Samuel and Hyman Belzberg, the two wealthy Canadian investors, reported today they now control 22.6 percent of the outstanding shares of the Bache Group Inc., a major brokerage firm.

The brothers who have said they intend to buy up to 25 percent of Bache's stock, also have been buying real estate in cities as diverse as Chicago, Miami and Philadelphia. The Belzbers reportedly are negotiating to buy a 642-apartment complex in Boston worth more than $30 million.

In filing with the Securities and Exchange Commission today, First City Financial Corp., the Vancouver-based investment firm controlled by the Belzbergs, said it bought 160,715 shares of Bache stock between Feb. 13 that brings the brothers' holdings of Bache to nearly 2.44 million shares. On Feb. 12 the brothers reported they owned 2.04 million shares, and last week they reported holdings of 2.28 million shares.

Wall Street sources there is no evidence of any further purchases by the Belzbergs in the last several days.

In 1979, when the Belzbergs first began to acquire Bache stock -- saying then they were not interested in controlling the nation's eighth-biggest broker -- Bache officials convinced their best customers, Nelson "friendly" basis to make it harder for the Canadians to buy a big block of the brokerage firm's stock.

The Hunt brothers' cash problems during last spring's silver crisis pushed Bache to the edge of bankruptcy, although the firm survived and had its most profitable year ever in 1980.

At one point last year the Hunts owned 6.6 percent of the company, but have since sold all of it -- half directly to the Balzbergs and the other half to a Philadelphia investor, Stanley Mann. Sources say they believe Mann has since sold his Bache holdings to the Belzbergs.

Bache officials will not comment on the latest purchases by the Belzbergs.

Bache has been the target of several takeover attempts in the past and, although the Belzbergs say they have no interest in controlling Bache, they have said they may change their minds.

Bache stockholders approved a management plan in late 1979 that makes it nearly impossible for the shareholders to gain management control of Bache unless they own 75 percent of the stock. More than 42 percent of Bache stock is in "friendly" hands -- including current management, directors and past employees -- and sources said there is no evidence that any Bache insiders have been selling their stock to the Belzbergs.

However, since the Belzbergs plan was approved by a majority of the shareholders, should the Belzbergs acquire more than 50 percent of Bache, presumably they could restructure the company to their own liking.

Last month the Belzbergs asked Bache for two seats on the company's board of directors, a request that was refused by the Bache nominating committee. The committee includes Bache chairman Harry A. Jacobs, President H. Virgil Sherrill and three outside directors. Bache directors decline to say why they refused the Belzberg request.