This is a group theory question. I am preparing a research paper. One result brought my attention. I am wondering if you know some paper or book listed this result. 


Let $G$ be a 2-group. Suppose there exists nonabelian subgroups of $G$(FYI, otherwise the structure of $G$ is known, see Huppert, Endliche Gruppen I, P309). If every nonabelian subgroup is a hamiltonian 2-group, then $G$ is hamiltonian 2-group.


If no book list this results, Do you think it is an interesting result or a tedious one? 


Thank you very much in advance for your comment.


Peter Tan 



Hamiltonian 2-groups
Groups with this property were studied by G.A. Miller in 1907: see [here](http://www.ams.org/journals/tran/1907-008-01/S0002-9947-1907-1500772-6/S0002-9947-1907-1500772-6.pdf).


It looks as though there is just one counterexample, the quaternion group of order $16$.


