Symmetry groups of field equations for spin 1/2

Methods for constructing the largest (in the S. Lie's sense) continuous symmetry groups of partial differential equations are developed. The equations and the transformations of the symmetry group are not supposed to be linear. The basic conception is that of the group of a differential operator $G_D$. Some important properties of this group are studied and used. For the fields with the spin 1/2 the group $G_D$ is constructed in an explicite form. With the aid of the formulas obtained, the maximal group of symmetry for an arbitrary system of free neutrinos is established. The general form of the conformal invariant interaction is also established and group classification of the Dirac equation with self-interactions is carried out.