← #72308236
Subgroups — #72308236
Order 4096.
Only the 2623 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 169 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72306591 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72304197 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #72303645 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #72303497 | C22 | 1 | 6 | yes | — |
| 5 | #72302892 | C22 | 1 | 6 | yes | complemented |
| 6 | #72258268 | C2 | 1 | 9 | yes | maximal, complemented |
| 7 | #72258256 | C22 | 1 | 9 | yes | complemented |
| 8 | #72258253 | C22 | 1 | 9 | yes | complemented |
| 9 | #72232895 | C22 | 1 | 18 | yes | complemented |
| 10 | #72227830 | C22 | 1 | 2 | yes | complemented |
| 11 | #72225836 | C2 | 1 | 9 | yes | maximal, complemented |
| 12 | #72225802 | C22 | 1 | 36 | yes | complemented |
| 13 | #72225797 | C22 | 1 | 18 | yes | complemented |
| 14 | #72225792 | C22 | 1 | 18 | yes | complemented |
| 15 | C2×#493474 | C22 | 1 | 18 | yes | complemented |
| 16 | #72219286 | C22 | 1 | 9 | yes | — |
| 17 | C2×#6499874 | C22 | 1 | 6 | yes | complemented |
| 18 | C2×#62817 | C23 | 1 | 6 | yes | — |
| 19 | C2×#60399 | C23 | 1 | 9 | yes | — |
| 20 | #7664542 | D4 | 1 | 6 | yes | complemented |
| 21 | #7664541 | C23 | 1 | 2 | yes | — |
| 22 | #7659310 | D4 | 1 | 36 | yes | complemented |
| 23 | #7659309 | D4 | 1 | 18 | yes | complemented |
| 24 | #7659307 | C23 | 1 | 18 | yes | — |
| 25 | #7643283 | D4 | 1 | 18 | yes | complemented |
| 26 | #7642897 | D4 | 1 | 9 | yes | complemented |
| 27 | #7642244 | D4 | 1 | 18 | yes | complemented |
| 28 | #7633646 | D4 | 1 | 6 | yes | complemented |
| 29 | C22×#2679 | D4 | 1 | 9 | yes | complemented |
| 30 | #7626264 | C23 | 1 | 9 | yes | — |
| 31 | C2×#33348 | C23 | 1 | 36 | yes | — |
| 32 | C2×#21778 | C23 | 1 | 9 | yes | — |
| 33 | C2×#21776 | C23 | 1 | 18 | yes | — |
| 34 | #6370747 | C23 | 1 | 6 | yes | — |
| 35 | #492908 | C23 | 1 | 6 | yes | — |
| 36 | #492900 | C23 | 1 | 18 | yes | — |
| 37 | #355935 | C23 | 1 | 18 | yes | — |
| 38 | C2×H(7,𝔽2) | C24 | 1 | 1 | yes | characteristic |
| 39 | C2×#3490 | C2×D4 | 1 | 36 | yes | — |
| 40 | C2×#3484 | C2×D4 | 1 | 18 | yes | — |
| 41 | C2×#3484 | C24 | 1 | 9 | yes | — |
| 42 | C23×#120 | C2×D4 | 1 | 18 | yes | — |
| 43 | C2×#2888 | C24 | 1 | 6 | yes | — |
| 44 | C2×#2883 | C24 | 1 | 9 | yes | — |
| 45 | #52291 | C2×D4 | 1 | 6 | yes | — |
| 46 | #52163 | C2×D4 | 1 | 18 | yes | — |
| 47 | C2×#2679 | C2×D4 | 1 | 36 | yes | — |
| 48 | #37306 | C2×D4 | 1 | 18 | yes | — |
| 49 | #37297 | C2×D4 | 1 | 18 | yes | — |
| 50 | #37269 | C2×D4 | 1 | 36 | yes | — |
| 51 | #37129 | C2×D4 | 1 | 36 | yes | — |
| 52 | #36714 | C2×D4 | 1 | 72 | yes | — |
| 53 | #34275 | C2×D4 | 1 | 18 | yes | — |
| 54 | #34269 | C2×D4 | 1 | 18 | yes | — |
| 55 | #34258 | C24 | 1 | 6 | yes | — |
| 56 | #34255 | C2×D4 | 1 | 18 | yes | — |
| 57 | #34200 | C2×D4 | 1 | 18 | yes | — |
| 58 | #34171 | C2×D4 | 1 | 9 | yes | — |
| 59 | C4×#525 | C2×D4 | 1 | 18 | yes | — |
| 60 | C22×#390 | C2×D4 | 1 | 9 | yes | — |
| 61 | C27 | #120 | 1 | 6 | yes | complemented |
| 62 | H(7,𝔽2) | H(5,𝔽2) | 1 | 2 | yes | complemented |
| 63 | C22×H(5,𝔽2) | #120 | 1 | 6 | yes | complemented |
| 64 | C22×H(5,𝔽2) | C25 | 1 | 1 | yes | characteristic |
| 65 | C24×D4 | C22×D4 | 1 | 9 | yes | — |
| 66 | C2×#543 | #120 | 1 | 12 | yes | complemented |
| 67 | C2×#535 | C22×D4 | 1 | 18 | yes | — |
| 68 | C2×#534 | C22×D4 | 1 | 36 | yes | — |
| 69 | C2×#525 | C22×D4 | 1 | 18 | yes | — |
| 70 | C22×#120 | #120 | 1 | 36 | yes | complemented |
| 71 | C22×#120 | C22×D4 | 1 | 36 | yes | — |
| 72 | C2×#520 | C22×D4 | 1 | 6 | yes | — |
| 73 | C2×#518 | #120 | 1 | 18 | yes | complemented |
| 74 | C2×#518 | #120 | 1 | 9 | yes | complemented |
| 75 | C2×#518 | #120 | 1 | 9 | yes | complemented |
| 76 | C2×#518 | C22×D4 | 1 | 9 | yes | — |
| 77 | C2×C4×#41 | C22×D4 | 1 | 6 | yes | — |
| 78 | C23×C4⋊C4 | #120 | 1 | 9 | yes | complemented |
| 79 | C23×C22⋊C4 | #120 | 1 | 18 | yes | complemented |
| 80 | C23×C42 | #120 | 1 | 9 | yes | complemented |
| 81 | #2883 | H(5,𝔽2) | 1 | 18 | yes | complemented |
| 82 | #2811 | #120 | 1 | 2 | yes | complemented |
| 83 | #2811 | #120 | 1 | 12 | yes | complemented |
| 84 | #2809 | #120 | 1 | 18 | yes | complemented |
| 85 | #2724 | #120 | 1 | 18 | yes | complemented |
| 86 | #2697 | #120 | 1 | 72 | yes | complemented |
| 87 | #2697 | #120 | 1 | 36 | yes | complemented |
| 88 | #2679 | #120 | 1 | 36 | yes | complemented |
| 89 | #2679 | #120 | 1 | 36 | yes | complemented |
| 90 | #2679 | #120 | 1 | 72 | yes | complemented |
| 91 | #2679 | #120 | 1 | 18 | yes | complemented |
| 92 | #2317 | #120 | 1 | 18 | yes | complemented |
| 93 | #2311 | C22×D4 | 1 | 18 | yes | — |
| 94 | #2309 | C22×D4 | 1 | 18 | yes | — |
| 95 | #2297 | C22×D4 | 1 | 18 | yes | — |
| 96 | #2296 | #120 | 1 | 18 | yes | complemented |
| 97 | C2×#390 | #120 | 1 | 18 | yes | complemented |
| 98 | C2×#390 | C22×D4 | 1 | 18 | yes | — |
| 99 | #2280 | #120 | 1 | 18 | yes | complemented |
| 100 | #2274 | #120 | 1 | 18 | yes | complemented |
| 101 | C4×#117 | #120 | 1 | 18 | yes | complemented |
| 102 | C26 | C2×#120 | 1 | 18 | yes | — |
| 103 | C2×H(5,𝔽2) | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 104 | C2×H(5,𝔽2) | C2×H(5,𝔽2) | 1 | 9 | yes | — |
| 105 | C2×H(5,𝔽2) | #585 | 1 | 6 | yes | — |
| 106 | C22×#41 | C23×D4 | 1 | 6 | yes | — |
| 107 | C23×D4 | C2×#120 | 1 | 18 | yes | — |
| 108 | C23×D4 | C2×#120 | 1 | 9 | yes | — |
| 109 | C23×D4 | C23×D4 | 1 | 9 | yes | — |
| 110 | C24×C4 | C2×#120 | 1 | 9 | yes | — |
| 111 | C2×#123 | C2×#120 | 1 | 36 | yes | — |
| 112 | C2×#120 | C2×#120 | 1 | 36 | yes | — |
| 113 | C2×#120 | C2×#120 | 1 | 72 | yes | — |
| 114 | C2×#117 | C2×#120 | 1 | 18 | yes | — |
| 115 | C2×#117 | C2×#120 | 1 | 18 | yes | — |
| 116 | C2×#117 | C2×#120 | 1 | 18 | yes | — |
| 117 | C22×C4⋊C4 | C2×#120 | 1 | 18 | yes | — |
| 118 | C22×C22⋊C4 | C2×#120 | 1 | 36 | yes | — |
| 119 | C22×C42 | C2×#120 | 1 | 18 | yes | — |
| 120 | #391 | C2×#120 | 1 | 18 | yes | — |
| 121 | #391 | C2×#120 | 1 | 6 | yes | — |
| 122 | #390 | C2×#120 | 1 | 18 | yes | — |
| 123 | #390 | C2×#120 | 1 | 36 | yes | — |
| 124 | #390 | C2×#120 | 1 | 18 | yes | — |
| 125 | C25 | #2846 | 1 | 9 | yes | — |
| 126 | C25 | #2846 | 1 | 18 | yes | — |
| 127 | C25 | C22×#120 | 1 | 6 | yes | — |
| 128 | C2×#41 | #3488 | 1 | 6 | yes | — |
| 129 | C2×#41 | #3488 | 1 | 18 | yes | — |
| 130 | C2×#41 | #3498 | 1 | 18 | yes | — |
| 131 | C2×#41 | #3500 | 1 | 6 | yes | — |
| 132 | C22×Q8 | C22×#120 | 1 | 2 | yes | — |
| 133 | C22×D4 | C22×#120 | 1 | 18 | yes | — |
| 134 | C22×D4 | #3484 | 1 | 9 | yes | — |
| 135 | C22×D4 | #3484 | 1 | 18 | yes | — |
| 136 | C22×D4 | #3485 | 1 | 9 | yes | — |
| 137 | C22×D4 | #3496 | 1 | 36 | yes | — |
| 138 | C23×C4 | #2846 | 1 | 9 | yes | — |
| 139 | C23×C4 | C22×#120 | 1 | 9 | yes | — |
| 140 | C2×C4⋊C4 | #2846 | 1 | 18 | yes | — |
| 141 | C2×C4⋊C4 | #2846 | 1 | 6 | yes | — |
| 142 | C2×C22⋊C4 | #2846 | 1 | 36 | yes | — |
| 143 | C2×C42 | #2846 | 1 | 18 | yes | — |
| 144 | C2×C42 | #2846 | 1 | 6 | yes | — |
| 145 | C24 | #35346 | 1 | 6 | yes | — |
| 146 | C24 | #35347 | 1 | 18 | yes | — |
| 147 | C24 | C2×#2846 | 1 | 9 | yes | — |
| 148 | C2×Q8 | #36082 | 1 | 2 | yes | — |
| 149 | C2×Q8 | #36091 | 1 | 6 | yes | — |
| 150 | C2×D4 | #35680 | 1 | 36 | yes | — |
| 151 | C2×D4 | #35680 | 1 | 18 | yes | — |
| 152 | C2×D4 | #35750 | 1 | 18 | yes | — |
| 153 | C22×C4 | #35512 | 1 | 9 | yes | — |
| 154 | C22×C4 | #35513 | 1 | 18 | yes | — |
| 155 | C22×C4 | #35527 | 1 | 9 | yes | — |
| 156 | C22×C4 | C2×#2846 | 1 | 6 | yes | — |
| 157 | C23 | #4928938 | 1 | 9 | yes | — |
| 158 | C23 | #4930494 | 1 | 9 | yes | — |
| 159 | C23 | #6342371 | 1 | 1 | yes | characteristic |
| 160 | C2×C4 | #4929082 | 1 | 6 | yes | — |
| 161 | C2×C4 | #4930608 | 1 | 6 | yes | — |
| 162 | C22 | #72210025 | 1 | 1 | yes | characteristic |
| 163 | C22 | #72210025 | 1 | 1 | yes | characteristic |
| 164 | C22 | #72250267 | 1 | 1 | yes | characteristic |
| 165 | C2 | #72258964 | 1 | 1 | yes | characteristic |
| 166 | C2 | #72265887 | 1 | 1 | yes | characteristic |
| 167 | C2 | #72308132 | 1 | 1 | yes | characteristic |
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