← #72310584
Subgroups — #72310584
Order 4096.
At least 10053 conjugacy classes of subgroups; only the 507 normal subgroups are shown.
The subgroup lattice has 215 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72310566 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #72310564 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72310558 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72310532 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72310531 | C22 | 1 | 4 | yes | complemented |
| 6 | #72310517 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #72309397 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#97555 | C22 | 1 | 2 | yes | — |
| 9 | #72247315 | C22 | 1 | 4 | yes | complemented |
| 10 | #72237035 | C22 | 1 | 4 | yes | complemented |
| 11 | C2×#97550 | C22 | 1 | 2 | yes | complemented |
| 12 | #72225781 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #72225778 | C22 | 1 | 2 | yes | — |
| 14 | #72225777 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #72225776 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #72225738 | C2 | 1 | 1 | yes | maximal, characteristic |
| 17 | #72225736 | C22 | 1 | 1 | yes | characteristic |
| 18 | #72225735 | C22 | 1 | 1 | yes | characteristic |
| 19 | #72225733 | C22 | 1 | 2 | yes | — |
| 20 | #72225732 | C4 | 1 | 4 | yes | complemented |
| 21 | #72225713 | C4 | 1 | 2 | yes | complemented |
| 22 | #72224136 | C4 | 1 | 2 | yes | complemented |
| 23 | #72221145 | C22 | 1 | 2 | yes | complemented |
| 24 | C2×#7670203 | C22 | 1 | 1 | yes | characteristic |
| 25 | #72219022 | C22 | 1 | 4 | yes | complemented |
| 26 | C2×#133822 | C22 | 1 | 2 | yes | complemented |
| 27 | #72217643 | C22 | 1 | 2 | yes | — |
| 28 | #10586404 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | C22×#3484 | D4 | 1 | 2 | yes | — |
| 30 | C24×#120 | D4 | 1 | 2 | yes | — |
| 31 | #7642273 | C23 | 1 | 2 | yes | — |
| 32 | C22×#2846 | C23 | 1 | 1 | yes | characteristic |
| 33 | C2×#35390 | C23 | 1 | 1 | yes | characteristic |
| 34 | C2×#35348 | D4 | 1 | 2 | yes | — |
| 35 | C2×#35346 | C23 | 1 | 1 | yes | characteristic |
| 36 | C2×#34981 | D4 | 1 | 2 | yes | — |
| 37 | C2×#34980 | C2×C4 | 1 | 2 | yes | — |
| 38 | C2×#34198 | C2×C4 | 1 | 2 | yes | — |
| 39 | #6451874 | C2×C4 | 1 | 4 | yes | — |
| 40 | C2×#23984 | C2×C4 | 1 | 4 | yes | complemented |
| 41 | #6374251 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 42 | #6374128 | C2×C4 | 1 | 2 | yes | complemented |
| 43 | #6372488 | C2×C4 | 1 | 2 | yes | complemented |
| 44 | #417896 | D4 | 1 | 2 | yes | — |
| 45 | #417896 | D4 | 1 | 2 | yes | — |
| 46 | #417896 | D4 | 1 | 4 | yes | — |
| 47 | #417824 | D4 | 1 | 2 | yes | — |
| 48 | #417824 | D4 | 1 | 2 | yes | — |
| 49 | #417824 | D4 | 1 | 4 | yes | — |
| 50 | #392368 | C2×C4 | 1 | 2 | yes | complemented |
| 51 | #382422 | C23 | 1 | 2 | yes | — |
| 52 | #359756 | C2×C4 | 1 | 4 | yes | complemented |
| 53 | #359705 | C2×C4 | 1 | 4 | yes | — |
| 54 | C2×#10965 | C23 | 1 | 4 | yes | — |
| 55 | C2×#8547 | C23 | 1 | 2 | yes | — |
| 56 | C2×#8541 | C23 | 1 | 2 | yes | — |
| 57 | #134025 | D4 | 1 | 8 | yes | complemented |
| 58 | C28 | C2×D4 | 1 | 1 | yes | characteristic |
| 59 | C23×H(5,𝔽2) | C2×D4 | 1 | 1 | yes | characteristic |
| 60 | C25×D4 | C22⋊C4 | 1 | 2 | yes | — |
| 61 | C2×#3490 | C22×C4 | 1 | 2 | yes | — |
| 62 | C22×#534 | C22⋊C4 | 1 | 2 | yes | — |
| 63 | C22×#534 | C22×C4 | 1 | 1 | yes | characteristic |
| 64 | C22×#534 | C2×D4 | 1 | 2 | yes | — |
| 65 | C23×#120 | C22⋊C4 | 1 | 2 | yes | — |
| 66 | C23×#120 | C22⋊C4 | 1 | 2 | yes | — |
| 67 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 68 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 69 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 70 | C23×#120 | C24 | 1 | 1 | yes | characteristic |
| 71 | C22×#518 | C22⋊C4 | 1 | 2 | yes | — |
| 72 | C24×C22⋊C4 | C22⋊C4 | 1 | 2 | yes | — |
| 73 | #35390 | C2×D4 | 1 | 2 | yes | — |
| 74 | #35390 | C2×D4 | 1 | 2 | yes | — |
| 75 | #35390 | C2×D4 | 1 | 4 | yes | — |
| 76 | #35390 | #41 | 1 | 4 | yes | — |
| 77 | #35367 | C2×D4 | 1 | 2 | yes | — |
| 78 | #35367 | C2×D4 | 1 | 2 | yes | — |
| 79 | #35346 | C2×D4 | 1 | 2 | yes | — |
| 80 | #35346 | C2×D4 | 1 | 2 | yes | — |
| 81 | #35346 | C2×D4 | 1 | 4 | yes | — |
| 82 | #34176 | C22×C4 | 1 | 2 | yes | — |
| 83 | C2×#2315 | C22⋊C4 | 1 | 2 | yes | — |
| 84 | C2×#2308 | C22⋊C4 | 1 | 2 | yes | — |
| 85 | C2×#2308 | C22×C4 | 1 | 2 | yes | — |
| 86 | C2×#2308 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C22×#379 | C22×C4 | 1 | 2 | yes | — |
| 88 | C22×#379 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C2×#2273 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | #23468 | C22⋊C4 | 1 | 4 | yes | complemented |
| 91 | #23468 | C22⋊C4 | 1 | 4 | yes | complemented |
| 92 | #23444 | C22⋊C4 | 1 | 4 | yes | complemented |
| 93 | #23444 | C22⋊C4 | 1 | 4 | yes | complemented |
| 94 | C2×#1819 | C22×C4 | 1 | 4 | yes | — |
| 95 | #10965 | C2×D4 | 1 | 2 | yes | — |
| 96 | #10965 | C2×D4 | 1 | 2 | yes | — |
| 97 | #10965 | C2×D4 | 1 | 4 | yes | — |
| 98 | #10938 | C22⋊C4 | 1 | 4 | yes | complemented |
| 99 | #10938 | C22⋊C4 | 1 | 4 | yes | complemented |
| 100 | #10938 | C22⋊C4 | 1 | 4 | yes | complemented |
| 101 | #10938 | C22⋊C4 | 1 | 4 | yes | complemented |
| 102 | #8547 | C2×D4 | 1 | 4 | yes | complemented |
| 103 | #8541 | C2×D4 | 1 | 4 | yes | complemented |
| 104 | C27 | #99 | 1 | 2 | yes | — |
| 105 | C27 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 106 | C27 | C22×D4 | 1 | 1 | yes | characteristic |
| 107 | C22×H(5,𝔽2) | #120 | 1 | 1 | yes | characteristic |
| 108 | C22×H(5,𝔽2) | #120 | 1 | 1 | yes | characteristic |
| 109 | C22×H(5,𝔽2) | #120 | 1 | 2 | yes | — |
| 110 | C24×D4 | #99 | 1 | 2 | yes | — |
| 111 | C24×D4 | #99 | 1 | 2 | yes | — |
| 112 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 113 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 114 | C24×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 115 | C24×D4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 116 | C25×C4 | #99 | 1 | 2 | yes | — |
| 117 | C2×#543 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 118 | C2×#534 | #99 | 1 | 4 | yes | — |
| 119 | C2×#534 | #99 | 1 | 4 | yes | — |
| 120 | C2×#534 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 121 | C2×#534 | C4×D4 | 1 | 4 | yes | — |
| 122 | C2×#534 | #120 | 1 | 4 | yes | — |
| 123 | C2×#534 | #123 | 1 | 4 | yes | — |
| 124 | C22×#120 | #120 | 1 | 4 | yes | — |
| 125 | C22×#120 | #120 | 1 | 4 | yes | — |
| 126 | C22×#120 | #121 | 1 | 8 | yes | — |
| 127 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 128 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 129 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 130 | C22×#120 | C2×#41 | 1 | 2 | yes | — |
| 131 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 132 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 133 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 134 | C23×C22⋊C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 135 | C23×C22⋊C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 136 | #2308 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 137 | #2308 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 138 | #2308 | #120 | 1 | 2 | yes | — |
| 139 | #2308 | #120 | 1 | 2 | yes | — |
| 140 | #2273 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 141 | #2273 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 142 | #2273 | C4×D4 | 1 | 4 | yes | — |
| 143 | C2×#342 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 144 | C2×#342 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 145 | C26 | C2×#99 | 1 | 2 | yes | — |
| 146 | C26 | C2×#99 | 1 | 2 | yes | — |
| 147 | C26 | C2×#99 | 1 | 2 | yes | — |
| 148 | C26 | C2×#99 | 1 | 2 | yes | — |
| 149 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C26 | C2×#120 | 1 | 2 | yes | — |
| 151 | C26 | C2×#121 | 1 | 2 | yes | — |
| 152 | C26 | #534 | 1 | 2 | yes | — |
| 153 | C26 | #534 | 1 | 1 | yes | characteristic |
| 154 | C23×D4 | #379 | 1 | 2 | yes | — |
| 155 | C23×D4 | #379 | 1 | 2 | yes | — |
| 156 | C23×D4 | #386 | 1 | 4 | yes | — |
| 157 | C23×D4 | C2×#99 | 1 | 4 | yes | — |
| 158 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 159 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 160 | C23×D4 | C2×#120 | 1 | 1 | yes | characteristic |
| 161 | C23×D4 | C2×#120 | 1 | 1 | yes | characteristic |
| 162 | C23×D4 | C2×#120 | 1 | 1 | yes | characteristic |
| 163 | C23×D4 | C2×#123 | 1 | 1 | yes | characteristic |
| 164 | C23×D4 | D42 | 1 | 4 | yes | — |
| 165 | C23×D4 | #546 | 1 | 4 | yes | — |
| 166 | C24×C4 | C2×#99 | 1 | 2 | yes | — |
| 167 | C24×C4 | C2×#99 | 1 | 2 | yes | — |
| 168 | C24×C4 | #518 | 1 | 2 | yes | — |
| 169 | C24×C4 | #534 | 1 | 1 | yes | characteristic |
| 170 | C22×C22⋊C4 | #379 | 1 | 4 | yes | — |
| 171 | C22×C22⋊C4 | #386 | 1 | 4 | yes | — |
| 172 | C22×C22⋊C4 | C2×#99 | 1 | 4 | yes | — |
| 173 | C22×C22⋊C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 174 | C22×C22⋊C4 | C2×C4×D4 | 1 | 2 | yes | — |
| 175 | C22×C22⋊C4 | D42 | 1 | 4 | yes | — |
| 176 | C22×C22⋊C4 | #546 | 1 | 4 | yes | — |
| 177 | C25 | #1781 | 1 | 2 | yes | — |
| 178 | C25 | #1781 | 1 | 2 | yes | — |
| 179 | C25 | #1898 | 1 | 4 | yes | — |
| 180 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 181 | C25 | C2×#386 | 1 | 1 | yes | characteristic |
| 182 | C25 | #2308 | 1 | 1 | yes | characteristic |
| 183 | C25 | #2403 | 1 | 1 | yes | characteristic |
| 184 | C25 | #2405 | 1 | 1 | yes | characteristic |
| 185 | C25 | #2410 | 1 | 4 | yes | — |
| 186 | C25 | C22×#99 | 1 | 2 | yes | — |
| 187 | C25 | C22×#99 | 1 | 2 | yes | — |
| 188 | C23×C4 | #1781 | 1 | 2 | yes | — |
| 189 | C23×C4 | #1781 | 1 | 2 | yes | — |
| 190 | C23×C4 | #1898 | 1 | 4 | yes | — |
| 191 | C23×C4 | D4×C22⋊C4 | 1 | 4 | yes | — |
| 192 | C23×C4 | #2403 | 1 | 1 | yes | characteristic |
| 193 | C23×C4 | #2405 | 1 | 1 | yes | characteristic |
| 194 | C24 | #12707 | 1 | 4 | yes | — |
| 195 | C24 | #13867 | 1 | 1 | yes | characteristic |
| 196 | C24 | C2×#1781 | 1 | 2 | yes | — |
| 197 | C24 | C2×#1898 | 1 | 2 | yes | — |
| 198 | C24 | #21746 | 1 | 1 | yes | characteristic |
| 199 | C24 | #21746 | 1 | 1 | yes | characteristic |
| 200 | C24 | #21776 | 1 | 4 | yes | — |
| 201 | C22×C4 | #12707 | 1 | 4 | yes | — |
| 202 | C23 | #213828 | 1 | 2 | yes | — |
| 203 | C23 | #213854 | 1 | 2 | yes | — |
| 204 | C23 | #359428 | 1 | 1 | yes | characteristic |
| 205 | C23 | #359591 | 1 | 2 | yes | — |
| 206 | C23 | C2×#12707 | 1 | 2 | yes | — |
| 207 | C23 | C2×#12707 | 1 | 2 | yes | — |
| 208 | C22 | #72216376 | 1 | 2 | yes | — |
| 209 | C22 | #72218057 | 1 | 2 | yes | — |
| 210 | C22 | #72219460 | 1 | 1 | yes | characteristic |
| 211 | C22 | #72258229 | 1 | 2 | yes | — |
| 212 | C2 | #72258350 | 1 | 2 | yes | — |
| 213 | C2 | #72266170 | 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