Symmetry groups of the Lagrangians of chiral fields with values on $S^2$

All the symmetry groups of the lagrangian of chiral field taking value in $S^2$ are constructed. It is shown that there are only seven different admissible point groups, five of which are infinite. The corresponding lagrangians are pointed out too. For three-dimensional space of the independent variables one of the groups acts transitively in the space of the solutions. This fact makes it possible to construct explicit (local) general solution if one of the partial solutions is given.