Some subgrid turbulence models are analysed according to the symmetry group of the Navier-Stokes equations. Since a major part of them destroy the symmetry properties of the equations, a new class of subgrid models is proposed. These new models are expected to restore the fundamental physical properties of the equations (conservation laws, scaling laws, ...) which are contained in the symmetries. Moreover, the derived models are conform with the second law of thermodynamics. A numerical test is presented.