← #72258185
Subgroups — #72258185
Order 1024.
62349 conjugacy classes of subgroups.
The subgroup lattice has 536 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #8093278 | C2 | 1 | 24 | yes | maximal, complemented |
| 2 | #8093263 | C2 | 1 | 24 | yes | maximal, complemented |
| 3 | #8093172 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #8093108 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #7702271 | C2 | 1 | 48 | yes | maximal, complemented |
| 6 | C2×#36614 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #7629133 | C2 | 1 | 9 | yes | maximal, complemented |
| 8 | #7629120 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C22×#585 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C26×C4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×#3458 | C22 | 1 | 3 | yes | complemented |
| 12 | C22×#525 | C22 | 1 | 9 | yes | — |
| 13 | #52301 | C22 | 1 | 96 | yes | complemented |
| 14 | #52294 | C22 | 1 | 96 | yes | complemented |
| 15 | #45667 | C22 | 1 | 144 | yes | complemented |
| 16 | #45645 | C22 | 1 | 144 | yes | complemented |
| 17 | #45601 | C22 | 1 | 288 | yes | complemented |
| 18 | #45568 | C22 | 1 | 288 | yes | complemented |
| 19 | #45539 | C22 | 1 | 288 | yes | complemented |
| 20 | #45509 | C22 | 1 | 96 | yes | complemented |
| 21 | #45494 | C22 | 1 | 48 | yes | complemented |
| 22 | #45479 | C22 | 1 | 48 | yes | complemented |
| 23 | #45458 | C22 | 1 | 96 | yes | complemented |
| 24 | #45439 | C22 | 1 | 96 | yes | complemented |
| 25 | #36675 | C22 | 1 | 32 | yes | complemented |
| 26 | #36614 | C22 | 1 | 48 | yes | complemented |
| 27 | #36614 | C22 | 1 | 48 | yes | complemented |
| 28 | C2×#2849 | C22 | 1 | 18 | yes | complemented |
| 29 | C2×#2848 | C22 | 1 | 12 | yes | complemented |
| 30 | C2×#2847 | C22 | 1 | 12 | yes | complemented |
| 31 | C2×#2846 | C22 | 1 | 6 | yes | complemented |
| 32 | #35659 | C22 | 1 | 36 | yes | complemented |
| 33 | #35644 | C22 | 1 | 36 | yes | complemented |
| 34 | #35584 | C22 | 1 | 36 | yes | complemented |
| 35 | #35542 | C22 | 1 | 144 | yes | complemented |
| 36 | #35512 | C22 | 1 | 36 | yes | complemented |
| 37 | #35455 | C22 | 1 | 36 | yes | complemented |
| 38 | #35446 | C22 | 1 | 12 | yes | complemented |
| 39 | #35367 | C22 | 1 | 36 | yes | complemented |
| 40 | #35346 | C22 | 1 | 12 | yes | — |
| 41 | #34946 | C22 | 1 | 72 | yes | complemented |
| 42 | #34813 | C22 | 1 | 144 | yes | complemented |
| 43 | #34736 | C22 | 1 | 72 | yes | complemented |
| 44 | C4×H(3,𝔽4) | C22 | 1 | 32 | yes | complemented |
| 45 | #34044 | C22 | 1 | 9 | yes | complemented |
| 46 | C2×C4×#120 | C22 | 1 | 24 | yes | complemented |
| 47 | C2×#2280 | C22 | 1 | 9 | yes | complemented |
| 48 | #33996 | C22 | 1 | 3 | yes | complemented |
| 49 | C27 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×#585 | — | 4 | 24 | no | — |
| 51 | C22×2−1+4 | C23 | 1 | 6 | yes | complemented |
| 52 | C22×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 53 | C22×H(5,𝔽2) | C23 | 1 | 6 | yes | complemented |
| 54 | C23×#41 | C23 | 1 | 3 | yes | — |
| 55 | C23×#41 | C23 | 1 | 12 | yes | complemented |
| 56 | C25×C4 | — | 4 | 24 | no | — |
| 57 | C25×C4 | C23 | 1 | 3 | yes | — |
| 58 | C25×C4 | C23 | 1 | 12 | yes | — |
| 59 | C25×C4 | C23 | 1 | 3 | yes | — |
| 60 | C25×C4 | C23 | 1 | 12 | yes | — |
| 61 | C2×H(3,𝔽4) | C23 | 1 | 32 | yes | — |
| 62 | #3458 | — | 4 | 24 | no | — |
| 63 | C2×#544 | C23 | 1 | 36 | yes | complemented |
| 64 | C2×#543 | C23 | 1 | 12 | yes | — |
| 65 | C2×#533 | C23 | 1 | 36 | yes | complemented |
| 66 | C2×#525 | — | 4 | 72 | no | — |
| 67 | C2×#525 | C23 | 1 | 72 | yes | — |
| 68 | C2×#525 | C23 | 1 | 72 | yes | — |
| 69 | C22×#123 | C23 | 1 | 18 | yes | — |
| 70 | C22×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 71 | C22×#121 | C23 | 1 | 18 | yes | — |
| 72 | C22×#120 | C23 | 1 | 24 | yes | — |
| 73 | C22×#120 | C23 | 1 | 18 | yes | — |
| 74 | C22×C4×D4 | C23 | 1 | 36 | yes | — |
| 75 | C22×#117 | C23 | 1 | 9 | yes | — |
| 76 | #2849 | C23 | 1 | 288 | yes | — |
| 77 | #2848 | C23 | 1 | 144 | yes | — |
| 78 | #2848 | C23 | 1 | 48 | yes | — |
| 79 | #2847 | C23 | 1 | 144 | yes | — |
| 80 | #2847 | C23 | 1 | 48 | yes | — |
| 81 | #2846 | C23 | 1 | 96 | yes | — |
| 82 | #2840 | C23 | 1 | 32 | yes | — |
| 83 | #2835 | C23 | 1 | 96 | yes | complemented |
| 84 | #2824 | C23 | 1 | 288 | yes | complemented |
| 85 | #2812 | C23 | 1 | 96 | yes | — |
| 86 | #2804 | C23 | 1 | 288 | yes | complemented |
| 87 | #2782 | C23 | 1 | 576 | yes | complemented |
| 88 | #2763 | C23 | 1 | 288 | yes | complemented |
| 89 | #2753 | C23 | 1 | 576 | yes | complemented |
| 90 | #2736 | C23 | 1 | 96 | yes | — |
| 91 | #2712 | C23 | 1 | 288 | yes | complemented |
| 92 | #2684 | C23 | 1 | 288 | yes | — |
| 93 | #2684 | C23 | 1 | 288 | yes | complemented |
| 94 | #2679 | C23 | 1 | 96 | yes | — |
| 95 | #2670 | C23 | 1 | 288 | yes | — |
| 96 | #2563 | C23 | 1 | 144 | yes | complemented |
| 97 | #2562 | C23 | 1 | 288 | yes | complemented |
| 98 | #2561 | C23 | 1 | 144 | yes | — |
| 99 | #2561 | C23 | 1 | 144 | yes | complemented |
| 100 | #2547 | C23 | 1 | 144 | yes | complemented |
| 101 | #2503 | C23 | 1 | 144 | yes | complemented |
| 102 | #2492 | C23 | 1 | 288 | yes | complemented |
| 103 | #2491 | C23 | 1 | 288 | yes | complemented |
| 104 | #2490 | C23 | 1 | 288 | yes | complemented |
| 105 | #2489 | C23 | 1 | 288 | yes | complemented |
| 106 | #2488 | C23 | 1 | 576 | yes | complemented |
| 107 | #2472 | C23 | 1 | 576 | yes | — |
| 108 | #2435 | C23 | 1 | 144 | yes | — |
| 109 | #2409 | C23 | 1 | 144 | yes | complemented |
| 110 | #2408 | C23 | 1 | 144 | yes | complemented |
| 111 | #2407 | C23 | 1 | 288 | yes | complemented |
| 112 | #2406 | C23 | 1 | 144 | yes | complemented |
| 113 | #2405 | C23 | 1 | 144 | yes | complemented |
| 114 | #2404 | C23 | 1 | 144 | yes | — |
| 115 | #2403 | C23 | 1 | 144 | yes | — |
| 116 | #2398 | C23 | 1 | 288 | yes | complemented |
| 117 | #2388 | C23 | 1 | 96 | yes | complemented |
| 118 | #2379 | C23 | 1 | 288 | yes | complemented |
| 119 | #2375 | C23 | 1 | 96 | yes | — |
| 120 | #2375 | C23 | 1 | 96 | yes | complemented |
| 121 | #2311 | C23 | 1 | 72 | yes | complemented |
| 122 | #2310 | C23 | 1 | 18 | yes | complemented |
| 123 | #2309 | C23 | 1 | 18 | yes | complemented |
| 124 | #2308 | C23 | 1 | 36 | yes | — |
| 125 | C4×#124 | C23 | 1 | 288 | yes | complemented |
| 126 | C4×#120 | C23 | 1 | 144 | yes | — |
| 127 | C4×#120 | C23 | 1 | 48 | yes | — |
| 128 | C4×#120 | C23 | 1 | 144 | yes | — |
| 129 | C4×#120 | C23 | 1 | 48 | yes | — |
| 130 | C4×#120 | C23 | 1 | 96 | yes | complemented |
| 131 | #2297 | C23 | 1 | 72 | yes | complemented |
| 132 | C2×#386 | C23 | 1 | 72 | yes | — |
| 133 | C2×#385 | C23 | 1 | 72 | yes | — |
| 134 | #2280 | C23 | 1 | 72 | yes | — |
| 135 | #2280 | C23 | 1 | 72 | yes | — |
| 136 | #2280 | C23 | 1 | 36 | yes | complemented |
| 137 | C2×#381 | C23 | 1 | 18 | yes | — |
| 138 | C2×#380 | C23 | 1 | 36 | yes | — |
| 139 | C2×#379 | C23 | 1 | 24 | yes | — |
| 140 | C2×#379 | C23 | 1 | 18 | yes | — |
| 141 | #2274 | C23 | 1 | 36 | yes | complemented |
| 142 | #2273 | C23 | 1 | 12 | yes | — |
| 143 | C4×#117 | C23 | 1 | 36 | yes | complemented |
| 144 | C2×C4×C22⋊C4 | C23 | 1 | 36 | yes | — |
| 145 | C26 | — | 4 | 12 | no | — |
| 146 | C26 | — | 4 | 16 | no | — |
| 147 | C26 | C24 | 1 | 3 | yes | — |
| 148 | C26 | C24 | 1 | 12 | yes | — |
| 149 | #585 | — | 4 | 256 | no | — |
| 150 | C2×2−1+4 | — | 4 | 72 | no | — |
| 151 | C2×H(5,𝔽2) | — | 4 | 48 | no | — |
| 152 | C2×H(5,𝔽2) | — | 4 | 72 | no | — |
| 153 | C22×#41 | — | 2 | 72 | no | — |
| 154 | C22×#41 | — | 4 | 144 | no | — |
| 155 | C22×#41 | C24 | 1 | 12 | yes | — |
| 156 | C22×#41 | C24 | 1 | 12 | yes | — |
| 157 | C22×#41 | C24 | 1 | 24 | yes | — |
| 158 | C22×#41 | C24 | 1 | 8 | yes | complemented |
| 159 | C22×#41 | C24 | 1 | 24 | yes | complemented |
| 160 | C23×Q8 | C24 | 1 | 3 | yes | — |
| 161 | C23×Q8 | C24 | 1 | 12 | yes | complemented |
| 162 | C23×D4 | C24 | 1 | 6 | yes | — |
| 163 | C23×D4 | C24 | 1 | 3 | yes | — |
| 164 | C23×D4 | C24 | 1 | 24 | yes | — |
| 165 | C23×D4 | C24 | 1 | 36 | yes | — |
| 166 | C23×D4 | C24 | 1 | 12 | yes | complemented |
| 167 | C24×C4 | — | 2 | 72 | no | — |
| 168 | C24×C4 | — | 4 | 144 | no | — |
| 169 | C24×C4 | — | 4 | 144 | no | — |
| 170 | C24×C4 | — | 4 | 36 | no | — |
| 171 | C24×C4 | — | 4 | 256 | no | — |
| 172 | C24×C4 | C24 | 1 | 18 | yes | — |
| 173 | C24×C4 | C24 | 1 | 18 | yes | — |
| 174 | C24×C4 | C24 | 1 | 3 | yes | — |
| 175 | C24×C4 | C24 | 1 | 6 | yes | — |
| 176 | C24×C4 | C24 | 1 | 36 | yes | — |
| 177 | C24×C4 | C24 | 1 | 12 | yes | — |
| 178 | C24×C4 | C24 | 1 | 36 | yes | — |
| 179 | C24×C4 | C24 | 1 | 12 | yes | — |
| 180 | C24×C4 | C24 | 1 | 4 | yes | — |
| 181 | C24×C4 | C24 | 1 | 1 | yes | characteristic |
| 182 | C24×C4 | C24 | 1 | 8 | yes | complemented |
| 183 | H(3,𝔽4) | — | 4 | 128 | no | — |
| 184 | #544 | — | 4 | 144 | no | — |
| 185 | #543 | — | 4 | 48 | no | — |
| 186 | #533 | — | 4 | 144 | no | — |
| 187 | C2×C4⋊Q8 | C24 | 1 | 72 | yes | complemented |
| 188 | C2×#125 | C24 | 1 | 72 | yes | complemented |
| 189 | C2×#124 | C24 | 1 | 288 | yes | — |
| 190 | #525 | — | 4 | 288 | no | — |
| 191 | #525 | — | 4 | 288 | no | — |
| 192 | C2×#123 | — | 4 | 72 | no | — |
| 193 | C2×#123 | C24 | 1 | 144 | yes | — |
| 194 | C2×C22⋊Q8 | — | 4 | 72 | no | — |
| 195 | C2×C22⋊Q8 | C24 | 1 | 144 | yes | — |
| 196 | C2×C22⋊Q8 | C24 | 1 | 144 | yes | — |
| 197 | C2×#121 | — | 4 | 72 | no | — |
| 198 | C2×#121 | C24 | 1 | 144 | yes | — |
| 199 | C2×#120 | — | 4 | 72 | no | — |
| 200 | C2×#120 | — | 4 | 96 | no | — |
| 201 | C2×#120 | C24 | 1 | 48 | yes | — |
| 202 | C2×#120 | C24 | 1 | 144 | yes | — |
| 203 | C2×#120 | C24 | 1 | 144 | yes | — |
| 204 | C2×#120 | C24 | 1 | 96 | yes | — |
| 205 | C2×C4×Q8 | C24 | 1 | 48 | yes | complemented |
| 206 | C2×C4×D4 | — | 4 | 144 | no | — |
| 207 | C2×C4×D4 | C24 | 1 | 144 | yes | — |
| 208 | C2×C4×D4 | C24 | 1 | 144 | yes | — |
| 209 | C2×#117 | — | 2 | 72 | no | — |
| 210 | C2×#117 | C24 | 1 | 36 | yes | — |
| 211 | C2×#117 | C24 | 1 | 36 | yes | — |
| 212 | C22×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 213 | C22×C4⋊C4 | C24 | 1 | 36 | yes | — |
| 214 | C22×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 215 | C22×C22⋊C4 | C24 | 1 | 36 | yes | — |
| 216 | C22×C22⋊C4 | C24 | 1 | 36 | yes | — |
| 217 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 218 | C22×C42 | C24 | 1 | 18 | yes | — |
| 219 | #400 | C24 | 1 | 576 | yes | complemented |
| 220 | #397 | C24 | 1 | 288 | yes | — |
| 221 | #397 | C24 | 1 | 288 | yes | complemented |
| 222 | #395 | C24 | 1 | 96 | yes | complemented |
| 223 | #394 | C24 | 1 | 576 | yes | — |
| 224 | #394 | C24 | 1 | 288 | yes | complemented |
| 225 | #393 | C24 | 1 | 288 | yes | — |
| 226 | #393 | C24 | 1 | 96 | yes | — |
| 227 | #393 | C24 | 1 | 288 | yes | complemented |
| 228 | #392 | C24 | 1 | 288 | yes | — |
| 229 | #391 | C24 | 1 | 144 | yes | complemented |
| 230 | #391 | C24 | 1 | 288 | yes | complemented |
| 231 | #390 | C24 | 1 | 288 | yes | — |
| 232 | #390 | C24 | 1 | 144 | yes | complemented |
| 233 | #388 | C24 | 1 | 576 | yes | — |
| 234 | #388 | C24 | 1 | 576 | yes | complemented |
| 235 | #386 | C24 | 1 | 288 | yes | — |
| 236 | #386 | C24 | 1 | 144 | yes | — |
| 237 | #386 | C24 | 1 | 288 | yes | — |
| 238 | #386 | C24 | 1 | 144 | yes | — |
| 239 | #386 | C24 | 1 | 288 | yes | — |
| 240 | #385 | C24 | 1 | 144 | yes | — |
| 241 | #385 | C24 | 1 | 144 | yes | — |
| 242 | #385 | C24 | 1 | 288 | yes | — |
| 243 | #385 | C24 | 1 | 288 | yes | complemented |
| 244 | #382 | C24 | 1 | 288 | yes | complemented |
| 245 | #381 | C24 | 1 | 72 | yes | — |
| 246 | #381 | C24 | 1 | 144 | yes | — |
| 247 | #380 | C24 | 1 | 144 | yes | — |
| 248 | #380 | C24 | 1 | 144 | yes | — |
| 249 | #380 | C24 | 1 | 144 | yes | complemented |
| 250 | #379 | C24 | 1 | 144 | yes | — |
| 251 | #379 | C24 | 1 | 72 | yes | — |
| 252 | #379 | C24 | 1 | 48 | yes | — |
| 253 | #379 | C24 | 1 | 144 | yes | — |
| 254 | #379 | C24 | 1 | 96 | yes | complemented |
| 255 | C4×C4⋊C4 | C24 | 1 | 144 | yes | complemented |
| 256 | C4×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 257 | C4×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 258 | C4×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 259 | C4×C22⋊C4 | C24 | 1 | 144 | yes | complemented |
| 260 | #376 | C24 | 1 | 24 | yes | complemented |
| 261 | C2×#95 | C24 | 1 | 72 | yes | — |
| 262 | C43 | C24 | 1 | 24 | yes | complemented |
| 263 | C25 | — | 2 | 36 | no | — |
| 264 | C25 | — | 2 | 48 | no | — |
| 265 | C25 | — | 4 | 72 | no | — |
| 266 | C25 | — | 4 | 24 | no | — |
| 267 | C25 | — | 4 | 72 | no | — |
| 268 | C25 | — | 4 | 64 | no | — |
| 269 | C25 | — | 4 | 384 | no | — |
| 270 | C25 | C25 | 1 | 18 | yes | — |
| 271 | C25 | C25 | 1 | 6 | yes | — |
| 272 | C25 | C25 | 1 | 12 | yes | — |
| 273 | C25 | C25 | 1 | 8 | yes | — |
| 274 | C25 | C25 | 1 | 4 | yes | — |
| 275 | C25 | C25 | 1 | 1 | yes | characteristic |
| 276 | 2−1+4 | — | 4 | 384 | no | — |
| 277 | H(5,𝔽2) | — | 4 | 384 | no | — |
| 278 | H(5,𝔽2) | — | 4 | 256 | no | — |
| 279 | C2×#41 | — | 2 | 144 | no | — |
| 280 | C2×#41 | — | 2 | 144 | no | — |
| 281 | C2×#41 | — | 4 | 48 | no | — |
| 282 | C2×#41 | — | 4 | 144 | no | — |
| 283 | C2×#41 | — | 4 | 144 | no | — |
| 284 | C2×#41 | — | 4 | 768 | no | — |
| 285 | C2×#41 | — | 4 | 192 | no | — |
| 286 | C22×Q8 | — | 2 | 36 | no | — |
| 287 | C22×Q8 | — | 4 | 72 | no | — |
| 288 | C22×Q8 | C25 | 1 | 12 | yes | — |
| 289 | C22×Q8 | C25 | 1 | 48 | yes | — |
| 290 | C22×Q8 | C25 | 1 | 8 | yes | — |
| 291 | C22×D4 | — | 2 | 72 | no | — |
| 292 | C22×D4 | — | 2 | 36 | no | — |
| 293 | C22×D4 | — | 4 | 72 | no | — |
| 294 | C22×D4 | — | 4 | 72 | no | — |
| 295 | C22×D4 | — | 4 | 144 | no | — |
| 296 | C22×D4 | — | 4 | 144 | no | — |
| 297 | C22×D4 | C25 | 1 | 24 | yes | — |
| 298 | C22×D4 | C25 | 1 | 12 | yes | — |
| 299 | C22×D4 | C25 | 1 | 144 | yes | — |
| 300 | C22×D4 | C25 | 1 | 24 | yes | — |
| 301 | C23×C4 | — | 2 | 36 | no | — |
| 302 | C23×C4 | — | 2 | 72 | no | — |
| 303 | C23×C4 | — | 2 | 72 | no | — |
| 304 | C23×C4 | — | 2 | 72 | no | — |
| 305 | C23×C4 | — | 2 | 144 | no | — |
| 306 | C23×C4 | — | 2 | 144 | no | — |
| 307 | C23×C4 | — | 4 | 24 | no | — |
| 308 | C23×C4 | — | 4 | 72 | no | — |
| 309 | C23×C4 | — | 4 | 72 | no | — |
| 310 | C23×C4 | — | 4 | 216 | no | — |
| 311 | C23×C4 | — | 4 | 48 | no | — |
| 312 | C23×C4 | — | 4 | 144 | no | — |
| 313 | C23×C4 | — | 4 | 72 | no | — |
| 314 | C23×C4 | — | 4 | 192 | no | — |
| 315 | C23×C4 | — | 4 | 768 | no | — |
| 316 | C23×C4 | — | 4 | 768 | no | — |
| 317 | C23×C4 | — | 4 | 192 | no | — |
| 318 | C23×C4 | H(5,𝔽2) | 1 | 24 | yes | — |
| 319 | C23×C4 | C25 | 1 | 6 | yes | — |
| 320 | C23×C4 | C25 | 1 | 18 | yes | — |
| 321 | C23×C4 | C25 | 1 | 12 | yes | — |
| 322 | C23×C4 | C25 | 1 | 36 | yes | — |
| 323 | C23×C4 | C25 | 1 | 12 | yes | — |
| 324 | C23×C4 | C25 | 1 | 12 | yes | — |
| 325 | C23×C4 | C25 | 1 | 36 | yes | — |
| 326 | C23×C4 | C25 | 1 | 12 | yes | — |
| 327 | C23×C4 | C25 | 1 | 36 | yes | — |
| 328 | C23×C4 | C25 | 1 | 24 | yes | — |
| 329 | C23×C4 | C25 | 1 | 3 | yes | — |
| 330 | C23×C4 | C25 | 1 | 3 | yes | — |
| 331 | C4⋊Q8 | — | 4 | 144 | no | — |
| 332 | #125 | — | 4 | 144 | no | — |
| 333 | #124 | — | 4 | 576 | no | — |
| 334 | #123 | — | 4 | 288 | no | — |
| 335 | C22⋊Q8 | — | 4 | 288 | no | — |
| 336 | C22⋊Q8 | — | 4 | 288 | no | — |
| 337 | #121 | — | 4 | 288 | no | — |
| 338 | #120 | — | 2 | 192 | no | — |
| 339 | #120 | — | 4 | 288 | no | — |
| 340 | #120 | — | 4 | 288 | no | — |
| 341 | #120 | — | 4 | 192 | no | — |
| 342 | C4×Q8 | — | 4 | 96 | no | — |
| 343 | C4×D4 | — | 4 | 288 | no | — |
| 344 | C4×D4 | — | 4 | 288 | no | — |
| 345 | #117 | — | 2 | 144 | no | — |
| 346 | #117 | — | 2 | 144 | no | — |
| 347 | C2×C4⋊C4 | — | 2 | 72 | no | — |
| 348 | C2×C4⋊C4 | — | 4 | 72 | no | — |
| 349 | C2×C4⋊C4 | C25 | 1 | 72 | yes | — |
| 350 | C2×C4⋊C4 | C25 | 1 | 144 | yes | — |
| 351 | C2×C4⋊C4 | C25 | 1 | 144 | yes | — |
| 352 | C2×C22⋊C4 | — | 2 | 72 | no | — |
| 353 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 354 | C2×C22⋊C4 | — | 4 | 72 | no | — |
| 355 | C2×C22⋊C4 | — | 4 | 72 | no | — |
| 356 | C2×C22⋊C4 | C25 | 1 | 72 | yes | — |
| 357 | C2×C22⋊C4 | C25 | 1 | 144 | yes | — |
| 358 | C2×C22⋊C4 | C25 | 1 | 144 | yes | — |
| 359 | C2×C22⋊C4 | C25 | 1 | 144 | yes | — |
| 360 | C2×C22⋊C4 | C25 | 1 | 144 | yes | — |
| 361 | C2×C22⋊C4 | C25 | 1 | 288 | yes | — |
| 362 | C2×C42 | — | 2 | 72 | no | — |
| 363 | C2×C42 | C25 | 1 | 36 | yes | — |
| 364 | C2×C42 | C25 | 1 | 36 | yes | — |
| 365 | C2×C42 | C25 | 1 | 96 | yes | — |
| 366 | #95 | C25 | 1 | 288 | yes | — |
| 367 | #95 | C25 | 1 | 96 | yes | — |
| 368 | #95 | C25 | 1 | 288 | yes | — |
| 369 | C24 | — | 2 | 36 | no | — |
| 370 | C24 | — | 2 | 72 | no | — |
| 371 | C24 | — | 2 | 72 | no | — |
| 372 | C24 | — | 2 | 72 | no | — |
| 373 | C24 | — | 2 | 36 | no | — |
| 374 | C24 | — | 4 | 12 | no | — |
| 375 | C24 | — | 4 | 36 | no | — |
| 376 | C24 | — | 4 | 4 | no | — |
| 377 | C24 | — | 4 | 36 | no | — |
| 378 | C24 | — | 4 | 12 | no | — |
| 379 | C24 | — | 4 | 12 | no | — |
| 380 | C24 | — | 4 | 24 | no | — |
| 381 | C24 | — | 4 | 24 | no | — |
| 382 | C24 | — | 4 | 32 | no | — |
| 383 | C24 | — | 4 | 288 | no | — |
| 384 | C24 | — | 4 | 576 | no | — |
| 385 | C24 | — | 4 | 192 | no | — |
| 386 | C24 | — | 4 | 576 | no | — |
| 387 | C24 | — | 4 | 1024 | no | — |
| 388 | C24 | — | 4 | 48 | no | — |
| 389 | C24 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 390 | C24 | #585 | 1 | 16 | yes | complemented |
| 391 | C24 | C26 | 1 | 12 | yes | — |
| 392 | C24 | C26 | 1 | 12 | yes | — |
| 393 | C24 | C26 | 1 | 3 | yes | — |
| 394 | #41 | — | 4 | 128 | no | — |
| 395 | #41 | — | 4 | 384 | no | — |
| 396 | #41 | — | 4 | 384 | no | — |
| 397 | #41 | — | 4 | 192 | no | — |
| 398 | #41 | — | 4 | 192 | no | — |
| 399 | C2×Q8 | — | 2 | 72 | no | — |
| 400 | C2×Q8 | — | 4 | 24 | no | — |
| 401 | C2×Q8 | — | 4 | 48 | no | — |
| 402 | C2×Q8 | — | 4 | 96 | no | — |
| 403 | C2×Q8 | — | 4 | 192 | no | — |
| 404 | C2×Q8 | — | 4 | 48 | no | — |
| 405 | C2×D4 | — | 2 | 144 | no | — |
| 406 | C2×D4 | — | 2 | 288 | no | — |
| 407 | C2×D4 | — | 2 | 72 | no | — |
| 408 | C2×D4 | — | 4 | 72 | no | — |
| 409 | C2×D4 | — | 4 | 144 | no | — |
| 410 | C2×D4 | — | 4 | 144 | no | — |
| 411 | C2×D4 | — | 4 | 384 | no | — |
| 412 | C2×D4 | — | 4 | 192 | no | — |
| 413 | C2×D4 | — | 4 | 96 | no | — |
| 414 | C2×D4 | — | 4 | 48 | no | — |
| 415 | C2×D4 | — | 8 | 288 | no | — |
| 416 | C22×C4 | — | 2 | 36 | no | — |
| 417 | C22×C4 | — | 2 | 36 | no | — |
| 418 | C22×C4 | — | 2 | 72 | no | — |
| 419 | C22×C4 | — | 2 | 72 | no | — |
| 420 | C22×C4 | — | 2 | 72 | no | — |
| 421 | C22×C4 | — | 2 | 72 | no | — |
| 422 | C22×C4 | — | 2 | 72 | no | — |
| 423 | C22×C4 | — | 2 | 72 | no | — |
| 424 | C22×C4 | — | 2 | 144 | no | — |
| 425 | C22×C4 | — | 4 | 36 | no | — |
| 426 | C22×C4 | — | 4 | 108 | no | — |
| 427 | C22×C4 | — | 4 | 72 | no | — |
| 428 | C22×C4 | — | 4 | 72 | no | — |
| 429 | C22×C4 | — | 4 | 576 | no | — |
| 430 | C22×C4 | — | 4 | 64 | no | — |
| 431 | C22×C4 | — | 4 | 192 | no | — |
| 432 | C22×C4 | — | 4 | 192 | no | — |
| 433 | C22×C4 | — | 4 | 576 | no | — |
| 434 | C22×C4 | — | 4 | 128 | no | — |
| 435 | C22×C4 | — | 4 | 48 | no | — |
| 436 | C22×C4 | — | 4 | 288 | no | — |
| 437 | C22×C4 | — | 4 | 288 | no | — |
| 438 | C22×C4 | — | 4 | 96 | no | — |
| 439 | C22×C4 | H(3,𝔽4) | 1 | 64 | yes | complemented |
| 440 | C22×C4 | C2×H(5,𝔽2) | 1 | 36 | yes | — |
| 441 | C22×C4 | C2×H(5,𝔽2) | 1 | 36 | yes | — |
| 442 | C22×C4 | C26 | 1 | 12 | yes | — |
| 443 | C22×C4 | C26 | 1 | 12 | yes | — |
| 444 | C22×C4 | C26 | 1 | 72 | yes | — |
| 445 | C22×C4 | C26 | 1 | 3 | yes | — |
| 446 | C22×C4 | C26 | 1 | 1 | yes | characteristic |
| 447 | C4⋊C4 | — | 2 | 144 | no | — |
| 448 | C4⋊C4 | — | 4 | 144 | no | — |
| 449 | C4⋊C4 | — | 4 | 144 | no | — |
| 450 | C22⋊C4 | — | 2 | 144 | no | — |
| 451 | C22⋊C4 | — | 2 | 288 | no | — |
| 452 | C22⋊C4 | — | 4 | 144 | no | — |
| 453 | C22⋊C4 | — | 4 | 144 | no | — |
| 454 | C22⋊C4 | — | 4 | 144 | no | — |
| 455 | C22⋊C4 | — | 4 | 288 | no | — |
| 456 | C42 | — | 2 | 72 | no | — |
| 457 | C42 | — | 2 | 72 | no | — |
| 458 | C42 | — | 4 | 96 | no | — |
| 459 | C23 | — | 2 | 12 | no | — |
| 460 | C23 | — | 2 | 144 | no | — |
| 461 | C23 | — | 2 | 36 | no | — |
| 462 | C23 | — | 2 | 36 | no | — |
| 463 | C23 | — | 2 | 36 | no | — |
| 464 | C23 | — | 2 | 48 | no | — |
| 465 | C23 | — | 4 | 24 | no | — |
| 466 | C23 | — | 4 | 48 | no | — |
| 467 | C23 | — | 4 | 288 | no | — |
| 468 | C23 | — | 4 | 144 | no | — |
| 469 | C23 | — | 4 | 72 | no | — |
| 470 | C23 | — | 4 | 144 | no | — |
| 471 | C23 | — | 4 | 16 | no | — |
| 472 | C23 | — | 4 | 48 | no | — |
| 473 | C23 | — | 4 | 384 | no | — |
| 474 | C23 | — | 4 | 1536 | no | — |
| 475 | C23 | — | 4 | 48 | no | — |
| 476 | C23 | — | 4 | 72 | no | — |
| 477 | C23 | — | 4 | 32 | no | — |
| 478 | C23 | — | 4 | 24 | no | — |
| 479 | C23 | — | 8 | 72 | no | — |
| 480 | C23 | — | 16 | 48 | no | — |
| 481 | C23 | C2×H(3,𝔽4) | 1 | 16 | yes | — |
| 482 | C23 | C22×H(5,𝔽2) | 1 | 18 | yes | — |
| 483 | C23 | C2×#585 | 1 | 24 | yes | — |
| 484 | C23 | C27 | 1 | 1 | yes | characteristic |
| 485 | Q8 | — | 4 | 32 | no | — |
| 486 | Q8 | — | 4 | 48 | no | — |
| 487 | Q8 | — | 16 | 48 | no | — |
| 488 | D4 | — | 4 | 96 | no | — |
| 489 | D4 | — | 4 | 96 | no | — |
| 490 | D4 | — | 4 | 48 | no | — |
| 491 | D4 | — | 8 | 288 | no | — |
| 492 | C2×C4 | — | 2 | 72 | no | — |
| 493 | C2×C4 | — | 2 | 36 | no | — |
| 494 | C2×C4 | — | 2 | 36 | no | — |
| 495 | C2×C4 | — | 2 | 144 | no | — |
| 496 | C2×C4 | — | 4 | 48 | no | — |
| 497 | C2×C4 | — | 4 | 144 | no | — |
| 498 | C2×C4 | — | 4 | 96 | no | — |
| 499 | C2×C4 | — | 4 | 72 | no | — |
| 500 | C2×C4 | — | 4 | 24 | no | — |
| 501 | C2×C4 | — | 4 | 48 | no | — |
| 502 | C2×C4 | — | 4 | 144 | no | — |
| 503 | C2×C4 | — | 4 | 48 | no | — |
| 504 | C2×C4 | — | 4 | 48 | no | — |
| 505 | C2×C4 | — | 8 | 72 | no | — |
| 506 | C2×C4 | C2×H(3,𝔽4) | 1 | 48 | yes | — |
| 507 | C2×C4 | C2×H(3,𝔽4) | 1 | 48 | yes | — |
| 508 | C2×C4 | C22×H(5,𝔽2) | 1 | 6 | yes | — |
| 509 | C2×C4 | C22×H(5,𝔽2) | 1 | 18 | yes | — |
| 510 | C22 | — | 2 | 36 | no | — |
| 511 | C22 | — | 2 | 72 | no | — |
| 512 | C22 | — | 4 | 16 | no | — |
| 513 | C22 | — | 4 | 288 | no | — |
| 514 | C22 | — | 4 | 64 | no | — |
| 515 | C22 | — | 4 | 192 | no | — |
| 516 | C22 | — | 4 | 36 | no | — |
| 517 | C22 | — | 4 | 12 | no | — |
| 518 | C22 | — | 4 | 72 | no | — |
| 519 | C22 | — | 4 | 12 | no | — |
| 520 | C22 | — | 16 | 24 | no | — |
| 521 | C22 | — | 16 | 32 | no | — |
| 522 | C22 | C22×H(3,𝔽4) | 1 | 12 | yes | — |
| 523 | C22 | C23×H(5,𝔽2) | 1 | 3 | yes | — |
| 524 | C22 | C22×#585 | 1 | 4 | yes | — |
| 525 | C4 | — | 4 | 72 | no | — |
| 526 | C4 | — | 4 | 12 | no | — |
| 527 | C4 | — | 4 | 12 | no | — |
| 528 | C4 | C22×H(3,𝔽4) | 1 | 4 | yes | — |
| 529 | C4 | C22×H(3,𝔽4) | 1 | 12 | yes | — |
| 530 | C2 | — | 2 | 12 | no | — |
| 531 | C2 | — | 4 | 24 | no | — |
| 532 | C2 | — | 8 | 12 | no | — |
| 533 | C2 | C23×H(3,𝔽4) | 1 | 1 | yes | characteristic |
| 534 | C2 | #10586169 | 1 | 6 | 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