A House subcommittee voted 8 to 3 yesterday to create a Cabinet-level Department of Education, but it stripped out $3.3 billion in child-feeding and Indian education programs that President Carter had sought to include in the new unit.

Committee Chairman Jack Brooks (D-Tex.) said he will put the education bill before the Government Operations Committee for a final vote today, then rush it to the Rules Committee, which has notified leaders it won't clear any more bills for floor action unless requested to do so by the end of this week.

As approved by the subcommittee, the bill would create a new department by shifting from existing departments programs with about 16,000 employes and a budget of just under $14 billion a year. The biggest unit is the existing education division of the Department of Health, Education and Welfare, which has a budget of about $12.9 billion a year and 3,600 employes.

The House bill also includes HEW civil rights functions (about 1,100 employes), Defense Department overseas schools ($350 million and 10,000 employes) and other, smaller units.

The Senate version of the bill, approved by the Governmental Affairs Committee and awaiting floor action, includes all the above plus $3 billion in child-feeding programs, $271-million in Indian education programs. $56 million in science education programs and $912 million in vocational rehabilitation, none of which is in the House bill. The Senate bill, totalling $18 billion in programs and 24,000 employes, is similar to Carter's request except that Carter didn't want vocational rehabilitation in the new department.

Opposition has come from Indian groups that want the $271 million Indian education programs left in the Interior Department's Bureau of Indian Affairs, and from agricultural groups and members of Congress from farm areas who oppose shifting the $3 billion school-lunch and related child-nutrition programs from the Agriculture Department to a new department.

In the Senate version of the bill, efforts to block the shift of Indian education and child-feeding to the new department failed in committee.

Yesterday, however, the House subcommittee approved by voice vote an amendment by Rep. Benjamin S. Rosenthal (D.N.Y.) to leave Indian education in Interior. Rosenthal said tribal groups representing "99 1/2 percent" of American Indians backed his amendment.

An amendment by Rep. Don Fuqua (D-Fla.) to leave the child-nutrition program in Agriculture also won by voice vote. Another Fuqua amendment leaving some $56 million in science education programs in the National Science Foundation was adopted, 5 to 2.

The success of the Rosenthal and Fuqua amendments could make it easier to pass the bill on the House floor by removing opposition from Indian and agricultural groups.

Carter first proposed a new Education Department at the National Education Association meeting during the 1976 presidential campaign. The NEA and other education groups have strongly supported the concept.

But the AFL-CIO and groups representing blacks and poor people have opposed it on grounds it would fragment their lobbying influence and tear apart HEW programs that unite social welfare efforts.