← #72317088
Subgroups — #72317088
Order 4096.
At least 17315 conjugacy classes of subgroups; only the 831 normal subgroups are shown.
The subgroup lattice has 366 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72317073 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #72266165 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72266163 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72265785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72265766 | C22 | 1 | 2 | yes | complemented |
| 6 | #72259029 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72259008 | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | #72259002 | C22 | 1 | 2 | yes | complemented |
| 9 | #72240489 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #72240132 | C22 | 1 | 4 | yes | complemented |
| 11 | #72240132 | C22 | 1 | 4 | yes | complemented |
| 12 | #72237629 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #72237608 | C22 | 1 | 2 | yes | complemented |
| 14 | #72235847 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #72234683 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #72234681 | C4 | 1 | 2 | yes | complemented |
| 17 | #72234681 | C22 | 1 | 2 | yes | — |
| 18 | #72234670 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #72234636 | C22 | 1 | 2 | yes | — |
| 20 | #72234618 | C4 | 1 | 2 | yes | complemented |
| 21 | #72234588 | C4 | 1 | 2 | yes | complemented |
| 22 | #72232723 | C22 | 1 | 4 | yes | complemented |
| 23 | #72232723 | C22 | 1 | 4 | yes | complemented |
| 24 | C2×#8932885 | C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#7670203 | C22 | 1 | 1 | yes | characteristic |
| 26 | #72218518 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #72218291 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #72217875 | C22 | 1 | 2 | yes | — |
| 29 | #72217789 | C22 | 1 | 2 | yes | complemented |
| 30 | C22×#3484 | D4 | 1 | 1 | yes | characteristic |
| 31 | C22×#3484 | D4 | 1 | 1 | yes | characteristic |
| 32 | C22×#3484 | D4 | 1 | 2 | yes | — |
| 33 | C24×#120 | D4 | 1 | 1 | yes | characteristic |
| 34 | C24×#120 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×#46996 | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×#46996 | C2×C4 | 1 | 2 | yes | — |
| 37 | C22×#2846 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×#35390 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×#35348 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C2×#35348 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×#35346 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C2×#35346 | C2×C4 | 1 | 2 | yes | — |
| 43 | C2×#35346 | D4 | 1 | 2 | yes | — |
| 44 | C2×#34981 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C2×#34981 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×#34980 | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×#34980 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×#34198 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×#34198 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×#21746 | C23 | 1 | 2 | yes | complemented |
| 51 | C2×#21746 | C23 | 1 | 2 | yes | complemented |
| 52 | #5024691 | D4 | 1 | 2 | yes | — |
| 53 | #5020751 | D4 | 1 | 2 | yes | — |
| 54 | #4932982 | D4 | 1 | 4 | yes | — |
| 55 | #4599104 | D4 | 1 | 4 | yes | — |
| 56 | #4466055 | D4 | 1 | 4 | yes | — |
| 57 | #4430405 | D4 | 1 | 2 | yes | — |
| 58 | #4335643 | C2×C4 | 1 | 4 | yes | — |
| 59 | #4321066 | C2×C4 | 1 | 4 | yes | — |
| 60 | #2805719 | D4 | 1 | 4 | yes | — |
| 61 | #2039146 | D4 | 1 | 4 | yes | — |
| 62 | #1465620 | D4 | 1 | 4 | yes | — |
| 63 | #648360 | D4 | 1 | 2 | yes | — |
| 64 | #616961 | D4 | 1 | 4 | yes | — |
| 65 | #616961 | C23 | 1 | 4 | yes | — |
| 66 | #612425 | C2×C4 | 1 | 4 | yes | — |
| 67 | #612425 | D4 | 1 | 4 | yes | — |
| 68 | #576189 | C2×C4 | 1 | 2 | yes | — |
| 69 | #576160 | C2×C4 | 1 | 2 | yes | — |
| 70 | #517411 | D4 | 1 | 2 | yes | — |
| 71 | #515285 | C2×C4 | 1 | 2 | yes | — |
| 72 | #515285 | D4 | 1 | 2 | yes | — |
| 73 | C2×#8547 | C23 | 1 | 2 | yes | complemented |
| 74 | C2×#8541 | C23 | 1 | 2 | yes | complemented |
| 75 | C28 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C23×H(5,𝔽2) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 77 | C23×H(5,𝔽2) | C22⋊C4 | 1 | 2 | yes | complemented |
| 78 | C25×D4 | C2×D4 | 1 | 2 | yes | — |
| 79 | C25×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 80 | C25×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C22×#535 | C2×D4 | 1 | 4 | yes | — |
| 82 | C22×#534 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 83 | C22×#534 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 84 | C22×#534 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C22×#534 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C22×#534 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C22×#525 | C22⋊C4 | 1 | 4 | yes | complemented |
| 88 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 89 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 90 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 91 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 92 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 93 | C23×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 94 | C23×#120 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 96 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 100 | C23×#120 | C24 | 1 | 1 | yes | characteristic |
| 101 | C22×#518 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 102 | C22×#518 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 103 | C22×#518 | C22⋊C4 | 1 | 2 | yes | complemented |
| 104 | C24×C22⋊C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 105 | C24×C22⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C24×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 107 | C2×#2760 | C22⋊C4 | 1 | 4 | yes | complemented |
| 108 | C2×#2760 | C22⋊C4 | 1 | 4 | yes | complemented |
| 109 | C2×#2840 | C22⋊C4 | 1 | 2 | yes | complemented |
| 110 | C2×#2840 | C22⋊C4 | 1 | 2 | yes | complemented |
| 111 | C2×#2849 | C2×D4 | 1 | 2 | yes | — |
| 112 | C2×#2846 | C2×D4 | 1 | 2 | yes | — |
| 113 | C2×#2404 | C22⋊C4 | 1 | 4 | yes | complemented |
| 114 | C2×#2404 | C22⋊C4 | 1 | 4 | yes | complemented |
| 115 | C2×#2404 | C22×C4 | 1 | 4 | yes | — |
| 116 | C2×#2404 | C2×D4 | 1 | 4 | yes | — |
| 117 | C2×#2412 | C2×D4 | 1 | 4 | yes | — |
| 118 | C2×#2410 | C2×D4 | 1 | 4 | yes | — |
| 119 | C2×#2403 | C22⋊C4 | 1 | 2 | yes | complemented |
| 120 | C2×#2403 | C22⋊C4 | 1 | 2 | yes | complemented |
| 121 | C2×#2613 | C2×D4 | 1 | 2 | yes | — |
| 122 | C2×#2613 | C2×D4 | 1 | 2 | yes | — |
| 123 | C2×#2315 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 124 | C2×#2315 | C22×C4 | 1 | 1 | yes | characteristic |
| 125 | C2×#2308 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 126 | C2×#2308 | C22⋊C4 | 1 | 2 | yes | complemented |
| 127 | C2×#2308 | C22⋊C4 | 1 | 2 | yes | complemented |
| 128 | C2×#2308 | C22×C4 | 1 | 1 | yes | characteristic |
| 129 | C2×#2308 | C22×C4 | 1 | 1 | yes | characteristic |
| 130 | C2×#2308 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | C2×#2308 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C22×#379 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 133 | C22×#379 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 134 | C22×#379 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×#2273 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | #15930 | C22⋊C4 | 1 | 4 | yes | complemented |
| 137 | #15635 | C22⋊C4 | 1 | 4 | yes | complemented |
| 138 | #15622 | C22⋊C4 | 1 | 4 | yes | complemented |
| 139 | #15568 | C22⋊C4 | 1 | 4 | yes | complemented |
| 140 | #15561 | C22⋊C4 | 1 | 4 | yes | complemented |
| 141 | #15467 | C22⋊C4 | 1 | 4 | yes | complemented |
| 142 | #15420 | C22⋊C4 | 1 | 4 | yes | complemented |
| 143 | #15267 | C22⋊C4 | 1 | 4 | yes | complemented |
| 144 | #15259 | C2×D4 | 1 | 4 | yes | — |
| 145 | #15259 | C2×D4 | 1 | 4 | yes | — |
| 146 | #15259 | C2×D4 | 1 | 4 | yes | — |
| 147 | #15259 | C2×D4 | 1 | 4 | yes | — |
| 148 | #15258 | C2×D4 | 1 | 4 | yes | — |
| 149 | #15258 | C2×D4 | 1 | 4 | yes | — |
| 150 | #15258 | C2×D4 | 1 | 4 | yes | — |
| 151 | #15258 | C2×D4 | 1 | 4 | yes | — |
| 152 | #14681 | C22⋊C4 | 1 | 4 | yes | complemented |
| 153 | #14507 | C22⋊C4 | 1 | 4 | yes | complemented |
| 154 | #14365 | C22⋊C4 | 1 | 4 | yes | complemented |
| 155 | #14335 | C2×D4 | 1 | 4 | yes | — |
| 156 | #13868 | C22⋊C4 | 1 | 4 | yes | complemented |
| 157 | #13868 | C22⋊C4 | 1 | 4 | yes | complemented |
| 158 | #13868 | C22×C4 | 1 | 4 | yes | — |
| 159 | #13868 | C2×D4 | 1 | 4 | yes | — |
| 160 | #13828 | C22⋊C4 | 1 | 2 | yes | complemented |
| 161 | #13827 | C22⋊C4 | 1 | 2 | yes | complemented |
| 162 | #13807 | C22⋊C4 | 1 | 2 | yes | complemented |
| 163 | C22⋊C42 | C22⋊C4 | 1 | 2 | yes | complemented |
| 164 | C27 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C27 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 166 | C27 | #120 | 1 | 2 | yes | — |
| 167 | C27 | #120 | 1 | 2 | yes | — |
| 168 | C27 | #120 | 1 | 1 | yes | characteristic |
| 169 | C27 | #120 | 1 | 1 | yes | characteristic |
| 170 | C27 | C22×D4 | 1 | 1 | yes | characteristic |
| 171 | C22×H(5,𝔽2) | #99 | 1 | 4 | yes | — |
| 172 | C23×#41 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 173 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 174 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 175 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 176 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 177 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 178 | C24×D4 | #120 | 1 | 1 | yes | characteristic |
| 179 | C24×D4 | #120 | 1 | 2 | yes | — |
| 180 | C24×D4 | #120 | 1 | 2 | yes | — |
| 181 | C24×D4 | #120 | 1 | 1 | yes | characteristic |
| 182 | C24×D4 | #120 | 1 | 2 | yes | — |
| 183 | C24×D4 | #120 | 1 | 1 | yes | characteristic |
| 184 | C24×D4 | #120 | 1 | 1 | yes | characteristic |
| 185 | C24×D4 | C22×D4 | 1 | 2 | yes | — |
| 186 | C24×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 187 | C25×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 188 | C25×C4 | #120 | 1 | 1 | yes | characteristic |
| 189 | C25×C4 | #120 | 1 | 1 | yes | characteristic |
| 190 | C22×#127 | #120 | 1 | 4 | yes | — |
| 191 | C22×#127 | #120 | 1 | 4 | yes | — |
| 192 | C22×#124 | #120 | 1 | 4 | yes | — |
| 193 | C22×#124 | #120 | 1 | 4 | yes | — |
| 194 | C22×#123 | #120 | 1 | 2 | yes | — |
| 195 | C22×#123 | #120 | 1 | 2 | yes | — |
| 196 | C22×#123 | #120 | 1 | 2 | yes | — |
| 197 | C22×#120 | #99 | 1 | 4 | yes | — |
| 198 | C22×#120 | #99 | 1 | 4 | yes | — |
| 199 | C22×#120 | #120 | 1 | 2 | yes | — |
| 200 | C22×#120 | #120 | 1 | 2 | yes | — |
| 201 | C22×#120 | #120 | 1 | 2 | yes | — |
| 202 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 203 | C22×#120 | C22×D4 | 1 | 4 | yes | — |
| 204 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 205 | C22×#117 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 206 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 207 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 208 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 209 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 210 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 211 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 212 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 213 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 214 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 215 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 216 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 217 | C23×C22⋊C4 | #120 | 1 | 4 | yes | — |
| 218 | C23×C22⋊C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 219 | C23×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 220 | C2×#393 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 221 | C2×#393 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 222 | C2×#393 | #120 | 1 | 4 | yes | — |
| 223 | C2×#393 | #120 | 1 | 4 | yes | — |
| 224 | C2×#392 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 225 | C2×#392 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 226 | C2×#392 | #120 | 1 | 4 | yes | — |
| 227 | C2×#392 | #120 | 1 | 4 | yes | — |
| 228 | #2308 | #99 | 1 | 4 | yes | — |
| 229 | C2×#386 | #120 | 1 | 4 | yes | — |
| 230 | C2×#385 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 231 | C2×#381 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 232 | C2×#381 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 233 | C2×#381 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 234 | C2×#381 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 235 | C2×#381 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 236 | C2×#379 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 237 | C2×#379 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 238 | C2×#379 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 239 | C2×#379 | #120 | 1 | 2 | yes | — |
| 240 | C2×#379 | #120 | 1 | 2 | yes | — |
| 241 | #1438 | #120 | 1 | 4 | yes | — |
| 242 | #1438 | #120 | 1 | 4 | yes | — |
| 243 | #1438 | #120 | 1 | 4 | yes | — |
| 244 | #1438 | #120 | 1 | 4 | yes | — |
| 245 | #1437 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 246 | #1437 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 247 | #1437 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 248 | #1437 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 249 | #1437 | #120 | 1 | 4 | yes | — |
| 250 | #1437 | #120 | 1 | 4 | yes | — |
| 251 | #1437 | #120 | 1 | 4 | yes | — |
| 252 | #1437 | #120 | 1 | 4 | yes | — |
| 253 | C26 | #379 | 1 | 1 | yes | characteristic |
| 254 | C26 | #379 | 1 | 1 | yes | characteristic |
| 255 | C26 | #379 | 1 | 2 | yes | — |
| 256 | C26 | #379 | 1 | 1 | yes | characteristic |
| 257 | C26 | #379 | 1 | 1 | yes | characteristic |
| 258 | C26 | #379 | 1 | 1 | yes | characteristic |
| 259 | C26 | #379 | 1 | 1 | yes | characteristic |
| 260 | C26 | C2×#99 | 1 | 2 | yes | — |
| 261 | C26 | C2×#99 | 1 | 2 | yes | — |
| 262 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 263 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 264 | C26 | C2×#120 | 1 | 2 | yes | — |
| 265 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 266 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 267 | C26 | C2×#120 | 1 | 2 | yes | — |
| 268 | C23×Q8 | #379 | 1 | 4 | yes | — |
| 269 | C23×D4 | #379 | 1 | 4 | yes | — |
| 270 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 271 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 272 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 273 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 274 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 275 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 276 | C23×D4 | B(4,𝔽2) | 1 | 4 | yes | — |
| 277 | C23×D4 | #458 | 1 | 4 | yes | — |
| 278 | C23×D4 | C2×#120 | 1 | 2 | yes | — |
| 279 | C23×D4 | C2×#120 | 1 | 2 | yes | — |
| 280 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 281 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 282 | C24×C4 | #379 | 1 | 1 | yes | characteristic |
| 283 | C24×C4 | #379 | 1 | 2 | yes | — |
| 284 | C24×C4 | #379 | 1 | 1 | yes | characteristic |
| 285 | C24×C4 | #379 | 1 | 2 | yes | — |
| 286 | C24×C4 | #379 | 1 | 1 | yes | characteristic |
| 287 | C24×C4 | #379 | 1 | 1 | yes | characteristic |
| 288 | C24×C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 289 | C24×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 290 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 291 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 292 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 293 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 294 | C22×C22⋊C4 | C2×#99 | 1 | 2 | yes | — |
| 295 | C22×C22⋊C4 | C2×#99 | 1 | 2 | yes | — |
| 296 | C22×C22⋊C4 | C2×#99 | 1 | 2 | yes | — |
| 297 | C22×C22⋊C4 | C2×#99 | 1 | 2 | yes | — |
| 298 | C22×C22⋊C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 299 | C22×C22⋊C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 300 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 301 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 302 | C22×C42 | #379 | 1 | 4 | yes | — |
| 303 | C22×C42 | #379 | 1 | 4 | yes | — |
| 304 | C2×#95 | #379 | 1 | 4 | yes | — |
| 305 | C2×#95 | #379 | 1 | 4 | yes | — |
| 306 | C2×#95 | #379 | 1 | 4 | yes | — |
| 307 | C2×#95 | #379 | 1 | 4 | yes | — |
| 308 | C25 | #1781 | 1 | 4 | yes | — |
| 309 | C25 | #1781 | 1 | 2 | yes | — |
| 310 | C25 | #1781 | 1 | 2 | yes | — |
| 311 | C25 | #1781 | 1 | 2 | yes | — |
| 312 | C25 | #1790 | 1 | 4 | yes | — |
| 313 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 314 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 315 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 316 | C25 | #2846 | 1 | 2 | yes | — |
| 317 | C25 | #2846 | 1 | 2 | yes | — |
| 318 | C25 | #2846 | 1 | 2 | yes | — |
| 319 | C25 | C22×#99 | 1 | 1 | yes | characteristic |
| 320 | C25 | C22×#99 | 1 | 1 | yes | characteristic |
| 321 | C25 | C22×#99 | 1 | 1 | yes | characteristic |
| 322 | C25 | C22×#99 | 1 | 1 | yes | characteristic |
| 323 | C25 | C2×B(4,𝔽2) | 1 | 2 | yes | — |
| 324 | C25 | C2×#458 | 1 | 2 | yes | — |
| 325 | C25 | #3026 | 1 | 2 | yes | — |
| 326 | C25 | #3026 | 1 | 2 | yes | — |
| 327 | C23×C4 | #1781 | 1 | 2 | yes | — |
| 328 | C23×C4 | #1781 | 1 | 2 | yes | — |
| 329 | C23×C4 | #1781 | 1 | 2 | yes | — |
| 330 | C23×C4 | #1790 | 1 | 4 | yes | — |
| 331 | C23×C4 | C2×#379 | 1 | 4 | yes | — |
| 332 | C23×C4 | #2846 | 1 | 2 | yes | — |
| 333 | C2×C22⋊C4 | #1781 | 1 | 4 | yes | — |
| 334 | C2×C22⋊C4 | #1781 | 1 | 4 | yes | — |
| 335 | C24 | #8534 | 1 | 4 | yes | — |
| 336 | C24 | #12707 | 1 | 4 | yes | complemented |
| 337 | C24 | #14679 | 1 | 1 | yes | characteristic |
| 338 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 339 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 340 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 341 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 342 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 343 | C24 | C2×#1781 | 1 | 1 | yes | characteristic |
| 344 | C24 | C2×#1790 | 1 | 2 | yes | — |
| 345 | C24 | #20609 | 1 | 2 | yes | — |
| 346 | C24 | #32898 | 1 | 2 | yes | — |
| 347 | C24 | #32898 | 1 | 2 | yes | — |
| 348 | C24 | #32900 | 1 | 2 | yes | — |
| 349 | C24 | #32900 | 1 | 2 | yes | — |
| 350 | C23 | C2×#8534 | 1 | 1 | yes | characteristic |
| 351 | C23 | #187928 | 1 | 2 | yes | — |
| 352 | C23 | #187944 | 1 | 1 | yes | characteristic |
| 353 | C23 | #392109 | 1 | 1 | yes | characteristic |
| 354 | C23 | #392125 | 1 | 2 | yes | — |
| 355 | C23 | C2×#12707 | 1 | 2 | yes | — |
| 356 | C23 | #493398 | 1 | 2 | yes | — |
| 357 | C23 | #511790 | 1 | 4 | yes | — |
| 358 | C22 | #72210555 | 1 | 1 | yes | characteristic |
| 359 | C22 | #72218467 | 1 | 1 | yes | characteristic |
| 360 | C22 | #72218475 | 1 | 2 | yes | — |
| 361 | C22 | #72237472 | 1 | 2 | yes | — |
| 362 | C22 | #72258026 | 1 | 1 | yes | characteristic |
| 363 | C2 | #72258242 | 1 | 2 | yes | — |
| 364 | C2 | #72266242 | 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