Groups of Order 8

Theorem
Let $G$ be a group of order 8.

Then $G$ is isomorphic to one of the following:


 * $\Z_8, \Z_4 \oplus \Z_2, \Z_2 \oplus \Z_2 \oplus \Z_2, D_4, Q_4$

where:


 * $\Z_n$ is the cyclic group of order $n$
 * $D_4$ is the dihedral group of order $8$
 * $Q_4$ is the dicyclic group of order $8$.