The Washington Post Co. plans to expand into cable television as well as broaden its interests in TV broadcasting, newspapers and magazines, Chairman Katharine Graham told shareholders at the company's annual meeting yesterday.

With the sale of two unprofitable publications earlier this year and a 177 percent gain in first-quarter profits, "We are now in the strongest position ever to capitalize on our growth opportunities--both by expanding and improving our existing businesses and by engaging in new businesses, either through acquisition or start-up," Graham said.

Noting that the Post Co. is in three of the media already, but not yet in cable TV, she said that "at the right price and in the right geographic area, cable could offer an interesting investment opportunity for us--as an ongoing communications business and as a laboratory to test consumer Videotext-type services. We certainly intend to be actively involved with any process that disseminates information to prospects in the Washington, D.C., area."

Adding to Post-Newsweek Stations' string of four TV stations may be difficult now because of the high price stations demand. But prices could fall as cable systems expand, cutting into the broadcast market, she predicted, saying the company is also interested in "acquisitions of major-market newspapers."

Although the firm lost several million dollars starting Inside Sports magazine and sold it earlier this year, the Post Co. is still interested in expanding its magazine publishing, Graham said.

"We hope to increase our activity there through acquisitions or start-up," she said. "Our strategy will be to pinpoint selected market niches where our expertise and the franchises we have already established give us a competitive edge."

Post Co. President Richard Simmons said raising profit margins will be a major goal in the year ahead. The poor performance of the Detroit station dragged down the profit margins of the TV stations last year, but the Detroit station has improved substantially its ratings, and profitability should also improve.

If Detroit can match the performance of the other stations, the whole group could post a 35 percent profit margin, Simmons said.

"At the Post newspaper, we aim to raise margins, which were a little over 10 percent at the end of 1981, to at least 15 percent," he said.

During the meeting, Evelyn Y. Davis, who speaks at many stockholder meetings, complained that her name had not been mentioned in The Washington Post.

The company at the meeting announced three corporate appointments: Edward N. Van Gombos as vice president-information systems, Howard E. Wall as vice president and chief accounting officer and Guyon Knight as director of corporate communications.

Van Gombos, 49, was previously senior vice president for information systems of Dun & Bradstreet Inc.; Wall, 52, had been executive vice president and chief financial officer of Field Enterprises; Knight, 34, had been director of public relations of Dun & Bradstreet.