  Given an endomorphism A over a finite dimensional vector space having
Jordan-Chevalley decomposition, the lattices of invariant and hyperinvariant
subspaces of A can be obtained from the nilpotent part of this decomposition.
We extend this result for lattices of characteristic subspaces. We also obtain
a generalization of Shoda's Theorem about the characterization of the existence
of characteristic non hyperinvariant subspaces.
