← #72316285
Subgroups — #72316285
Order 4096.
At least 10642 conjugacy classes of subgroups; only the 431 normal subgroups are shown.
The subgroup lattice has 162 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72313138 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72310380 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72265678 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72264862 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #72237032 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72225652 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72225619 | C22 | 1 | 4 | yes | — |
| 8 | #72219418 | C22 | 1 | 4 | yes | complemented |
| 9 | #72219242 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #72219237 | C22 | 1 | 4 | yes | complemented |
| 11 | #72219229 | C22 | 1 | 2 | yes | complemented |
| 12 | C22×#8541 | C22 | 1 | 2 | yes | complemented |
| 13 | C22×#15947 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#359428 | C22 | 1 | 1 | yes | characteristic |
| 15 | #72218518 | C22 | 1 | 2 | yes | — |
| 16 | #72218375 | C22 | 1 | 1 | yes | characteristic |
| 17 | #72218057 | C22 | 1 | 8 | yes | complemented |
| 18 | #72217511 | C22 | 1 | 2 | yes | — |
| 19 | #72215858 | C22 | 1 | 4 | yes | complemented |
| 20 | C2×#62817 | D4 | 1 | 2 | yes | complemented |
| 21 | C24×#120 | D4 | 1 | 2 | yes | complemented |
| 22 | C24×#120 | C23 | 1 | 1 | yes | characteristic |
| 23 | C24×#120 | C23 | 1 | 1 | yes | characteristic |
| 24 | #7642244 | D4 | 1 | 4 | yes | complemented |
| 25 | #7630939 | C23 | 1 | 4 | yes | — |
| 26 | #7626202 | D4 | 1 | 2 | yes | complemented |
| 27 | C23×#379 | D4 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×#23895 | D4 | 1 | 4 | yes | complemented |
| 29 | C22×#1781 | C23 | 1 | 2 | yes | — |
| 30 | C22×#1781 | C23 | 1 | 2 | yes | — |
| 31 | C2×#14679 | D4 | 1 | 1 | yes | characteristic, complemented |
| 32 | C22×#1438 | D4 | 1 | 2 | yes | complemented |
| 33 | C22×#1438 | C23 | 1 | 1 | yes | characteristic |
| 34 | #392109 | C23 | 1 | 4 | yes | — |
| 35 | #373637 | D4 | 1 | 4 | yes | complemented |
| 36 | #359549 | D4 | 1 | 8 | yes | complemented |
| 37 | C2×#10725 | D4 | 1 | 2 | yes | complemented |
| 38 | C2×#8541 | D4 | 1 | 8 | yes | complemented |
| 39 | C28 | C2×D4 | 1 | 1 | yes | characteristic |
| 40 | C28 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 41 | C25×D4 | C2×D4 | 1 | 2 | yes | — |
| 42 | C25×D4 | C24 | 1 | 1 | yes | characteristic |
| 43 | C2×#3484 | C2×D4 | 1 | 4 | yes | — |
| 44 | C2×#3484 | C2×D4 | 1 | 8 | yes | — |
| 45 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 46 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 47 | C23×#120 | C2×D4 | 1 | 4 | yes | — |
| 48 | C24×C22⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 49 | C24×C22⋊C4 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 50 | C24×C22⋊C4 | C2×D4 | 1 | 2 | yes | complemented |
| 51 | C24×C22⋊C4 | #41 | 1 | 2 | yes | — |
| 52 | #34171 | C2×D4 | 1 | 4 | yes | — |
| 53 | #34171 | C2×D4 | 1 | 8 | yes | — |
| 54 | C22×#379 | C2×D4 | 1 | 2 | yes | — |
| 55 | C22×#379 | C2×D4 | 1 | 2 | yes | — |
| 56 | C2×#1781 | C2×D4 | 1 | 4 | yes | — |
| 57 | C2×#1781 | C2×D4 | 1 | 4 | yes | — |
| 58 | C2×#1781 | C2×D4 | 1 | 8 | yes | complemented |
| 59 | C27 | #120 | 1 | 1 | yes | characteristic |
| 60 | C27 | #120 | 1 | 1 | yes | characteristic |
| 61 | C27 | #121 | 1 | 2 | yes | — |
| 62 | C27 | #127 | 1 | 2 | yes | — |
| 63 | C27 | C22×D4 | 1 | 1 | yes | characteristic |
| 64 | C27 | C22×D4 | 1 | 1 | yes | characteristic |
| 65 | C22×H(5,𝔽2) | #120 | 1 | 4 | yes | — |
| 66 | C24×D4 | #120 | 1 | 4 | yes | — |
| 67 | C24×D4 | #120 | 1 | 4 | yes | — |
| 68 | C24×D4 | C22×D4 | 1 | 2 | yes | — |
| 69 | C24×D4 | C22×D4 | 1 | 2 | yes | — |
| 70 | C24×D4 | C22×D4 | 1 | 4 | yes | — |
| 71 | C24×D4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 72 | C25×C4 | #121 | 1 | 2 | yes | — |
| 73 | C25×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 74 | C2×#518 | #120 | 1 | 4 | yes | — |
| 75 | C2×#518 | #120 | 1 | 8 | yes | — |
| 76 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 77 | C23×C22⋊C4 | #121 | 1 | 4 | yes | — |
| 78 | C23×C22⋊C4 | #121 | 1 | 4 | yes | — |
| 79 | C23×C22⋊C4 | #127 | 1 | 2 | yes | — |
| 80 | C2×#379 | #120 | 1 | 4 | yes | — |
| 81 | C2×#379 | #120 | 1 | 2 | yes | — |
| 82 | C2×#379 | #120 | 1 | 2 | yes | — |
| 83 | C26 | #392 | 1 | 2 | yes | — |
| 84 | C26 | #392 | 1 | 2 | yes | — |
| 85 | C26 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 86 | C26 | B(4,𝔽2) | 1 | 2 | yes | — |
| 87 | C26 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 88 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 89 | C26 | C2×#120 | 1 | 2 | yes | — |
| 90 | C26 | C2×#120 | 1 | 2 | yes | — |
| 91 | C26 | C2×#121 | 1 | 1 | yes | characteristic |
| 92 | C26 | C2×#127 | 1 | 1 | yes | characteristic |
| 93 | C26 | #535 | 1 | 2 | yes | — |
| 94 | C26 | D42 | 1 | 4 | yes | — |
| 95 | C23×D4 | B(4,𝔽2) | 1 | 8 | yes | — |
| 96 | C23×D4 | B(4,𝔽2) | 1 | 8 | yes | — |
| 97 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 98 | C23×D4 | #534 | 1 | 4 | yes | — |
| 99 | C23×D4 | D42 | 1 | 8 | yes | — |
| 100 | C24×C4 | #392 | 1 | 4 | yes | — |
| 101 | C24×C4 | C2×#121 | 1 | 2 | yes | — |
| 102 | C24×C4 | #546 | 1 | 4 | yes | — |
| 103 | #379 | B(4,𝔽2) | 1 | 4 | yes | complemented |
| 104 | C25 | #2021 | 1 | 2 | yes | — |
| 105 | C25 | #2021 | 1 | 4 | yes | — |
| 106 | C25 | #2021 | 1 | 2 | yes | — |
| 107 | C25 | #2021 | 1 | 4 | yes | — |
| 108 | C25 | C2×#392 | 1 | 1 | yes | characteristic |
| 109 | C25 | #2403 | 1 | 4 | yes | — |
| 110 | C25 | #2408 | 1 | 2 | yes | — |
| 111 | C25 | #2433 | 1 | 2 | yes | — |
| 112 | C25 | #2613 | 1 | 1 | yes | characteristic |
| 113 | C25 | #2846 | 1 | 1 | yes | characteristic |
| 114 | C25 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 115 | C25 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 116 | C25 | C2×B(4,𝔽2) | 1 | 8 | yes | — |
| 117 | C25 | C2×B(4,𝔽2) | 1 | 2 | yes | — |
| 118 | C25 | #3025 | 1 | 2 | yes | — |
| 119 | C25 | #3026 | 1 | 1 | yes | characteristic |
| 120 | C25 | #3026 | 1 | 1 | yes | characteristic |
| 121 | C25 | #3026 | 1 | 2 | yes | — |
| 122 | C25 | #3027 | 1 | 2 | yes | — |
| 123 | C23×C4 | #2021 | 1 | 8 | yes | — |
| 124 | C23×C4 | #2410 | 1 | 4 | yes | — |
| 125 | C24 | #10336 | 1 | 4 | yes | — |
| 126 | C24 | #10336 | 1 | 2 | yes | — |
| 127 | C24 | #10336 | 1 | 2 | yes | — |
| 128 | C24 | #14715 | 1 | 1 | yes | characteristic |
| 129 | C24 | C2×#2021 | 1 | 1 | yes | characteristic |
| 130 | C24 | C2×#2021 | 1 | 4 | yes | — |
| 131 | C24 | #23444 | 1 | 1 | yes | characteristic |
| 132 | C24 | #23900 | 1 | 8 | yes | — |
| 133 | C24 | #24260 | 1 | 2 | yes | — |
| 134 | C24 | #24262 | 1 | 2 | yes | — |
| 135 | C24 | #25771 | 1 | 2 | yes | — |
| 136 | C24 | #25773 | 1 | 2 | yes | — |
| 137 | C24 | #29634 | 1 | 1 | yes | characteristic |
| 138 | C24 | #29634 | 1 | 1 | yes | characteristic |
| 139 | C24 | #32898 | 1 | 1 | yes | characteristic |
| 140 | C24 | #32898 | 1 | 1 | yes | characteristic |
| 141 | C24 | #32898 | 1 | 2 | yes | — |
| 142 | C24 | #32899 | 1 | 2 | yes | — |
| 143 | C23 | #144378 | 1 | 4 | yes | complemented |
| 144 | C23 | C2×#10336 | 1 | 2 | yes | — |
| 145 | C23 | #233541 | 1 | 2 | yes | — |
| 146 | C23 | #347042 | 1 | 1 | yes | characteristic |
| 147 | C23 | #347043 | 1 | 2 | yes | — |
| 148 | C23 | #347044 | 1 | 1 | yes | characteristic |
| 149 | C23 | #393929 | 1 | 1 | yes | characteristic |
| 150 | C23 | #393933 | 1 | 2 | yes | — |
| 151 | C23 | #393934 | 1 | 2 | yes | — |
| 152 | C23 | #394058 | 1 | 2 | yes | — |
| 153 | C22 | #72214549 | 1 | 1 | yes | characteristic |
| 154 | C22 | C2×#144378 | 1 | 2 | yes | — |
| 155 | C22 | #72225661 | 1 | 1 | yes | characteristic |
| 156 | C22 | #72234155 | 1 | 4 | yes | — |
| 157 | C22 | #72236508 | 1 | 2 | yes | — |
| 158 | C22 | #72258515 | 1 | 1 | yes | characteristic |
| 159 | C2 | #72236528 | 1 | 2 | yes | — |
| 160 | C2 | #72266377 | 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