Financial General Bankshares, Inc., a large bank holding company with major subsidiaries in metropolitan Washington, yesterday reported a 64 per cent increase in profits during 1976 and announced plans to sell its controlling interest in H. G. Smithy Co., a local real estate and magagement firm.

Earnings for the year totaled $10.4 million ($1.76 a share) compared with $6.4 million ($1.07) in 1975. Included in the 1976 profits was an after-tax gain of $2 million (34 cents) from the sale of four Chicago area banks and a bank service firm.

Without the gain from selling Illinois investments, Financial General's profits for the year would have been up 33 per cent over 1975.

According to the banking firm, profits also aided by a $5.5 million pre-tax increase in the interest margin -the spread between interest earned from securities and loans and the interest paid out of time deposits and borrowed money.

Total equity capital increased by 10 per cent to $93 million, and deposits of member banks rose by 4 per cent to a record $1.4 billion. Reflecting a sluggish commercial loan demand at many banks,

Financial General said it plans to sell its 68 per cent interest in the Smithy company to a private firm which has selected one of its members, Edmund B. Cronin Jr., to be a principal officer.

Smithy had to sold: Bank holding company laws require divestment of non-banking businesses by Dec. 31, 1978.

Financial General operates 141 banking locations with total assests of more than $1.9 billion, mainly in Maryland, Virginia and the District. Subsidiaries here include Union First National Bank, Alexandria National Bank, Arlington Trust Co., Clarendon Bank & Trust, American National Bank in Silver Spring, Round Hill National and Peoples National of Leesburg.

Criterion Insurance Co., an automobile insurance firm, yesterday reported a continued rebound in profitability during the final quarter last year. Criterion profits totaled $113,000 (7 cents a share) in the recent quarter compared with a net loss of $2.8 million during the same period in 1975. For the full year, Criterion lost $4 million compared with a 1975 loss of $5.3 million. Most of the 1976 loss occurred in the first and second quarters.

An affiliate of Government Employees Insurance Co., Criterion sells auto policies to drivers considered to be greater risks than those accepted by Geico.

On the business of underwriting auto insurance, Criterion still operated with a loss in the recent quarter of $715,000 but that much improved from an underwriting loss of $3.8 million in the 1975 period. The 1976 underwriting loss was estimated at $8.3 million in 1975, with 95 per cent of last year's underwriting loses occurring in the first six months.