The controversial plan to extend the west front of the Capitol and cover over the last remaining sections of the original 177-year-old building won its first legislative support yesterday from a House appropriations subcommittee.

With barely a mention and no discussion, the Legislative Branch Appropriations for Congress, approved a $55 million outlay for the project.

But it debated and agreed by a split vote of 5 to 3 to support another project that has aroused bitter opposition from Capitol Hill residents - the creation of a parking lot for House employees on the vacant site at 2d and D Streets SE once occupied by Providence Hospital.

Several residents of the area listened silently, unable to participate, as the subcommittee debated the issue and took its action. As they left the meeting, they denounced the decision and said they would try to persuade other House members and senators to block it.

The project would add 400 parking spaces to the 5,000 free spaces now available on the House side of Capitol Hill. This ratio of nearly one space for every two persons is far more generous than the government provides for executive agencies.

"The current proposal could be interpreted by the public as an invitation to increase the use of private cars and a negation of energy conservation efforts," one opponent, Phoebe Bannister, charged in a prepared statement.

Ironically, she and others said, the proposal comes just before the scheduled July 1 opening of a Metro subway station, located just one block from the Cannon House Office Building, that will provide convenient transportation for some congressional workers. The Capitol Hill residents principal objection is to traffic and dangers to neighborhood school children.

Rep. George [WORDS ILLEGIBLE] Subcommittee chairman, strongly supported the proposal for the parking lot, which would be temporary until the land is used for other purposes. It was acquired as a site for a school for Capitol pages, which has not been authorized.

"I think we need the parking spaces," Rep. John P. Murtha (D-Pa.) commented. "That's one of the biggest problems we have . . . I've got people who won't work for me because they can't get a parking space."

Opposition to the project was led by Rep. Lawrence Coughlin (R-Pa.), who was supported by Reps. William L. Armstrong (R-Colo.) and Bob Traxler (D-Mich.).

Rep. George H. Mahon (D-Tex.), chairman of the full Appropriations Committee, who attended only a few minutes of the session, voted for the parking lot, joining Reps. Shipley, Murtha, Adam Benjamin (D-Ind.) and John J. McFall (D-Calif.).

The extention of the Capitol is a project that has been proposed several times in recent years, has won almost routine support from the House and has been blocked chiefly by opposition in the Senate.Yesterday's action was significant chiefly because it puts the project into the legislative pipeline.

This year, Capitol Architect George M. White propsed a scaled-down version of earlier plans. The earlier plans called for extending as much as 80 feet from the center of the structure but not from the House or Senate wings.

White's plan would add between 19 and 60 feet and leave the broad terraces untouched. The original sandstone walls of the Capitol, which would be covered from exterior view, would remains as interior walls.

White said restoration of the deteriorated west front, without adding the new space, would cost $45 million. The extension project would add floor space. The project has sparked strong opposition from the American Institute of Architects.

At yesterday's meeting, Shipley, the chairman, made only a passing mention of "a little item of $55 million for the extension of the West front," and it was approved by the mere absence of objections.