  We construct large families of characteristically nilpotent Lie algebras by
considering deformations of the Lie algebra g_{m,m-1}^{4} of type Q_{n},and
which arises as a central extension fo the filiform Lie algebra L_{n}. By
studying the graded cohomology spaces we obtain that the sill algebras are
isomorphic to the nilradicals of solvable, complete Lie algebra laws. For
extremal cocycles these laws are also rigid. Considering supplementary cocycles
we construcy, for dimensions n>8, nonfiliform characteristically nilpotent Lie
algebras and show that for certain deformations these are compatible with
central extensions.
