After livening up an otherwise dull election this month, Australia's growing antinuclear lobby threatens further trouble for the reelected Labor government of Prime Minister Robert Hawke and possibly for U.S. interests here, according to Australian political analysts.

Among the issues in the recent campaign -- and potentially at stake if the antinuclear activists gain strength -- were the presence of three key U.S. communications bases in Australia, the mining and export of uranium and port calls by nuclear-armed or nuclear-powered U.S. warships.

Although not mentioned directly as a campaign issue, the ANZUS defense treaty linking Australia, New Zealand and the United States would be affected by any moves against the bases or port calls, according to U.S. officials. They say the alliance has already suffered a setback from the decision of New Zealand's Labor government elected in July to ban all visits by nuclear ships and seek renegotiation of the ANZUS pact to "denuclearize" the alliance.

While two small opposition parties with antinuclear platforms appear to have gained only seven of 76 Senate seats between them, the issue may have contributed to disenchantment among some Labor voters and the shrinkage of the governing party's majority in the more important House of Representatives, political analysts say.

Other fallout from the rise of the antinuclear issue has included the emergence on the political scene of a 31-year-old rock star, Peter Garrett, and reports of a U.S.-Australian diplomatic rift.

The antinuclear issue "probably had more impact on the election than any single issue," said Sen. Donald Chipp, the leader of the Australian Democrats, the other small opposition party. His party appears to have captured six Senate seats with a platform that included opposition to visits by nuclear warships and to the presence of "foreign bases that contribute to nuclear war" and allegedly make Australia a target for Soviet nuclear attack.

Because of Australia's complicated weighted voting system, final results of the Dec. 1 election are not expected to be known until January. But data now available indicate that Hawke's reelected government will emerge with a 16-seat house majority, down from 25 in the 1982 elections.

Polls before this month's election had predicted a landslide Hawke victory, with an increased majority in the new house. The chamber has 23 new seats, for a total of 148.

Chipp charged that the Hawke government had made Australians "craven puppets" of the United States and its "lying American diplomats" by backing the U.S. position that the warship visits and the communications bases were vital to the survival of ANZUS, which he called "the most useless document in the Australian government archives."

But Chipp also had harsh words for Garrett's Nuclear Disarmament Party, which emerged two months before the election and may have denied the Democrats some gains by splitting the antinuclear vote. Chipp asserted that the party was "simply a front for the communist left."

Garrett, who appears to have narrowly lost his bid for a Senate seat from New South Wales, according to the latest poll data, said Chipp's charge was regrettable and insisted that his party also opposed the Soviet nuclear buildup.

Garrett said the next two years would determine "whether the peoples of the world are prepared to say no to nuclear weapons. That's a decision that has to be made as much by Australians as by anybody else, and we are saying no to the Soviet Union as well as to the United States."

More than 500,000 of Australia's 9 million voters -- or about 6 percent of the electorate -- cast primary votes for the Nuclear Disarmament Party, electing at least one Senate candidate from Western Australia. Garrett said his party received support from a political cross section of concerned people, including Labor supporters who "felt betrayed" by the Hawke government's reversal of Labor Party opposition to uranium mining earlier this year and its "total accommodation to U.S. policy."

He said New Zealand's ban on nuclear warships was "a very encouraging sign" for Australians and had served as an impetus for the antinuclear movement here.

The United States and Australia operate three bases officially termed "joint defense facilities" at Pine Gap near Alice Springs in central Australia, at Nurrungar to the south and at North West Cape on the coast of Western Australia.

The Pine Gap and Nurrungar bases receive a variety of data from U.S. satellites that provides early warning of Soviet missile launches and helps to monitor arms control agreements. The North West Cape facility serves as a communications relay station for U.S. Navy ships and submarines.

According to the head of Australia's Center for Strategic Studies, Desmond Ball, the same data received by the Pine Gap and Nurrungar bases to verify arms control agreements also help the United States to plan nuclear strikes in the event of war. The "basic dilemma" for peace groups is that the uses of these data cannot be separated, said Ball, who is regarded as Australia's leading expert on the bases.

"If you think that arms control treaties are important, then you can't close down Pine Gap," ball said. Nevertheless, the Nuclear Disarmament Party wants to do just that, insisting that the United States is using the bases to carry out "first-strike nuclear war-winning policies" on Australian soil.

While antinuclear activists like Garrett maintain that the party is evenhanded in its opposition to the U.S.-Soviet arms race, its platform, campaign literature and leaders' pronouncements make clear that its protest activities are mainly directed against the United States.

Standing 6 foot 4, with a shaven head and deep-set, piercing eyes, Garrett cuts an imposing figure. Opponents charge that, as the lead singer of the Australian rock band Midnight Oil, he benefited from extraordinary media attention during the campaign, although his party is a single-issue group and contested only two House seats (unsuccessfully) in addition to Senate seats in four of eight states.

But Garrett, who holds university degrees in politics and law, emerged as an articulate and well-versed spokesman for antinuclear issues, and he said he plans to continue his political activism.

Besides producing some of the livelier campaign rhetoric, the antinuclear issue appeared to increase internal left-wing pressure on the Labor government, which already has been trying to assert itself on global arms control matters.

That effort has led to what newspapers here called a major diplomatic row between senior Reagan administration officials and Foreign Minister Bill Hayden over his efforts to promote a comprehensive test-ban treaty in the United Nations and other nuclear arms control measures.

Neither government would confirm or deny reports that Washington recently lodged a formal complaint with the prime minister's foreign relations adviser charging that Hayden had violated understandings on the test-ban issue, publicly misrepresented U.S. policy and promoted measures that would weaken the West's nuclear deterrence.

The United States has insisted that a comprehensive test ban must be linked to obtaining reductions of both U.S. and Soviet nuclear weapons as a long-term goal, not as a separate matter to be negotiated urgently, as advocated by Hayden.

In response to the reported rift, the U.S. Embassy in Canberra last week issued a statement denying that "the purported remarks" about Hayden by U.S. officials "reflect the views of the United States government." However, the statement noted that "differences of view on specific issues may arise at various times" between the United States and Australia, which maintain "a very close and comprehensive working relationship."

Hayden said he was satisfied with the U.S. Embassy statement. However, he reacted sharply when the head of the opposition Liberal Party, Andrew Peacock, described the alleged rift as "an indictment of the conduct of foreign policy under the Labor government" and called on Hawke to "pluck up the courage to control Mr. Hayden and his center-left faction."

Hayden countercharged that Peacock "has made a fool of himself by condemning me" on the basis of "half-baked fiction."

Peacock's Liberal Party appears to have been the main gainer in the election, picking up 12 of the additional 23 seats in the new House of Representatives, for a total of 45.

According to the latest projections, the opposition in the House -- consisting of the Liberals and the National Party -- will have 66 seats, compared with 82 for Labor.