← #72227055
Subgroups — #72227055
Order 2048.
550 conjugacy classes of subgroups.
The subgroup lattice has 508 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225527 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225426 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72225338 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72225316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225158 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72216390 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72216302 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #496112 | C22 | 1 | 1 | yes | characteristic |
| 9 | #151981 | C22 | 1 | 1 | yes | characteristic |
| 10 | C4×#1398 | C22 | 1 | 1 | yes | characteristic |
| 11 | #150950 | C4 | 1 | 1 | yes | characteristic |
| 12 | #150947 | C4 | 1 | 1 | yes | characteristic |
| 13 | C2×#7389 | — | 2 | 1 | no | — |
| 14 | C2×#7389 | — | 2 | 1 | no | — |
| 15 | #149504 | — | 2 | 1 | no | — |
| 16 | #140841 | — | 2 | 1 | no | — |
| 17 | #140390 | — | 2 | 1 | no | — |
| 18 | #135715 | C22 | 1 | 1 | yes | characteristic |
| 19 | #129101 | C22 | 1 | 1 | yes | characteristic |
| 20 | #129088 | C22 | 1 | 1 | yes | characteristic |
| 21 | #129051 | C22 | 1 | 1 | yes | characteristic |
| 22 | #124213 | — | 2 | 1 | no | — |
| 23 | #94366 | C4 | 1 | 1 | yes | characteristic |
| 24 | #94365 | C4 | 1 | 1 | yes | characteristic |
| 25 | #93996 | — | 2 | 1 | no | — |
| 26 | #93444 | — | 2 | 1 | no | — |
| 27 | #33713 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C2×#2179 | — | 2 | 1 | no | — |
| 29 | C2×#2179 | — | 2 | 1 | no | — |
| 30 | #21705 | — | 2 | 1 | no | — |
| 31 | C2×#1422 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C2×#1422 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C2×#1398 | — | 2 | 1 | no | — |
| 34 | C2×#1398 | — | 2 | 1 | no | — |
| 35 | C2×#1398 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×#1398 | D4 | 1 | 1 | yes | characteristic |
| 37 | C4×M64 | — | 2 | 1 | no | — |
| 38 | #13242 | — | 2 | 1 | no | — |
| 39 | #13242 | — | 2 | 1 | no | — |
| 40 | #13208 | — | 2 | 1 | no | — |
| 41 | #12909 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C4×#364 | — | 2 | 1 | no | — |
| 43 | C4×#364 | D4 | 1 | 1 | yes | characteristic |
| 44 | C4×#346 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #12000 | — | 4 | 1 | no | — |
| 48 | #11999 | — | 2 | 1 | no | — |
| 49 | C2×#1368 | — | 2 | 1 | no | — |
| 50 | C2×#1368 | — | 2 | 1 | no | — |
| 51 | #11604 | — | 4 | 1 | no | — |
| 52 | #11602 | — | 4 | 1 | no | — |
| 53 | #11405 | — | 2 | 1 | no | — |
| 54 | #8805 | — | 2 | 1 | no | — |
| 55 | #8266 | — | 2 | 1 | no | — |
| 56 | #8266 | D4 | 1 | 1 | yes | characteristic |
| 57 | #7468 | — | 2 | 1 | no | — |
| 58 | #7449 | C8 | 1 | 2 | yes | complemented |
| 59 | #7448 | C8 | 1 | 2 | yes | complemented |
| 60 | #7447 | — | 2 | 2 | no | — |
| 61 | #7389 | — | 4 | 2 | no | — |
| 62 | #7389 | — | 4 | 2 | no | — |
| 63 | #7333 | — | 4 | 2 | no | — |
| 64 | #7160 | — | 2 | 1 | no | — |
| 65 | #7158 | — | 4 | 1 | no | — |
| 66 | #7157 | — | 2 | 1 | no | — |
| 67 | #7140 | — | 2 | 1 | no | — |
| 68 | #7106 | — | 4 | 2 | no | — |
| 69 | C2×#508 | — | 2 | 1 | no | — |
| 70 | C2×#508 | — | 2 | 1 | no | — |
| 71 | #3147 | — | 2 | 1 | no | — |
| 72 | C2×#443 | — | 4 | 1 | no | — |
| 73 | C2×#443 | — | 4 | 1 | no | — |
| 74 | #2931 | — | 4 | 1 | no | — |
| 75 | C2×M64 | — | 2 | 1 | no | — |
| 76 | C2×M64 | — | 2 | 1 | no | — |
| 77 | C2×M64 | — | 2 | 1 | no | — |
| 78 | C2×M64 | — | 2 | 1 | no | — |
| 79 | #2249 | — | 2 | 1 | no | — |
| 80 | #2249 | — | 2 | 1 | no | — |
| 81 | #2248 | — | 2 | 1 | no | — |
| 82 | #2247 | C2×C8 | 1 | 1 | yes | characteristic |
| 83 | #2246 | C2×C8 | 1 | 1 | yes | characteristic |
| 84 | #2179 | — | 4 | 1 | no | — |
| 85 | #2179 | — | 4 | 1 | no | — |
| 86 | #2179 | — | 4 | 1 | no | — |
| 87 | #2179 | — | 4 | 1 | no | — |
| 88 | #2179 | — | 8 | 1 | no | — |
| 89 | #2179 | — | 8 | 1 | no | — |
| 90 | C2×#368 | — | 2 | 1 | no | — |
| 91 | C2×#368 | — | 2 | 1 | no | — |
| 92 | C2×#364 | — | 2 | 1 | no | — |
| 93 | C2×#364 | — | 2 | 1 | no | — |
| 94 | C2×#364 | — | 2 | 1 | no | — |
| 95 | C2×#359 | — | 4 | 1 | no | — |
| 96 | C2×#359 | — | 4 | 1 | no | — |
| 97 | C4×M32 | — | 2 | 1 | no | — |
| 98 | C4×M32 | — | 4 | 1 | no | — |
| 99 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 101 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 102 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 103 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C16 | #41 | 1 | 1 | yes | characteristic |
| 105 | #1974 | — | 4 | 1 | no | — |
| 106 | #1974 | — | 4 | 1 | no | — |
| 107 | #1962 | — | 4 | 1 | no | — |
| 108 | #1848 | — | 2 | 1 | no | — |
| 109 | #1842 | — | 4 | 1 | no | — |
| 110 | C42×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | #1564 | — | 2 | 1 | no | — |
| 112 | #1564 | — | 4 | 1 | no | — |
| 113 | C2×#334 | — | 4 | 1 | no | — |
| 114 | C2×#334 | — | 4 | 1 | no | — |
| 115 | #1450 | — | 2 | 1 | no | — |
| 116 | #1450 | — | 4 | 1 | no | — |
| 117 | #1422 | — | 2 | 1 | no | — |
| 118 | #1422 | — | 2 | 1 | no | — |
| 119 | #1422 | C2×C8 | 1 | 2 | yes | — |
| 120 | #1422 | M16 | 1 | 2 | yes | — |
| 121 | #1398 | — | 2 | 1 | no | — |
| 122 | #1398 | — | 2 | 1 | no | — |
| 123 | #1398 | — | 2 | 1 | no | — |
| 124 | #1398 | — | 4 | 2 | no | — |
| 125 | #1398 | — | 4 | 1 | no | — |
| 126 | #1398 | — | 4 | 1 | no | — |
| 127 | #1398 | SD16 | 1 | 2 | yes | — |
| 128 | #1397 | — | 4 | 1 | no | — |
| 129 | C4×C32 | — | 4 | 1 | no | — |
| 130 | #1376 | — | 2 | 1 | no | — |
| 131 | #1376 | — | 4 | 1 | no | — |
| 132 | #1373 | — | 2 | 1 | no | — |
| 133 | #1373 | — | 2 | 1 | no | — |
| 134 | #1373 | — | 2 | 1 | no | — |
| 135 | #1373 | C2×C8 | 1 | 2 | yes | — |
| 136 | #1368 | — | 2 | 2 | no | — |
| 137 | #1368 | — | 4 | 1 | no | — |
| 138 | #1368 | — | 4 | 1 | no | — |
| 139 | #1368 | — | 4 | 1 | no | — |
| 140 | #1368 | — | 8 | 2 | no | — |
| 141 | #1368 | — | 8 | 1 | no | — |
| 142 | #1336 | — | 8 | 2 | no | — |
| 143 | #1335 | — | 8 | 2 | no | — |
| 144 | #1313 | — | 4 | 1 | no | — |
| 145 | #1313 | — | 4 | 1 | no | — |
| 146 | #1276 | — | 2 | 1 | no | — |
| 147 | #1276 | — | 4 | 1 | no | — |
| 148 | C2×#135 | — | 4 | 1 | no | — |
| 149 | C2×#135 | — | 4 | 1 | no | — |
| 150 | C2×#131 | — | 8 | 1 | no | — |
| 151 | #532 | — | 4 | 1 | no | — |
| 152 | #508 | — | 4 | 1 | no | — |
| 153 | #508 | — | 4 | 1 | no | — |
| 154 | #508 | — | 4 | 1 | no | — |
| 155 | #508 | — | 4 | 1 | no | — |
| 156 | #508 | — | 8 | 1 | no | — |
| 157 | #508 | — | 8 | 1 | no | — |
| 158 | C2×Q32 | — | 2 | 1 | no | — |
| 159 | C2×Q32 | — | 2 | 1 | no | — |
| 160 | C2×SD32 | — | 4 | 1 | no | — |
| 161 | C2×SD32 | — | 4 | 1 | no | — |
| 162 | C2×D16 | — | 2 | 1 | no | — |
| 163 | C2×D16 | — | 2 | 1 | no | — |
| 164 | C2×M32 | — | 4 | 1 | no | — |
| 165 | C2×M32 | — | 4 | 1 | no | — |
| 166 | C2×M32 | — | 4 | 1 | no | — |
| 167 | C22×C16 | #117 | 1 | 1 | yes | characteristic |
| 168 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 169 | C22×C16 | #123 | 1 | 1 | yes | characteristic |
| 170 | C22×C16 | #126 | 1 | 1 | yes | characteristic |
| 171 | #495 | — | 4 | 1 | no | — |
| 172 | #495 | — | 4 | 1 | no | — |
| 173 | #494 | — | 2 | 1 | no | — |
| 174 | #493 | — | 2 | 1 | no | — |
| 175 | #492 | — | 4 | 1 | no | — |
| 176 | #443 | — | 8 | 1 | no | — |
| 177 | #443 | — | 8 | 1 | no | — |
| 178 | #443 | — | 8 | 1 | no | — |
| 179 | #443 | — | 8 | 1 | no | — |
| 180 | #443 | — | 8 | 1 | no | — |
| 181 | #443 | — | 8 | 1 | no | — |
| 182 | #443 | — | 8 | 1 | no | — |
| 183 | #443 | — | 8 | 1 | no | — |
| 184 | #436 | — | 16 | 1 | no | — |
| 185 | C8×D4 | — | 16 | 1 | no | — |
| 186 | #431 | — | 4 | 1 | no | — |
| 187 | #431 | — | 8 | 1 | no | — |
| 188 | C2×#108 | — | 4 | 1 | no | — |
| 189 | C2×#108 | — | 4 | 1 | no | — |
| 190 | #423 | — | 4 | 1 | no | — |
| 191 | C2×C4⋊C8 | — | 8 | 1 | no | — |
| 192 | C2×C4⋊C8 | — | 16 | 1 | no | — |
| 193 | C2×#104 | — | 8 | 1 | no | — |
| 194 | C2×#104 | — | 8 | 1 | no | — |
| 195 | #408 | — | 8 | 1 | no | — |
| 196 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×C8 | #121 | 1 | 1 | yes | characteristic |
| 198 | C2×C4×C8 | #124 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 200 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 201 | C2×C4×C8 | #137 | 1 | 1 | yes | characteristic |
| 202 | C43 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 203 | M64 | — | 2 | 2 | no | — |
| 204 | M64 | — | 2 | 2 | no | — |
| 205 | M64 | — | 2 | 2 | no | — |
| 206 | M64 | — | 2 | 2 | no | — |
| 207 | M64 | — | 4 | 1 | no | — |
| 208 | M64 | — | 4 | 1 | no | — |
| 209 | M64 | — | 4 | 1 | no | — |
| 210 | M64 | — | 4 | 1 | no | — |
| 211 | C2×C32 | — | 4 | 1 | no | — |
| 212 | C2×C32 | — | 4 | 1 | no | — |
| 213 | C2×C32 | — | 4 | 1 | no | — |
| 214 | C2×C32 | — | 4 | 1 | no | — |
| 215 | #368 | — | 4 | 1 | no | — |
| 216 | #368 | — | 4 | 1 | no | — |
| 217 | #368 | — | 8 | 1 | no | — |
| 218 | #364 | — | 2 | 2 | no | — |
| 219 | #364 | — | 4 | 1 | no | — |
| 220 | #364 | — | 4 | 1 | no | — |
| 221 | #364 | — | 4 | 1 | no | — |
| 222 | #364 | — | 4 | 1 | no | — |
| 223 | #364 | — | 4 | 1 | no | — |
| 224 | #359 | — | 8 | 2 | no | — |
| 225 | #359 | — | 8 | 1 | no | — |
| 226 | #359 | — | 8 | 1 | no | — |
| 227 | #346 | — | 2 | 1 | no | — |
| 228 | #346 | — | 2 | 1 | no | — |
| 229 | #346 | — | 2 | 1 | no | — |
| 230 | #346 | — | 2 | 1 | no | — |
| 231 | #346 | — | 4 | 1 | no | — |
| 232 | #346 | — | 4 | 1 | no | — |
| 233 | #346 | — | 8 | 1 | no | — |
| 234 | #346 | C2×SD16 | 1 | 1 | yes | characteristic |
| 235 | #346 | #135 | 1 | 1 | yes | characteristic |
| 236 | #346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 237 | #346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 238 | C4×C16 | — | 2 | 1 | no | — |
| 239 | C4×C16 | — | 2 | 1 | no | — |
| 240 | C4×C16 | — | 4 | 1 | no | — |
| 241 | C4×C16 | — | 8 | 1 | no | — |
| 242 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 243 | C4×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 244 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 245 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 246 | #335 | — | 4 | 1 | no | — |
| 247 | #335 | — | 8 | 1 | no | — |
| 248 | #334 | — | 4 | 1 | no | — |
| 249 | #334 | — | 4 | 2 | no | — |
| 250 | #334 | — | 8 | 1 | no | — |
| 251 | #334 | — | 8 | 1 | no | — |
| 252 | #334 | — | 8 | 1 | no | — |
| 253 | #334 | — | 8 | 1 | no | — |
| 254 | #322 | — | 4 | 1 | no | — |
| 255 | #322 | — | 8 | 1 | no | — |
| 256 | C82 | — | 4 | 1 | no | — |
| 257 | C82 | — | 8 | 1 | no | — |
| 258 | C2×#41 | — | 8 | 1 | no | — |
| 259 | #135 | — | 8 | 1 | no | — |
| 260 | #135 | — | 8 | 1 | no | — |
| 261 | #135 | — | 8 | 1 | no | — |
| 262 | #135 | — | 8 | 1 | no | — |
| 263 | #135 | — | 8 | 1 | no | — |
| 264 | #135 | — | 8 | 1 | no | — |
| 265 | #135 | — | 8 | 1 | no | — |
| 266 | #135 | — | 8 | 1 | no | — |
| 267 | C2×Q16 | — | 4 | 1 | no | — |
| 268 | C2×Q16 | — | 4 | 1 | no | — |
| 269 | C2×SD16 | — | 8 | 1 | no | — |
| 270 | C2×SD16 | — | 8 | 1 | no | — |
| 271 | C2×D8 | — | 4 | 1 | no | — |
| 272 | C2×D8 | — | 4 | 1 | no | — |
| 273 | #131 | — | 16 | 1 | no | — |
| 274 | #131 | — | 16 | 1 | no | — |
| 275 | #131 | — | 16 | 1 | no | — |
| 276 | #131 | — | 16 | 1 | no | — |
| 277 | C2×M16 | — | 8 | 1 | no | — |
| 278 | C2×M16 | — | 16 | 1 | no | — |
| 279 | C22×C8 | — | 16 | 1 | no | — |
| 280 | C22×C8 | — | 16 | 1 | no | — |
| 281 | C22×C8 | #388 | 1 | 1 | yes | characteristic |
| 282 | C22×C8 | #442 | 1 | 1 | yes | characteristic |
| 283 | C22×C8 | #468 | 1 | 1 | yes | characteristic |
| 284 | C22×C8 | #489 | 1 | 1 | yes | characteristic |
| 285 | C4⋊Q8 | — | 4 | 1 | no | — |
| 286 | #127 | — | 4 | 1 | no | — |
| 287 | #124 | — | 8 | 1 | no | — |
| 288 | #121 | — | 16 | 1 | no | — |
| 289 | C4×D4 | — | 16 | 1 | no | — |
| 290 | C2×C42 | — | 4 | 1 | no | — |
| 291 | C2×C42 | #440 | 1 | 1 | yes | characteristic |
| 292 | C2×C42 | #469 | 1 | 1 | yes | characteristic |
| 293 | C2×C42 | #490 | 1 | 1 | yes | characteristic |
| 294 | Q32 | — | 4 | 1 | no | — |
| 295 | Q32 | — | 4 | 1 | no | — |
| 296 | Q32 | — | 8 | 1 | no | — |
| 297 | SD32 | — | 8 | 2 | no | — |
| 298 | SD32 | — | 8 | 1 | no | — |
| 299 | SD32 | — | 8 | 1 | no | — |
| 300 | D16 | — | 4 | 1 | no | — |
| 301 | D16 | — | 4 | 1 | no | — |
| 302 | D16 | — | 8 | 1 | no | — |
| 303 | M32 | — | 4 | 2 | no | — |
| 304 | M32 | — | 8 | 1 | no | — |
| 305 | M32 | — | 8 | 1 | no | — |
| 306 | M32 | — | 8 | 1 | no | — |
| 307 | M32 | — | 8 | 1 | no | — |
| 308 | M32 | — | 8 | 1 | no | — |
| 309 | C2×C16 | — | 2 | 1 | no | — |
| 310 | C2×C16 | — | 2 | 1 | no | — |
| 311 | C2×C16 | — | 2 | 1 | no | — |
| 312 | C2×C16 | — | 2 | 1 | no | — |
| 313 | C2×C16 | — | 2 | 1 | no | — |
| 314 | C2×C16 | — | 2 | 1 | no | — |
| 315 | C2×C16 | — | 2 | 1 | no | — |
| 316 | C2×C16 | — | 8 | 1 | no | — |
| 317 | C2×C16 | — | 8 | 1 | no | — |
| 318 | C2×C16 | — | 8 | 1 | no | — |
| 319 | C2×C16 | #431 | 1 | 1 | yes | characteristic |
| 320 | C2×C16 | #433 | 1 | 1 | yes | characteristic |
| 321 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 322 | C2×C16 | #435 | 1 | 1 | yes | characteristic |
| 323 | C2×C16 | C4×SD16 | 1 | 1 | yes | characteristic |
| 324 | C2×C16 | #442 | 1 | 1 | yes | characteristic |
| 325 | C2×C16 | #443 | 1 | 1 | yes | characteristic |
| 326 | C2×C16 | #444 | 1 | 1 | yes | characteristic |
| 327 | C2×C16 | #481 | 1 | 1 | yes | characteristic |
| 328 | C2×C16 | #482 | 1 | 1 | yes | characteristic |
| 329 | #108 | — | 8 | 1 | no | — |
| 330 | #108 | — | 8 | 1 | no | — |
| 331 | #108 | — | 8 | 1 | no | — |
| 332 | #108 | — | 8 | 1 | no | — |
| 333 | C4⋊C8 | — | 8 | 1 | no | — |
| 334 | C4⋊C8 | — | 8 | 2 | no | — |
| 335 | C4⋊C8 | — | 16 | 1 | no | — |
| 336 | C4⋊C8 | — | 16 | 1 | no | — |
| 337 | C4⋊C8 | — | 16 | 1 | no | — |
| 338 | C4⋊C8 | — | 32 | 2 | no | — |
| 339 | #104 | — | 16 | 1 | no | — |
| 340 | #104 | — | 16 | 1 | no | — |
| 341 | #104 | — | 16 | 1 | no | — |
| 342 | #104 | — | 16 | 1 | no | — |
| 343 | C22⋊C8 | — | 8 | 1 | no | — |
| 344 | C22⋊C8 | — | 16 | 2 | no | — |
| 345 | C22⋊C8 | — | 16 | 1 | no | — |
| 346 | C4×C8 | — | 2 | 1 | no | — |
| 347 | C4×C8 | — | 2 | 1 | no | — |
| 348 | C4×C8 | — | 2 | 1 | no | — |
| 349 | C4×C8 | — | 2 | 1 | no | — |
| 350 | C4×C8 | — | 2 | 1 | no | — |
| 351 | C4×C8 | — | 2 | 1 | no | — |
| 352 | C4×C8 | — | 4 | 1 | no | — |
| 353 | C4×C8 | — | 8 | 1 | no | — |
| 354 | C4×C8 | — | 16 | 1 | no | — |
| 355 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 356 | C4×C8 | #436 | 1 | 1 | yes | characteristic |
| 357 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 358 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 359 | C4×C8 | #460 | 1 | 1 | yes | characteristic |
| 360 | C4×C8 | #463 | 1 | 1 | yes | characteristic |
| 361 | C4×C8 | #471 | 1 | 1 | yes | characteristic |
| 362 | C4×C8 | #472 | 1 | 1 | yes | characteristic |
| 363 | C32 | — | 4 | 2 | no | — |
| 364 | C32 | — | 4 | 2 | no | — |
| 365 | C32 | — | 4 | 2 | no | — |
| 366 | C32 | — | 4 | 2 | no | — |
| 367 | #41 | — | 16 | 1 | no | — |
| 368 | #41 | — | 16 | 1 | no | — |
| 369 | #41 | — | 16 | 1 | no | — |
| 370 | #41 | — | 16 | 1 | no | — |
| 371 | C2×Q8 | — | 8 | 1 | no | — |
| 372 | C2×D4 | — | 8 | 1 | no | — |
| 373 | C2×D4 | — | 16 | 1 | no | — |
| 374 | C2×D4 | — | 16 | 1 | no | — |
| 375 | C22×C4 | — | 2 | 1 | no | — |
| 376 | C22×C4 | — | 2 | 1 | no | — |
| 377 | C22×C4 | — | 2 | 1 | no | — |
| 378 | C22×C4 | — | 16 | 1 | no | — |
| 379 | C22×C4 | #1936 | 1 | 1 | yes | characteristic |
| 380 | Q16 | — | 8 | 1 | no | — |
| 381 | Q16 | — | 8 | 1 | no | — |
| 382 | Q16 | — | 8 | 1 | no | — |
| 383 | Q16 | — | 8 | 1 | no | — |
| 384 | SD16 | — | 16 | 1 | no | — |
| 385 | SD16 | — | 16 | 1 | no | — |
| 386 | SD16 | — | 16 | 1 | no | — |
| 387 | SD16 | — | 16 | 1 | no | — |
| 388 | D8 | — | 8 | 1 | no | — |
| 389 | D8 | — | 8 | 1 | no | — |
| 390 | D8 | — | 8 | 1 | no | — |
| 391 | D8 | — | 8 | 1 | no | — |
| 392 | M16 | — | 16 | 1 | no | — |
| 393 | M16 | — | 16 | 1 | no | — |
| 394 | M16 | — | 32 | 1 | no | — |
| 395 | M16 | — | 32 | 1 | no | — |
| 396 | C2×C8 | — | 2 | 1 | no | — |
| 397 | C2×C8 | — | 2 | 1 | no | — |
| 398 | C2×C8 | — | 2 | 1 | no | — |
| 399 | C2×C8 | — | 2 | 1 | no | — |
| 400 | C2×C8 | — | 2 | 1 | no | — |
| 401 | C2×C8 | — | 16 | 1 | no | — |
| 402 | C2×C8 | — | 16 | 2 | no | — |
| 403 | C2×C8 | — | 16 | 1 | no | — |
| 404 | C2×C8 | — | 32 | 1 | no | — |
| 405 | C2×C8 | — | 32 | 1 | no | — |
| 406 | C2×C8 | — | 32 | 1 | no | — |
| 407 | C2×C8 | — | 32 | 2 | no | — |
| 408 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 409 | C2×C8 | #1594 | 1 | 1 | yes | characteristic |
| 410 | C2×C8 | #1686 | 1 | 1 | yes | characteristic |
| 411 | C2×C8 | #1697 | 1 | 1 | yes | characteristic |
| 412 | C2×C8 | #1923 | 1 | 1 | yes | characteristic |
| 413 | C2×C8 | #1926 | 1 | 1 | yes | characteristic |
| 414 | C2×C8 | #1929 | 1 | 1 | yes | characteristic |
| 415 | C2×C8 | #1931 | 1 | 1 | yes | characteristic |
| 416 | C2×C8 | #1932 | 1 | 1 | yes | characteristic |
| 417 | C2×C8 | #1938 | 1 | 1 | yes | characteristic |
| 418 | C2×C8 | #2180 | 1 | 1 | yes | characteristic |
| 419 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 420 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 421 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 422 | C4⋊C4 | — | 16 | 1 | no | — |
| 423 | C22⋊C4 | — | 16 | 2 | no | — |
| 424 | C42 | — | 2 | 1 | no | — |
| 425 | C42 | — | 2 | 1 | no | — |
| 426 | C42 | — | 2 | 1 | no | — |
| 427 | C42 | — | 2 | 1 | no | — |
| 428 | C42 | — | 8 | 2 | no | — |
| 429 | C42 | SD16⋊C8 | 1 | 1 | yes | characteristic |
| 430 | C42 | #1592 | 1 | 1 | yes | characteristic |
| 431 | C42 | #1688 | 1 | 1 | yes | characteristic |
| 432 | C42 | #1701 | 1 | 1 | yes | characteristic |
| 433 | C16 | — | 2 | 1 | no | — |
| 434 | C16 | — | 2 | 1 | no | — |
| 435 | C16 | — | 2 | 1 | no | — |
| 436 | C16 | — | 2 | 1 | no | — |
| 437 | C16 | — | 4 | 1 | no | — |
| 438 | C16 | — | 8 | 2 | no | — |
| 439 | C16 | — | 16 | 1 | no | — |
| 440 | C16 | — | 16 | 1 | no | — |
| 441 | C16 | C8×SD16 | 1 | 1 | yes | characteristic |
| 442 | C16 | #1580 | 1 | 1 | yes | characteristic |
| 443 | C16 | #1583 | 1 | 1 | yes | characteristic |
| 444 | C16 | #1586 | 1 | 1 | yes | characteristic |
| 445 | C23 | — | 16 | 1 | no | — |
| 446 | C23 | #13156 | 1 | 1 | yes | characteristic |
| 447 | Q8 | — | 16 | 1 | no | — |
| 448 | Q8 | — | 16 | 1 | no | — |
| 449 | D4 | — | 16 | 1 | no | — |
| 450 | D4 | — | 16 | 1 | no | — |
| 451 | D4 | — | 32 | 2 | no | — |
| 452 | D4 | — | 32 | 1 | no | — |
| 453 | D4 | — | 32 | 1 | no | — |
| 454 | C2×C4 | — | 2 | 1 | no | — |
| 455 | C2×C4 | — | 2 | 1 | no | — |
| 456 | C2×C4 | — | 2 | 1 | no | — |
| 457 | C2×C4 | — | 2 | 1 | no | — |
| 458 | C2×C4 | — | 4 | 2 | no | — |
| 459 | C2×C4 | — | 4 | 1 | no | — |
| 460 | C2×C4 | — | 8 | 1 | no | — |
| 461 | C2×C4 | — | 8 | 1 | no | — |
| 462 | C2×C4 | — | 16 | 1 | no | — |
| 463 | C2×C4 | — | 32 | 1 | no | — |
| 464 | C2×C4 | — | 32 | 1 | no | — |
| 465 | C2×C4 | #9556 | 1 | 1 | yes | characteristic |
| 466 | C2×C4 | #9572 | 1 | 1 | yes | characteristic |
| 467 | C2×C4 | #9592 | 1 | 1 | yes | characteristic |
| 468 | C2×C4 | #13153 | 1 | 1 | yes | characteristic |
| 469 | C2×C4 | #13155 | 1 | 1 | yes | characteristic |
| 470 | C2×C4 | #13158 | 1 | 1 | yes | characteristic |
| 471 | C8 | — | 2 | 1 | no | — |
| 472 | C8 | — | 2 | 1 | no | — |
| 473 | C8 | — | 4 | 1 | no | — |
| 474 | C8 | — | 32 | 1 | no | — |
| 475 | C8 | — | 32 | 2 | no | — |
| 476 | C8 | — | 32 | 1 | no | — |
| 477 | C8 | — | 64 | 1 | no | — |
| 478 | C8 | #9542 | 1 | 1 | yes | characteristic |
| 479 | C8 | #9550 | 1 | 1 | yes | characteristic |
| 480 | C8 | #9582 | 1 | 1 | yes | characteristic |
| 481 | C8 | #9588 | 1 | 1 | yes | characteristic |
| 482 | C8 | #12065 | 1 | 1 | yes | characteristic |
| 483 | C8 | #12067 | 1 | 1 | yes | characteristic |
| 484 | C8 | #12087 | 1 | 1 | yes | characteristic |
| 485 | C8 | #12089 | 1 | 1 | yes | characteristic |
| 486 | C22 | — | 4 | 1 | no | — |
| 487 | C22 | — | 32 | 2 | no | — |
| 488 | C22 | — | 32 | 1 | no | — |
| 489 | C22 | #140190 | 1 | 1 | yes | characteristic |
| 490 | C22 | #140290 | 1 | 1 | yes | characteristic |
| 491 | C22 | #140332 | 1 | 1 | yes | characteristic |
| 492 | C4 | — | 2 | 2 | no | — |
| 493 | C4 | — | 4 | 1 | no | — |
| 494 | C4 | — | 4 | 1 | no | — |
| 495 | C4 | — | 4 | 1 | no | — |
| 496 | C4 | — | 8 | 1 | no | — |
| 497 | C4 | — | 32 | 1 | no | — |
| 498 | C4 | #101906 | 1 | 1 | yes | characteristic |
| 499 | C4 | #140188 | 1 | 1 | yes | characteristic |
| 500 | C4 | #140292 | 1 | 1 | yes | characteristic |
| 501 | C4 | #140334 | 1 | 1 | yes | characteristic |
| 502 | C2 | — | 2 | 1 | no | — |
| 503 | C2 | — | 2 | 1 | no | — |
| 504 | C2 | — | 2 | 1 | no | — |
| 505 | C2 | — | 64 | 1 | no | — |
| 506 | C2 | #72227054 | 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