Finite-Frattini-realizable group

Symbol-free definition
A finite group is termed finite-Frattini-realizable if it can be realized as the Frattini subgroup of some finite group.

Definition with symbols
A finite group $$G$$ is termed finite-Frattini-realizable if there exists a finite group $$K$$ such that $$\Phi(K) \cong G$$ where $$\Phi(K)$$ denotes the Frattini subgroup of $$K$$.

Weaker properties

 * Finite ACIC-group:
 * Finite nilpotent group
 * Frattini-realizable group: A group that can be realized as the Frattini subgroup of a not necessarily finite group
 * Finite-(Frattini-embedded normal)-realizable group