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## Find the subgroup lattice of the cyclic group of order 48

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: