Hello!!
We have that $\mathbb{Z}_{14}^{\star}=\{1,3,5,9,11,13\}$. From these elements we get the cyclic subgroups $\langle 1\rangle, \langle 13\rangle, \langle 3\rangle=\langle 5\rangle, \langle 9\rangle=\langle 11\rangle$. How can we show that $\mathbb{Z}_{14}^{\star}$ has no other subgroups?