Control Data Corp., the troubled Minneapolis computer maker, said yesterday it may sell its giant financial services unit, Commercial Credit Co., and use the proceeds to buy "a substantial portion" of its own common stock.

The announcement sent the company's stock soaring 3 3/8 to 38 1/4, with 3.37 million shares changing hands in the most active trading of any New York Stock Exchange issue yesterday. The stock rose 1 1/2 on Tuesday as rumors about yesterday's announcement circulated on Wall Street, analysts said.

Control Data said it may sell the financial services subsidiary, which has a net worth of $828 million, because it wants to focus its efforts on its computer businesses.

Yesterday's announcement followed a recent decision by the company to halt production of disk drives for large computers made by International Business Machines Corp. That decision resulted in a one-time $70.3 million after-tax charge to earnings, largely responsible for a $54.5 million third-quarter loss.

Analysts said both moves were designed to improve the company's long-run profitability.

"The announcement yesterday confirms some of the rumors that have been around for the last two months that there would be major changes at Control Data," said Duff & Phelps analyst George J. Podrasky Jr. "The sale of Commercial Credit is a logical move because the business has not been growing, has not been consistently profitable, and no longer fits with the rest of Control Data."

Control Data acquired Commercial Credit in 1968 to help its computer customers finance leases of the company's hardware and to stabilize erratic earnings caused by cyclical changes in the computer business. As leasing has become less prevalent in the computer business and purchasing more common, the importance of the financial services operation to Control Data has diminished.

"The idea that they will use the funds from the sale of Commercial Credit to buy their own stock certainly helps to put a floor under the stock's price," said Gartner Group analyst Thomas J. Crotty. "Presumably, the company's offer to buy shares would be at a price above market value, and that would certainly be positive."

Control Data stock traded as high as 48 1/2 in the last year, before disappointing earnings pushed the price of the shares down. The company would not say if it would use all of the proceeds from the Commercial Credit sale to purchase its shares, nor did it indicate what else it might do with the proceeds if the unit is sold.

The timing of yesterday's announcement indicates that Control Data and its financial adviser, Goldman, Sachs & Co., believe Commercial Credit's earnings will continue to improve, since the subsidiary could be expected to command a higher price during a period when earnings are expected to improve.

Several analysts said they expect Commercial Credit's earnings to improve dramatically next year, supporting the wisdom of the timing of the proposed sale. They speculated that the company would probably be sold for a price near its net worth of $828 million, but emphasized that the diversity of Commercial's insurance, and consumer and industrial finance operations makes it difficult to predict a sale price.

In 1983, Commercial Credit had revenue of $1.1 billion and net income of about $30 million, one analyst said, which was a significant decline from the subsidiary's pre-tax earnings of $87.7 million in '82 and $99 million in '81.

But during the first nine months of 1984, Commercial Credit's pre-tax income rose to $55 million from $38.3 million a year earlier, and favorable results are expected in the fourth quarter.

Control Data is the nation's fourth-largest computer company bsed on 1983 revenue of $3.5 billion from data-processing activities, according to Datamation, a trade journal published by Dun & Bradstreet Corp., winning their respective regional title soccer matches at Richard Mont