If $G$ is any group, then by $\text{Sub}(G)$ we denote the collection of all subgroups, ordered by $\subseteq$. If $(P,\leq)$ is a partially ordered set we let $\text{Max}(P)$ and the set of maximal elements.

Let $\frak{S}$ be the group of all bijections $f:\omega\to\omega$ together with composition.

Is there a member of $\text{Sub}(\frak{S}) \setminus \{\frak{S}\}$ that is not contained in some member of $\text{Max}\big(\text{Sub}(\frak{S})\setminus \{\frak{S}\}\big)$?