← #72225534
Subgroups — #72225534
Order 4096.
594 conjugacy classes of subgroups.
The subgroup lattice has 483 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225485 | — | 2 | 1 | no | — |
| 3 | #72225484 | — | 2 | 1 | no | — |
| 4 | #72225472 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72225470 | — | 2 | 1 | no | — |
| 6 | #72225468 | — | 2 | 1 | no | — |
| 7 | #72225457 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72225436 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #72225433 | C4 | 1 | 2 | yes | complemented |
| 10 | #72225432 | C4 | 1 | 2 | yes | complemented |
| 11 | #72225410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #72225395 | C22 | 1 | 1 | yes | characteristic |
| 13 | #72225395 | C22 | 1 | 1 | yes | characteristic |
| 14 | #72225378 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #72225363 | — | 2 | 1 | no | — |
| 16 | #72225352 | C22 | 1 | 1 | yes | characteristic |
| 17 | #72225313 | C22 | 1 | 1 | yes | characteristic |
| 18 | #72216535 | — | 2 | 1 | no | — |
| 19 | #72216326 | C2 | 1 | 1 | yes | maximal, characteristic |
| 20 | #72216296 | C22 | 1 | 1 | yes | characteristic |
| 21 | #72216283 | — | 2 | 1 | no | — |
| 22 | #72216261 | C22 | 1 | 1 | yes | characteristic |
| 23 | #72216244 | — | 2 | 1 | no | — |
| 24 | #72216226 | C22 | 1 | 1 | yes | characteristic |
| 25 | #513082 | — | 2 | 1 | no | — |
| 26 | #513082 | — | 2 | 1 | no | — |
| 27 | #491485 | — | 2 | 1 | no | — |
| 28 | #153582 | — | 2 | 1 | no | — |
| 29 | #153582 | — | 2 | 1 | no | — |
| 30 | #151998 | D4 | 1 | 1 | yes | characteristic |
| 31 | #151989 | — | 4 | 1 | no | — |
| 32 | #151732 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | #151724 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | #151718 | — | 2 | 1 | no | — |
| 35 | #151715 | — | 2 | 1 | no | — |
| 36 | #151715 | — | 2 | 1 | no | — |
| 37 | #151055 | — | 2 | 1 | no | — |
| 38 | #151055 | — | 2 | 1 | no | — |
| 39 | #151040 | D4 | 1 | 1 | yes | characteristic |
| 40 | C2×#7459 | — | 2 | 1 | no | — |
| 41 | #150160 | — | 4 | 1 | no | — |
| 42 | #150160 | — | 4 | 1 | no | — |
| 43 | C8×M64 | D4 | 1 | 1 | yes | characteristic |
| 44 | C8×M64 | C23 | 1 | 1 | yes | characteristic |
| 45 | #141812 | — | 4 | 1 | no | — |
| 46 | #141671 | — | 4 | 1 | no | — |
| 47 | #135796 | — | 2 | 1 | no | — |
| 48 | #129142 | — | 2 | 1 | no | — |
| 49 | C2×#7052 | D4 | 1 | 1 | yes | characteristic |
| 50 | #94754 | — | 4 | 2 | no | — |
| 51 | #94748 | — | 2 | 1 | no | — |
| 52 | #94748 | C2×C4 | 1 | 2 | yes | — |
| 53 | #94746 | — | 2 | 1 | no | — |
| 54 | #94746 | — | 2 | 1 | no | — |
| 55 | #94696 | — | 4 | 1 | no | — |
| 56 | #94694 | — | 4 | 1 | no | — |
| 57 | #94614 | — | 4 | 2 | no | — |
| 58 | #94053 | — | 2 | 1 | no | — |
| 59 | #94041 | — | 4 | 1 | no | — |
| 60 | #93882 | — | 2 | 1 | no | — |
| 61 | #93882 | C2×C4 | 1 | 2 | yes | — |
| 62 | #93666 | — | 2 | 1 | no | — |
| 63 | #93666 | — | 2 | 1 | no | — |
| 64 | #33733 | — | 4 | 1 | no | — |
| 65 | #33733 | — | 4 | 1 | no | — |
| 66 | #19603 | — | 4 | 1 | no | — |
| 67 | #13733 | — | 2 | 1 | no | — |
| 68 | #13733 | — | 2 | 1 | no | — |
| 69 | #13725 | — | 2 | 1 | no | — |
| 70 | #13725 | — | 2 | 1 | no | — |
| 71 | #13719 | — | 4 | 1 | no | — |
| 72 | #13719 | — | 4 | 1 | no | — |
| 73 | #13697 | — | 4 | 1 | no | — |
| 74 | #13697 | — | 4 | 1 | no | — |
| 75 | #13697 | — | 8 | 1 | no | — |
| 76 | #13654 | — | 4 | 1 | no | — |
| 77 | #13654 | — | 4 | 1 | no | — |
| 78 | #13654 | — | 8 | 1 | no | — |
| 79 | #13638 | — | 2 | 1 | no | — |
| 80 | C2×#1422 | — | 4 | 1 | no | — |
| 81 | #13551 | — | 8 | 1 | no | — |
| 82 | C4×M64 | D8 | 1 | 1 | yes | characteristic |
| 83 | C4×M64 | D8 | 1 | 1 | yes | characteristic |
| 84 | C4×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C4×M64 | #41 | 1 | 1 | yes | characteristic |
| 86 | #13208 | — | 8 | 2 | no | — |
| 87 | #12670 | — | 2 | 1 | no | — |
| 88 | #12664 | — | 4 | 1 | no | — |
| 89 | #12521 | — | 2 | 1 | no | — |
| 90 | #12515 | — | 2 | 1 | no | — |
| 91 | #12509 | — | 4 | 1 | no | — |
| 92 | #12503 | — | 4 | 1 | no | — |
| 93 | #12503 | — | 4 | 1 | no | — |
| 94 | #12023 | — | 4 | 1 | no | — |
| 95 | #12023 | — | 4 | 1 | no | — |
| 96 | C2×#1373 | — | 2 | 1 | no | — |
| 97 | #11671 | — | 8 | 2 | no | — |
| 98 | C2×C8×C16 | — | 2 | 1 | no | — |
| 99 | C2×C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | #8823 | — | 4 | 1 | no | — |
| 101 | #7544 | — | 2 | 2 | no | — |
| 102 | #7544 | — | 4 | 1 | no | — |
| 103 | #7513 | — | 4 | 1 | no | — |
| 104 | #7513 | — | 4 | 1 | no | — |
| 105 | #7511 | — | 4 | 1 | no | — |
| 106 | #7511 | — | 4 | 1 | no | — |
| 107 | #7476 | SD16 | 1 | 1 | yes | characteristic |
| 108 | #7475 | SD16 | 1 | 1 | yes | characteristic |
| 109 | #7469 | — | 8 | 1 | no | — |
| 110 | #7464 | — | 2 | 1 | no | — |
| 111 | #7464 | D8 | 1 | 2 | yes | — |
| 112 | #7463 | — | 4 | 1 | no | — |
| 113 | #7463 | — | 4 | 1 | no | — |
| 114 | #7463 | — | 8 | 1 | no | — |
| 115 | #7459 | — | 2 | 2 | no | — |
| 116 | #7459 | — | 4 | 1 | no | — |
| 117 | #7385 | — | 8 | 2 | no | — |
| 118 | #7385 | — | 8 | 2 | no | — |
| 119 | #7329 | — | 2 | 1 | no | — |
| 120 | #7329 | #41 | 1 | 1 | yes | characteristic |
| 121 | #7329 | #41 | 1 | 1 | yes | characteristic |
| 122 | C8×C32 | — | 2 | 1 | no | — |
| 123 | C8×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 124 | C8×C32 | #41 | 1 | 1 | yes | characteristic |
| 125 | #7179 | — | 4 | 1 | no | — |
| 126 | #7052 | — | 2 | 1 | no | — |
| 127 | #7052 | — | 2 | 1 | no | — |
| 128 | #3169 | — | 8 | 1 | no | — |
| 129 | #3169 | — | 8 | 1 | no | — |
| 130 | #3147 | — | 8 | 1 | no | — |
| 131 | C2×D32 | — | 4 | 1 | no | — |
| 132 | C2×D32 | — | 4 | 1 | no | — |
| 133 | C2×D32 | — | 8 | 1 | no | — |
| 134 | C2×M64 | — | 2 | 1 | no | — |
| 135 | C2×M64 | — | 2 | 1 | no | — |
| 136 | C2×M64 | — | 2 | 1 | no | — |
| 137 | C2×M64 | — | 8 | 1 | no | — |
| 138 | C2×M64 | C2×SD16 | 1 | 1 | yes | characteristic |
| 139 | C2×M64 | #135 | 1 | 1 | yes | characteristic |
| 140 | #2252 | — | 4 | 1 | no | — |
| 141 | #2252 | — | 4 | 1 | no | — |
| 142 | #2246 | — | 4 | 1 | no | — |
| 143 | #2246 | — | 4 | 1 | no | — |
| 144 | #2240 | — | 8 | 1 | no | — |
| 145 | #2240 | — | 8 | 1 | no | — |
| 146 | #2215 | — | 8 | 1 | no | — |
| 147 | #2215 | — | 8 | 1 | no | — |
| 148 | #2215 | — | 8 | 1 | no | — |
| 149 | #2215 | — | 8 | 1 | no | — |
| 150 | C4×D16 | — | 8 | 1 | no | — |
| 151 | C4×D16 | — | 8 | 1 | no | — |
| 152 | C4×D16 | — | 8 | 1 | no | — |
| 153 | C4×D16 | — | 8 | 1 | no | — |
| 154 | C2×#368 | — | 2 | 1 | no | — |
| 155 | #2158 | — | 2 | 1 | no | — |
| 156 | C2×#364 | — | 4 | 1 | no | — |
| 157 | C2×#359 | — | 16 | 4 | no | — |
| 158 | #2108 | — | 8 | 1 | no | — |
| 159 | C2×C4×C16 | — | 2 | 2 | no | — |
| 160 | C2×C4×C16 | #121 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 162 | #1848 | — | 8 | 1 | no | — |
| 163 | #1772 | — | 4 | 1 | no | — |
| 164 | #1713 | — | 4 | 1 | no | — |
| 165 | #1712 | — | 4 | 1 | no | — |
| 166 | #1709 | — | 8 | 1 | no | — |
| 167 | #1706 | — | 8 | 1 | no | — |
| 168 | #1706 | — | 8 | 1 | no | — |
| 169 | #1567 | — | 8 | 1 | no | — |
| 170 | #1567 | — | 8 | 1 | no | — |
| 171 | C2×C82 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 172 | M128 | — | 4 | 2 | no | — |
| 173 | M128 | — | 8 | 1 | no | — |
| 174 | #1426 | — | 4 | 2 | no | — |
| 175 | #1424 | — | 4 | 1 | no | — |
| 176 | #1424 | — | 4 | 1 | no | — |
| 177 | #1424 | — | 8 | 1 | no | — |
| 178 | #1422 | — | 4 | 2 | no | — |
| 179 | #1422 | — | 8 | 1 | no | — |
| 180 | #1415 | — | 8 | 2 | no | — |
| 181 | #1415 | — | 8 | 1 | no | — |
| 182 | #1415 | — | 8 | 1 | no | — |
| 183 | #1398 | — | 16 | 2 | no | — |
| 184 | #1397 | — | 2 | 1 | no | — |
| 185 | #1397 | — | 2 | 1 | no | — |
| 186 | #1397 | SD32 | 1 | 2 | yes | — |
| 187 | #1397 | C2×D8 | 1 | 1 | yes | characteristic |
| 188 | #1397 | #135 | 1 | 1 | yes | characteristic |
| 189 | C4×C32 | — | 2 | 1 | no | — |
| 190 | C4×C32 | — | 2 | 1 | no | — |
| 191 | C4×C32 | #117 | 1 | 1 | yes | characteristic |
| 192 | C4×C32 | C4×D4 | 1 | 1 | yes | characteristic |
| 193 | C4×C32 | #124 | 1 | 1 | yes | characteristic |
| 194 | C4×C32 | #126 | 1 | 1 | yes | characteristic |
| 195 | #1382 | — | 4 | 1 | no | — |
| 196 | #1379 | — | 8 | 1 | no | — |
| 197 | #1373 | — | 2 | 2 | no | — |
| 198 | #1373 | — | 4 | 1 | no | — |
| 199 | #1372 | — | 8 | 1 | no | — |
| 200 | #1372 | — | 8 | 1 | no | — |
| 201 | #1372 | — | 8 | 1 | no | — |
| 202 | #1372 | — | 8 | 1 | no | — |
| 203 | #1331 | — | 16 | 4 | no | — |
| 204 | C8×C16 | — | 4 | 1 | no | — |
| 205 | C8×C16 | — | 4 | 1 | no | — |
| 206 | C8×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 207 | C8×C16 | #123 | 1 | 1 | yes | characteristic |
| 208 | C8×C16 | #135 | 1 | 1 | yes | characteristic |
| 209 | C8×C16 | #137 | 1 | 1 | yes | characteristic |
| 210 | C2×#135 | — | 16 | 2 | no | — |
| 211 | #532 | — | 16 | 1 | no | — |
| 212 | C2×D16 | — | 8 | 1 | no | — |
| 213 | C2×D16 | — | 8 | 1 | no | — |
| 214 | C2×D16 | — | 8 | 1 | no | — |
| 215 | C2×D16 | — | 8 | 1 | no | — |
| 216 | C2×M32 | — | 8 | 1 | no | — |
| 217 | C22×C16 | — | 4 | 2 | no | — |
| 218 | C22×C16 | #465 | 1 | 1 | yes | characteristic |
| 219 | C22×C16 | #471 | 1 | 1 | yes | characteristic |
| 220 | C22×C16 | #508 | 1 | 1 | yes | characteristic |
| 221 | C22×C16 | #509 | 1 | 1 | yes | characteristic |
| 222 | #500 | — | 8 | 1 | no | — |
| 223 | #500 | — | 8 | 1 | no | — |
| 224 | #495 | — | 16 | 2 | no | — |
| 225 | #494 | — | 8 | 1 | no | — |
| 226 | #493 | — | 8 | 1 | no | — |
| 227 | #493 | — | 8 | 1 | no | — |
| 228 | #493 | — | 8 | 1 | no | — |
| 229 | #492 | — | 16 | 1 | no | — |
| 230 | #486 | — | 16 | 1 | no | — |
| 231 | #486 | — | 16 | 1 | no | — |
| 232 | #466 | — | 16 | 2 | no | — |
| 233 | #466 | — | 16 | 1 | no | — |
| 234 | #466 | — | 16 | 1 | no | — |
| 235 | C4×D8 | — | 16 | 2 | no | — |
| 236 | C4×D8 | — | 16 | 1 | no | — |
| 237 | C4×D8 | — | 16 | 1 | no | — |
| 238 | C2×#108 | — | 4 | 1 | no | — |
| 239 | C2×#108 | — | 16 | 2 | no | — |
| 240 | #427 | — | 4 | 1 | no | — |
| 241 | #423 | — | 16 | 1 | no | — |
| 242 | #405 | — | 8 | 1 | no | — |
| 243 | C2×C4×C8 | — | 2 | 1 | no | — |
| 244 | C2×C4×C8 | #459 | 1 | 1 | yes | characteristic |
| 245 | D32 | — | 8 | 2 | no | — |
| 246 | D32 | — | 16 | 1 | no | — |
| 247 | D32 | — | 16 | 2 | no | — |
| 248 | M64 | — | 2 | 2 | no | — |
| 249 | M64 | — | 4 | 1 | no | — |
| 250 | M64 | — | 4 | 2 | no | — |
| 251 | M64 | — | 4 | 1 | no | — |
| 252 | M64 | — | 4 | 1 | no | — |
| 253 | M64 | — | 8 | 1 | no | — |
| 254 | M64 | — | 8 | 2 | no | — |
| 255 | M64 | — | 16 | 1 | no | — |
| 256 | C2×C32 | — | 2 | 1 | no | — |
| 257 | C2×C32 | — | 2 | 1 | no | — |
| 258 | C2×C32 | — | 2 | 2 | no | — |
| 259 | C2×C32 | — | 4 | 1 | no | — |
| 260 | C2×C32 | — | 16 | 1 | no | — |
| 261 | C2×C32 | C4×D8 | 1 | 1 | yes | characteristic |
| 262 | C2×C32 | C4×SD16 | 1 | 1 | yes | characteristic |
| 263 | C2×C32 | #486 | 1 | 1 | yes | characteristic |
| 264 | C2×C32 | #488 | 1 | 1 | yes | characteristic |
| 265 | #368 | — | 4 | 1 | no | — |
| 266 | #368 | — | 4 | 1 | no | — |
| 267 | #367 | — | 4 | 1 | no | — |
| 268 | #366 | — | 4 | 1 | no | — |
| 269 | #366 | — | 8 | 1 | no | — |
| 270 | #366 | — | 8 | 1 | no | — |
| 271 | #366 | — | 8 | 1 | no | — |
| 272 | #366 | — | 8 | 1 | no | — |
| 273 | #364 | — | 4 | 2 | no | — |
| 274 | #364 | — | 8 | 1 | no | — |
| 275 | #359 | — | 32 | 8 | no | — |
| 276 | #357 | — | 16 | 1 | no | — |
| 277 | #357 | — | 16 | 1 | no | — |
| 278 | #357 | — | 16 | 1 | no | — |
| 279 | #357 | — | 16 | 1 | no | — |
| 280 | #346 | — | 16 | 1 | no | — |
| 281 | C4×C16 | — | 4 | 2 | no | — |
| 282 | C4×C16 | — | 4 | 2 | no | — |
| 283 | C4×C16 | — | 16 | 1 | no | — |
| 284 | C4×C16 | #388 | 1 | 1 | yes | characteristic |
| 285 | C4×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 286 | C4×C16 | #464 | 1 | 1 | yes | characteristic |
| 287 | C4×C16 | #466 | 1 | 1 | yes | characteristic |
| 288 | C4×C16 | #472 | 1 | 1 | yes | characteristic |
| 289 | C4×C16 | #480 | 1 | 1 | yes | characteristic |
| 290 | C4×C16 | C2×SD32 | 1 | 1 | yes | characteristic |
| 291 | C4×C16 | #509 | 1 | 1 | yes | characteristic |
| 292 | #339 | — | 8 | 1 | no | — |
| 293 | #335 | — | 16 | 2 | no | — |
| 294 | #335 | — | 16 | 1 | no | — |
| 295 | #335 | — | 16 | 1 | no | — |
| 296 | C82 | — | 2 | 1 | no | — |
| 297 | C82 | #440 | 1 | 1 | yes | characteristic |
| 298 | C82 | #482 | 1 | 1 | yes | characteristic |
| 299 | C64 | — | 8 | 2 | no | — |
| 300 | C64 | — | 16 | 1 | no | — |
| 301 | C2×#41 | — | 32 | 1 | no | — |
| 302 | #135 | — | 32 | 4 | no | — |
| 303 | #135 | — | 32 | 4 | no | — |
| 304 | C2×Q16 | — | 16 | 2 | no | — |
| 305 | C2×SD16 | — | 32 | 2 | no | — |
| 306 | C2×D8 | — | 16 | 2 | no | — |
| 307 | C2×D8 | — | 16 | 2 | no | — |
| 308 | C2×D8 | — | 16 | 1 | no | — |
| 309 | C2×D8 | — | 16 | 1 | no | — |
| 310 | C2×M16 | — | 8 | 1 | no | — |
| 311 | C2×M16 | — | 32 | 1 | no | — |
| 312 | C22×C8 | — | 2 | 2 | no | — |
| 313 | C22×C8 | #1665 | 1 | 1 | yes | characteristic |
| 314 | C22×C8 | #2210 | 1 | 1 | yes | characteristic |
| 315 | C4⋊Q8 | — | 16 | 1 | no | — |
| 316 | #127 | — | 16 | 1 | no | — |
| 317 | #124 | — | 32 | 1 | no | — |
| 318 | #121 | — | 32 | 1 | no | — |
| 319 | #121 | — | 32 | 1 | no | — |
| 320 | C4×D4 | — | 32 | 1 | no | — |
| 321 | C4×D4 | — | 32 | 1 | no | — |
| 322 | #117 | — | 8 | 1 | no | — |
| 323 | C2×C42 | #2213 | 1 | 1 | yes | characteristic |
| 324 | D16 | — | 16 | 2 | no | — |
| 325 | D16 | — | 16 | 2 | no | — |
| 326 | D16 | — | 16 | 1 | no | — |
| 327 | D16 | — | 16 | 1 | no | — |
| 328 | D16 | — | 16 | 1 | no | — |
| 329 | D16 | — | 16 | 1 | no | — |
| 330 | M32 | — | 8 | 2 | no | — |
| 331 | M32 | — | 16 | 1 | no | — |
| 332 | C2×C16 | — | 2 | 1 | no | — |
| 333 | C2×C16 | — | 2 | 1 | no | — |
| 334 | C2×C16 | — | 2 | 1 | no | — |
| 335 | C2×C16 | — | 2 | 1 | no | — |
| 336 | C2×C16 | — | 4 | 1 | no | — |
| 337 | C2×C16 | — | 4 | 1 | no | — |
| 338 | C2×C16 | — | 8 | 2 | no | — |
| 339 | C2×C16 | — | 8 | 4 | no | — |
| 340 | C2×C16 | — | 16 | 1 | no | — |
| 341 | C2×C16 | #1678 | 1 | 1 | yes | characteristic |
| 342 | C2×C16 | #1682 | 1 | 1 | yes | characteristic |
| 343 | C2×C16 | #1931 | 1 | 1 | yes | characteristic |
| 344 | C2×C16 | #1934 | 1 | 1 | yes | characteristic |
| 345 | C2×C16 | C4×SD32 | 1 | 1 | yes | characteristic |
| 346 | C2×C16 | #2177 | 1 | 1 | yes | characteristic |
| 347 | C2×C16 | #2233 | 1 | 1 | yes | characteristic |
| 348 | C2×C16 | #2234 | 1 | 1 | yes | characteristic |
| 349 | #108 | — | 8 | 1 | no | — |
| 350 | #108 | — | 8 | 1 | no | — |
| 351 | #108 | — | 32 | 4 | no | — |
| 352 | #107 | — | 8 | 1 | no | — |
| 353 | #107 | — | 16 | 2 | no | — |
| 354 | #107 | — | 16 | 1 | no | — |
| 355 | #107 | — | 16 | 1 | no | — |
| 356 | #106 | — | 8 | 1 | no | — |
| 357 | C4⋊C8 | — | 32 | 1 | no | — |
| 358 | C4⋊C8 | — | 32 | 1 | no | — |
| 359 | #102 | — | 32 | 2 | no | — |
| 360 | #102 | — | 32 | 1 | no | — |
| 361 | #102 | — | 32 | 1 | no | — |
| 362 | #97 | — | 16 | 1 | no | — |
| 363 | C4×C8 | — | 2 | 2 | no | — |
| 364 | C4×C8 | — | 2 | 1 | no | — |
| 365 | C4×C8 | — | 2 | 1 | no | — |
| 366 | C4×C8 | — | 16 | 1 | no | — |
| 367 | C4×C8 | #1667 | 1 | 1 | yes | characteristic |
| 368 | C4×C8 | #1925 | 1 | 1 | yes | characteristic |
| 369 | C4×C8 | #2207 | 1 | 1 | yes | characteristic |
| 370 | C4×C8 | #2212 | 1 | 1 | yes | characteristic |
| 371 | C32 | — | 2 | 2 | no | — |
| 372 | C32 | — | 2 | 1 | no | — |
| 373 | C32 | — | 2 | 1 | no | — |
| 374 | C32 | — | 2 | 1 | no | — |
| 375 | C32 | — | 4 | 1 | no | — |
| 376 | C32 | — | 4 | 2 | no | — |
| 377 | C32 | — | 8 | 1 | no | — |
| 378 | C32 | — | 16 | 2 | no | — |
| 379 | C32 | #2179 | 1 | 2 | yes | — |
| 380 | #41 | — | 64 | 2 | no | — |
| 381 | #41 | — | 64 | 2 | no | — |
| 382 | C2×Q8 | — | 32 | 1 | no | — |
| 383 | C2×D4 | — | 32 | 1 | no | — |
| 384 | C2×D4 | — | 32 | 1 | no | — |
| 385 | C2×D4 | — | 32 | 1 | no | — |
| 386 | C2×D4 | — | 64 | 1 | no | — |
| 387 | C22×C4 | — | 2 | 1 | no | — |
| 388 | C22×C4 | — | 64 | 1 | no | — |
| 389 | C22×C4 | #12418 | 1 | 1 | yes | characteristic |
| 390 | Q16 | — | 32 | 4 | no | — |
| 391 | SD16 | — | 64 | 4 | no | — |
| 392 | D8 | — | 32 | 4 | no | — |
| 393 | D8 | — | 32 | 4 | no | — |
| 394 | D8 | — | 32 | 1 | no | — |
| 395 | D8 | — | 32 | 1 | no | — |
| 396 | D8 | — | 32 | 1 | no | — |
| 397 | D8 | — | 32 | 1 | no | — |
| 398 | M16 | — | 16 | 1 | no | — |
| 399 | M16 | — | 16 | 1 | no | — |
| 400 | M16 | — | 64 | 2 | no | — |
| 401 | C2×C8 | — | 2 | 2 | no | — |
| 402 | C2×C8 | — | 2 | 1 | no | — |
| 403 | C2×C8 | — | 2 | 1 | no | — |
| 404 | C2×C8 | — | 2 | 1 | no | — |
| 405 | C2×C8 | — | 2 | 1 | no | — |
| 406 | C2×C8 | — | 2 | 2 | no | — |
| 407 | C2×C8 | — | 4 | 4 | no | — |
| 408 | C2×C8 | — | 16 | 1 | no | — |
| 409 | C2×C8 | — | 64 | 1 | no | — |
| 410 | C2×C8 | #9563 | 1 | 1 | yes | characteristic |
| 411 | C2×C8 | #12417 | 1 | 1 | yes | characteristic |
| 412 | C2×C8 | #12428 | 1 | 1 | yes | characteristic |
| 413 | C2×C8 | #13131 | 1 | 1 | yes | characteristic |
| 414 | C4⋊C4 | — | 16 | 1 | no | — |
| 415 | C4⋊C4 | — | 32 | 1 | no | — |
| 416 | C4⋊C4 | — | 32 | 1 | no | — |
| 417 | C22⋊C4 | — | 16 | 1 | no | — |
| 418 | C22⋊C4 | — | 64 | 1 | no | — |
| 419 | C22⋊C4 | — | 64 | 1 | no | — |
| 420 | C42 | — | 2 | 1 | no | — |
| 421 | C42 | — | 16 | 1 | no | — |
| 422 | C42 | #12425 | 1 | 1 | yes | characteristic |
| 423 | C42 | #13136 | 1 | 1 | yes | characteristic |
| 424 | C16 | — | 2 | 1 | no | — |
| 425 | C16 | — | 2 | 1 | no | — |
| 426 | C16 | — | 2 | 1 | no | — |
| 427 | C16 | — | 2 | 1 | no | — |
| 428 | C16 | — | 2 | 1 | no | — |
| 429 | C16 | — | 2 | 1 | no | — |
| 430 | C16 | — | 16 | 2 | no | — |
| 431 | C16 | — | 16 | 2 | no | — |
| 432 | C16 | #13146 | 1 | 1 | yes | characteristic |
| 433 | C16 | #13152 | 1 | 1 | yes | characteristic |
| 434 | C16 | #13657 | 1 | 1 | yes | characteristic |
| 435 | C16 | #13658 | 1 | 1 | yes | characteristic |
| 436 | C23 | — | 64 | 1 | no | — |
| 437 | C23 | #151626 | 1 | 1 | yes | characteristic |
| 438 | Q8 | — | 64 | 2 | no | — |
| 439 | D4 | — | 64 | 2 | no | — |
| 440 | D4 | — | 64 | 2 | no | — |
| 441 | D4 | — | 64 | 1 | no | — |
| 442 | D4 | — | 64 | 1 | no | — |
| 443 | D4 | — | 128 | 2 | no | — |
| 444 | C2×C4 | — | 2 | 1 | no | — |
| 445 | C2×C4 | — | 2 | 1 | no | — |
| 446 | C2×C4 | — | 2 | 1 | no | — |
| 447 | C2×C4 | — | 2 | 1 | no | — |
| 448 | C2×C4 | — | 4 | 2 | no | — |
| 449 | C2×C4 | — | 32 | 1 | no | — |
| 450 | C2×C4 | — | 64 | 1 | no | — |
| 451 | C2×C4 | — | 128 | 1 | no | — |
| 452 | C2×C4 | — | 128 | 1 | no | — |
| 453 | C2×C4 | #140224 | 1 | 1 | yes | characteristic |
| 454 | C2×C4 | #151626 | 1 | 1 | yes | characteristic |
| 455 | C8 | — | 2 | 4 | no | — |
| 456 | C8 | — | 2 | 1 | no | — |
| 457 | C8 | — | 2 | 1 | no | — |
| 458 | C8 | — | 4 | 2 | no | — |
| 459 | C8 | — | 32 | 1 | no | — |
| 460 | C8 | — | 128 | 1 | no | — |
| 461 | C8 | #140230 | 1 | 1 | yes | characteristic |
| 462 | C8 | #140236 | 1 | 1 | yes | characteristic |
| 463 | C8 | #152826 | 1 | 1 | yes | characteristic |
| 464 | C8 | #152829 | 1 | 1 | yes | characteristic |
| 465 | C22 | — | 2 | 1 | no | — |
| 466 | C22 | — | 4 | 1 | no | — |
| 467 | C22 | — | 128 | 1 | no | — |
| 468 | C22 | — | 128 | 1 | no | — |
| 469 | C22 | — | 128 | 1 | no | — |
| 470 | C22 | #72216271 | 1 | 1 | yes | characteristic |
| 471 | C4 | — | 2 | 2 | no | — |
| 472 | C4 | — | 2 | 1 | no | — |
| 473 | C4 | — | 4 | 1 | no | — |
| 474 | C4 | — | 64 | 1 | no | — |
| 475 | C4 | — | 128 | 1 | no | — |
| 476 | C4 | #72225530 | 1 | 1 | yes | characteristic |
| 477 | C4 | #72225531 | 1 | 1 | yes | characteristic |
| 478 | C2 | — | 256 | 1 | no | — |
| 479 | C2 | — | 2 | 1 | no | — |
| 480 | C2 | — | 4 | 1 | no | — |
| 481 | C2 | #72225533 | 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