← #72334328
Subgroups — #72334328
Order 8192.
Only the 2746 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 163 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72334284 | C2 | 1 | 9 | yes | maximal, complemented |
| 2 | #72317060 | C2 | 1 | 9 | yes | maximal, complemented |
| 3 | #72317052 | C22 | 1 | 18 | yes | complemented |
| 4 | #72309401 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #72309397 | C22 | 1 | 9 | yes | complemented |
| 6 | #72306611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72236520 | C22 | 1 | 36 | yes | complemented |
| 8 | #72234683 | C22 | 1 | 9 | yes | — |
| 9 | #72234682 | D4 | 1 | 18 | yes | complemented |
| 10 | #72234670 | D4 | 1 | 9 | yes | complemented |
| 11 | #72234618 | D4 | 1 | 36 | yes | complemented |
| 12 | C2×#8932885 | D4 | 1 | 9 | yes | complemented |
| 13 | #72225731 | C2 | 1 | 6 | yes | maximal, complemented |
| 14 | #72225676 | C22 | 1 | 18 | yes | complemented |
| 15 | #72225652 | C22 | 1 | 6 | yes | complemented |
| 16 | #72225629 | C22 | 1 | 18 | yes | complemented |
| 17 | #72225615 | C22 | 1 | 6 | yes | — |
| 18 | #72221195 | C22 | 1 | 6 | yes | complemented |
| 19 | #72221145 | C23 | 1 | 18 | yes | complemented |
| 20 | #72219291 | C22 | 1 | 2 | yes | complemented |
| 21 | #72219257 | D4 | 1 | 18 | yes | complemented |
| 22 | #72219254 | D4 | 1 | 6 | yes | complemented |
| 23 | #72219227 | C23 | 1 | 6 | yes | complemented |
| 24 | #72219225 | D4 | 1 | 18 | yes | complemented |
| 25 | C22×#15947 | C23 | 1 | 2 | yes | — |
| 26 | C2×#72217546 | C22 | 1 | 9 | yes | complemented |
| 27 | C2×#374022 | C23 | 1 | 9 | yes | complemented |
| 28 | C2×#359428 | C23 | 1 | 18 | yes | complemented |
| 29 | C2×#7670203 | C23 | 1 | 9 | yes | — |
| 30 | #72219166 | C23 | 1 | 6 | yes | — |
| 31 | C22×#62817 | D4 | 1 | 6 | yes | complemented |
| 32 | #72218799 | C22 | 1 | 18 | yes | complemented |
| 33 | #72218744 | C23 | 1 | 36 | yes | complemented |
| 34 | #72218375 | C23 | 1 | 18 | yes | complemented |
| 35 | #72217875 | C23 | 1 | 18 | yes | — |
| 36 | C23×#2846 | C23 | 1 | 6 | yes | complemented |
| 37 | C2×#6342371 | C23 | 1 | 9 | yes | complemented |
| 38 | C29 | C24 | 1 | 1 | yes | characteristic, complemented |
| 39 | C22×#3484 | C2×D4 | 1 | 18 | yes | — |
| 40 | C22×#3484 | C2×D4 | 1 | 18 | yes | — |
| 41 | C24×#120 | C2×D4 | 1 | 6 | yes | — |
| 42 | C24×#120 | C24 | 1 | 6 | yes | — |
| 43 | C22×#2846 | C24 | 1 | 9 | yes | — |
| 44 | C2×#35390 | C2×D4 | 1 | 9 | yes | — |
| 45 | C2×#35348 | C2×D4 | 1 | 18 | yes | — |
| 46 | C2×#35346 | C2×D4 | 1 | 9 | yes | — |
| 47 | C2×#35346 | C2×D4 | 1 | 36 | yes | — |
| 48 | C2×#35346 | C2×D4 | 1 | 18 | yes | — |
| 49 | C2×#34981 | C2×D4 | 1 | 18 | yes | — |
| 50 | C2×#34980 | C2×D4 | 1 | 18 | yes | — |
| 51 | C2×#34198 | C2×D4 | 1 | 18 | yes | — |
| 52 | C23×#379 | C24 | 1 | 6 | yes | complemented |
| 53 | #5955309 | C2×D4 | 1 | 36 | yes | — |
| 54 | #5955303 | C2×D4 | 1 | 72 | yes | — |
| 55 | C2×#14679 | C24 | 1 | 9 | yes | complemented |
| 56 | #517411 | C2×D4 | 1 | 18 | yes | — |
| 57 | #516383 | C2×D4 | 1 | 36 | yes | — |
| 58 | #515326 | C2×D4 | 1 | 18 | yes | — |
| 59 | #515285 | C2×D4 | 1 | 36 | yes | — |
| 60 | C22×#1438 | C2×D4 | 1 | 18 | yes | — |
| 61 | C28 | #120 | 1 | 2 | yes | complemented |
| 62 | C28 | C25 | 1 | 1 | yes | characteristic |
| 63 | C23×H(5,𝔽2) | #120 | 1 | 9 | yes | — |
| 64 | C23×H(5,𝔽2) | #120 | 1 | 18 | yes | complemented |
| 65 | C23×H(5,𝔽2) | #120 | 1 | 6 | yes | complemented |
| 66 | C25×D4 | C22×D4 | 1 | 18 | yes | — |
| 67 | C22×#534 | #120 | 1 | 18 | yes | — |
| 68 | C22×#534 | #120 | 1 | 18 | yes | — |
| 69 | C22×#534 | #120 | 1 | 9 | yes | — |
| 70 | C22×#534 | #120 | 1 | 36 | yes | complemented |
| 71 | C23×#120 | C22×D4 | 1 | 6 | yes | — |
| 72 | C23×#120 | C22×D4 | 1 | 6 | yes | — |
| 73 | C23×#120 | C22×D4 | 1 | 18 | yes | — |
| 74 | C23×#120 | C22×D4 | 1 | 18 | yes | — |
| 75 | C23×#120 | C22×D4 | 1 | 18 | yes | — |
| 76 | C23×#120 | C22×D4 | 1 | 9 | yes | — |
| 77 | C23×#120 | C22×D4 | 1 | 36 | yes | — |
| 78 | C22×#518 | #120 | 1 | 18 | yes | — |
| 79 | C22×#518 | #120 | 1 | 18 | yes | complemented |
| 80 | C24×C22⋊C4 | #120 | 1 | 18 | yes | complemented |
| 81 | C24×C22⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 82 | C2×#2315 | #120 | 1 | 18 | yes | — |
| 83 | C2×#2315 | #120 | 1 | 18 | yes | complemented |
| 84 | C2×#2308 | #120 | 1 | 18 | yes | — |
| 85 | C2×#2308 | #120 | 1 | 18 | yes | — |
| 86 | C2×#2308 | #120 | 1 | 9 | yes | — |
| 87 | C2×#2308 | #120 | 1 | 72 | yes | complemented |
| 88 | C2×#2308 | #120 | 1 | 36 | yes | complemented |
| 89 | C2×#2308 | #120 | 1 | 36 | yes | complemented |
| 90 | C2×#2308 | #120 | 1 | 18 | yes | complemented |
| 91 | C2×#2308 | #120 | 1 | 36 | yes | complemented |
| 92 | C22×#379 | C22×D4 | 1 | 18 | yes | — |
| 93 | C22×#379 | C22×D4 | 1 | 9 | yes | — |
| 94 | C22×#379 | C22×D4 | 1 | 36 | yes | — |
| 95 | C2×#2273 | #120 | 1 | 9 | yes | — |
| 96 | C2×#2273 | #120 | 1 | 6 | yes | complemented |
| 97 | C23×#95 | #120 | 1 | 12 | yes | complemented |
| 98 | #13794 | #120 | 1 | 72 | yes | complemented |
| 99 | #13794 | #120 | 1 | 12 | yes | complemented |
| 100 | C27 | C2×#120 | 1 | 6 | yes | — |
| 101 | C27 | C23×D4 | 1 | 6 | yes | — |
| 102 | C27 | C23×D4 | 1 | 9 | yes | — |
| 103 | C22×H(5,𝔽2) | B(4,𝔽2) | 1 | 36 | yes | complemented |
| 104 | C24×D4 | C2×#120 | 1 | 18 | yes | — |
| 105 | C24×D4 | C2×#120 | 1 | 9 | yes | — |
| 106 | C24×D4 | C2×#120 | 1 | 18 | yes | — |
| 107 | C24×D4 | C2×#120 | 1 | 18 | yes | — |
| 108 | C24×D4 | C2×#120 | 1 | 18 | yes | — |
| 109 | C24×D4 | C2×#120 | 1 | 36 | yes | — |
| 110 | C24×D4 | C2×#120 | 1 | 18 | yes | — |
| 111 | C25×C4 | C2×#120 | 1 | 18 | yes | — |
| 112 | C23×C22⋊C4 | C2×#120 | 1 | 18 | yes | — |
| 113 | C23×C22⋊C4 | C2×#120 | 1 | 18 | yes | — |
| 114 | C23×C22⋊C4 | C2×#120 | 1 | 18 | yes | — |
| 115 | C23×C22⋊C4 | C2×#120 | 1 | 18 | yes | — |
| 116 | C23×C22⋊C4 | C2×#120 | 1 | 36 | yes | — |
| 117 | C23×C22⋊C4 | C2×#120 | 1 | 36 | yes | — |
| 118 | C23×C22⋊C4 | C2×#120 | 1 | 36 | yes | — |
| 119 | C23×C22⋊C4 | C2×#120 | 1 | 9 | yes | — |
| 120 | C23×C22⋊C4 | C2×#120 | 1 | 72 | yes | — |
| 121 | C26 | #2846 | 1 | 6 | yes | — |
| 122 | C26 | #2846 | 1 | 9 | yes | — |
| 123 | C26 | #2846 | 1 | 6 | yes | — |
| 124 | C26 | C22×#120 | 1 | 2 | yes | — |
| 125 | C26 | C22×#120 | 1 | 18 | yes | — |
| 126 | C26 | C22×#120 | 1 | 6 | yes | — |
| 127 | C26 | C22×#120 | 1 | 9 | yes | — |
| 128 | C23×D4 | C2×B(4,𝔽2) | 1 | 18 | yes | — |
| 129 | C23×D4 | C2×B(4,𝔽2) | 1 | 36 | yes | — |
| 130 | C23×D4 | #3026 | 1 | 18 | yes | — |
| 131 | C23×D4 | #3026 | 1 | 36 | yes | — |
| 132 | C24×C4 | #2846 | 1 | 18 | yes | — |
| 133 | C24×C4 | #2846 | 1 | 9 | yes | — |
| 134 | C24×C4 | #2846 | 1 | 18 | yes | — |
| 135 | C24×C4 | #2846 | 1 | 36 | yes | — |
| 136 | C24×C4 | #2846 | 1 | 18 | yes | — |
| 137 | C25 | #32898 | 1 | 18 | yes | — |
| 138 | C25 | #32898 | 1 | 36 | yes | — |
| 139 | C25 | C2×#2846 | 1 | 6 | yes | — |
| 140 | C25 | C2×#2846 | 1 | 9 | yes | — |
| 141 | C25 | C22×B(4,𝔽2) | 1 | 9 | yes | — |
| 142 | C25 | C2×#3026 | 1 | 18 | yes | — |
| 143 | C25 | C2×#3026 | 1 | 9 | yes | — |
| 144 | C23×C4 | #32898 | 1 | 36 | yes | — |
| 145 | C23×C4 | #32898 | 1 | 18 | yes | — |
| 146 | C24 | #347042 | 1 | 24 | yes | complemented |
| 147 | C24 | #6342371 | 1 | 1 | yes | characteristic |
| 148 | C24 | C2×#32898 | 1 | 18 | yes | — |
| 149 | C24 | C2×#32898 | 1 | 9 | yes | — |
| 150 | C24 | #6628892 | 1 | 18 | yes | — |
| 151 | C24 | #6628892 | 1 | 9 | yes | — |
| 152 | C23 | #72210025 | 1 | 6 | yes | — |
| 153 | C23 | C2×#347042 | 1 | 6 | yes | — |
| 154 | C23 | #72219118 | 1 | 9 | yes | — |
| 155 | C23 | #72233581 | 1 | 18 | yes | — |
| 156 | C22 | #72228235 | 1 | 2 | yes | — |
| 157 | C22 | #72255884 | 1 | 6 | yes | — |
| 158 | C22 | #72258972 | 1 | 18 | yes | — |
| 159 | C22 | #72265938 | 1 | 9 | yes | — |
| 160 | C2 | #72266466 | 1 | 9 | yes | — |
| 161 | C2 | #72334288 | 1 | 6 | 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