← #72320679
Subgroups — #72320679
Order 2048.
1956 conjugacy classes of subgroups.
The subgroup lattice has 703 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72320649 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72320634 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72320603 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72320539 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72320449 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72320349 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #72320305 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #72286801 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #72231861 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #7625194 | C4 | 1 | 1 | yes | characteristic |
| 11 | #7622627 | C22 | 1 | 2 | yes | — |
| 12 | #512775 | — | 2 | 2 | no | — |
| 13 | #512775 | C4 | 1 | 2 | yes | — |
| 14 | #512774 | — | 2 | 2 | no | — |
| 15 | #512774 | C4 | 1 | 2 | yes | — |
| 16 | #512773 | — | 2 | 2 | no | — |
| 17 | #512773 | C22 | 1 | 2 | yes | — |
| 18 | C2×#13656 | — | 2 | 2 | no | — |
| 19 | C2×#13656 | C22 | 1 | 2 | yes | — |
| 20 | #512731 | C22 | 1 | 1 | yes | characteristic |
| 21 | #512721 | C4 | 1 | 1 | yes | characteristic |
| 22 | #512695 | C4 | 1 | 2 | yes | — |
| 23 | #512545 | C22 | 1 | 1 | yes | characteristic |
| 24 | #496302 | — | 2 | 2 | no | — |
| 25 | #483413 | C22 | 1 | 2 | yes | — |
| 26 | #481289 | — | 2 | 2 | no | — |
| 27 | #479917 | C22 | 1 | 1 | yes | characteristic |
| 28 | #151058 | — | 2 | 2 | no | — |
| 29 | #151057 | — | 2 | 2 | no | — |
| 30 | C2×#7464 | C22 | 1 | 2 | yes | complemented |
| 31 | #151035 | C22 | 1 | 2 | yes | complemented |
| 32 | #150145 | — | 2 | 4 | no | — |
| 33 | #150144 | — | 2 | 4 | no | — |
| 34 | C2×#7388 | C22 | 1 | 4 | yes | complemented |
| 35 | #150067 | C22 | 1 | 4 | yes | complemented |
| 36 | #149509 | — | 2 | 2 | no | — |
| 37 | #149508 | — | 2 | 2 | no | — |
| 38 | #149502 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #149501 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #149496 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#7330 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #140788 | — | 2 | 2 | no | — |
| 43 | #140787 | — | 2 | 2 | no | — |
| 44 | #140733 | C22 | 1 | 4 | yes | complemented |
| 45 | #140732 | C22 | 1 | 4 | yes | complemented |
| 46 | #62635 | C2×C4 | 1 | 2 | yes | — |
| 47 | #60183 | — | 2 | 2 | no | — |
| 48 | #33984 | — | 2 | 2 | no | — |
| 49 | #33983 | — | 2 | 4 | no | — |
| 50 | #33982 | — | 2 | 2 | no | — |
| 51 | #33981 | — | 2 | 2 | no | — |
| 52 | #33981 | C2×C4 | 1 | 2 | yes | — |
| 53 | C2×#2262 | — | 2 | 2 | no | — |
| 54 | C2×#2262 | C2×C4 | 1 | 2 | yes | — |
| 55 | C2×#2258 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C2×#2258 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | #33465 | — | 2 | 4 | no | — |
| 58 | #33465 | C2×C4 | 1 | 4 | yes | — |
| 59 | #33464 | — | 2 | 4 | no | — |
| 60 | #33464 | — | 2 | 2 | no | — |
| 61 | #33463 | — | 2 | 2 | no | — |
| 62 | #33463 | — | 2 | 4 | no | — |
| 63 | C2×#2178 | — | 2 | 4 | no | — |
| 64 | C2×#2178 | C23 | 1 | 4 | yes | — |
| 65 | #33428 | — | 2 | 2 | no | — |
| 66 | #33420 | D4 | 1 | 1 | yes | characteristic |
| 67 | #33414 | C2×C4 | 1 | 2 | yes | — |
| 68 | #33385 | — | 2 | 2 | no | — |
| 69 | C4×#504 | C23 | 1 | 1 | yes | characteristic |
| 70 | #17335 | D4 | 1 | 1 | yes | characteristic |
| 71 | #13656 | — | 2 | 4 | no | — |
| 72 | #13656 | — | 2 | 4 | no | — |
| 73 | #13656 | — | 2 | 2 | no | — |
| 74 | #13656 | — | 2 | 4 | no | — |
| 75 | #13656 | — | 2 | 2 | no | — |
| 76 | #13656 | — | 2 | 2 | no | — |
| 77 | #13656 | — | 2 | 2 | no | — |
| 78 | #13655 | — | 2 | 4 | no | — |
| 79 | #13655 | — | 2 | 4 | no | — |
| 80 | #13655 | — | 2 | 4 | no | — |
| 81 | #13641 | D4 | 1 | 4 | yes | — |
| 82 | #13640 | — | 2 | 2 | no | — |
| 83 | #13636 | — | 2 | 2 | no | — |
| 84 | #13636 | C2×C4 | 1 | 2 | yes | — |
| 85 | C2×#1425 | — | 2 | 2 | no | — |
| 86 | C2×#1425 | C2×C4 | 1 | 2 | yes | — |
| 87 | #13628 | — | 2 | 1 | no | — |
| 88 | #13620 | — | 2 | 4 | no | — |
| 89 | #13620 | C2×C4 | 1 | 4 | yes | — |
| 90 | C2×#1417 | — | 2 | 4 | no | — |
| 91 | C2×#1417 | C2×C4 | 1 | 4 | yes | — |
| 92 | #13554 | — | 2 | 1 | no | — |
| 93 | #13549 | C2×C4 | 1 | 1 | yes | characteristic |
| 94 | #13549 | C2×C4 | 1 | 1 | yes | characteristic |
| 95 | #13549 | D4 | 1 | 2 | yes | — |
| 96 | #13549 | D4 | 1 | 2 | yes | — |
| 97 | C4×M64 | D4 | 1 | 2 | yes | — |
| 98 | C4×M64 | C23 | 1 | 1 | yes | characteristic |
| 99 | C4×M64 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×#1397 | D4 | 1 | 2 | yes | — |
| 101 | C2×#1397 | C23 | 1 | 1 | yes | characteristic |
| 102 | C2×#1397 | C23 | 1 | 1 | yes | characteristic |
| 103 | #13199 | — | 4 | 2 | no | — |
| 104 | #13198 | — | 4 | 2 | no | — |
| 105 | #13197 | — | 2 | 4 | no | — |
| 106 | #13195 | — | 2 | 4 | no | — |
| 107 | #12685 | — | 4 | 2 | no | — |
| 108 | #12684 | — | 4 | 2 | no | — |
| 109 | #12027 | — | 2 | 4 | no | — |
| 110 | #12026 | — | 2 | 4 | no | — |
| 111 | C2×#1373 | C23 | 1 | 4 | yes | — |
| 112 | #12002 | — | 2 | 2 | no | — |
| 113 | #11670 | — | 4 | 4 | no | — |
| 114 | #11669 | — | 4 | 4 | no | — |
| 115 | #11604 | — | 2 | 4 | no | — |
| 116 | C2×#1335 | — | 2 | 4 | no | — |
| 117 | #11409 | — | 2 | 2 | no | — |
| 118 | #11408 | — | 2 | 2 | no | — |
| 119 | #11402 | D4 | 1 | 1 | yes | characteristic |
| 120 | #11401 | D4 | 1 | 1 | yes | characteristic |
| 121 | #11399 | C23 | 1 | 1 | yes | characteristic |
| 122 | C2×#1311 | C23 | 1 | 1 | yes | characteristic |
| 123 | #7464 | — | 2 | 2 | no | — |
| 124 | #7464 | — | 2 | 2 | no | — |
| 125 | #7462 | — | 2 | 4 | no | — |
| 126 | #7388 | — | 2 | 4 | no | — |
| 127 | #7388 | — | 2 | 4 | no | — |
| 128 | #7387 | — | 2 | 8 | no | — |
| 129 | #7332 | — | 2 | 2 | no | — |
| 130 | #7332 | — | 2 | 2 | no | — |
| 131 | #7330 | — | 2 | 1 | no | — |
| 132 | #7330 | — | 2 | 1 | no | — |
| 133 | #7330 | — | 2 | 1 | no | — |
| 134 | #7330 | — | 2 | 1 | no | — |
| 135 | #3584 | — | 2 | 2 | no | — |
| 136 | #3573 | — | 4 | 2 | no | — |
| 137 | #3417 | — | 2 | 4 | no | — |
| 138 | #3416 | — | 4 | 4 | no | — |
| 139 | #3415 | — | 2 | 4 | no | — |
| 140 | #3414 | — | 2 | 2 | no | — |
| 141 | #3414 | — | 2 | 4 | no | — |
| 142 | C2×#508 | — | 2 | 4 | no | — |
| 143 | C2×#508 | C22×C4 | 1 | 4 | yes | — |
| 144 | C2×#504 | C22×C4 | 1 | 1 | yes | characteristic |
| 145 | C2×#504 | #41 | 1 | 1 | yes | characteristic |
| 146 | #2965 | — | 2 | 1 | no | — |
| 147 | #2957 | — | 2 | 4 | no | — |
| 148 | #2957 | — | 4 | 4 | no | — |
| 149 | #2956 | — | 4 | 2 | no | — |
| 150 | #2956 | — | 4 | 4 | no | — |
| 151 | #2955 | — | 4 | 2 | no | — |
| 152 | #2955 | — | 4 | 4 | no | — |
| 153 | C2×#443 | — | 2 | 4 | no | — |
| 154 | C2×#443 | — | 4 | 4 | no | — |
| 155 | #2916 | — | 2 | 2 | no | — |
| 156 | #2901 | — | 4 | 2 | no | — |
| 157 | C4×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | #2264 | — | 2 | 8 | no | — |
| 159 | #2264 | — | 2 | 4 | no | — |
| 160 | #2263 | — | 2 | 8 | no | — |
| 161 | #2263 | — | 2 | 4 | no | — |
| 162 | #2262 | — | 2 | 4 | no | — |
| 163 | #2262 | — | 2 | 4 | no | — |
| 164 | #2262 | — | 2 | 4 | no | — |
| 165 | #2262 | — | 2 | 2 | no | — |
| 166 | #2262 | — | 2 | 2 | no | — |
| 167 | #2262 | — | 2 | 2 | no | — |
| 168 | #2262 | — | 2 | 2 | no | — |
| 169 | C2×Q64 | — | 2 | 2 | no | — |
| 170 | C2×Q64 | M16 | 1 | 2 | yes | complemented |
| 171 | C2×SD64 | — | 2 | 4 | no | — |
| 172 | C2×SD64 | M16 | 1 | 4 | yes | complemented |
| 173 | C2×D32 | — | 2 | 2 | no | — |
| 174 | C2×D32 | M16 | 1 | 2 | yes | complemented |
| 175 | #2258 | — | 2 | 2 | no | — |
| 176 | #2258 | — | 2 | 2 | no | — |
| 177 | #2258 | — | 4 | 2 | no | — |
| 178 | C2×M64 | — | 2 | 1 | no | — |
| 179 | C2×M64 | C22⋊C4 | 1 | 2 | yes | — |
| 180 | C2×M64 | C22⋊C4 | 1 | 2 | yes | — |
| 181 | C2×M64 | C22×C4 | 1 | 1 | yes | characteristic |
| 182 | C2×M64 | C22×C4 | 1 | 1 | yes | characteristic |
| 183 | C22×C32 | — | 2 | 1 | no | — |
| 184 | C22×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 185 | C22×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 186 | C22×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 187 | C22×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 188 | #2179 | — | 2 | 8 | no | — |
| 189 | #2179 | — | 4 | 4 | no | — |
| 190 | #2179 | — | 4 | 4 | no | — |
| 191 | #2178 | — | 2 | 8 | no | — |
| 192 | #2178 | — | 2 | 4 | no | — |
| 193 | #2178 | — | 2 | 4 | no | — |
| 194 | #2178 | — | 2 | 4 | no | — |
| 195 | #2178 | — | 2 | 4 | no | — |
| 196 | #2178 | — | 4 | 4 | no | — |
| 197 | #2178 | — | 4 | 4 | no | — |
| 198 | #2166 | — | 4 | 4 | no | — |
| 199 | #2165 | — | 4 | 4 | no | — |
| 200 | #2164 | — | 2 | 2 | no | — |
| 201 | #2162 | — | 2 | 2 | no | — |
| 202 | #2161 | — | 2 | 4 | no | — |
| 203 | #2161 | — | 2 | 2 | no | — |
| 204 | C2×#368 | — | 2 | 4 | no | — |
| 205 | C2×#368 | C22×C4 | 1 | 4 | yes | — |
| 206 | C2×#364 | — | 2 | 4 | no | — |
| 207 | #2151 | D8 | 1 | 2 | yes | — |
| 208 | #2143 | — | 2 | 4 | no | — |
| 209 | #2143 | — | 4 | 4 | no | — |
| 210 | C2×#359 | — | 2 | 4 | no | — |
| 211 | C2×#359 | — | 4 | 4 | no | — |
| 212 | #2117 | — | 4 | 4 | no | — |
| 213 | C2×#350 | — | 4 | 4 | no | — |
| 214 | #2115 | — | 4 | 4 | no | — |
| 215 | #2115 | — | 4 | 2 | no | — |
| 216 | #2113 | — | 4 | 4 | no | — |
| 217 | #2113 | D8 | 1 | 2 | yes | — |
| 218 | #2110 | — | 4 | 2 | no | — |
| 219 | #2108 | C22×C4 | 1 | 1 | yes | characteristic |
| 220 | #2108 | C2×D4 | 1 | 2 | yes | — |
| 221 | #2108 | C2×D4 | 1 | 2 | yes | — |
| 222 | #2108 | #41 | 1 | 1 | yes | characteristic |
| 223 | C4×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C4×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C4×M32 | #41 | 1 | 2 | yes | — |
| 226 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C2×C4×C16 | C2×D4 | 1 | 2 | yes | — |
| 228 | C2×C4×C16 | C24 | 1 | 1 | yes | characteristic |
| 229 | #1455 | D8 | 1 | 2 | yes | — |
| 230 | #1453 | D8 | 1 | 2 | yes | — |
| 231 | #1451 | — | 2 | 1 | no | — |
| 232 | #1450 | C2×D4 | 1 | 1 | yes | characteristic |
| 233 | C8×M16 | — | 2 | 2 | no | — |
| 234 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | #1425 | — | 2 | 2 | no | — |
| 236 | #1425 | — | 2 | 4 | no | — |
| 237 | #1425 | — | 2 | 2 | no | — |
| 238 | C4⋊C32 | — | 2 | 4 | no | — |
| 239 | #1417 | — | 2 | 4 | no | — |
| 240 | #1417 | — | 2 | 8 | no | — |
| 241 | #1417 | — | 2 | 4 | no | — |
| 242 | C22⋊C32 | — | 2 | 4 | no | — |
| 243 | #1397 | — | 2 | 1 | no | — |
| 244 | #1397 | — | 2 | 1 | no | — |
| 245 | #1397 | C22⋊C4 | 1 | 2 | yes | — |
| 246 | #1397 | C22⋊C4 | 1 | 2 | yes | — |
| 247 | #1397 | C2×D4 | 1 | 2 | yes | — |
| 248 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 252 | #1397 | C2×D4 | 1 | 2 | yes | — |
| 253 | C4×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 254 | C4×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 255 | C4×C32 | C2×D4 | 1 | 2 | yes | — |
| 256 | C4×C32 | C2×D4 | 1 | 2 | yes | — |
| 257 | #1373 | — | 2 | 4 | no | — |
| 258 | #1373 | — | 2 | 4 | no | — |
| 259 | #1369 | — | 4 | 4 | no | — |
| 260 | #1336 | — | 4 | 8 | no | — |
| 261 | #1335 | — | 4 | 4 | no | — |
| 262 | #1335 | — | 4 | 4 | no | — |
| 263 | #1312 | — | 2 | 2 | no | — |
| 264 | #1312 | — | 2 | 2 | no | — |
| 265 | #1311 | — | 2 | 1 | no | — |
| 266 | #1311 | — | 2 | 1 | no | — |
| 267 | #1311 | — | 2 | 1 | no | — |
| 268 | C8×C16 | — | 2 | 1 | no | — |
| 269 | #585 | — | 4 | 2 | no | — |
| 270 | #578 | — | 4 | 4 | no | — |
| 271 | #577 | — | 8 | 4 | no | — |
| 272 | #576 | — | 4 | 4 | no | — |
| 273 | #575 | — | 4 | 4 | no | — |
| 274 | #575 | — | 4 | 2 | no | — |
| 275 | C2×#135 | — | 2 | 4 | no | — |
| 276 | C2×#135 | — | 4 | 4 | no | — |
| 277 | #568 | — | 4 | 2 | no | — |
| 278 | #568 | — | 4 | 4 | no | — |
| 279 | #568 | — | 8 | 4 | no | — |
| 280 | #568 | — | 16 | 4 | no | — |
| 281 | C2×#131 | — | 4 | 4 | no | — |
| 282 | C2×#131 | — | 8 | 4 | no | — |
| 283 | C2×#131 | — | 16 | 4 | no | — |
| 284 | C2×#131 | C4×D4 | 1 | 1 | yes | characteristic |
| 285 | C2×#131 | C2×D8 | 1 | 1 | yes | characteristic |
| 286 | C4×#41 | #135 | 1 | 1 | yes | characteristic |
| 287 | #510 | — | 4 | 8 | no | — |
| 288 | #510 | — | 4 | 4 | no | — |
| 289 | #509 | — | 4 | 8 | no | — |
| 290 | #509 | — | 4 | 4 | no | — |
| 291 | #508 | — | 2 | 8 | no | — |
| 292 | #508 | — | 2 | 4 | no | — |
| 293 | #508 | — | 2 | 4 | no | — |
| 294 | #508 | — | 2 | 4 | no | — |
| 295 | #508 | — | 2 | 4 | no | — |
| 296 | #508 | — | 4 | 4 | no | — |
| 297 | #508 | — | 4 | 4 | no | — |
| 298 | C2×Q32 | — | 2 | 4 | no | — |
| 299 | C2×Q32 | C2×M16 | 1 | 4 | yes | — |
| 300 | C2×SD32 | — | 2 | 4 | no | — |
| 301 | C2×SD32 | — | 4 | 4 | no | — |
| 302 | C2×D16 | — | 2 | 4 | no | — |
| 303 | C2×D16 | C2×M16 | 1 | 4 | yes | — |
| 304 | #504 | — | 2 | 2 | no | — |
| 305 | #504 | — | 2 | 2 | no | — |
| 306 | #504 | — | 4 | 2 | no | — |
| 307 | C2×M32 | — | 4 | 4 | no | — |
| 308 | C2×M32 | C4×D4 | 1 | 2 | yes | — |
| 309 | C2×M32 | C4×D4 | 1 | 1 | yes | characteristic |
| 310 | C2×M32 | C4×D4 | 1 | 1 | yes | characteristic |
| 311 | C2×M32 | #124 | 1 | 2 | yes | — |
| 312 | C2×M32 | C2×D8 | 1 | 2 | yes | — |
| 313 | C22×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 314 | C22×C16 | #121 | 1 | 2 | yes | — |
| 315 | C22×C16 | C2×D8 | 1 | 2 | yes | — |
| 316 | C22×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 317 | C22×C16 | C2×#41 | 1 | 1 | yes | characteristic |
| 318 | #446 | — | 4 | 1 | no | — |
| 319 | #444 | — | 4 | 8 | no | — |
| 320 | #444 | — | 8 | 4 | no | — |
| 321 | #444 | — | 8 | 4 | no | — |
| 322 | #443 | — | 4 | 4 | no | — |
| 323 | #443 | — | 4 | 4 | no | — |
| 324 | #443 | — | 4 | 4 | no | — |
| 325 | #443 | — | 4 | 4 | no | — |
| 326 | #443 | — | 4 | 8 | no | — |
| 327 | #443 | — | 8 | 4 | no | — |
| 328 | #443 | — | 8 | 4 | no | — |
| 329 | #436 | — | 4 | 1 | no | — |
| 330 | #435 | — | 4 | 2 | no | — |
| 331 | #431 | — | 2 | 1 | no | — |
| 332 | #431 | — | 2 | 2 | no | — |
| 333 | #430 | — | 4 | 4 | no | — |
| 334 | #430 | — | 4 | 2 | no | — |
| 335 | C2×#108 | — | 2 | 4 | no | — |
| 336 | C2×#108 | — | 4 | 4 | no | — |
| 337 | #421 | — | 4 | 4 | no | — |
| 338 | #421 | — | 8 | 4 | no | — |
| 339 | C2×#104 | — | 4 | 4 | no | — |
| 340 | C2×#104 | — | 8 | 4 | no | — |
| 341 | #405 | C4×D4 | 1 | 1 | yes | characteristic |
| 342 | #405 | #127 | 1 | 2 | yes | — |
| 343 | #405 | C2×D8 | 1 | 1 | yes | characteristic |
| 344 | #405 | #135 | 1 | 2 | yes | — |
| 345 | C4×M16 | — | 2 | 2 | no | — |
| 346 | C4×M16 | C2×D8 | 1 | 2 | yes | — |
| 347 | C4×M16 | #135 | 1 | 1 | yes | characteristic |
| 348 | C2×C4×C8 | — | 2 | 1 | no | — |
| 349 | C2×C4×C8 | #121 | 1 | 2 | yes | — |
| 350 | C2×C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 351 | Q64 | — | 2 | 4 | no | — |
| 352 | Q64 | — | 2 | 2 | no | — |
| 353 | Q64 | — | 2 | 2 | no | — |
| 354 | SD64 | — | 2 | 8 | no | — |
| 355 | SD64 | — | 2 | 4 | no | — |
| 356 | SD64 | — | 2 | 4 | no | — |
| 357 | D32 | — | 2 | 4 | no | — |
| 358 | D32 | — | 2 | 2 | no | — |
| 359 | D32 | — | 2 | 2 | no | — |
| 360 | M64 | — | 2 | 2 | no | — |
| 361 | M64 | — | 2 | 2 | no | — |
| 362 | M64 | — | 2 | 4 | no | — |
| 363 | M64 | — | 4 | 2 | no | — |
| 364 | M64 | — | 4 | 2 | no | — |
| 365 | C2×C32 | — | 2 | 2 | no | — |
| 366 | C2×C32 | — | 2 | 2 | no | — |
| 367 | C2×C32 | — | 2 | 2 | no | — |
| 368 | C2×C32 | — | 2 | 2 | no | — |
| 369 | C2×C32 | — | 2 | 2 | no | — |
| 370 | C2×C32 | — | 4 | 2 | no | — |
| 371 | C2×C32 | — | 4 | 2 | no | — |
| 372 | C2×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 373 | C2×C32 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 374 | C2×C32 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 375 | C2×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 376 | C2×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 377 | C2×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 378 | C2×C32 | C2×M16 | 1 | 2 | yes | — |
| 379 | C2×C32 | C2×M16 | 1 | 2 | yes | — |
| 380 | #368 | — | 2 | 4 | no | — |
| 381 | #368 | — | 2 | 4 | no | — |
| 382 | #368 | — | 4 | 4 | no | — |
| 383 | #364 | — | 4 | 4 | no | — |
| 384 | #364 | — | 4 | 4 | no | — |
| 385 | C4⋊C16 | — | 2 | 4 | no | — |
| 386 | #359 | — | 4 | 4 | no | — |
| 387 | #359 | — | 4 | 4 | no | — |
| 388 | #359 | — | 4 | 8 | no | — |
| 389 | #350 | — | 16 | 4 | no | — |
| 390 | #350 | — | 16 | 4 | no | — |
| 391 | #349 | — | 8 | 4 | no | — |
| 392 | #349 | — | 16 | 4 | no | — |
| 393 | C22⋊C16 | — | 2 | 4 | no | — |
| 394 | C22⋊C16 | — | 16 | 4 | no | — |
| 395 | #347 | — | 8 | 4 | no | — |
| 396 | #346 | — | 2 | 1 | no | — |
| 397 | #346 | C4×D4 | 1 | 2 | yes | — |
| 398 | #346 | #124 | 1 | 2 | yes | — |
| 399 | #346 | #127 | 1 | 2 | yes | — |
| 400 | C4×C16 | — | 2 | 1 | no | — |
| 401 | C4×C16 | — | 2 | 1 | no | — |
| 402 | C4×C16 | — | 2 | 1 | no | — |
| 403 | C4×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 404 | C4×C16 | #121 | 1 | 2 | yes | — |
| 405 | C4×C16 | #121 | 1 | 2 | yes | — |
| 406 | C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 407 | C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 408 | C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 409 | C4×C16 | C2×#41 | 1 | 1 | yes | characteristic |
| 410 | #322 | — | 2 | 2 | no | — |
| 411 | #322 | — | 2 | 2 | no | — |
| 412 | #322 | C2×D8 | 1 | 2 | yes | — |
| 413 | C82 | — | 2 | 1 | no | — |
| 414 | C82 | — | 2 | 1 | no | — |
| 415 | C82 | C2×D8 | 1 | 1 | yes | characteristic |
| 416 | C82 | C2×D8 | 1 | 1 | yes | characteristic |
| 417 | 2−1+4 | — | 8 | 4 | no | — |
| 418 | 2−1+4 | — | 8 | 2 | no | — |
| 419 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 420 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 421 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 422 | C2×#41 | — | 4 | 4 | no | — |
| 423 | C2×#41 | — | 8 | 4 | no | — |
| 424 | C2×#41 | — | 16 | 4 | no | — |
| 425 | C2×#41 | C4×D8 | 1 | 1 | yes | characteristic |
| 426 | #137 | — | 8 | 8 | no | — |
| 427 | #137 | — | 8 | 4 | no | — |
| 428 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 429 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 430 | #135 | — | 4 | 8 | no | — |
| 431 | #135 | — | 4 | 4 | no | — |
| 432 | #135 | — | 4 | 4 | no | — |
| 433 | #135 | — | 4 | 4 | no | — |
| 434 | #135 | — | 4 | 4 | no | — |
| 435 | #135 | — | 8 | 4 | no | — |
| 436 | #135 | — | 8 | 4 | no | — |
| 437 | C2×Q16 | — | 2 | 4 | no | — |
| 438 | C2×Q16 | — | 4 | 4 | no | — |
| 439 | C2×SD16 | — | 4 | 4 | no | — |
| 440 | C2×SD16 | — | 8 | 4 | no | — |
| 441 | C2×D8 | — | 2 | 4 | no | — |
| 442 | C2×D8 | — | 4 | 4 | no | — |
| 443 | #131 | — | 2 | 4 | no | — |
| 444 | #131 | — | 2 | 2 | no | — |
| 445 | #131 | — | 2 | 2 | no | — |
| 446 | #131 | — | 8 | 4 | no | — |
| 447 | #131 | — | 8 | 4 | no | — |
| 448 | #131 | — | 8 | 4 | no | — |
| 449 | #131 | — | 8 | 8 | no | — |
| 450 | #131 | — | 8 | 4 | no | — |
| 451 | #131 | — | 16 | 4 | no | — |
| 452 | #131 | — | 16 | 4 | no | — |
| 453 | #131 | — | 16 | 4 | no | — |
| 454 | #131 | — | 16 | 4 | no | — |
| 455 | #131 | — | 16 | 8 | no | — |
| 456 | C2×M16 | — | 4 | 2 | no | — |
| 457 | C2×M16 | — | 4 | 4 | no | — |
| 458 | C2×M16 | — | 8 | 4 | no | — |
| 459 | C2×M16 | — | 8 | 4 | no | — |
| 460 | C2×M16 | — | 16 | 4 | no | — |
| 461 | C2×M16 | — | 16 | 4 | no | — |
| 462 | C2×M16 | — | 16 | 8 | no | — |
| 463 | C2×M16 | C4×D8 | 1 | 2 | yes | — |
| 464 | C2×M16 | C4×D8 | 1 | 1 | yes | characteristic |
| 465 | C2×M16 | C4×D8 | 1 | 1 | yes | characteristic |
| 466 | C2×M16 | #493 | 1 | 2 | yes | — |
| 467 | C22×C8 | — | 4 | 1 | no | — |
| 468 | C22×C8 | — | 8 | 4 | no | — |
| 469 | C22×C8 | — | 16 | 4 | no | — |
| 470 | C22×C8 | #390 | 1 | 2 | yes | — |
| 471 | C22×C8 | #466 | 1 | 2 | yes | — |
| 472 | C22×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 473 | C22×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 474 | C4×Q8 | — | 2 | 1 | no | — |
| 475 | C4×D4 | — | 2 | 2 | no | — |
| 476 | C4×D4 | — | 2 | 1 | no | — |
| 477 | #117 | C4×D8 | 1 | 1 | yes | characteristic |
| 478 | #117 | #495 | 1 | 2 | yes | — |
| 479 | C2×C42 | #466 | 1 | 2 | yes | — |
| 480 | C2×C42 | C2×#135 | 1 | 1 | yes | characteristic |
| 481 | Q32 | — | 2 | 4 | no | — |
| 482 | Q32 | — | 2 | 4 | no | — |
| 483 | Q32 | — | 4 | 4 | no | — |
| 484 | SD32 | — | 4 | 8 | no | — |
| 485 | SD32 | — | 4 | 4 | no | — |
| 486 | SD32 | — | 4 | 4 | no | — |
| 487 | D16 | — | 2 | 4 | no | — |
| 488 | D16 | — | 2 | 4 | no | — |
| 489 | D16 | — | 4 | 4 | no | — |
| 490 | M32 | — | 2 | 2 | no | — |
| 491 | M32 | — | 2 | 2 | no | — |
| 492 | M32 | — | 2 | 4 | no | — |
| 493 | M32 | — | 2 | 4 | no | — |
| 494 | M32 | — | 4 | 2 | no | — |
| 495 | M32 | — | 8 | 4 | no | — |
| 496 | M32 | — | 8 | 4 | no | — |
| 497 | C2×C16 | — | 2 | 2 | no | — |
| 498 | C2×C16 | — | 2 | 2 | no | — |
| 499 | C2×C16 | — | 2 | 2 | no | — |
| 500 | C2×C16 | — | 2 | 4 | no | — |
| 501 | C2×C16 | — | 2 | 2 | no | — |
| 502 | C2×C16 | — | 2 | 2 | no | — |
| 503 | C2×C16 | — | 4 | 2 | no | — |
| 504 | C2×C16 | — | 8 | 4 | no | — |
| 505 | C2×C16 | #390 | 1 | 2 | yes | — |
| 506 | C2×C16 | #390 | 1 | 2 | yes | — |
| 507 | C2×C16 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 508 | C2×C16 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 509 | C2×C16 | C2×#121 | 1 | 1 | yes | characteristic |
| 510 | C2×C16 | C2×#124 | 1 | 1 | yes | characteristic |
| 511 | C2×C16 | C22×M16 | 1 | 2 | yes | — |
| 512 | C2×C16 | #568 | 1 | 2 | yes | — |
| 513 | #108 | — | 4 | 4 | no | — |
| 514 | #108 | — | 4 | 4 | no | — |
| 515 | #108 | — | 8 | 4 | no | — |
| 516 | C4⋊C8 | — | 4 | 2 | no | — |
| 517 | C4⋊C8 | — | 4 | 1 | no | — |
| 518 | #104 | — | 8 | 4 | no | — |
| 519 | #104 | — | 8 | 8 | no | — |
| 520 | #104 | — | 8 | 4 | no | — |
| 521 | C22⋊C8 | — | 4 | 1 | no | — |
| 522 | C22⋊C8 | — | 4 | 2 | no | — |
| 523 | #97 | — | 4 | 2 | no | — |
| 524 | #97 | C4×D8 | 1 | 2 | yes | — |
| 525 | #97 | #493 | 1 | 2 | yes | — |
| 526 | #97 | #495 | 1 | 2 | yes | — |
| 527 | C4×C8 | — | 2 | 1 | no | — |
| 528 | C4×C8 | — | 2 | 1 | no | — |
| 529 | C4×C8 | — | 2 | 2 | no | — |
| 530 | C4×C8 | — | 4 | 1 | no | — |
| 531 | C4×C8 | #390 | 1 | 2 | yes | — |
| 532 | C4×C8 | #466 | 1 | 2 | yes | — |
| 533 | C4×C8 | #466 | 1 | 2 | yes | — |
| 534 | C4×C8 | C2×#121 | 1 | 1 | yes | characteristic |
| 535 | C4×C8 | C2×#127 | 1 | 1 | yes | characteristic |
| 536 | C4×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 537 | C4×C8 | C2×#135 | 1 | 1 | yes | characteristic |
| 538 | C32 | — | 2 | 2 | no | — |
| 539 | C32 | — | 2 | 1 | no | — |
| 540 | C32 | — | 2 | 1 | no | — |
| 541 | C32 | — | 2 | 2 | no | — |
| 542 | C32 | — | 4 | 2 | no | — |
| 543 | C32 | — | 4 | 2 | no | — |
| 544 | C32 | #407 | 1 | 1 | yes | characteristic |
| 545 | C32 | #407 | 1 | 1 | yes | characteristic |
| 546 | C32 | #407 | 1 | 2 | yes | — |
| 547 | #41 | — | 2 | 2 | no | — |
| 548 | #41 | — | 2 | 2 | no | — |
| 549 | #41 | — | 8 | 8 | no | — |
| 550 | #41 | — | 8 | 4 | no | — |
| 551 | #41 | — | 8 | 4 | no | — |
| 552 | #41 | — | 8 | 4 | no | — |
| 553 | #41 | — | 8 | 4 | no | — |
| 554 | #41 | — | 16 | 4 | no | — |
| 555 | #41 | — | 16 | 8 | no | — |
| 556 | #41 | — | 16 | 4 | no | — |
| 557 | #41 | — | 16 | 4 | no | — |
| 558 | #41 | — | 16 | 4 | no | — |
| 559 | C2×Q8 | — | 4 | 4 | no | — |
| 560 | C2×Q8 | — | 8 | 4 | no | — |
| 561 | C2×Q8 | — | 16 | 4 | no | — |
| 562 | C2×Q8 | #2179 | 1 | 1 | yes | characteristic |
| 563 | C2×D4 | — | 4 | 4 | no | — |
| 564 | C2×D4 | — | 8 | 4 | no | — |
| 565 | C2×D4 | — | 8 | 4 | no | — |
| 566 | C2×D4 | — | 16 | 4 | no | — |
| 567 | C2×D4 | — | 16 | 8 | no | — |
| 568 | C2×D4 | — | 16 | 4 | no | — |
| 569 | C2×D4 | #2179 | 1 | 1 | yes | characteristic |
| 570 | C2×D4 | #2179 | 1 | 2 | yes | — |
| 571 | C22×C4 | — | 2 | 1 | no | — |
| 572 | C22×C4 | — | 2 | 2 | no | — |
| 573 | C22×C4 | — | 8 | 4 | no | — |
| 574 | C22×C4 | — | 16 | 4 | no | — |
| 575 | C22×C4 | #1970 | 1 | 2 | yes | — |
| 576 | C22×C4 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 577 | Q16 | — | 4 | 4 | no | — |
| 578 | Q16 | — | 4 | 4 | no | — |
| 579 | Q16 | — | 8 | 4 | no | — |
| 580 | SD16 | — | 8 | 8 | no | — |
| 581 | SD16 | — | 8 | 4 | no | — |
| 582 | SD16 | — | 8 | 4 | no | — |
| 583 | D8 | — | 4 | 4 | no | — |
| 584 | D8 | — | 4 | 4 | no | — |
| 585 | D8 | — | 8 | 4 | no | — |
| 586 | M16 | — | 2 | 2 | no | — |
| 587 | M16 | — | 2 | 2 | no | — |
| 588 | M16 | — | 2 | 4 | no | — |
| 589 | M16 | — | 2 | 4 | no | — |
| 590 | M16 | — | 8 | 4 | no | — |
| 591 | M16 | — | 8 | 4 | no | — |
| 592 | M16 | — | 16 | 8 | no | — |
| 593 | M16 | — | 16 | 2 | no | — |
| 594 | M16 | — | 16 | 4 | no | — |
| 595 | M16 | — | 16 | 4 | no | — |
| 596 | M16 | — | 16 | 4 | no | — |
| 597 | C2×C8 | — | 2 | 4 | no | — |
| 598 | C2×C8 | — | 2 | 2 | no | — |
| 599 | C2×C8 | — | 2 | 2 | no | — |
| 600 | C2×C8 | — | 4 | 1 | no | — |
| 601 | C2×C8 | — | 4 | 1 | no | — |
| 602 | C2×C8 | — | 4 | 2 | no | — |
| 603 | C2×C8 | — | 8 | 4 | no | — |
| 604 | C2×C8 | — | 16 | 8 | no | — |
| 605 | C2×C8 | — | 16 | 1 | no | — |
| 606 | C2×C8 | — | 16 | 4 | no | — |
| 607 | C2×C8 | — | 16 | 4 | no | — |
| 608 | C2×C8 | — | 16 | 4 | no | — |
| 609 | C2×C8 | #1970 | 1 | 2 | yes | — |
| 610 | C2×C8 | #1970 | 1 | 2 | yes | — |
| 611 | C2×C8 | C2×#390 | 1 | 1 | yes | characteristic |
| 612 | C2×C8 | D4×M16 | 1 | 2 | yes | — |
| 613 | C2×C8 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 614 | C2×C8 | #2957 | 1 | 2 | yes | — |
| 615 | C2×C8 | C2×#466 | 1 | 1 | yes | characteristic |
| 616 | C2×C8 | C2×#493 | 1 | 1 | yes | characteristic |
| 617 | C2×C8 | #3415 | 1 | 4 | yes | — |
| 618 | C4⋊C4 | — | 2 | 1 | no | — |
| 619 | C4⋊C4 | — | 2 | 2 | no | — |
| 620 | C22⋊C4 | — | 2 | 1 | no | — |
| 621 | C22⋊C4 | — | 2 | 2 | no | — |
| 622 | C42 | — | 2 | 1 | no | — |
| 623 | C42 | — | 2 | 2 | no | — |
| 624 | C42 | #1970 | 1 | 2 | yes | — |
| 625 | C42 | C2×#466 | 1 | 1 | yes | characteristic |
| 626 | C42 | C2×#495 | 1 | 1 | yes | characteristic |
| 627 | C16 | — | 2 | 2 | no | — |
| 628 | C16 | — | 2 | 1 | no | — |
| 629 | C16 | — | 2 | 1 | no | — |
| 630 | C16 | — | 2 | 2 | no | — |
| 631 | C16 | — | 4 | 2 | no | — |
| 632 | C16 | — | 4 | 2 | no | — |
| 633 | C16 | — | 16 | 4 | no | — |
| 634 | C16 | C2×#407 | 1 | 1 | yes | characteristic |
| 635 | C16 | #2879 | 1 | 1 | yes | characteristic |
| 636 | C16 | D4×M16 | 1 | 2 | yes | — |
| 637 | C23 | — | 8 | 4 | no | — |
| 638 | C23 | — | 16 | 4 | no | — |
| 639 | C23 | #13242 | 1 | 2 | yes | — |
| 640 | C23 | C2×#2179 | 1 | 1 | yes | characteristic |
| 641 | Q8 | — | 2 | 2 | no | — |
| 642 | Q8 | — | 8 | 4 | no | — |
| 643 | Q8 | — | 8 | 4 | no | — |
| 644 | Q8 | — | 16 | 4 | no | — |
| 645 | D4 | — | 2 | 4 | no | — |
| 646 | D4 | — | 2 | 2 | no | — |
| 647 | D4 | — | 8 | 4 | no | — |
| 648 | D4 | — | 8 | 4 | no | — |
| 649 | D4 | — | 16 | 4 | no | — |
| 650 | D4 | — | 16 | 8 | no | — |
| 651 | D4 | — | 16 | 4 | no | — |
| 652 | D4 | — | 16 | 4 | no | — |
| 653 | C2×C4 | — | 2 | 2 | no | — |
| 654 | C2×C4 | — | 2 | 2 | no | — |
| 655 | C2×C4 | — | 2 | 1 | no | — |
| 656 | C2×C4 | — | 2 | 1 | no | — |
| 657 | C2×C4 | — | 2 | 2 | no | — |
| 658 | C2×C4 | — | 8 | 1 | no | — |
| 659 | C2×C4 | — | 8 | 2 | no | — |
| 660 | C2×C4 | — | 8 | 4 | no | — |
| 661 | C2×C4 | — | 16 | 8 | no | — |
| 662 | C2×C4 | — | 16 | 4 | no | — |
| 663 | C2×C4 | — | 16 | 4 | no | — |
| 664 | C2×C4 | — | 16 | 4 | no | — |
| 665 | C2×C4 | #13242 | 1 | 2 | yes | — |
| 666 | C2×C4 | M16×D8 | 1 | 2 | yes | — |
| 667 | C2×C4 | C2×#1970 | 1 | 1 | yes | characteristic |
| 668 | C2×C4 | #33456 | 1 | 2 | yes | — |
| 669 | C2×C4 | C2×#2179 | 1 | 1 | yes | characteristic |
| 670 | C8 | — | 2 | 2 | no | — |
| 671 | C8 | — | 2 | 2 | no | — |
| 672 | C8 | — | 8 | 1 | no | — |
| 673 | C8 | — | 8 | 1 | no | — |
| 674 | C8 | — | 8 | 2 | no | — |
| 675 | C8 | — | 16 | 4 | no | — |
| 676 | C8 | M16×D8 | 1 | 2 | yes | — |
| 677 | C8 | #21190 | 1 | 1 | yes | characteristic |
| 678 | C8 | #21240 | 1 | 1 | yes | characteristic |
| 679 | C8 | #33607 | 1 | 2 | yes | — |
| 680 | C8 | #33720 | 1 | 2 | yes | — |
| 681 | C22 | — | 2 | 2 | no | — |
| 682 | C22 | — | 4 | 1 | no | — |
| 683 | C22 | — | 4 | 2 | no | — |
| 684 | C22 | — | 16 | 4 | no | — |
| 685 | C22 | — | 32 | 4 | no | — |
| 686 | C22 | — | 64 | 4 | no | — |
| 687 | C22 | #484093 | 1 | 2 | yes | — |
| 688 | C22 | C2×#13242 | 1 | 1 | yes | characteristic |
| 689 | C4 | — | 2 | 2 | no | — |
| 690 | C4 | — | 4 | 1 | no | — |
| 691 | C4 | — | 4 | 1 | no | — |
| 692 | C4 | — | 4 | 2 | no | — |
| 693 | C4 | — | 16 | 4 | no | — |
| 694 | C4 | #204348 | 1 | 1 | yes | characteristic |
| 695 | C4 | #484093 | 1 | 2 | yes | — |
| 696 | C4 | #495215 | 1 | 1 | yes | characteristic |
| 697 | C2 | — | 2 | 1 | no | — |
| 698 | C2 | — | 2 | 2 | no | — |
| 699 | C2 | — | 4 | 2 | no | — |
| 700 | C2 | — | 32 | 4 | no | — |
| 701 | C2 | #72320212 | 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