Section InjmAut.
Variables (gT rT : finGroupType) (G D : {group gT}) (f : {morphism D >-> rT}).
Hypotheses (injf : 'injm f) (sGD : G \subset D).
Let domG := subsetP sGD.
Canonical conj_aut_morphism := Morphism conj_aut_morphM.
(* Characteristic subgroup properties : composition, relational properties *)

Lemma lone_subgroup_char G H :
H \subset G -> (forall K, K \subset G -> K \isog H -> K \subset H) ->
H \char G.