The definition of the symmetry group as a group of unitary operators that commute with the hamiltonian is insufficient. Concepts of maximal, minimal, incomplete, and exce ssive symmetry groups are introduced. A procedure for setting up the minimal symmetry group is proposed. For this purpose it is sufficient to choose a group with the required dimensions of irreducible representations. As an illustration the problem posed by Jauch and Hill is solved. The symmetry group of an anisotropic oscillator is determined. (auth)