One knows that any countable group can be embedded in a 2-generated group. Also, any finite group is a subgroup of a 2-generated finite group, namely by the Cayley embedding. Does the same hold if we restrict to finite $p$-groups, where $p$ is some prime, i.e. is any finite $p$-group a subgroup of a 2-generated finite $p$-group?
Note that the minimal number of generators of the Sylow subgroup of the symmetric groups grow with their order. Thus the Cayley embedding would not suffice.