← #72310419
Subgroups — #72310419
Order 2048.
Only the 924 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 128 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72219237 | C2 | 1 | 12 | yes | maximal, complemented |
| 2 | #72219227 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72218518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72217511 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C2×#62817 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C24×#120 | C22 | 1 | 1 | yes | characteristic |
| 7 | #7642244 | C4 | 1 | 6 | yes | complemented |
| 8 | #7630939 | C22 | 1 | 6 | yes | — |
| 9 | #7626202 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C22×#1438 | C22 | 1 | 6 | yes | complemented |
| 11 | #392675 | C22 | 1 | 16 | yes | complemented |
| 12 | #392109 | C22 | 1 | 6 | yes | complemented |
| 13 | C28 | D4 | 1 | 1 | yes | characteristic |
| 14 | C25×D4 | C23 | 1 | 3 | yes | — |
| 15 | C2×#3484 | C2×C4 | 1 | 6 | yes | — |
| 16 | C2×#3484 | D4 | 1 | 12 | yes | — |
| 17 | C23×#120 | C2×C4 | 1 | 1 | yes | characteristic |
| 18 | C23×#120 | C2×C4 | 1 | 3 | yes | — |
| 19 | C23×#120 | D4 | 1 | 1 | yes | characteristic |
| 20 | C23×#120 | D4 | 1 | 3 | yes | — |
| 21 | C24×C22⋊C4 | D4 | 1 | 3 | yes | — |
| 22 | C24×C22⋊C4 | C23 | 1 | 4 | yes | complemented |
| 23 | C2×#2846 | C23 | 1 | 4 | yes | — |
| 24 | #34980 | C2×C4 | 1 | 12 | yes | — |
| 25 | #34980 | D4 | 1 | 24 | yes | — |
| 26 | #34171 | C2×C4 | 1 | 6 | yes | — |
| 27 | #34171 | D4 | 1 | 12 | yes | — |
| 28 | #14679 | C23 | 1 | 4 | yes | complemented |
| 29 | C27 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 30 | C27 | C22⋊C4 | 1 | 3 | yes | — |
| 31 | C27 | C2×D4 | 1 | 3 | yes | — |
| 32 | C27 | C24 | 1 | 1 | yes | characteristic |
| 33 | C22×H(5,𝔽2) | C22⋊C4 | 1 | 6 | yes | complemented |
| 34 | C24×D4 | C22×C4 | 1 | 3 | yes | — |
| 35 | C24×D4 | C22×C4 | 1 | 3 | yes | — |
| 36 | C24×D4 | C2×D4 | 1 | 3 | yes | — |
| 37 | C24×D4 | C2×D4 | 1 | 3 | yes | — |
| 38 | C24×D4 | C2×D4 | 1 | 12 | yes | — |
| 39 | C24×D4 | C2×D4 | 1 | 12 | yes | — |
| 40 | C25×C4 | C2×D4 | 1 | 3 | yes | — |
| 41 | C2×#534 | C22⋊C4 | 1 | 12 | yes | complemented |
| 42 | C2×#534 | C22⋊C4 | 1 | 24 | yes | complemented |
| 43 | C22×#120 | C22×C4 | 1 | 4 | yes | — |
| 44 | C22×#120 | C2×D4 | 1 | 24 | yes | — |
| 45 | C2×#518 | C22⋊C4 | 1 | 6 | yes | complemented |
| 46 | C2×#518 | C22⋊C4 | 1 | 12 | yes | complemented |
| 47 | C23×C22⋊C4 | C22⋊C4 | 1 | 3 | yes | — |
| 48 | C23×C22⋊C4 | C22⋊C4 | 1 | 6 | yes | — |
| 49 | C23×C22⋊C4 | C22⋊C4 | 1 | 3 | yes | — |
| 50 | #2308 | C22⋊C4 | 1 | 12 | yes | complemented |
| 51 | #2308 | C22⋊C4 | 1 | 24 | yes | complemented |
| 52 | C2×#379 | C22×C4 | 1 | 4 | yes | — |
| 53 | C2×#379 | C2×D4 | 1 | 24 | yes | — |
| 54 | C26 | #99 | 1 | 4 | yes | complemented |
| 55 | C26 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 56 | C26 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 57 | C26 | #120 | 1 | 6 | yes | — |
| 58 | C26 | #120 | 1 | 6 | yes | — |
| 59 | C26 | C23×C4 | 1 | 1 | yes | characteristic |
| 60 | C26 | C22×D4 | 1 | 1 | yes | characteristic |
| 61 | C26 | C22×D4 | 1 | 1 | yes | characteristic |
| 62 | C26 | C22×D4 | 1 | 12 | yes | — |
| 63 | C23×D4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 64 | C23×D4 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 65 | C23×D4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 66 | C23×D4 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 67 | C23×D4 | #120 | 1 | 12 | yes | — |
| 68 | C23×D4 | #120 | 1 | 6 | yes | — |
| 69 | C23×D4 | #120 | 1 | 6 | yes | — |
| 70 | C23×D4 | #120 | 1 | 16 | yes | — |
| 71 | C24×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 72 | C24×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 73 | C24×C4 | #120 | 1 | 12 | yes | — |
| 74 | C22×C22⋊C4 | #99 | 1 | 12 | yes | complemented |
| 75 | C22×C22⋊C4 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 76 | C22×C22⋊C4 | C2×C22⋊C4 | 1 | 24 | yes | — |
| 77 | C22×C22⋊C4 | #120 | 1 | 48 | yes | — |
| 78 | C25 | #379 | 1 | 3 | yes | — |
| 79 | C25 | #379 | 1 | 3 | yes | — |
| 80 | C25 | #379 | 1 | 6 | yes | — |
| 81 | C25 | #379 | 1 | 4 | yes | complemented |
| 82 | C25 | C2×#99 | 1 | 6 | yes | — |
| 83 | C25 | C2×#99 | 1 | 6 | yes | — |
| 84 | C25 | B(4,𝔽2) | 1 | 12 | yes | — |
| 85 | C25 | #458 | 1 | 12 | yes | — |
| 86 | C25 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 87 | C25 | C22×C22⋊C4 | 1 | 6 | yes | — |
| 88 | C25 | C2×#120 | 1 | 6 | yes | — |
| 89 | C25 | C2×#120 | 1 | 16 | yes | — |
| 90 | C25 | C2×#120 | 1 | 6 | yes | — |
| 91 | C23×C4 | #379 | 1 | 6 | yes | — |
| 92 | C23×C4 | #379 | 1 | 6 | yes | — |
| 93 | C23×C4 | #379 | 1 | 16 | yes | complemented |
| 94 | C23×C4 | #379 | 1 | 12 | yes | complemented |
| 95 | C23×C4 | C2×#99 | 1 | 12 | yes | — |
| 96 | C24 | #1781 | 1 | 6 | yes | — |
| 97 | C24 | #1781 | 1 | 6 | yes | — |
| 98 | C24 | #1790 | 1 | 12 | yes | — |
| 99 | C24 | #1790 | 1 | 12 | yes | — |
| 100 | C24 | C2×#379 | 1 | 4 | yes | — |
| 101 | C24 | C2×#379 | 1 | 3 | yes | — |
| 102 | C24 | #2846 | 1 | 4 | yes | — |
| 103 | C24 | #2846 | 1 | 4 | yes | — |
| 104 | C24 | C22×#99 | 1 | 3 | yes | — |
| 105 | C24 | C22×#99 | 1 | 1 | yes | characteristic |
| 106 | C24 | C2×B(4,𝔽2) | 1 | 6 | yes | — |
| 107 | C24 | C2×#458 | 1 | 6 | yes | — |
| 108 | C24 | #3026 | 1 | 12 | yes | — |
| 109 | C22×C4 | #1781 | 1 | 12 | yes | — |
| 110 | C23 | #8534 | 1 | 12 | yes | complemented |
| 111 | C23 | #14679 | 1 | 1 | yes | characteristic |
| 112 | C23 | C2×#1781 | 1 | 3 | yes | — |
| 113 | C23 | C2×#1781 | 1 | 3 | yes | — |
| 114 | C23 | C2×#1790 | 1 | 6 | yes | — |
| 115 | C23 | #20609 | 1 | 6 | yes | — |
| 116 | C23 | #32898 | 1 | 12 | yes | — |
| 117 | C23 | #32900 | 1 | 12 | yes | — |
| 118 | C22 | C2×#8534 | 1 | 3 | yes | — |
| 119 | C22 | #187928 | 1 | 6 | yes | — |
| 120 | C22 | #187944 | 1 | 3 | yes | — |
| 121 | C22 | #347042 | 1 | 4 | yes | — |
| 122 | C22 | #347048 | 1 | 12 | yes | — |
| 123 | C22 | #392109 | 1 | 1 | yes | characteristic |
| 124 | C22 | #392125 | 1 | 6 | yes | — |
| 125 | C2 | #72218467 | 1 | 3 | yes | — |
| 126 | C2 | #72219045 | 1 | 4 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta