Undersecretary of Education Gary L. Bauer has been named chairman of a White House study group on the impact of government policies and social trends on the American family.

The panel was set up by Attorney General Edwin Meese III, who heads the White House Domestic Policy Council, after President Reagan announced in his State of the Union address that he was asking for such a study.

Although Reagan said the study would focus on the "financial, educational, social and safety concerns of poor families," Meese said in a speech last week that the group will seek ways to strengthen all "nuclear families," not just poor ones, that are composed of "one husband and one wife, monogamous and heterosexual, together with their child or children."

Terry Eastland, a spokesman for Meese, said a separate working group, headed by Charles D. Hobbs, a White House staffer, is studying possible changes in the welfare system and the impact welfare has had on the stability of poor families.

Bauer, 39, worked for Meese on the White House staff for two years before moving to the Education Department, where he has been an outspoken advocate of school prayer and aid to private schools. He also has called for curbs on pornography and has criticized school curriculums as "value-free" and school textbooks as "hyper-critical" of the United States.

His panel, composed of officials from several departments along with White House staffers, is expected to report to Reagan by Dec. 1. Bauer will keep his Education post, a department spokesman said, while working part-time on the family study.