Every 1-completed subgroup is contained in a maximal subgroup

Verbal statement
Every fact about::1-completed subgroup is contained in a fact about::maximal subgroup.

Statement with symbols
Suppose $$G$$ is a group and $$H$$ is a subgroup of $$G$$ such that there exists $$x \in G$$ such that $$\langle H, x \rangle = G$$. Then, $$H$$ is contained in a maximal subgroup.