The Reagan administration yesterday came out on the side of women's groups and urged the Supreme Court to allow discrimination suits against the hiring and promotion policies of the nation's large law firms.

The government told the justices that the firms should not be "protected enclaves," immune to civil rights laws. The government's position, if adopted by the court, could subject sensitive and often secretive partnership decisions to legal scrutiny for the first time.

It was the second time this year that the administration has joined a major Supreme Court case in support of women's rights. Earlier, it joined in a challenge to discriminatory pension and insurance plans. Both actions contrast sharply with the administration's controversial opposition to affirmative action quotas, busing and denial of tax exemptions to discriminatory private schools.

The immediate beneficiary of the "friend-of-the-court" brief released yesterday by Solicitor General Rex E. Lee was Elizabeth Anderson Hishon, a Columbia University Law School graduate who sued the prominent Atlanta law firm of King & Spalding in 1979 after being rejected as a partner and forced to leave the firm under an "up-or-out" policy.

A U.S. District Court, upheld by the 11th U.S. Circuit Court of Appeals, threw out her suit on grounds that law firm partnership decisions are not covered by federal job discrimination laws.

The lower courts said that partnerships are "voluntary associations," more akin to marriages than to the conventional employment relationships governed by the Civil Rights Act of 1964.

The issue goes to the heart of the intensely competitive process by which law firms choose young associates, usually after five to seven years, for elevation to full partnership. Promotion means money and job security. Those who are rejected often have to leave the firm. Complaints about discrimination in that process have been made for years by blacks and women, but there was little they could do about it.

Lee, joined by the Equal Employment Opportunity Commission and William Bradford Reynolds, head of the Justice Department's Civil Rights Division, said it was "immaterial" whether partnerships are covered by the law. Associates in a firm are employes like any other, the brief said, and thus protected against job discrimination in hiring and promotion.

"The prospect of advancement is a critical element in most employment relationships," the brief said. "The relationship between associates and law firms is no exception.

"The prospect of becoming a partner remains a central preoccupation of both the firm and the associate during the associate's period of employment," the brief said. "An associate's professional development is both shaped and evaluated with the prospect of advancement to partnership in mind.

"In view of the pervasive influence that the opportunity to become a partner has on the associate's choice of a firm, the firm's ability to recruit associates, and the associates' working lives," Lee told the court, "it is difficult to imagine a more obvious" example of an employment decision as defined by civil rights law.

Lee noted that a close-knit law firm would not be affected by a ruling because the civil rights act does not apply to employers of fewer than 15 people.

The most significant change in the makeup of the legal profession in the past decade has been the influx of women, according to recent studies. In 1970 only 2.8 percent of all lawyers were women, compared with 7.5 percent in 1980. More significantly, women represent about one-third of lawyers under age 26--those who will be competing for partnership status during the next decade.

The court is expected to rule in Hishon vs. King & Spalding next year.