Find the smallest n such that $S_4 \times S_8$ is isomorphic to a subgroup in $S_n$.
Answer
By Lagrange, we know that the minimum $n$ has to be at least $12$. But also if $n=12$ then this is easy to find a subgroup of $S_{12}$ by permuting first 4 numbers juxtaposed with permuting last 8 numbers.