File:D8latticeofsubgroups.png

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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"];
}

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current20:36, 1 December 2008Thumbnail for version as of 20:36, 1 December 20081,643 × 400 (102 KB)Vipul (talk | contribs)
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