Potentially characteristic not implies characteristic-potentially characteristic

Statement
A potentially characteristic subgroup of a group need not be a characteristic-potentially characteristic subgroup.

Facts used

 * 1) uses::Potentially characteristic not implies normal-potentially characteristic, which in turn uses uses::potentially characteristic not implies normal-extensible automorphism-invariant, which in turn uses uses::normal not implies normal-extensible automorphism-invariant in finite

Proof
The proof follows directly from fact (1), and the observation that any characteristic-potentially characteristic subgroup is also normal-potentially characteristic.