Submerged in the drama of President Reagan's successful drive to win Senate approval of the $8.5 billion aircraft sale to Saudi Arabia was a highly effective lobbying effort by conservative groups, key elements of the oil and aerospace industries and an ad hoc collection of corporations that do business with Arab countries.

Many of these interests were major supporters of the election campaigns of freshman Republicans and have facilities in the states of southern senators who abandoned their opposition or indecision in the final days before the vote Wednesday and put the sale over the top, 52 to 48.

From this perspective, just one aspect of the complex tale of President Reagan's first foreign policy victory in Congress, it was a test of strength between the Israeli lobby and core elements of the Reagan coalition, and the Israeli lobby was the clear loser.

The lobbying drive in behalf of the arms deal, which includes selling the Saudis Airborne Warning and Control System (AWACS) radar planes, became a concerted effort about a month before the vote--at a time when prospects for a Reagan victory were dim.

On the business side, the initiative was taken by Richard M. Hunt, director of government relations for NL Industries, a major manufacturer of petroleum equipment and supplies. He put together a group of Washington representatives from about 40 companies with Mideast ties to form an ad hoc AWACS coalition.

"We believed in it," Hunt declared. Among the corporations were Boeing Co. and Pratt & Whitney division of United Technologies Corp., both of which had a direct financial stake in the sale as prime contractor and engine builder, respectively. The coalition also included such major oil companies as Exxon and Mobil, and two international construction firms, Brown & Root and Bechtel, both of which do extensive work in the Middle East.

Many of the firms are members of the Business Roundtable, perhaps the most influential business lobbying group in Washington, and some of the meetings were held in the Roundtable's Washington offices. The Roundtable, an organization of major U.S. corporations, never took a formal stand on the sale.

Working in parallel and sometimes in cooperation with the business alliance was a lobbying effort coordinated by Richard Sellers, director of congressional relations for the American Security Council and Washington director for the Coalition for Peace Through Strength.

He put together the leaders of 34 diverse groups such as the Young Americans for Freedom, American Military Retirees Association, Catholics for Christian Political Action, Conservative Victory Fund, National Christian Action Committee and Veterans of Foreign Wars.

"We created an environment in which it was possible" for certain key, wavering senators to change their minds and support the sale or to drop an uncommitted stance and come out behind President Reagan, Sellers said.

Similarly, the Stanton Group, part of the network of conservative organizations run by Paul Weyrich, the best known of which is the Committee for the Survival of a Free Congress, pressed for the sale among its sympathizers, particularly junior Republicans who have strong ties to the right wing.

These varying corporate and ideological interests have become increasingly potent. They were important not only in the election of Reagan, but also in the growth of conservatism as a political force and in the election of Republican senators with deep commitments to the political right.

In private, some of the leaders of these groups claim at least partial credit for the AWACS conversion of such senators as William Armstrong (R-Colo.), Roger Jepsen (R-Iowa) and Charles Grassley (R-Iowa).

While giving credit for the overall victory to President Reagan, Sellers argued that, when changes by three senators could have brought defeat, conservative senators held "the key to victory, period."

The Sellers group provided briefings on the sale, and also used such tactics as organizing four planeloads of Alabama businessmen to come to Washington to lobby Sen. Howell Heflin (D-Ala.) and persuading campaign supporters and contributors to back the sale. (In the case of Heflin, the effort proved futile.)

The business groups lobbied senators directly and also pressured their subcontractors, vendors and suppliers to join in.

Brown & Root, for instance, supplied position papers to senators, particularly to those from the band of southern and southwestern states--Texas, Oklahoma, Louisiana, Alabama, Mississippi and Arkansas--where Brown & Root and affiliated companies have facilities.

The presidents of both the Boeing commercial aircraft division and Pratt & Whitney sent telegrams by the hundreds.

Boeing president E. H. Boullioun, in wires to 1,600 firms that do business with the Washington state aircraft producer, said: "Without this sale, and with present budget planning, the AWACS production line will be ended. It is our belief that a negative decision on this issue may affect Saudi Arabia's attitude towards other U.S. products such as commercial aircraft."

In a similar telegram, Harry J. Gray, head of Pratt & Whitney, wrote: "I strongly support the sale to Saudi Arabia...A Senate veto of the president's plan would only cause the Saudis to turn to other aircraft producers . This would cost the U.S. both exports and jobs."