Each department shall maintain a central office in Springfield, in space provided by the Secretary of State, the Department of Central Management Services, or the Architect of the Capitol, excepting the Department of Agriculture, which shall maintain a central office at the State fair grounds at Springfield, and the Department of Transportation, which shall also maintain a Division of Aeronautics at Capital Airport. The director of each department (see Section 5-10 of this Law for the definition of “director”) may, in the director’s discretion and with the approval of the Governor, establish and maintain, at places other than the seat of government, branch offices for the conduct of any one or more functions of the director’s department.