File:D8latticeofsubgroups.png

This is the lattice of subgroups of dihedral group:D8. For more information, see subgroup structure of dihedral group:D8.

This file was created using Graphviz. The generating code is given below:

digraph G{       rankdir = "BT"; Wholegroup[peripheries=3]; Trivialsubgroup[peripheries=3]; Center[peripheries=2]; Involutionone; Involutiontwo; Involutionthree; Involutionfour; Cyclicfour; ElementaryAbelianone; ElementaryAbeliantwo; Trivialsubgroup -> Center; Trivialsubgroup -> Involutionone; Trivialsubgroup -> Involutiontwo; Trivialsubgroup -> Involutionthree; Trivialsubgroup -> Involutionfour; Involutionone -> ElementaryAbelianone; Involutionthree -> ElementaryAbelianone; Involutiontwo -> ElementaryAbeliantwo; Involutionfour -> ElementaryAbeliantwo; Center -> ElementaryAbelianone; Center -> Cyclicfour; Center -> ElementaryAbeliantwo; ElementaryAbelianone -> Wholegroup; ElementaryAbeliantwo -> Wholegroup; Cyclicfour -> Wholegroup; Wholegroup[label="Whole group {e, a, a^2, a^3, ax, a^2x, a^3x }"]; Center[label="Center {e, a^2}, Order two, characteristic"]; Trivialsubgroup[label="Trivial subgroup {e}"]; Involutionone[label = "{e, x}, Order two, 2-subnormal"]; Involutiontwo[label = "{e, ax}, Order two, 2-subnormal"]; Involutionthree[label = "{e, a^2x}, Order two, 2-subnormal"]; Involutionfour[label = "{e, a^3x}, Order two, 2-subnormal"]; ElementaryAbelianone[label = "{e, x, a^2, a^2x}, Order four, normal"]; ElementaryAbeliantwo[label = "{e, ax, a^2, a^3x}, Order four, normal"]; Cyclicfour[label = "{e, a, a^2, a^3}, Order four, characteristic"]; }