<math>a = (1,2,3,4), \qquad x = (1,3)</math>.
Graphical description== ===Lattice of all subgroups=== [[File:D8latticeofsubgroups.png|300px]]
===Lattice of normal subgroups=== [[File: D8latticeofnormalsubgroups.png| 1000px]] The lattice of normal subgroups fits into the following general picture, which is the general picture of the lattice of normal subgroups for [[groups having the same Hall-Senior genus]] as this (namely, this and the [[quaternion group]]). The Hall-Senior genus is <math>8\Gamma_2a</math>. [[File:8Gamma2a.png|1000px]] ==Tables for quick information==
===Table classifying subgroups up to automorphisms===