D8 is not potentially fully invariant in D16
This article gives the statement, and possibly proof, of a particular subgroup or type of subgroup (namely, Dihedral group:D8 (?)) not satisfying a particular subgroup property (namely, Potentially fully invariant subgroup (?)) in a particular group or type of group (namely, Dihedral group:D16 (?)).
Suppose is the dihedral group of order 16:
and is a subgroup isomorphic to the dihedral group of order 8:
Then, is not a potentially fully invariant subgroup of .