Potentially characteristic not implies characteristic-potentially characteristic

This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., potentially characteristic subgroup) need not satisfy the second subgroup property (i.e., characteristic-potentially characteristic subgroup)
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Statement

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

Facts used

1. Potentially characteristic not implies normal-potentially characteristic, which in turn uses potentially characteristic not implies normal-extensible automorphism-invariant, which in turn 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.