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## Compute the subgroup lattice of quaternion group

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.3 Compute the lattice of subgroups of $Q_8$. Solution: Every $\subseteq$-minimal subgroup of $Q_8$ is cyclic; disregarding…

## The subgroup lattice of a symmetric group on three elements

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.2 Find the lattice of subgroups of $S_3$. Solution: Every (nontrivial) $\subseteq$-minimal subgroup of $S_3$ is cyclic…

## Compute the subgroup lattice of a quotient of modular group of order 16

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.3 Exercise 3.3.6 Let $M = \langle u,v \rangle$ be the modular group of order 16 described in Exercise…

## Draw subgroup lattice of a quotient of quasi-dihedral group of order 16

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.3 Exercise 3.3.5 Let $QD_{16} = \langle \sigma, \tau \rangle$ be the quasidihedral group of order 16 described in…