← #72272577
Subgroups — #72272577
Order 2048.
Only the 2294 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 182 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72272576 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #72272573 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #72272570 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #72272568 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #72272564 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #72272561 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #72272519 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10586977 | C22 | 1 | 4 | yes | — |
| 9 | #10586964 | C22 | 1 | 8 | yes | — |
| 10 | #10586797 | C22 | 1 | 3 | yes | — |
| 11 | #6516740 | C22 | 1 | 6 | yes | complemented |
| 12 | #6351882 | C22 | 1 | 4 | yes | complemented |
| 13 | #6349116 | C22 | 1 | 12 | yes | complemented |
| 14 | #6347408 | C22 | 1 | 12 | yes | complemented |
| 15 | #5021378 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #188170 | C22 | 1 | 3 | yes | complemented |
| 17 | #187922 | C22 | 1 | 4 | yes | complemented |
| 18 | #187745 | C22 | 1 | 8 | yes | complemented |
| 19 | #187544 | C22 | 1 | 24 | yes | complemented |
| 20 | #187378 | C22 | 1 | 24 | yes | complemented |
| 21 | #187093 | C22 | 1 | 12 | yes | complemented |
| 22 | #186843 | C22 | 1 | 6 | yes | complemented |
| 23 | #186596 | C22 | 1 | 12 | yes | complemented |
| 24 | #185284 | C22 | 1 | 12 | yes | complemented |
| 25 | #63036 | D4 | 1 | 8 | yes | complemented |
| 26 | #63014 | D4 | 1 | 24 | yes | complemented |
| 27 | #62979 | D4 | 1 | 8 | yes | complemented |
| 28 | #62977 | D4 | 1 | 24 | yes | complemented |
| 29 | #62976 | D4 | 1 | 8 | yes | complemented |
| 30 | #62975 | D4 | 1 | 24 | yes | complemented |
| 31 | #62840 | C23 | 1 | 4 | yes | — |
| 32 | #62832 | C23 | 1 | 6 | yes | — |
| 33 | #62826 | C23 | 1 | 12 | yes | — |
| 34 | #62820 | D4 | 1 | 6 | yes | — |
| 35 | #62818 | D4 | 1 | 12 | yes | — |
| 36 | #62817 | D4 | 1 | 6 | yes | — |
| 37 | #62762 | C23 | 1 | 12 | yes | — |
| 38 | C22×#560 | C23 | 1 | 1 | yes | characteristic |
| 39 | #60798 | C23 | 1 | 12 | yes | complemented |
| 40 | C2×#2818 | C23 | 1 | 2 | yes | — |
| 41 | C2×#2867 | C23 | 1 | 1 | yes | characteristic |
| 42 | #21797 | C23 | 1 | 6 | yes | — |
| 43 | #21415 | C23 | 1 | 12 | yes | complemented |
| 44 | #17757 | C23 | 1 | 12 | yes | complemented |
| 45 | #17665 | C23 | 1 | 12 | yes | complemented |
| 46 | #17593 | C23 | 1 | 24 | yes | complemented |
| 47 | #17499 | C23 | 1 | 24 | yes | complemented |
| 48 | #17398 | C23 | 1 | 12 | yes | — |
| 49 | #14711 | C23 | 1 | 2 | yes | — |
| 50 | #14661 | C23 | 1 | 1 | yes | characteristic |
| 51 | #3567 | C2×D4 | 1 | 8 | yes | — |
| 52 | #3567 | C2×D4 | 1 | 24 | yes | — |
| 53 | #3564 | C2×D4 | 1 | 24 | yes | — |
| 54 | #3564 | C2×D4 | 1 | 24 | yes | — |
| 55 | #3560 | C2×D4 | 1 | 24 | yes | — |
| 56 | #3560 | C2×D4 | 1 | 24 | yes | — |
| 57 | #3556 | C2×D4 | 1 | 4 | yes | — |
| 58 | #3555 | C2×D4 | 1 | 24 | yes | — |
| 59 | #3554 | C2×D4 | 1 | 24 | yes | — |
| 60 | #3548 | C2×D4 | 1 | 12 | yes | — |
| 61 | #3547 | C2×D4 | 1 | 24 | yes | — |
| 62 | #3546 | C2×D4 | 1 | 24 | yes | — |
| 63 | #3508 | C2×D4 | 1 | 24 | yes | — |
| 64 | #3498 | C2×D4 | 1 | 24 | yes | — |
| 65 | #3492 | C2×D4 | 1 | 24 | yes | — |
| 66 | #3490 | C2×D4 | 1 | 12 | yes | — |
| 67 | #3490 | C2×D4 | 1 | 12 | yes | — |
| 68 | #3484 | C2×D4 | 1 | 12 | yes | — |
| 69 | #3484 | C2×D4 | 1 | 12 | yes | — |
| 70 | #3483 | C2×D4 | 1 | 12 | yes | — |
| 71 | #3482 | C2×D4 | 1 | 24 | yes | — |
| 72 | #3481 | C2×D4 | 1 | 12 | yes | — |
| 73 | #3444 | C24 | 1 | 12 | yes | — |
| 74 | C22×#127 | C24 | 1 | 1 | yes | characteristic |
| 75 | C22×#127 | C24 | 1 | 1 | yes | characteristic |
| 76 | C22×#126 | C24 | 1 | 2 | yes | — |
| 77 | C22×#123 | C2×D4 | 1 | 3 | yes | — |
| 78 | C22×#121 | C2×D4 | 1 | 6 | yes | — |
| 79 | C22×#120 | C2×D4 | 1 | 3 | yes | — |
| 80 | #2920 | C24 | 1 | 12 | yes | — |
| 81 | C2×#383 | C24 | 1 | 2 | yes | — |
| 82 | C2×C43 | C24 | 1 | 1 | yes | characteristic |
| 83 | C26 | #120 | 1 | 1 | yes | characteristic |
| 84 | C2×H(5,𝔽2) | #120 | 1 | 12 | yes | — |
| 85 | C2×H(5,𝔽2) | #120 | 1 | 12 | yes | — |
| 86 | C23×D4 | #120 | 1 | 6 | yes | — |
| 87 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 88 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 89 | C24×C4 | #120 | 1 | 3 | yes | — |
| 90 | #564 | #120 | 1 | 4 | yes | complemented |
| 91 | #564 | #120 | 1 | 12 | yes | complemented |
| 92 | #562 | #120 | 1 | 24 | yes | complemented |
| 93 | #562 | #120 | 1 | 24 | yes | complemented |
| 94 | #559 | #120 | 1 | 12 | yes | complemented |
| 95 | Q82 | #120 | 1 | 12 | yes | complemented |
| 96 | #557 | #120 | 1 | 24 | yes | complemented |
| 97 | #556 | #120 | 1 | 24 | yes | complemented |
| 98 | #555 | #120 | 1 | 12 | yes | complemented |
| 99 | #554 | #120 | 1 | 24 | yes | complemented |
| 100 | #550 | #120 | 1 | 24 | yes | complemented |
| 101 | D4×Q8 | #120 | 1 | 24 | yes | complemented |
| 102 | #547 | #120 | 1 | 24 | yes | complemented |
| 103 | D42 | #120 | 1 | 12 | yes | complemented |
| 104 | #544 | #120 | 1 | 24 | yes | — |
| 105 | #543 | #120 | 1 | 12 | yes | — |
| 106 | #543 | #120 | 1 | 12 | yes | — |
| 107 | #539 | #120 | 1 | 24 | yes | — |
| 108 | #539 | #120 | 1 | 24 | yes | — |
| 109 | #538 | #120 | 1 | 24 | yes | — |
| 110 | #538 | #120 | 1 | 24 | yes | — |
| 111 | #537 | #120 | 1 | 24 | yes | — |
| 112 | #535 | #120 | 1 | 24 | yes | — |
| 113 | #535 | #120 | 1 | 24 | yes | — |
| 114 | #534 | #120 | 1 | 12 | yes | — |
| 115 | #534 | #120 | 1 | 12 | yes | — |
| 116 | #533 | C22×D4 | 1 | 12 | yes | — |
| 117 | #533 | C22×D4 | 1 | 24 | yes | — |
| 118 | #532 | C22×D4 | 1 | 24 | yes | — |
| 119 | #532 | C22×D4 | 1 | 12 | yes | — |
| 120 | C2×#127 | C22×D4 | 1 | 8 | yes | — |
| 121 | #529 | C22×D4 | 1 | 24 | yes | — |
| 122 | #529 | C22×D4 | 1 | 24 | yes | — |
| 123 | C2×#126 | C22×D4 | 1 | 8 | yes | — |
| 124 | C2×#126 | C22×D4 | 1 | 8 | yes | — |
| 125 | #525 | C22×D4 | 1 | 24 | yes | — |
| 126 | #518 | #120 | 1 | 12 | yes | — |
| 127 | #518 | #120 | 1 | 12 | yes | — |
| 128 | C4×#41 | C22×D4 | 1 | 24 | yes | — |
| 129 | C22×C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 130 | C22×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 131 | C22×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 132 | C22×C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 133 | C22×C42 | C25 | 1 | 1 | yes | characteristic |
| 134 | C25 | C2×#120 | 1 | 1 | yes | characteristic |
| 135 | C25 | C2×#120 | 1 | 3 | yes | — |
| 136 | C25 | C2×#120 | 1 | 2 | yes | — |
| 137 | C2×#41 | C2×#120 | 1 | 24 | yes | — |
| 138 | C22×D4 | C2×#120 | 1 | 12 | yes | — |
| 139 | C22×D4 | C2×#120 | 1 | 12 | yes | — |
| 140 | C23×C4 | C2×#120 | 1 | 6 | yes | — |
| 141 | C23×C4 | C23×D4 | 1 | 3 | yes | — |
| 142 | C4⋊Q8 | C2×#120 | 1 | 24 | yes | — |
| 143 | C4⋊Q8 | C2×#120 | 1 | 12 | yes | — |
| 144 | #127 | C2×#120 | 1 | 12 | yes | — |
| 145 | #125 | C2×#120 | 1 | 12 | yes | — |
| 146 | #125 | C2×#120 | 1 | 12 | yes | — |
| 147 | #124 | C2×#120 | 1 | 24 | yes | — |
| 148 | C22⋊Q8 | C2×#120 | 1 | 24 | yes | — |
| 149 | C22⋊Q8 | C2×#120 | 1 | 24 | yes | — |
| 150 | #121 | C2×#120 | 1 | 24 | yes | — |
| 151 | #121 | C2×#120 | 1 | 24 | yes | — |
| 152 | C4×Q8 | C2×#120 | 1 | 24 | yes | — |
| 153 | C4×Q8 | C2×#120 | 1 | 24 | yes | — |
| 154 | C4×D4 | C2×#120 | 1 | 24 | yes | — |
| 155 | C4×D4 | C2×#120 | 1 | 24 | yes | — |
| 156 | #117 | C2×#120 | 1 | 24 | yes | — |
| 157 | C2×C4⋊C4 | C2×#120 | 1 | 24 | yes | — |
| 158 | C2×C22⋊C4 | C2×#120 | 1 | 12 | yes | — |
| 159 | C2×C22⋊C4 | C2×#120 | 1 | 12 | yes | — |
| 160 | C2×C42 | C23×D4 | 1 | 4 | yes | — |
| 161 | C2×C42 | C23×D4 | 1 | 8 | yes | — |
| 162 | C24 | #2846 | 1 | 2 | yes | — |
| 163 | C24 | #2846 | 1 | 2 | yes | — |
| 164 | C24 | #2846 | 1 | 2 | yes | — |
| 165 | C24 | #2846 | 1 | 6 | yes | — |
| 166 | C24 | C22×#120 | 1 | 1 | yes | characteristic |
| 167 | C2×Q8 | #2846 | 1 | 24 | yes | — |
| 168 | C2×D4 | #2846 | 1 | 24 | yes | — |
| 169 | C22×C4 | #2846 | 1 | 12 | yes | — |
| 170 | C22×C4 | C22×#120 | 1 | 12 | yes | — |
| 171 | C22×C4 | C22×#120 | 1 | 6 | yes | — |
| 172 | C4⋊C4 | #2846 | 1 | 24 | yes | — |
| 173 | C4⋊C4 | #2846 | 1 | 24 | yes | — |
| 174 | C42 | C22×#120 | 1 | 12 | yes | — |
| 175 | C42 | C22×#120 | 1 | 4 | yes | — |
| 176 | C23 | C2×#2846 | 1 | 2 | yes | — |
| 177 | C23 | C2×#2846 | 1 | 1 | yes | characteristic |
| 178 | C2×C4 | C2×#2846 | 1 | 12 | yes | — |
| 179 | C22 | #6342371 | 1 | 1 | yes | characteristic |
| 180 | C2 | #72227588 | 1 | 3 | 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