Every Hamiltonian group contains a subgroup isomorphic to $Q_8$

Question

I read somewhere that every Hamiltonian group (a non abelian group with every subgroup normal) contains a subgroup isomorphic to quaternion group.

But I cannot find its proof anywhere on net or in book. This does not look easy when I tried. In which book/notes can I found a proof of this statement

Answer 1

For a reference for proof you can see Group Theory By W. R. Scott. In page 253.

(Baer) A group $G$ is Hamiltonian iff $G$ is a direct sum of $A,B,D$ where $A$ is a quaternion group, $B$ is a elementary abelian $2$-group, and $D$ is a periodic abelian group with all elements are odd order.