FACPC-subgroup

Definition
Suppose $$G$$ is a finite abelian group (i.e., a group that is both finite and abelian) and $$H$$ is a subgroup of $$G$$. We say that $$H$$ is a FACPC-subgroup or finite-abelian-characteristic-potentially characteristic subgroup of $$G$$ if there exists a finite abelian group $$K$$ containing $$G$$ such that both $$H$$ and $$G$$ are characteristic subgroups of $$K$$.