Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.7
Let $Z_{48} = \langle x \rangle$ and use the isomorphism $\mathbb{Z}/(48) \cong Z_{48}$ given by $\overline{1} \mapsto x$ to list all subgroups of $Z_{48}$ as computed in Exercise 2.3.6.
Solution:
![Subgroup lattice of the cyclic group of order 48](https://cdn.jsdelivr.net/gh/MathPage/gitalk/img/subgroups-of-c-48.png)