  We study SUSY $N$-supergroups, $N=1,2$, their classification and explicit
realization, together with their real forms. In the end, we give the supergroup
of SUSY preserving automorphism of $\mathbf{C}^{1|1}$ and we identify it with a
subsupergroup of the SUSY preserving automorphisms of $\mathbf{P}^{1|1}$.
