File:Symmetric group S4; lattice of subgroups Hasse diagram; all 30 subgroups.svg
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DescriptionSymmetric group S4; lattice of subgroups Hasse diagram; all 30 subgroups.svg |
The lattice of subgroups of the Symmetric group S4, represented in a Hasse diagram These are A005432(4) = 30 distinct subgroups. They belong to A000638(4) = 11 different types, which are shown on the right. S4: Symmetric group of order 24 The C2 knots are marked with the index numbers (compare this table) of the transpositions (1, 6, 5, 14, 2, 21) and double transpositions (7, 16, 23) each has as its non-identity element. Edge colors indicate the quotient of the connected groups' orders: red 2, green 3, blue 4 |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 18:50, 7 May 2017 | 1,054 × 1,012 (224 KB) | Watchduck (talk | contribs) | layout | |
13:47, 16 November 2016 | 1,054 × 1,012 (222 KB) | Watchduck (talk | contribs) | color edges | ||
22:30, 30 October 2016 | 1,054 × 1,012 (221 KB) | Watchduck (talk | contribs) | {{Information |Description ={{en|1=The lattice of subgroups of the Symmetric group S<sub>4</sub>, represented in a Hasse diagram S4: Symmetric group of order 24 A4: Alternating group of order 12 Dih4... |
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