  We obtain some results on symmetries of sub-Riemannian surfaces. In case of
contact sub-Riemannian surface we base on invariants found by Hughen
\cite{Hughen}. Using these invariants, we find conditions under which a
sub-Riemannian surface does not admit symmetries. If a surface admits
symmetries, we show how invariants help to find them. It is worth noting, that
the obtained conditions can be explicitly checked for a given contact
sub-Riemannian surface. Also, we consider sub-Riemannian surfaces which are not
contact and find their invariants along the surface where the distribution
fails to be contact.
