← #72225387
Subgroups — #72225387
Order 2048.
581 conjugacy classes of subgroups.
The subgroup lattice has 423 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225373 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225353 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72225311 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72216535 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#93752 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72216226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #512751 | — | 2 | 1 | no | — |
| 9 | C2×#12046 | C22 | 1 | 1 | yes | characteristic |
| 10 | #151989 | — | 2 | 1 | no | — |
| 11 | #151968 | C4 | 1 | 1 | yes | characteristic |
| 12 | #151073 | — | 2 | 2 | no | — |
| 13 | #151072 | C4 | 1 | 4 | yes | complemented |
| 14 | C2×#7459 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#7459 | C22 | 1 | 1 | yes | characteristic |
| 16 | #150069 | C4 | 1 | 1 | yes | characteristic |
| 17 | #150051 | — | 2 | 1 | no | — |
| 18 | C8×M64 | C22 | 1 | 1 | yes | characteristic |
| 19 | C8×M64 | C22 | 1 | 1 | yes | characteristic |
| 20 | #129142 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#7052 | C22 | 1 | 1 | yes | characteristic |
| 22 | #94054 | C4 | 1 | 1 | yes | characteristic |
| 23 | #94041 | — | 2 | 1 | no | — |
| 24 | #94029 | C4 | 1 | 1 | yes | characteristic |
| 25 | #93752 | C4 | 1 | 4 | yes | complemented |
| 26 | #93666 | — | 2 | 2 | no | — |
| 27 | #33974 | — | 4 | 1 | no | — |
| 28 | C2×#2178 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C2×#2170 | — | 2 | 1 | no | — |
| 30 | #13648 | — | 4 | 2 | no | — |
| 31 | #13647 | — | 2 | 4 | no | — |
| 32 | C2×#1422 | — | 2 | 1 | no | — |
| 33 | C2×#1422 | — | 2 | 1 | no | — |
| 34 | #13625 | C8 | 1 | 1 | yes | characteristic |
| 35 | #13622 | C8 | 1 | 1 | yes | characteristic |
| 36 | #13558 | — | 4 | 1 | no | — |
| 37 | #13551 | — | 4 | 1 | no | — |
| 38 | C4×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C4×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 41 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 42 | #12670 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | #12664 | — | 2 | 1 | no | — |
| 44 | #12046 | — | 2 | 1 | no | — |
| 45 | #12046 | — | 2 | 1 | no | — |
| 46 | #12046 | C2×C4 | 1 | 2 | yes | — |
| 47 | #12046 | C2×C4 | 1 | 2 | yes | — |
| 48 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×#1335 | — | 2 | 1 | no | — |
| 51 | C2×C8×C16 | — | 2 | 1 | no | — |
| 52 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 53 | #7480 | C8 | 1 | 1 | yes | characteristic |
| 54 | #7479 | C8 | 1 | 1 | yes | characteristic |
| 55 | #7469 | — | 4 | 1 | no | — |
| 56 | #7459 | — | 2 | 1 | no | — |
| 57 | #7459 | — | 2 | 1 | no | — |
| 58 | #7459 | C2×C4 | 1 | 2 | yes | — |
| 59 | #7459 | C2×C4 | 1 | 2 | yes | — |
| 60 | #7388 | C8 | 1 | 4 | yes | — |
| 61 | #7381 | — | 2 | 4 | no | — |
| 62 | #7329 | — | 2 | 1 | no | — |
| 63 | #7329 | D4 | 1 | 2 | yes | — |
| 64 | C8×C32 | — | 2 | 1 | no | — |
| 65 | C8×C32 | C2×C4 | 1 | 2 | yes | — |
| 66 | #7179 | — | 2 | 1 | no | — |
| 67 | #7052 | — | 2 | 1 | no | — |
| 68 | #7052 | C2×C4 | 1 | 2 | yes | — |
| 69 | C2×#508 | C2×C8 | 1 | 1 | yes | characteristic |
| 70 | C2×#504 | — | 4 | 1 | no | — |
| 71 | C2×#443 | — | 2 | 1 | no | — |
| 72 | #2258 | — | 4 | 4 | no | — |
| 73 | #2258 | — | 8 | 2 | no | — |
| 74 | C2×M64 | — | 2 | 1 | no | — |
| 75 | C2×M64 | — | 2 | 1 | no | — |
| 76 | C2×M64 | — | 4 | 1 | no | — |
| 77 | C2×M64 | — | 4 | 1 | no | — |
| 78 | C2×M64 | — | 8 | 2 | no | — |
| 79 | C2×M64 | C2×C8 | 1 | 1 | yes | characteristic |
| 80 | C2×M64 | C2×C8 | 1 | 1 | yes | characteristic |
| 81 | C2×M64 | D8 | 1 | 1 | yes | characteristic |
| 82 | C2×M64 | D8 | 1 | 1 | yes | characteristic |
| 83 | #2178 | — | 2 | 1 | no | — |
| 84 | #2178 | — | 2 | 1 | no | — |
| 85 | #2178 | C42 | 1 | 2 | yes | — |
| 86 | #2178 | C2×C8 | 1 | 2 | yes | — |
| 87 | #2170 | — | 2 | 2 | no | — |
| 88 | #2170 | — | 2 | 2 | no | — |
| 89 | #2170 | — | 4 | 1 | no | — |
| 90 | #2170 | — | 4 | 1 | no | — |
| 91 | C2×#368 | C2×C8 | 1 | 1 | yes | characteristic |
| 92 | C2×#368 | C2×C8 | 1 | 1 | yes | characteristic |
| 93 | #2158 | C2×C8 | 1 | 1 | yes | characteristic |
| 94 | C2×#364 | — | 2 | 1 | no | — |
| 95 | C2×#364 | — | 2 | 1 | no | — |
| 96 | C2×#359 | — | 2 | 1 | no | — |
| 97 | C2×#350 | — | 4 | 1 | no | — |
| 98 | #2108 | — | 4 | 1 | no | — |
| 99 | C2×C4×C16 | — | 2 | 2 | no | — |
| 100 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | #1772 | — | 2 | 1 | no | — |
| 103 | C2×C82 | #41 | 1 | 1 | yes | characteristic |
| 104 | #1422 | — | 2 | 2 | no | — |
| 105 | #1422 | — | 2 | 2 | no | — |
| 106 | #1422 | — | 4 | 1 | no | — |
| 107 | #1422 | — | 4 | 1 | no | — |
| 108 | #1420 | — | 2 | 1 | no | — |
| 109 | #1419 | — | 2 | 1 | no | — |
| 110 | #1418 | — | 2 | 2 | no | — |
| 111 | #1401 | — | 4 | 4 | no | — |
| 112 | #1398 | — | 8 | 2 | no | — |
| 113 | #1397 | — | 2 | 1 | no | — |
| 114 | #1397 | — | 2 | 1 | no | — |
| 115 | #1397 | C2×C8 | 1 | 2 | yes | — |
| 116 | #1397 | SD16 | 1 | 2 | yes | — |
| 117 | C4×C32 | — | 2 | 1 | no | — |
| 118 | C4×C32 | — | 2 | 1 | no | — |
| 119 | C4×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 120 | C4×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 121 | #1382 | — | 2 | 1 | no | — |
| 122 | #1379 | — | 4 | 1 | no | — |
| 123 | #1373 | — | 2 | 1 | no | — |
| 124 | #1373 | — | 2 | 1 | no | — |
| 125 | #1373 | C42 | 1 | 2 | yes | — |
| 126 | #1373 | C2×C8 | 1 | 2 | yes | — |
| 127 | #1335 | — | 2 | 2 | no | — |
| 128 | #1335 | — | 2 | 2 | no | — |
| 129 | C8×C16 | — | 2 | 2 | no | — |
| 130 | C8×C16 | — | 2 | 2 | no | — |
| 131 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 132 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 133 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 135 | C2×#135 | — | 2 | 1 | no | — |
| 136 | C2×#131 | — | 4 | 1 | no | — |
| 137 | #508 | — | 2 | 1 | no | — |
| 138 | #508 | — | 2 | 1 | no | — |
| 139 | #508 | C4×C8 | 1 | 2 | yes | — |
| 140 | #508 | M32 | 1 | 2 | yes | — |
| 141 | C2×Q32 | M32 | 1 | 1 | yes | characteristic |
| 142 | C2×SD32 | — | 2 | 1 | no | — |
| 143 | C2×D16 | M32 | 1 | 1 | yes | characteristic |
| 144 | #504 | — | 4 | 2 | no | — |
| 145 | #504 | — | 4 | 2 | no | — |
| 146 | #504 | — | 8 | 1 | no | — |
| 147 | #504 | — | 8 | 1 | no | — |
| 148 | C2×M32 | — | 4 | 1 | no | — |
| 149 | C2×M32 | — | 4 | 1 | no | — |
| 150 | C2×M32 | — | 8 | 1 | no | — |
| 151 | C22×C16 | — | 4 | 2 | no | — |
| 152 | C22×C16 | — | 8 | 1 | no | — |
| 153 | C22×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 154 | C22×C16 | #131 | 1 | 1 | yes | characteristic |
| 155 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 156 | C22×C16 | #135 | 1 | 1 | yes | characteristic |
| 157 | #443 | — | 2 | 2 | no | — |
| 158 | #443 | — | 2 | 2 | no | — |
| 159 | #443 | — | 4 | 1 | no | — |
| 160 | #443 | — | 4 | 1 | no | — |
| 161 | C2×#108 | — | 2 | 1 | no | — |
| 162 | C2×#108 | — | 2 | 1 | no | — |
| 163 | #427 | — | 2 | 1 | no | — |
| 164 | C2×#104 | — | 4 | 1 | no | — |
| 165 | #405 | — | 4 | 1 | no | — |
| 166 | C2×C4×C8 | — | 2 | 1 | no | — |
| 167 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 168 | M64 | — | 2 | 2 | no | — |
| 169 | M64 | — | 2 | 2 | no | — |
| 170 | M64 | — | 2 | 1 | no | — |
| 171 | M64 | — | 2 | 1 | no | — |
| 172 | M64 | — | 2 | 1 | no | — |
| 173 | M64 | — | 2 | 1 | no | — |
| 174 | M64 | — | 2 | 1 | no | — |
| 175 | M64 | — | 2 | 1 | no | — |
| 176 | M64 | — | 4 | 1 | no | — |
| 177 | M64 | — | 4 | 1 | no | — |
| 178 | M64 | — | 4 | 2 | no | — |
| 179 | M64 | — | 4 | 2 | no | — |
| 180 | M64 | — | 8 | 1 | no | — |
| 181 | M64 | — | 8 | 1 | no | — |
| 182 | M64 | — | 8 | 4 | no | — |
| 183 | M64 | D16 | 1 | 2 | yes | — |
| 184 | M64 | SD32 | 1 | 2 | yes | — |
| 185 | C2×C32 | — | 2 | 2 | no | — |
| 186 | C2×C32 | — | 2 | 1 | no | — |
| 187 | C2×C32 | — | 2 | 1 | no | — |
| 188 | C2×C32 | — | 2 | 2 | no | — |
| 189 | C2×C32 | — | 8 | 1 | no | — |
| 190 | C2×C32 | — | 8 | 1 | no | — |
| 191 | C2×C32 | — | 8 | 4 | no | — |
| 192 | C2×C32 | #102 | 1 | 2 | yes | — |
| 193 | C2×C32 | #102 | 1 | 2 | yes | — |
| 194 | #368 | — | 2 | 1 | no | — |
| 195 | #368 | — | 2 | 1 | no | — |
| 196 | #368 | — | 2 | 1 | no | — |
| 197 | #368 | C4×C8 | 1 | 2 | yes | — |
| 198 | #367 | — | 2 | 1 | no | — |
| 199 | #366 | — | 2 | 1 | no | — |
| 200 | #364 | — | 2 | 2 | no | — |
| 201 | #364 | — | 2 | 2 | no | — |
| 202 | #364 | — | 4 | 1 | no | — |
| 203 | #364 | — | 4 | 1 | no | — |
| 204 | #359 | — | 2 | 2 | no | — |
| 205 | #359 | — | 2 | 2 | no | — |
| 206 | #350 | — | 4 | 2 | no | — |
| 207 | #350 | — | 4 | 2 | no | — |
| 208 | #346 | — | 8 | 1 | no | — |
| 209 | C4×C16 | — | 2 | 4 | no | — |
| 210 | C4×C16 | — | 4 | 2 | no | — |
| 211 | C4×C16 | — | 8 | 1 | no | — |
| 212 | C4×C16 | C2×C42 | 1 | 1 | yes | characteristic |
| 213 | C4×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 214 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 215 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 216 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 217 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 218 | C4×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 219 | C4×C16 | #135 | 1 | 1 | yes | characteristic |
| 220 | #339 | — | 4 | 1 | no | — |
| 221 | C82 | — | 2 | 1 | no | — |
| 222 | C82 | #117 | 1 | 1 | yes | characteristic |
| 223 | C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×#41 | — | 4 | 1 | no | — |
| 225 | #135 | — | 2 | 2 | no | — |
| 226 | #135 | — | 2 | 2 | no | — |
| 227 | #135 | — | 4 | 1 | no | — |
| 228 | #135 | — | 4 | 1 | no | — |
| 229 | C2×Q16 | — | 2 | 1 | no | — |
| 230 | C2×SD16 | — | 4 | 1 | no | — |
| 231 | C2×D8 | — | 2 | 1 | no | — |
| 232 | #131 | — | 4 | 2 | no | — |
| 233 | #131 | — | 4 | 2 | no | — |
| 234 | #131 | — | 8 | 1 | no | — |
| 235 | #131 | — | 8 | 1 | no | — |
| 236 | C2×M16 | — | 4 | 1 | no | — |
| 237 | C2×M16 | — | 4 | 1 | no | — |
| 238 | C2×M16 | — | 8 | 1 | no | — |
| 239 | C22×C8 | — | 2 | 2 | no | — |
| 240 | C22×C8 | — | 8 | 1 | no | — |
| 241 | C22×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 242 | C22×C8 | C4×D8 | 1 | 1 | yes | characteristic |
| 243 | #117 | — | 4 | 1 | no | — |
| 244 | C2×C42 | #443 | 1 | 1 | yes | characteristic |
| 245 | Q32 | — | 2 | 1 | no | — |
| 246 | Q32 | #346 | 1 | 2 | yes | — |
| 247 | SD32 | — | 2 | 2 | no | — |
| 248 | SD32 | — | 2 | 2 | no | — |
| 249 | D16 | — | 2 | 1 | no | — |
| 250 | D16 | #346 | 1 | 2 | yes | — |
| 251 | M32 | — | 4 | 2 | no | — |
| 252 | M32 | — | 4 | 2 | no | — |
| 253 | M32 | — | 8 | 1 | no | — |
| 254 | M32 | — | 8 | 1 | no | — |
| 255 | M32 | — | 8 | 2 | no | — |
| 256 | M32 | — | 8 | 2 | no | — |
| 257 | C2×C16 | — | 2 | 1 | no | — |
| 258 | C2×C16 | — | 2 | 1 | no | — |
| 259 | C2×C16 | — | 2 | 1 | no | — |
| 260 | C2×C16 | — | 2 | 1 | no | — |
| 261 | C2×C16 | — | 4 | 4 | no | — |
| 262 | C2×C16 | — | 8 | 4 | no | — |
| 263 | C2×C16 | — | 8 | 1 | no | — |
| 264 | C2×C16 | — | 8 | 1 | no | — |
| 265 | C2×C16 | — | 8 | 2 | no | — |
| 266 | C2×C16 | — | 8 | 2 | no | — |
| 267 | C2×C16 | C2×C4×C8 | 1 | 1 | yes | characteristic |
| 268 | C2×C16 | #405 | 1 | 1 | yes | characteristic |
| 269 | C2×C16 | C2×#102 | 1 | 1 | yes | characteristic |
| 270 | C2×C16 | #416 | 1 | 1 | yes | characteristic |
| 271 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 272 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 273 | C2×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 274 | C2×C16 | C4×SD16 | 1 | 1 | yes | characteristic |
| 275 | C2×C16 | C2×M32 | 1 | 1 | yes | characteristic |
| 276 | C2×C16 | C2×M32 | 1 | 1 | yes | characteristic |
| 277 | C2×C16 | #504 | 1 | 1 | yes | characteristic |
| 278 | C2×C16 | #504 | 1 | 1 | yes | characteristic |
| 279 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 280 | C2×C16 | C2×SD32 | 1 | 1 | yes | characteristic |
| 281 | C2×C16 | #508 | 1 | 1 | yes | characteristic |
| 282 | C2×C16 | #508 | 1 | 1 | yes | characteristic |
| 283 | #108 | — | 2 | 2 | no | — |
| 284 | #108 | — | 4 | 1 | no | — |
| 285 | #108 | — | 4 | 1 | no | — |
| 286 | #108 | — | 4 | 1 | no | — |
| 287 | #107 | — | 4 | 1 | no | — |
| 288 | #106 | — | 4 | 1 | no | — |
| 289 | #104 | — | 4 | 2 | no | — |
| 290 | #104 | — | 4 | 2 | no | — |
| 291 | #97 | — | 8 | 1 | no | — |
| 292 | C4×C8 | — | 2 | 2 | no | — |
| 293 | C4×C8 | — | 2 | 1 | no | — |
| 294 | C4×C8 | — | 2 | 1 | no | — |
| 295 | C4×C8 | — | 8 | 1 | no | — |
| 296 | C4×C8 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 297 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 298 | C4×C8 | C4×SD16 | 1 | 1 | yes | characteristic |
| 299 | C4×C8 | #443 | 1 | 1 | yes | characteristic |
| 300 | C32 | — | 2 | 4 | no | — |
| 301 | C32 | — | 2 | 2 | no | — |
| 302 | C32 | — | 4 | 2 | no | — |
| 303 | C32 | — | 4 | 1 | no | — |
| 304 | C32 | — | 4 | 1 | no | — |
| 305 | C32 | — | 8 | 2 | no | — |
| 306 | C32 | — | 8 | 2 | no | — |
| 307 | C32 | #357 | 1 | 4 | yes | — |
| 308 | #41 | — | 4 | 2 | no | — |
| 309 | #41 | — | 4 | 2 | no | — |
| 310 | #41 | — | 8 | 1 | no | — |
| 311 | #41 | — | 8 | 1 | no | — |
| 312 | C2×Q8 | — | 4 | 1 | no | — |
| 313 | C2×D4 | — | 4 | 1 | no | — |
| 314 | C2×D4 | — | 8 | 1 | no | — |
| 315 | C22×C4 | — | 2 | 1 | no | — |
| 316 | C22×C4 | — | 8 | 1 | no | — |
| 317 | C22×C4 | C8×D8 | 1 | 1 | yes | characteristic |
| 318 | Q16 | — | 2 | 2 | no | — |
| 319 | Q16 | — | 4 | 1 | no | — |
| 320 | SD16 | — | 4 | 2 | no | — |
| 321 | SD16 | — | 4 | 2 | no | — |
| 322 | D8 | — | 2 | 2 | no | — |
| 323 | D8 | — | 4 | 1 | no | — |
| 324 | M16 | — | 4 | 2 | no | — |
| 325 | M16 | — | 8 | 1 | no | — |
| 326 | M16 | — | 8 | 2 | no | — |
| 327 | M16 | — | 8 | 2 | no | — |
| 328 | M16 | — | 8 | 1 | no | — |
| 329 | M16 | — | 8 | 1 | no | — |
| 330 | C2×C8 | — | 2 | 2 | no | — |
| 331 | C2×C8 | — | 2 | 2 | no | — |
| 332 | C2×C8 | — | 4 | 4 | no | — |
| 333 | C2×C8 | — | 8 | 1 | no | — |
| 334 | C2×C8 | — | 8 | 2 | no | — |
| 335 | C2×C8 | — | 8 | 2 | no | — |
| 336 | C2×C8 | — | 8 | 1 | no | — |
| 337 | C2×C8 | C8×D8 | 1 | 1 | yes | characteristic |
| 338 | C2×C8 | C8×SD16 | 1 | 1 | yes | characteristic |
| 339 | C2×C8 | C8×C22⋊C4 | 1 | 1 | yes | characteristic |
| 340 | C2×C8 | C4×#102 | 1 | 1 | yes | characteristic |
| 341 | C2×C8 | #2168 | 1 | 1 | yes | characteristic |
| 342 | C2×C8 | #2168 | 1 | 1 | yes | characteristic |
| 343 | C2×C8 | #2171 | 1 | 1 | yes | characteristic |
| 344 | C2×C8 | #2171 | 1 | 1 | yes | characteristic |
| 345 | C2×C8 | C4×D16 | 1 | 1 | yes | characteristic |
| 346 | C2×C8 | C4×SD32 | 1 | 1 | yes | characteristic |
| 347 | C2×C8 | #2178 | 1 | 1 | yes | characteristic |
| 348 | C2×C8 | #2178 | 1 | 1 | yes | characteristic |
| 349 | C4⋊C4 | — | 8 | 1 | no | — |
| 350 | C22⋊C4 | — | 8 | 1 | no | — |
| 351 | C42 | — | 2 | 1 | no | — |
| 352 | C42 | — | 8 | 1 | no | — |
| 353 | C42 | C8×SD16 | 1 | 1 | yes | characteristic |
| 354 | C42 | #1764 | 1 | 1 | yes | characteristic |
| 355 | C16 | — | 2 | 1 | no | — |
| 356 | C16 | — | 2 | 1 | no | — |
| 357 | C16 | — | 2 | 1 | no | — |
| 358 | C16 | — | 2 | 1 | no | — |
| 359 | C16 | — | 8 | 4 | no | — |
| 360 | C16 | — | 8 | 2 | no | — |
| 361 | C16 | — | 8 | 2 | no | — |
| 362 | C16 | C2×#346 | 1 | 1 | yes | characteristic |
| 363 | C16 | #2108 | 1 | 1 | yes | characteristic |
| 364 | C16 | C2×#357 | 1 | 1 | yes | characteristic |
| 365 | C16 | #2138 | 1 | 1 | yes | characteristic |
| 366 | C16 | #2168 | 1 | 1 | yes | characteristic |
| 367 | C16 | #2168 | 1 | 1 | yes | characteristic |
| 368 | C16 | C4×D16 | 1 | 1 | yes | characteristic |
| 369 | C16 | C4×SD32 | 1 | 1 | yes | characteristic |
| 370 | C23 | — | 8 | 1 | no | — |
| 371 | C23 | #12047 | 1 | 1 | yes | characteristic |
| 372 | Q8 | — | 4 | 2 | no | — |
| 373 | Q8 | — | 8 | 1 | no | — |
| 374 | D4 | — | 4 | 2 | no | — |
| 375 | D4 | — | 8 | 2 | no | — |
| 376 | D4 | — | 8 | 2 | no | — |
| 377 | D4 | — | 8 | 1 | no | — |
| 378 | C2×C4 | — | 2 | 1 | no | — |
| 379 | C2×C4 | — | 2 | 1 | no | — |
| 380 | C2×C4 | — | 4 | 2 | no | — |
| 381 | C2×C4 | — | 8 | 1 | no | — |
| 382 | C2×C4 | — | 8 | 2 | no | — |
| 383 | C2×C4 | — | 8 | 2 | no | — |
| 384 | C2×C4 | — | 16 | 1 | no | — |
| 385 | C2×C4 | C8×#102 | 1 | 1 | yes | characteristic |
| 386 | C2×C4 | #12038 | 1 | 1 | yes | characteristic |
| 387 | C2×C4 | #12038 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | C8×D16 | 1 | 1 | yes | characteristic |
| 389 | C2×C4 | C8×SD32 | 1 | 1 | yes | characteristic |
| 390 | C2×C4 | #12047 | 1 | 1 | yes | characteristic |
| 391 | C8 | — | 2 | 4 | no | — |
| 392 | C8 | — | 4 | 2 | no | — |
| 393 | C8 | — | 8 | 2 | no | — |
| 394 | C8 | — | 16 | 1 | no | — |
| 395 | C8 | C8×D16 | 1 | 1 | yes | characteristic |
| 396 | C8 | C8×SD32 | 1 | 1 | yes | characteristic |
| 397 | C8 | #12049 | 1 | 1 | yes | characteristic |
| 398 | C8 | #12049 | 1 | 1 | yes | characteristic |
| 399 | C8 | #12611 | 1 | 1 | yes | characteristic |
| 400 | C8 | #12615 | 1 | 1 | yes | characteristic |
| 401 | C8 | C4×#357 | 1 | 1 | yes | characteristic |
| 402 | C8 | #12641 | 1 | 1 | yes | characteristic |
| 403 | C22 | — | 4 | 1 | no | — |
| 404 | C22 | — | 8 | 2 | no | — |
| 405 | C22 | — | 32 | 1 | no | — |
| 406 | C22 | #122953 | 1 | 1 | yes | characteristic |
| 407 | C22 | #122954 | 1 | 1 | yes | characteristic |
| 408 | C22 | #128674 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 2 | 2 | no | — |
| 410 | C4 | — | 4 | 1 | no | — |
| 411 | C4 | — | 8 | 2 | no | — |
| 412 | C4 | — | 32 | 1 | no | — |
| 413 | C4 | #122953 | 1 | 1 | yes | characteristic |
| 414 | C4 | #122954 | 1 | 1 | yes | characteristic |
| 415 | C4 | #128659 | 1 | 1 | yes | characteristic |
| 416 | C4 | C8×#357 | 1 | 1 | yes | characteristic |
| 417 | C2 | — | 2 | 1 | no | — |
| 418 | C2 | — | 2 | 1 | no | — |
| 419 | C2 | — | 2 | 1 | no | — |
| 420 | C2 | — | 16 | 2 | no | — |
| 421 | C2 | #72225386 | 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