← #72227134
Subgroups — #72227134
Order 2048.
774 conjugacy classes of subgroups.
The subgroup lattice has 515 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72227044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72227004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72226994 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72225597 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72225492 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72225461 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72216298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #497870 | — | 2 | 1 | no | — |
| 9 | C2×C8×D16 | C22 | 1 | 1 | yes | characteristic |
| 10 | D8×#107 | — | 2 | 1 | no | — |
| 11 | #152407 | — | 2 | 2 | no | — |
| 12 | #152276 | — | 2 | 1 | no | — |
| 13 | #151026 | C22 | 1 | 1 | yes | characteristic |
| 14 | C8×M64 | C22 | 1 | 1 | yes | characteristic |
| 15 | #140490 | — | 2 | 1 | no | — |
| 16 | #140429 | — | 2 | 1 | no | — |
| 17 | #136339 | — | 2 | 2 | no | — |
| 18 | #135781 | C22 | 1 | 1 | yes | characteristic |
| 19 | #135778 | C22 | 1 | 1 | yes | characteristic |
| 20 | #134950 | — | 2 | 1 | no | — |
| 21 | #129140 | C22 | 1 | 1 | yes | characteristic |
| 22 | #122930 | C22 | 1 | 1 | yes | characteristic |
| 23 | #94358 | — | 2 | 1 | no | — |
| 24 | #93747 | C4 | 1 | 4 | yes | complemented |
| 25 | #93071 | — | 2 | 1 | no | — |
| 26 | C2×#2177 | — | 4 | 1 | no | — |
| 27 | C2×C4×D16 | D4 | 1 | 1 | yes | characteristic |
| 28 | C4⋊C4×D8 | — | 2 | 2 | no | — |
| 29 | D4×#107 | — | 4 | 1 | no | — |
| 30 | C2×C8×D8 | — | 2 | 1 | no | — |
| 31 | C2×#1426 | — | 4 | 4 | no | — |
| 32 | #13627 | — | 2 | 1 | no | — |
| 33 | C2×#1419 | — | 4 | 1 | no | — |
| 34 | C4×M64 | — | 2 | 1 | no | — |
| 35 | #13168 | — | 4 | 1 | no | — |
| 36 | #12937 | — | 4 | 2 | no | — |
| 37 | #12909 | — | 2 | 1 | no | — |
| 38 | #12909 | — | 2 | 1 | no | — |
| 39 | #12906 | — | 2 | 1 | no | — |
| 40 | #12906 | D4 | 1 | 2 | yes | — |
| 41 | #12811 | — | 2 | 2 | no | — |
| 42 | #12662 | — | 2 | 1 | no | — |
| 43 | C8×D16 | — | 2 | 1 | no | — |
| 44 | C8×D16 | — | 2 | 1 | no | — |
| 45 | C8×D16 | C2×C4 | 1 | 2 | yes | — |
| 46 | C8×D16 | Q8 | 1 | 2 | yes | — |
| 47 | #12033 | — | 4 | 1 | no | — |
| 48 | #12012 | — | 2 | 1 | no | — |
| 49 | C2×#1371 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×#1370 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×#1331 | — | 2 | 1 | no | — |
| 52 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 53 | #9614 | — | 2 | 2 | no | — |
| 54 | #8882 | — | 4 | 2 | no | — |
| 55 | #8823 | — | 2 | 1 | no | — |
| 56 | #8818 | — | 2 | 1 | no | — |
| 57 | #8644 | — | 4 | 1 | no | — |
| 58 | C8×#107 | D4 | 1 | 1 | yes | characteristic |
| 59 | #7478 | — | 4 | 1 | no | — |
| 60 | #7458 | — | 2 | 1 | no | — |
| 61 | #7458 | — | 2 | 1 | no | — |
| 62 | #7329 | — | 2 | 1 | no | — |
| 63 | C8×C32 | C2×C4 | 1 | 2 | yes | complemented |
| 64 | #7296 | — | 4 | 1 | no | — |
| 65 | #7274 | — | 2 | 2 | no | — |
| 66 | #7167 | — | 2 | 1 | no | — |
| 67 | #7101 | — | 2 | 1 | no | — |
| 68 | #7100 | C2×C4 | 1 | 2 | yes | complemented |
| 69 | C22×D16 | D8 | 1 | 1 | yes | characteristic |
| 70 | C2×C4×D8 | — | 2 | 1 | no | — |
| 71 | C2×C4×D8 | — | 4 | 2 | no | — |
| 72 | C2×C8×D4 | — | 4 | 1 | no | — |
| 73 | C22×#107 | — | 8 | 1 | no | — |
| 74 | D4×C4⋊C4 | — | 4 | 2 | no | — |
| 75 | C2×M64 | — | 2 | 2 | no | — |
| 76 | C2×M64 | — | 4 | 1 | no | — |
| 77 | #2177 | — | 8 | 2 | no | — |
| 78 | #2177 | — | 8 | 2 | no | — |
| 79 | C4×D16 | — | 2 | 1 | no | — |
| 80 | C4×D16 | — | 2 | 1 | no | — |
| 81 | C4×D16 | C4⋊C4 | 1 | 2 | yes | — |
| 82 | C4×D16 | Q16 | 1 | 2 | yes | — |
| 83 | #2162 | — | 4 | 1 | no | — |
| 84 | C2×#368 | — | 4 | 2 | no | — |
| 85 | C2×#368 | — | 4 | 1 | no | — |
| 86 | C2×#368 | — | 4 | 1 | no | — |
| 87 | C2×#367 | — | 4 | 1 | no | — |
| 88 | C2×#367 | — | 4 | 2 | no | — |
| 89 | C2×#367 | — | 4 | 1 | no | — |
| 90 | C2×#366 | D8 | 1 | 1 | yes | characteristic |
| 91 | C2×C4⋊C16 | — | 2 | 1 | no | — |
| 92 | C2×#357 | — | 2 | 1 | no | — |
| 93 | C2×#357 | — | 4 | 2 | no | — |
| 94 | C2×#346 | — | 4 | 1 | no | — |
| 95 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | #1947 | — | 4 | 2 | no | — |
| 98 | #1942 | — | 4 | 2 | no | — |
| 99 | #1862 | — | 8 | 2 | no | — |
| 100 | #1852 | — | 8 | 2 | no | — |
| 101 | #1848 | — | 4 | 1 | no | — |
| 102 | #1845 | — | 2 | 2 | no | — |
| 103 | #1845 | — | 4 | 1 | no | — |
| 104 | #1845 | — | 4 | 1 | no | — |
| 105 | #1808 | — | 8 | 1 | no | — |
| 106 | #1802 | — | 4 | 2 | no | — |
| 107 | C4×#107 | D8 | 1 | 1 | yes | characteristic |
| 108 | C8×C4⋊C4 | — | 2 | 1 | no | — |
| 109 | C8×D8 | — | 2 | 2 | no | — |
| 110 | C8×D8 | — | 2 | 2 | no | — |
| 111 | C8×D8 | — | 4 | 1 | no | — |
| 112 | C8×D8 | — | 4 | 1 | no | — |
| 113 | #1567 | — | 4 | 1 | no | — |
| 114 | #1567 | — | 4 | 1 | no | — |
| 115 | C2×#335 | — | 2 | 1 | no | — |
| 116 | C2×#335 | D8 | 1 | 1 | yes | characteristic |
| 117 | C2×D4⋊C8 | — | 4 | 1 | no | — |
| 118 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | #1426 | — | 8 | 8 | no | — |
| 120 | C4⋊C32 | — | 4 | 1 | no | — |
| 121 | C4⋊C32 | — | 4 | 1 | no | — |
| 122 | #1419 | — | 8 | 2 | no | — |
| 123 | #1397 | — | 2 | 2 | no | — |
| 124 | C4×C32 | — | 2 | 2 | no | — |
| 125 | #1380 | — | 4 | 2 | no | — |
| 126 | #1374 | — | 4 | 1 | no | — |
| 127 | #1372 | — | 8 | 2 | no | — |
| 128 | #1371 | — | 2 | 1 | no | — |
| 129 | #1371 | C4⋊C4 | 1 | 2 | yes | — |
| 130 | #1370 | — | 2 | 2 | no | — |
| 131 | #1370 | — | 2 | 1 | no | — |
| 132 | #1370 | — | 2 | 1 | no | — |
| 133 | #1367 | — | 4 | 1 | no | — |
| 134 | #1331 | — | 2 | 2 | no | — |
| 135 | #1331 | — | 2 | 2 | no | — |
| 136 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 137 | C8×C16 | C2×Q8 | 1 | 1 | yes | characteristic |
| 138 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 139 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 140 | #1296 | — | 4 | 2 | no | — |
| 141 | #1279 | — | 2 | 1 | no | — |
| 142 | C22×D8 | — | 2 | 1 | no | — |
| 143 | C23×C8 | — | 8 | 1 | no | — |
| 144 | C2×C4×D4 | — | 4 | 1 | no | — |
| 145 | C2×C4×D4 | — | 8 | 2 | no | — |
| 146 | C22×C4⋊C4 | — | 8 | 2 | no | — |
| 147 | C2×D16 | — | 2 | 1 | no | — |
| 148 | C2×D16 | — | 2 | 1 | no | — |
| 149 | C2×D16 | — | 2 | 1 | no | — |
| 150 | C2×D16 | #107 | 1 | 2 | yes | — |
| 151 | C2×D16 | SD32 | 1 | 2 | yes | — |
| 152 | C2×D16 | SD32 | 1 | 2 | yes | — |
| 153 | C22×C16 | — | 2 | 1 | no | — |
| 154 | C22×C16 | — | 4 | 1 | no | — |
| 155 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 156 | C22×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 157 | C4×D8 | — | 2 | 2 | no | — |
| 158 | C4×D8 | — | 2 | 2 | no | — |
| 159 | C4×D8 | — | 4 | 1 | no | — |
| 160 | C4×D8 | — | 4 | 1 | no | — |
| 161 | C4×D8 | — | 8 | 4 | no | — |
| 162 | C4×D8 | — | 16 | 2 | no | — |
| 163 | C8×D4 | — | 4 | 2 | no | — |
| 164 | C8×D4 | — | 4 | 2 | no | — |
| 165 | C8×D4 | — | 8 | 1 | no | — |
| 166 | C8×D4 | — | 8 | 1 | no | — |
| 167 | C2×#108 | — | 8 | 1 | no | — |
| 168 | C2×#108 | — | 8 | 1 | no | — |
| 169 | C2×#107 | — | 2 | 1 | no | — |
| 170 | C2×#107 | — | 2 | 1 | no | — |
| 171 | C2×#107 | — | 4 | 2 | no | — |
| 172 | C2×#107 | — | 4 | 2 | no | — |
| 173 | C2×#107 | — | 8 | 2 | no | — |
| 174 | C2×#107 | — | 8 | 1 | no | — |
| 175 | C2×#107 | — | 8 | 1 | no | — |
| 176 | C2×#107 | — | 16 | 4 | no | — |
| 177 | C2×#107 | — | 16 | 1 | no | — |
| 178 | #423 | — | 8 | 1 | no | — |
| 179 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 180 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 181 | C2×#102 | — | 4 | 1 | no | — |
| 182 | C2×#102 | — | 8 | 2 | no | — |
| 183 | C2×C22⋊C8 | — | 8 | 1 | no | — |
| 184 | C2×C4×C8 | — | 4 | 1 | no | — |
| 185 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 186 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 187 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 188 | #389 | — | 8 | 2 | no | — |
| 189 | #385 | — | 16 | 2 | no | — |
| 190 | #384 | — | 4 | 2 | no | — |
| 191 | #380 | — | 8 | 2 | no | — |
| 192 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 193 | M64 | — | 2 | 4 | no | — |
| 194 | M64 | — | 2 | 4 | no | — |
| 195 | M64 | — | 8 | 1 | no | — |
| 196 | M64 | — | 8 | 1 | no | — |
| 197 | C2×C32 | — | 2 | 4 | no | — |
| 198 | C2×C32 | — | 8 | 1 | no | — |
| 199 | #368 | — | 8 | 4 | no | — |
| 200 | #368 | — | 8 | 1 | no | — |
| 201 | #368 | — | 8 | 1 | no | — |
| 202 | #368 | — | 16 | 1 | no | — |
| 203 | #367 | — | 8 | 1 | no | — |
| 204 | #367 | — | 8 | 1 | no | — |
| 205 | #367 | — | 8 | 4 | no | — |
| 206 | #367 | — | 16 | 1 | no | — |
| 207 | #366 | — | 2 | 1 | no | — |
| 208 | #366 | #107 | 1 | 2 | yes | — |
| 209 | C4⋊C16 | — | 4 | 2 | no | — |
| 210 | C4⋊C16 | — | 4 | 1 | no | — |
| 211 | C4⋊C16 | — | 4 | 1 | no | — |
| 212 | #357 | — | 2 | 2 | no | — |
| 213 | #357 | — | 2 | 2 | no | — |
| 214 | #357 | — | 8 | 4 | no | — |
| 215 | C22⋊C16 | — | 8 | 1 | no | — |
| 216 | #346 | — | 8 | 1 | no | — |
| 217 | #346 | — | 8 | 1 | no | — |
| 218 | C4×C16 | — | 2 | 1 | no | — |
| 219 | C4×C16 | — | 8 | 1 | no | — |
| 220 | C4×C16 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 221 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 222 | C4×C16 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 223 | C4×C16 | #123 | 1 | 1 | yes | characteristic |
| 224 | C4×C16 | C2×Q16 | 1 | 1 | yes | characteristic |
| 225 | C4×C16 | #137 | 1 | 1 | yes | characteristic |
| 226 | #340 | — | 8 | 2 | no | — |
| 227 | #340 | — | 8 | 2 | no | — |
| 228 | #340 | SD32 | 1 | 2 | yes | — |
| 229 | #336 | — | 4 | 1 | no | — |
| 230 | #335 | — | 2 | 2 | no | — |
| 231 | #335 | — | 2 | 1 | no | — |
| 232 | #335 | — | 2 | 1 | no | — |
| 233 | #335 | — | 4 | 1 | no | — |
| 234 | #335 | — | 8 | 1 | no | — |
| 235 | #335 | — | 8 | 1 | no | — |
| 236 | #335 | — | 16 | 1 | no | — |
| 237 | D4⋊C8 | — | 4 | 2 | no | — |
| 238 | D4⋊C8 | — | 4 | 2 | no | — |
| 239 | C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 240 | C82 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 241 | C82 | #135 | 1 | 1 | yes | characteristic |
| 242 | C82 | #137 | 1 | 1 | yes | characteristic |
| 243 | C22×D4 | — | 4 | 1 | no | — |
| 244 | C23×C4 | — | 8 | 1 | no | — |
| 245 | C23×C4 | — | 16 | 2 | no | — |
| 246 | C2×D8 | — | 2 | 2 | no | — |
| 247 | C2×D8 | — | 2 | 2 | no | — |
| 248 | C2×D8 | — | 2 | 2 | no | — |
| 249 | C2×D8 | — | 4 | 1 | no | — |
| 250 | C2×D8 | — | 4 | 1 | no | — |
| 251 | C2×D8 | — | 4 | 1 | no | — |
| 252 | C2×M16 | — | 16 | 1 | no | — |
| 253 | C22×C8 | — | 2 | 1 | no | — |
| 254 | C22×C8 | — | 4 | 1 | no | — |
| 255 | C22×C8 | — | 8 | 1 | no | — |
| 256 | C22×C8 | — | 8 | 2 | no | — |
| 257 | C22×C8 | — | 8 | 2 | no | — |
| 258 | C22×C8 | — | 16 | 2 | no | — |
| 259 | C22×C8 | — | 16 | 2 | no | — |
| 260 | C22×C8 | #447 | 1 | 1 | yes | characteristic |
| 261 | C22×C8 | #453 | 1 | 1 | yes | characteristic |
| 262 | C22×C8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 263 | C22×C8 | #509 | 1 | 1 | yes | characteristic |
| 264 | C4×D4 | — | 4 | 2 | no | — |
| 265 | C4×D4 | — | 4 | 2 | no | — |
| 266 | C4×D4 | — | 8 | 1 | no | — |
| 267 | C4×D4 | — | 8 | 1 | no | — |
| 268 | C4×D4 | — | 16 | 4 | no | — |
| 269 | C4×D4 | — | 32 | 2 | no | — |
| 270 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 271 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 272 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 273 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 274 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 275 | C2×C4⋊C4 | — | 16 | 4 | no | — |
| 276 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 277 | C2×C4⋊C4 | — | 32 | 2 | no | — |
| 278 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 279 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 280 | C2×C42 | — | 4 | 1 | no | — |
| 281 | C2×C42 | #447 | 1 | 1 | yes | characteristic |
| 282 | D16 | — | 2 | 2 | no | — |
| 283 | D16 | — | 2 | 2 | no | — |
| 284 | D16 | — | 2 | 2 | no | — |
| 285 | D16 | #367 | 1 | 4 | yes | — |
| 286 | C2×C16 | — | 2 | 2 | no | — |
| 287 | C2×C16 | — | 2 | 2 | no | — |
| 288 | C2×C16 | — | 2 | 1 | no | — |
| 289 | C2×C16 | — | 2 | 1 | no | — |
| 290 | C2×C16 | — | 2 | 1 | no | — |
| 291 | C2×C16 | — | 2 | 1 | no | — |
| 292 | C2×C16 | — | 8 | 1 | no | — |
| 293 | C2×C16 | — | 8 | 2 | no | — |
| 294 | C2×C16 | — | 8 | 1 | no | — |
| 295 | C2×C16 | — | 8 | 1 | no | — |
| 296 | C2×C16 | C2×#107 | 1 | 1 | yes | characteristic |
| 297 | C2×C16 | #428 | 1 | 1 | yes | characteristic |
| 298 | C2×C16 | #480 | 1 | 1 | yes | characteristic |
| 299 | C2×C16 | #484 | 1 | 1 | yes | characteristic |
| 300 | C2×C16 | C2×SD32 | 1 | 1 | yes | characteristic |
| 301 | C2×C16 | C2×SD32 | 1 | 1 | yes | characteristic |
| 302 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 303 | C2×C16 | #510 | 1 | 1 | yes | characteristic |
| 304 | #108 | — | 16 | 2 | no | — |
| 305 | #108 | — | 16 | 1 | no | — |
| 306 | #108 | — | 16 | 1 | no | — |
| 307 | #107 | — | 2 | 2 | no | — |
| 308 | #107 | — | 4 | 2 | no | — |
| 309 | #107 | — | 4 | 1 | no | — |
| 310 | #107 | — | 8 | 2 | no | — |
| 311 | #107 | — | 8 | 2 | no | — |
| 312 | #107 | — | 16 | 4 | no | — |
| 313 | #107 | — | 16 | 2 | no | — |
| 314 | #107 | — | 16 | 2 | no | — |
| 315 | #107 | — | 32 | 1 | no | — |
| 316 | #107 | — | 32 | 2 | no | — |
| 317 | C4⋊C8 | — | 4 | 2 | no | — |
| 318 | C4⋊C8 | — | 4 | 1 | no | — |
| 319 | C4⋊C8 | — | 4 | 1 | no | — |
| 320 | C4⋊C8 | — | 8 | 1 | no | — |
| 321 | C4⋊C8 | — | 16 | 1 | no | — |
| 322 | C4⋊C8 | — | 16 | 1 | no | — |
| 323 | #102 | — | 4 | 2 | no | — |
| 324 | #102 | — | 4 | 2 | no | — |
| 325 | #102 | — | 16 | 4 | no | — |
| 326 | C22⋊C8 | — | 8 | 2 | no | — |
| 327 | C22⋊C8 | — | 8 | 2 | no | — |
| 328 | C4×C8 | — | 2 | 1 | no | — |
| 329 | C4×C8 | — | 8 | 1 | no | — |
| 330 | C4×C8 | — | 8 | 1 | no | — |
| 331 | C4×C8 | #385 | 1 | 1 | yes | characteristic |
| 332 | C4×C8 | C4×D8 | 1 | 1 | yes | characteristic |
| 333 | C4×C8 | #440 | 1 | 1 | yes | characteristic |
| 334 | C4×C8 | #451 | 1 | 1 | yes | characteristic |
| 335 | C4×C8 | #452 | 1 | 1 | yes | characteristic |
| 336 | C4×C8 | #456 | 1 | 1 | yes | characteristic |
| 337 | C4×C8 | #474 | 1 | 1 | yes | characteristic |
| 338 | C4×C8 | #478 | 1 | 1 | yes | characteristic |
| 339 | C4×C8 | #508 | 1 | 1 | yes | characteristic |
| 340 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 341 | #95 | — | 4 | 1 | no | — |
| 342 | #95 | — | 16 | 2 | no | — |
| 343 | C32 | — | 2 | 8 | no | — |
| 344 | C32 | — | 16 | 1 | no | — |
| 345 | C24 | — | 8 | 1 | no | — |
| 346 | C2×D4 | — | 4 | 2 | no | — |
| 347 | C2×D4 | — | 4 | 2 | no | — |
| 348 | C2×D4 | — | 4 | 2 | no | — |
| 349 | C2×D4 | — | 8 | 1 | no | — |
| 350 | C2×D4 | — | 8 | 1 | no | — |
| 351 | C2×D4 | — | 8 | 1 | no | — |
| 352 | C22×C4 | — | 4 | 2 | no | — |
| 353 | C22×C4 | — | 8 | 1 | no | — |
| 354 | C22×C4 | — | 8 | 2 | no | — |
| 355 | C22×C4 | — | 8 | 2 | no | — |
| 356 | C22×C4 | — | 16 | 1 | no | — |
| 357 | C22×C4 | — | 16 | 1 | no | — |
| 358 | C22×C4 | — | 16 | 1 | no | — |
| 359 | C22×C4 | — | 16 | 1 | no | — |
| 360 | C22×C4 | — | 16 | 2 | no | — |
| 361 | C22×C4 | — | 32 | 4 | no | — |
| 362 | C22×C4 | — | 32 | 4 | no | — |
| 363 | C22×C4 | — | 64 | 2 | no | — |
| 364 | C22×C4 | #1619 | 1 | 1 | yes | characteristic |
| 365 | C22×C4 | #2187 | 1 | 1 | yes | characteristic |
| 366 | C22×C4 | #2194 | 1 | 1 | yes | characteristic |
| 367 | D8 | — | 2 | 4 | no | — |
| 368 | D8 | — | 4 | 2 | no | — |
| 369 | D8 | — | 4 | 2 | no | — |
| 370 | D8 | — | 4 | 2 | no | — |
| 371 | M16 | — | 32 | 1 | no | — |
| 372 | M16 | — | 32 | 1 | no | — |
| 373 | C2×C8 | — | 2 | 1 | no | — |
| 374 | C2×C8 | — | 2 | 1 | no | — |
| 375 | C2×C8 | — | 2 | 1 | no | — |
| 376 | C2×C8 | — | 2 | 2 | no | — |
| 377 | C2×C8 | — | 2 | 1 | no | — |
| 378 | C2×C8 | — | 4 | 1 | no | — |
| 379 | C2×C8 | — | 4 | 2 | no | — |
| 380 | C2×C8 | — | 8 | 1 | no | — |
| 381 | C2×C8 | — | 8 | 1 | no | — |
| 382 | C2×C8 | — | 8 | 1 | no | — |
| 383 | C2×C8 | — | 8 | 2 | no | — |
| 384 | C2×C8 | — | 16 | 4 | no | — |
| 385 | C2×C8 | — | 16 | 1 | no | — |
| 386 | C2×C8 | — | 16 | 1 | no | — |
| 387 | C2×C8 | — | 16 | 4 | no | — |
| 388 | C2×C8 | — | 32 | 1 | no | — |
| 389 | C2×C8 | #1632 | 1 | 1 | yes | characteristic |
| 390 | C2×C8 | #1647 | 1 | 1 | yes | characteristic |
| 391 | C2×C8 | #1852 | 1 | 1 | yes | characteristic |
| 392 | C2×C8 | #1859 | 1 | 1 | yes | characteristic |
| 393 | C2×C8 | C4×SD32 | 1 | 1 | yes | characteristic |
| 394 | C2×C8 | #2177 | 1 | 1 | yes | characteristic |
| 395 | C2×C8 | #2185 | 1 | 1 | yes | characteristic |
| 396 | C2×C8 | #2187 | 1 | 1 | yes | characteristic |
| 397 | C2×C8 | #2193 | 1 | 1 | yes | characteristic |
| 398 | C2×C8 | #2194 | 1 | 1 | yes | characteristic |
| 399 | C2×C8 | #2226 | 1 | 1 | yes | characteristic |
| 400 | C2×C8 | #2228 | 1 | 1 | yes | characteristic |
| 401 | C4⋊C4 | — | 4 | 2 | no | — |
| 402 | C4⋊C4 | — | 4 | 2 | no | — |
| 403 | C4⋊C4 | — | 4 | 2 | no | — |
| 404 | C4⋊C4 | — | 8 | 1 | no | — |
| 405 | C4⋊C4 | — | 16 | 2 | no | — |
| 406 | C4⋊C4 | — | 16 | 2 | no | — |
| 407 | C4⋊C4 | — | 16 | 2 | no | — |
| 408 | C4⋊C4 | — | 16 | 2 | no | — |
| 409 | C4⋊C4 | — | 32 | 2 | no | — |
| 410 | C4⋊C4 | — | 32 | 4 | no | — |
| 411 | C22⋊C4 | — | 8 | 2 | no | — |
| 412 | C22⋊C4 | — | 8 | 2 | no | — |
| 413 | C22⋊C4 | — | 32 | 4 | no | — |
| 414 | C42 | — | 8 | 1 | no | — |
| 415 | C42 | — | 8 | 1 | no | — |
| 416 | C42 | #1649 | 1 | 1 | yes | characteristic |
| 417 | C42 | #1862 | 1 | 1 | yes | characteristic |
| 418 | C42 | #2186 | 1 | 1 | yes | characteristic |
| 419 | C42 | #2193 | 1 | 1 | yes | characteristic |
| 420 | C16 | — | 2 | 2 | no | — |
| 421 | C16 | — | 2 | 2 | no | — |
| 422 | C16 | — | 2 | 1 | no | — |
| 423 | C16 | — | 2 | 1 | no | — |
| 424 | C16 | — | 16 | 2 | no | — |
| 425 | C16 | — | 16 | 1 | no | — |
| 426 | C16 | C2×#367 | 1 | 1 | yes | characteristic |
| 427 | C16 | #2159 | 1 | 1 | yes | characteristic |
| 428 | C16 | #2233 | 1 | 1 | yes | characteristic |
| 429 | C16 | #2235 | 1 | 1 | yes | characteristic |
| 430 | C23 | — | 8 | 2 | no | — |
| 431 | C23 | — | 8 | 2 | no | — |
| 432 | C23 | — | 8 | 2 | no | — |
| 433 | C23 | — | 16 | 1 | no | — |
| 434 | C23 | — | 16 | 1 | no | — |
| 435 | C23 | — | 16 | 1 | no | — |
| 436 | C23 | — | 16 | 1 | no | — |
| 437 | C23 | #12320 | 1 | 1 | yes | characteristic |
| 438 | D4 | — | 4 | 4 | no | — |
| 439 | D4 | — | 8 | 2 | no | — |
| 440 | D4 | — | 8 | 2 | no | — |
| 441 | D4 | — | 8 | 2 | no | — |
| 442 | C2×C4 | — | 2 | 1 | no | — |
| 443 | C2×C4 | — | 2 | 1 | no | — |
| 444 | C2×C4 | — | 4 | 1 | no | — |
| 445 | C2×C4 | — | 8 | 2 | no | — |
| 446 | C2×C4 | — | 8 | 2 | no | — |
| 447 | C2×C4 | — | 8 | 2 | no | — |
| 448 | C2×C4 | — | 8 | 2 | no | — |
| 449 | C2×C4 | — | 16 | 2 | no | — |
| 450 | C2×C4 | — | 16 | 2 | no | — |
| 451 | C2×C4 | — | 16 | 1 | no | — |
| 452 | C2×C4 | — | 16 | 1 | no | — |
| 453 | C2×C4 | — | 16 | 2 | no | — |
| 454 | C2×C4 | — | 16 | 2 | no | — |
| 455 | C2×C4 | — | 32 | 2 | no | — |
| 456 | C2×C4 | — | 32 | 2 | no | — |
| 457 | C2×C4 | — | 32 | 2 | no | — |
| 458 | C2×C4 | — | 64 | 8 | no | — |
| 459 | C2×C4 | #8882 | 1 | 1 | yes | characteristic |
| 460 | C2×C4 | #12310 | 1 | 1 | yes | characteristic |
| 461 | C2×C4 | #12313 | 1 | 1 | yes | characteristic |
| 462 | C2×C4 | #12318 | 1 | 1 | yes | characteristic |
| 463 | C2×C4 | #12319 | 1 | 1 | yes | characteristic |
| 464 | C2×C4 | #12320 | 1 | 1 | yes | characteristic |
| 465 | C2×C4 | #12407 | 1 | 1 | yes | characteristic |
| 466 | C2×C4 | #12408 | 1 | 1 | yes | characteristic |
| 467 | C2×C4 | #12937 | 1 | 1 | yes | characteristic |
| 468 | C2×C4 | #12946 | 1 | 1 | yes | characteristic |
| 469 | C8 | — | 2 | 2 | no | — |
| 470 | C8 | — | 2 | 1 | no | — |
| 471 | C8 | — | 2 | 1 | no | — |
| 472 | C8 | — | 2 | 1 | no | — |
| 473 | C8 | — | 2 | 1 | no | — |
| 474 | C8 | — | 2 | 1 | no | — |
| 475 | C8 | — | 4 | 1 | no | — |
| 476 | C8 | — | 16 | 2 | no | — |
| 477 | C8 | — | 16 | 1 | no | — |
| 478 | C8 | — | 64 | 1 | no | — |
| 479 | C8 | #12394 | 1 | 1 | yes | characteristic |
| 480 | C8 | #12396 | 1 | 1 | yes | characteristic |
| 481 | C8 | #12920 | 1 | 1 | yes | characteristic |
| 482 | C8 | #12926 | 1 | 1 | yes | characteristic |
| 483 | C8 | #13658 | 1 | 2 | yes | — |
| 484 | C22 | — | 2 | 1 | no | — |
| 485 | C22 | — | 2 | 1 | no | — |
| 486 | C22 | — | 8 | 4 | no | — |
| 487 | C22 | — | 16 | 2 | no | — |
| 488 | C22 | — | 16 | 2 | no | — |
| 489 | C22 | — | 16 | 2 | no | — |
| 490 | C22 | — | 16 | 2 | no | — |
| 491 | C22 | — | 16 | 2 | no | — |
| 492 | C22 | — | 16 | 2 | no | — |
| 493 | C22 | #123285 | 1 | 1 | yes | characteristic |
| 494 | C22 | #123307 | 1 | 1 | yes | characteristic |
| 495 | C22 | #136339 | 1 | 1 | yes | characteristic |
| 496 | C4 | — | 2 | 1 | no | — |
| 497 | C4 | — | 2 | 1 | no | — |
| 498 | C4 | — | 2 | 1 | no | — |
| 499 | C4 | — | 16 | 2 | no | — |
| 500 | C4 | — | 16 | 2 | no | — |
| 501 | C4 | — | 64 | 2 | no | — |
| 502 | C4 | #123278 | 1 | 1 | yes | characteristic |
| 503 | C4 | #123310 | 1 | 1 | yes | characteristic |
| 504 | C4 | #136324 | 1 | 1 | yes | characteristic |
| 505 | C4 | #136331 | 1 | 1 | yes | characteristic |
| 506 | C4 | #152447 | 1 | 1 | yes | characteristic |
| 507 | C4 | #152454 | 1 | 1 | yes | characteristic |
| 508 | C2 | — | 2 | 1 | no | — |
| 509 | C2 | — | 2 | 1 | no | — |
| 510 | C2 | — | 16 | 4 | no | — |
| 511 | C2 | #72225193 | 1 | 1 | yes | characteristic |
| 512 | C2 | #72225594 | 1 | 1 | yes | characteristic |
| 513 | C2 | #72227133 | 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