  Let G a group of germs of analytic diffeomorphisms in (C^2,0). We find some
remarkable properties supposing that
  G is finite, linearizable, abelian nilpotent and solvable. In particular, if
the group is abelian and has a generic dicritic diffeomorphisms, then the group
is a subgroup of a 1-parametric group. In addition, we study the topological
behaviour of the orbits of a dicritic diffeomorphisms. Last, we find some
invariants in order to know when two diffeomorphisms are formally conjugates.
