A House trade subcommittee will make an 11th-hour effort next week to help the U.S. auto industry find a legislative solution to its problems -- problems many in the industry blame on imports.

Rep. Charles A. Vanik (D-Ohio), who is retiring at the end of this Congress, scheduled the hearings only hours after the International Trade Commission ruled by a 3-to-2 vote that imported cars aren't the major cause of Detroit's problems.

The ITC's decision Monday virtually shut the door on the industry's hopes of getting temporary relief from imported cars, particularly those from Japan.

"One thing we have to do is make it clear to the public, to the Congress and the administration that, merely because the ITC has found under their statute imports weren't the substantial cause of injury," this doesn't mean Detroit's problems will go away, a United Auto Workers union spokesman said yesterday. "We have people who are exhausting their benefits . . . suicide rates are up, [alcoholism] rates are up, divorce rates are up" as a result of the auto industry's difficulties.

The hearing next Tuesday will concentrate on legislation giving President Carter authority to negotiate an agreement with the Japanese to reduce their auto exports to the United States as well as other legislative proposals, such as tax or regulation changes to aid the industry, according to a spokesman for the House Ways and Means subcommittee on trade which is holding the hearing. "Everyone was pinning their hopes on the ITC," the spokesman said.

But what the hearing may boil down to is what authority Carter will have to help the auto industry.

The UAW and the Ford Motor Co. this summer had asked the ITC to find that imports were the substantial cause of their recent difficulties including 200,000 auto workers permanently laid off this year and record losses reported by major auto companies. The UAW and Ford needed a positive ITC decision to have imposed any import quotas, increased tariffs or an orderly marketing agreement between Japan and the United States limiting imports.

The restrictions would have been for a maximum of five years, the time the industry said it needs for its $80 billion retooling and modernizing program to help it build new small cars to compete with Japan.

But the ITC said that the recession -- which reduced consumer income -- high gasoline prices and consumers' shift away from gas guzzlers were more important factors in Detroit's dilemma than were imports.

Yesterday, spokesmen for both Ford andf the UAW said the ITC's decision won't stop their drive. They said their efforts will focus on the Carter administration and the lameduck Congress rather than President-elect Ronald Reagan's administration.

"Our hope is Carter will act," a Ford spokesman said from Detroit yesterday. "Whatever happens, we need broad bipartisan support."

Government lawyers, however, contend that Carter is prohibited from negotiating with the Japanese to curb imports because, without a mandate from the ITC, he would be violating antitrust laws. Ford and the UAW are hoping to get passed, with impetus from the hearing next week, legislation authorizing the president to negotiate for such curbs.

"For us with hundreds of thousands of people unemployed and with communities devastated" by plant shutdowns and unemployment, "the problem is festering," the UAW spokesman said.

Everyone, however, doesn't favor legislative action to curb imports. Bart S. Fisher, an attorney representing the American Imported Automobile Dealers Association, said on Monday that he anticipated Ford and the UAW would take their case to Congress. But he said, "Congress will reject those attempts. Their constituent support isn't there either."

The UAW's and Ford's efforts will be particularly hard because a government agency already has determined that imports aren't Detroit's problem, Fisher said.

Alexander Trowbridge, head of the National Association of Manufacturers, said yesterday that his group supports a trade agreement to limit Japanese imports, but the association of thousands of the nation's manufacturers is against import quotas.