← #72265792
Subgroups — #72265792
Order 2048.
At least 6172 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
The subgroup lattice has 173 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72265603 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72219457 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72219414 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72219294 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72218846 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72218381 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72218198 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#2403 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×#1781 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×#1781 | C22 | 1 | 1 | yes | characteristic |
| 11 | #517411 | C22 | 1 | 1 | yes | characteristic |
| 12 | #392113 | C22 | 1 | 1 | yes | characteristic |
| 13 | #392109 | C4 | 1 | 2 | yes | complemented |
| 14 | #392109 | C22 | 1 | 1 | yes | characteristic |
| 15 | #392109 | C22 | 1 | 1 | yes | characteristic |
| 16 | C22⋊#1304 | C4 | 1 | 2 | yes | complemented |
| 17 | C25×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 18 | C25×D4 | C23 | 1 | 1 | yes | characteristic |
| 19 | C23×#120 | D4 | 1 | 1 | yes | characteristic |
| 20 | C23×#120 | Q8 | 1 | 1 | yes | characteristic |
| 21 | C23×#99 | D4 | 1 | 1 | yes | characteristic |
| 22 | C23×#99 | D4 | 1 | 1 | yes | characteristic |
| 23 | C2×#2308 | D4 | 1 | 1 | yes | characteristic |
| 24 | C2×#2308 | D4 | 1 | 1 | yes | characteristic |
| 25 | C22×#386 | D4 | 1 | 1 | yes | characteristic |
| 26 | C22×#386 | Q8 | 1 | 1 | yes | characteristic |
| 27 | C22×#379 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C22×#379 | D4 | 1 | 1 | yes | characteristic |
| 29 | C22×#379 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×#1783 | D4 | 1 | 2 | yes | — |
| 31 | C2×#1781 | D4 | 1 | 2 | yes | — |
| 32 | #14679 | C2×C4 | 1 | 2 | yes | — |
| 33 | #14679 | C2×C4 | 1 | 2 | yes | — |
| 34 | #14335 | D4 | 1 | 2 | yes | — |
| 35 | C27 | C4⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 36 | C27 | C22×C4 | 1 | 1 | yes | characteristic |
| 37 | C27 | C2×D4 | 1 | 1 | yes | characteristic |
| 38 | C24×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 39 | C24×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 40 | C24×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 41 | C24×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 42 | C24×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 43 | C24×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 44 | C24×D4 | C2×Q8 | 1 | 1 | yes | characteristic |
| 45 | C24×D4 | #41 | 1 | 1 | yes | characteristic |
| 46 | C24×D4 | #41 | 1 | 1 | yes | characteristic |
| 47 | C24×D4 | #41 | 1 | 1 | yes | characteristic |
| 48 | C24×D4 | #41 | 1 | 1 | yes | characteristic |
| 49 | C24×D4 | #41 | 1 | 1 | yes | characteristic |
| 50 | C25×C4 | C4⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 51 | C25×C4 | #41 | 1 | 1 | yes | characteristic |
| 52 | C23×C22⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 53 | C23×C22⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 54 | C2×#379 | C22⋊C4 | 1 | 2 | yes | — |
| 55 | C2×#379 | C22⋊C4 | 1 | 2 | yes | — |
| 56 | C26 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 57 | C26 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 58 | C26 | #117 | 1 | 1 | yes | characteristic |
| 59 | C26 | C4×D4 | 1 | 1 | yes | characteristic |
| 60 | C26 | C4×D4 | 1 | 1 | yes | characteristic |
| 61 | C26 | C4×D4 | 1 | 1 | yes | characteristic |
| 62 | C26 | C4×D4 | 1 | 1 | yes | characteristic |
| 63 | C26 | #120 | 1 | 1 | yes | characteristic |
| 64 | C26 | #120 | 1 | 1 | yes | characteristic |
| 65 | C26 | #121 | 1 | 1 | yes | characteristic |
| 66 | C26 | #121 | 1 | 1 | yes | characteristic |
| 67 | C26 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 68 | C26 | #124 | 1 | 1 | yes | characteristic |
| 69 | C23×D4 | #120 | 1 | 1 | yes | characteristic |
| 70 | C23×D4 | #121 | 1 | 1 | yes | characteristic |
| 71 | C23×D4 | #121 | 1 | 1 | yes | characteristic |
| 72 | C23×D4 | #121 | 1 | 1 | yes | characteristic |
| 73 | C23×D4 | #121 | 1 | 1 | yes | characteristic |
| 74 | C23×D4 | #121 | 1 | 1 | yes | characteristic |
| 75 | C23×D4 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 76 | C23×D4 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 77 | C23×D4 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 78 | C23×D4 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 79 | C23×D4 | #123 | 1 | 1 | yes | characteristic |
| 80 | C23×D4 | #123 | 1 | 1 | yes | characteristic |
| 81 | C23×D4 | #124 | 1 | 1 | yes | characteristic |
| 82 | C23×D4 | #124 | 1 | 1 | yes | characteristic |
| 83 | C23×D4 | #126 | 1 | 1 | yes | characteristic |
| 84 | C23×D4 | #127 | 1 | 1 | yes | characteristic |
| 85 | C24×C4 | #121 | 1 | 1 | yes | characteristic |
| 86 | C24×C4 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 87 | C24×C4 | #123 | 1 | 1 | yes | characteristic |
| 88 | C24×C4 | #123 | 1 | 1 | yes | characteristic |
| 89 | C24×C4 | #123 | 1 | 1 | yes | characteristic |
| 90 | C24×C4 | #126 | 1 | 1 | yes | characteristic |
| 91 | C22×C22⋊C4 | #99 | 1 | 4 | yes | complemented |
| 92 | C25 | #380 | 1 | 1 | yes | characteristic |
| 93 | C25 | #385 | 1 | 1 | yes | characteristic |
| 94 | C25 | #385 | 1 | 1 | yes | characteristic |
| 95 | C25 | #386 | 1 | 1 | yes | characteristic |
| 96 | C25 | #388 | 1 | 1 | yes | characteristic |
| 97 | C25 | #388 | 1 | 1 | yes | characteristic |
| 98 | C25 | #390 | 1 | 1 | yes | characteristic |
| 99 | C25 | #392 | 1 | 1 | yes | characteristic |
| 100 | C25 | #393 | 1 | 1 | yes | characteristic |
| 101 | C25 | #394 | 1 | 1 | yes | characteristic |
| 102 | C25 | #396 | 1 | 1 | yes | characteristic |
| 103 | C25 | C2×#99 | 1 | 2 | yes | — |
| 104 | C25 | #410 | 1 | 2 | yes | — |
| 105 | C25 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 106 | C25 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 107 | C25 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 108 | C25 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 109 | C25 | B(4,𝔽2) | 1 | 2 | yes | — |
| 110 | C25 | #458 | 1 | 2 | yes | — |
| 111 | C22×D4 | B(4,𝔽2) | 1 | 2 | yes | — |
| 112 | C22×D4 | #458 | 1 | 2 | yes | — |
| 113 | C23×C4 | #394 | 1 | 1 | yes | characteristic |
| 114 | C23×C4 | #396 | 1 | 1 | yes | characteristic |
| 115 | C23×C4 | #397 | 1 | 1 | yes | characteristic |
| 116 | C23×C4 | #399 | 1 | 1 | yes | characteristic |
| 117 | C24 | #1439 | 1 | 1 | yes | characteristic |
| 118 | C24 | #1799 | 1 | 2 | yes | — |
| 119 | C24 | #1867 | 1 | 2 | yes | — |
| 120 | C24 | #1867 | 1 | 2 | yes | — |
| 121 | C24 | #1889 | 1 | 1 | yes | characteristic |
| 122 | C24 | #1889 | 1 | 1 | yes | characteristic |
| 123 | C24 | #1898 | 1 | 1 | yes | characteristic |
| 124 | C24 | #1899 | 1 | 1 | yes | characteristic |
| 125 | C24 | #1913 | 1 | 1 | yes | characteristic |
| 126 | C24 | #1913 | 1 | 1 | yes | characteristic |
| 127 | C24 | #1964 | 1 | 2 | yes | — |
| 128 | C24 | #2021 | 1 | 1 | yes | characteristic |
| 129 | C24 | #2021 | 1 | 1 | yes | characteristic |
| 130 | C24 | #2021 | 1 | 1 | yes | characteristic |
| 131 | C24 | #2021 | 1 | 1 | yes | characteristic |
| 132 | C24 | #2022 | 1 | 1 | yes | characteristic |
| 133 | C24 | #2022 | 1 | 1 | yes | characteristic |
| 134 | C24 | #2029 | 1 | 1 | yes | characteristic |
| 135 | C24 | #2029 | 1 | 1 | yes | characteristic |
| 136 | C24 | #2032 | 1 | 1 | yes | characteristic |
| 137 | C24 | #2032 | 1 | 1 | yes | characteristic |
| 138 | C24 | #2032 | 1 | 1 | yes | characteristic |
| 139 | C24 | #2032 | 1 | 1 | yes | characteristic |
| 140 | C24 | #2044 | 1 | 2 | yes | — |
| 141 | C22×C4 | #2044 | 1 | 2 | yes | — |
| 142 | C23 | #9495 | 1 | 1 | yes | characteristic |
| 143 | C23 | #9496 | 1 | 1 | yes | characteristic |
| 144 | C23 | #9497 | 1 | 1 | yes | characteristic |
| 145 | C23 | #9498 | 1 | 1 | yes | characteristic |
| 146 | C23 | #10336 | 1 | 1 | yes | characteristic |
| 147 | C23 | #10337 | 1 | 1 | yes | characteristic |
| 148 | C23 | #10337 | 1 | 1 | yes | characteristic |
| 149 | C23 | #10338 | 1 | 1 | yes | characteristic |
| 150 | C23 | #10390 | 1 | 1 | yes | characteristic |
| 151 | C23 | #10392 | 1 | 1 | yes | characteristic |
| 152 | C23 | #10392 | 1 | 1 | yes | characteristic |
| 153 | C23 | #10392 | 1 | 1 | yes | characteristic |
| 154 | C23 | #11043 | 1 | 1 | yes | characteristic |
| 155 | C23 | #11046 | 1 | 1 | yes | characteristic |
| 156 | C23 | #11069 | 1 | 1 | yes | characteristic |
| 157 | C23 | #11087 | 1 | 1 | yes | characteristic |
| 158 | C23 | #11087 | 1 | 1 | yes | characteristic |
| 159 | C23 | #11089 | 1 | 1 | yes | characteristic |
| 160 | C23 | #11089 | 1 | 1 | yes | characteristic |
| 161 | C22 | #115723 | 1 | 1 | yes | characteristic |
| 162 | C22 | #115995 | 1 | 1 | yes | characteristic |
| 163 | C22 | #115995 | 1 | 1 | yes | characteristic |
| 164 | C22 | #116022 | 1 | 1 | yes | characteristic |
| 165 | C22 | #116022 | 1 | 1 | yes | characteristic |
| 166 | C22 | #116351 | 1 | 1 | yes | characteristic |
| 167 | C22 | #116356 | 1 | 1 | yes | characteristic |
| 168 | C22 | #139750 | 1 | 2 | yes | — |
| 169 | C2 | #72255838 | 1 | 1 | yes | characteristic |
| 170 | C2 | #72255867 | 1 | 1 | yes | characteristic |
| 171 | C2 | #72264957 | 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