How do I compute the subgroup of $(\Bbb Z\_{17}^\times, \*\_{17})$ generated by $\{2,3\}$, where $\Bbb Z\_{17}^\times = \{1,2,3,\dots,16\}$?

I believe I understand how to calculate it for all the cyclical subgroups but I'm not too sure how to do it with this criteria. I've tried finding similar examples but go off but I couldn't seem to find any.