p-groups embedded into Sylow subgroups

Let $$p$$ be a prime number, $$q$$ a power of $$p$$ and $$P$$ be a finite $$p$$-group. $$P$$ is isomorphic to a subroup of p-Sylow subgroup of

• the symmetric group $$S_{\mid P\mid}$$ (Theorem of Cayley)

• the general linear group $$GL(\mid P\mid, GF(q))$$ (a theorem of ?)

• the unit group $$U(GF(q)P)$$ of the modular group algebra $$GF(q)P$$ (based on a theorem of Wallace).

My question is whether there are some more non-trivial series of $$p$$-Sylow subgroups which let $$P$$ be embedded as a subgroup, too. All of them are grandfathers of all $$p$$-groups.

My second question is if there are some connections between these grandfather series.