← #72226838
Subgroups — #72226838
Order 4096.
1580 conjugacy classes of subgroups.
The subgroup lattice has 680 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72226834 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72225607 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72225606 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72225604 | — | 2 | 2 | no | — |
| 5 | #72225603 | — | 2 | 2 | no | — |
| 6 | #72225602 | — | 2 | 2 | no | — |
| 7 | #72225601 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72225599 | C22 | 1 | 2 | yes | — |
| 9 | #72225598 | C2 | 1 | 2 | yes | maximal |
| 10 | #72225596 | — | 2 | 2 | no | — |
| 11 | #72225595 | — | 2 | 2 | no | — |
| 12 | #72225594 | — | 2 | 2 | no | — |
| 13 | #72225564 | — | 2 | 2 | no | — |
| 14 | #72225556 | — | 2 | 2 | no | — |
| 15 | #72225401 | C22 | 1 | 2 | yes | — |
| 16 | #72225366 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #72225363 | C22 | 1 | 2 | yes | — |
| 18 | #72225362 | C22 | 1 | 1 | yes | characteristic |
| 19 | #72225360 | C2 | 1 | 1 | yes | maximal, characteristic |
| 20 | #72225356 | C4 | 1 | 4 | yes | complemented |
| 21 | #72225355 | C4 | 1 | 4 | yes | complemented |
| 22 | #72225353 | C22 | 1 | 2 | yes | — |
| 23 | #72225352 | C22 | 1 | 1 | yes | characteristic |
| 24 | #72225342 | C22 | 1 | 2 | yes | — |
| 25 | #72225341 | C22 | 1 | 2 | yes | — |
| 26 | #72225313 | C22 | 1 | 1 | yes | characteristic |
| 27 | #72225308 | C22 | 1 | 1 | yes | characteristic |
| 28 | #72225194 | C2 | 1 | 2 | yes | maximal, complemented |
| 29 | #72216560 | C22 | 1 | 2 | yes | — |
| 30 | #72216534 | C22 | 1 | 2 | yes | — |
| 31 | C2×#93751 | C22 | 1 | 2 | yes | — |
| 32 | #72216413 | C22 | 1 | 2 | yes | — |
| 33 | #72216379 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 34 | #72216298 | C22 | 1 | 2 | yes | — |
| 35 | #72216298 | C22 | 1 | 2 | yes | — |
| 36 | #72216273 | C22 | 1 | 2 | yes | — |
| 37 | #72216267 | C22 | 1 | 2 | yes | — |
| 38 | #72216239 | C22 | 1 | 1 | yes | characteristic |
| 39 | C16×M64 | C22 | 1 | 1 | yes | characteristic |
| 40 | #72216197 | C22 | 1 | 1 | yes | characteristic |
| 41 | #512779 | — | 4 | 2 | no | — |
| 42 | #512773 | D4 | 1 | 1 | yes | characteristic |
| 43 | #512751 | — | 2 | 2 | no | — |
| 44 | #512724 | — | 4 | 2 | no | — |
| 45 | #497894 | — | 2 | 2 | no | — |
| 46 | #497891 | — | 2 | 2 | no | — |
| 47 | #497857 | — | 2 | 2 | no | — |
| 48 | #497855 | — | 2 | 2 | no | — |
| 49 | C2×#12046 | C23 | 1 | 2 | yes | — |
| 50 | #152874 | — | 2 | 2 | no | — |
| 51 | #152873 | — | 2 | 2 | no | — |
| 52 | #152861 | — | 4 | 2 | no | — |
| 53 | #152447 | — | 4 | 2 | no | — |
| 54 | #152446 | — | 4 | 2 | no | — |
| 55 | #152432 | — | 4 | 2 | no | — |
| 56 | #152431 | — | 4 | 2 | no | — |
| 57 | #152407 | — | 2 | 2 | no | — |
| 58 | #152407 | — | 2 | 2 | no | — |
| 59 | #152407 | — | 2 | 2 | no | — |
| 60 | #152407 | — | 2 | 2 | no | — |
| 61 | #152301 | — | 4 | 2 | no | — |
| 62 | #152283 | — | 2 | 2 | no | — |
| 63 | #152282 | — | 2 | 2 | no | — |
| 64 | #151998 | D4 | 1 | 1 | yes | characteristic |
| 65 | #151989 | — | 2 | 2 | no | — |
| 66 | #151082 | Q8 | 1 | 4 | yes | — |
| 67 | #151081 | C2×C4 | 1 | 4 | yes | — |
| 68 | #151073 | — | 2 | 4 | no | — |
| 69 | #151072 | C2×C4 | 1 | 8 | yes | complemented |
| 70 | #151040 | D4 | 1 | 1 | yes | characteristic |
| 71 | #151035 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×#7459 | C23 | 1 | 2 | yes | — |
| 73 | C2×#7459 | C23 | 1 | 2 | yes | — |
| 74 | #150067 | D4 | 1 | 2 | yes | — |
| 75 | #150051 | — | 2 | 2 | no | — |
| 76 | C8×M64 | C23 | 1 | 1 | yes | characteristic |
| 77 | C8×M64 | C23 | 1 | 1 | yes | characteristic |
| 78 | #140438 | — | 2 | 2 | no | — |
| 79 | #140437 | — | 2 | 2 | no | — |
| 80 | #136326 | — | 4 | 2 | no | — |
| 81 | #136324 | — | 4 | 2 | no | — |
| 82 | #135796 | — | 4 | 1 | no | — |
| 83 | #135781 | C23 | 1 | 2 | yes | — |
| 84 | #135778 | — | 4 | 1 | no | — |
| 85 | #135778 | C23 | 1 | 2 | yes | — |
| 86 | #134971 | — | 2 | 2 | no | — |
| 87 | #134970 | — | 2 | 2 | no | — |
| 88 | #129142 | C23 | 1 | 2 | yes | — |
| 89 | C2×C162 | C23 | 1 | 1 | yes | characteristic |
| 90 | #94366 | — | 2 | 2 | no | — |
| 91 | #94365 | — | 2 | 2 | no | — |
| 92 | #94364 | — | 2 | 2 | no | — |
| 93 | #94364 | — | 2 | 2 | no | — |
| 94 | #94053 | D4 | 1 | 2 | yes | — |
| 95 | #94041 | — | 2 | 2 | no | — |
| 96 | #93885 | — | 2 | 2 | no | — |
| 97 | #93882 | C2×C4 | 1 | 4 | yes | complemented |
| 98 | #93751 | C2×C4 | 1 | 4 | yes | complemented |
| 99 | #93751 | C2×C4 | 1 | 4 | yes | complemented |
| 100 | #93664 | C2×C4 | 1 | 2 | yes | complemented |
| 101 | C16×C32 | C2×C4 | 1 | 2 | yes | complemented |
| 102 | #33981 | D8 | 1 | 1 | yes | characteristic |
| 103 | #33974 | — | 4 | 2 | no | — |
| 104 | #33465 | — | 4 | 2 | no | — |
| 105 | C2×#2178 | C2×D4 | 1 | 2 | yes | — |
| 106 | #33460 | — | 4 | 2 | no | — |
| 107 | C2×#2170 | — | 2 | 2 | no | — |
| 108 | #33414 | — | 4 | 2 | no | — |
| 109 | #33411 | — | 4 | 2 | no | — |
| 110 | #22694 | — | 4 | 2 | no | — |
| 111 | #22692 | — | 4 | 2 | no | — |
| 112 | #13658 | — | 8 | 4 | no | — |
| 113 | #13657 | — | 8 | 4 | no | — |
| 114 | #13656 | Q16 | 1 | 4 | yes | — |
| 115 | #13655 | C4⋊C4 | 1 | 4 | yes | — |
| 116 | #13648 | — | 4 | 4 | no | — |
| 117 | #13647 | — | 2 | 8 | no | — |
| 118 | #13638 | — | 4 | 2 | no | — |
| 119 | #13638 | — | 8 | 4 | no | — |
| 120 | #13638 | D8 | 1 | 2 | yes | — |
| 121 | C2×#1426 | — | 4 | 2 | no | — |
| 122 | C2×#1426 | — | 4 | 2 | no | — |
| 123 | C2×#1426 | — | 4 | 2 | no | — |
| 124 | C2×#1426 | — | 4 | 2 | no | — |
| 125 | C2×#1426 | — | 4 | 2 | no | — |
| 126 | C2×#1426 | — | 8 | 2 | no | — |
| 127 | C2×#1426 | — | 8 | 2 | no | — |
| 128 | C2×#1426 | — | 8 | 4 | no | — |
| 129 | #13636 | D8 | 1 | 1 | yes | characteristic |
| 130 | C2×#1422 | — | 2 | 2 | no | — |
| 131 | C2×#1422 | — | 2 | 2 | no | — |
| 132 | #13625 | — | 4 | 2 | no | — |
| 133 | C2×#1418 | — | 4 | 2 | no | — |
| 134 | #13620 | D8 | 1 | 2 | yes | — |
| 135 | #13558 | — | 4 | 2 | no | — |
| 136 | #13551 | — | 4 | 2 | no | — |
| 137 | C4×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C4×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C4×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C4×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | #13182 | — | 4 | 2 | no | — |
| 142 | #13181 | — | 4 | 2 | no | — |
| 143 | #13173 | — | 4 | 2 | no | — |
| 144 | #13172 | — | 4 | 2 | no | — |
| 145 | #12947 | — | 8 | 2 | no | — |
| 146 | #12946 | — | 8 | 2 | no | — |
| 147 | #12927 | — | 8 | 2 | no | — |
| 148 | #12926 | — | 8 | 2 | no | — |
| 149 | #12909 | — | 2 | 2 | no | — |
| 150 | #12909 | — | 2 | 2 | no | — |
| 151 | #12906 | — | 2 | 2 | no | — |
| 152 | #12906 | — | 2 | 2 | no | — |
| 153 | #12906 | — | 8 | 2 | no | — |
| 154 | #12843 | — | 4 | 2 | no | — |
| 155 | #12841 | — | 4 | 2 | no | — |
| 156 | #12822 | — | 4 | 2 | no | — |
| 157 | #12821 | — | 4 | 2 | no | — |
| 158 | #12670 | C2×D4 | 1 | 2 | yes | — |
| 159 | #12664 | — | 2 | 2 | no | — |
| 160 | #12046 | — | 2 | 2 | no | — |
| 161 | #12046 | — | 2 | 2 | no | — |
| 162 | #12046 | C22×C4 | 1 | 4 | yes | — |
| 163 | #12046 | C2×Q8 | 1 | 4 | yes | — |
| 164 | #12023 | — | 8 | 2 | no | — |
| 165 | C2×#1373 | C2×D4 | 1 | 2 | yes | — |
| 166 | C2×#1373 | C2×D4 | 1 | 2 | yes | — |
| 167 | C2×#1335 | — | 2 | 2 | no | — |
| 168 | C2×C8×C16 | — | 2 | 1 | no | — |
| 169 | C2×C8×C16 | C24 | 1 | 1 | yes | characteristic |
| 170 | #8823 | — | 2 | 2 | no | — |
| 171 | #8818 | — | 2 | 2 | no | — |
| 172 | #7479 | — | 4 | 2 | no | — |
| 173 | #7477 | — | 4 | 2 | no | — |
| 174 | #7476 | — | 4 | 2 | no | — |
| 175 | #7476 | D8 | 1 | 1 | yes | characteristic |
| 176 | #7475 | D8 | 1 | 1 | yes | characteristic |
| 177 | #7474 | — | 4 | 2 | no | — |
| 178 | #7469 | — | 4 | 2 | no | — |
| 179 | #7464 | — | 2 | 2 | no | — |
| 180 | #7462 | C4⋊C4 | 1 | 4 | yes | — |
| 181 | #7459 | — | 2 | 2 | no | — |
| 182 | #7459 | — | 2 | 2 | no | — |
| 183 | #7459 | — | 2 | 2 | no | — |
| 184 | #7459 | C22×C4 | 1 | 4 | yes | — |
| 185 | #7387 | C4⋊C4 | 1 | 8 | yes | — |
| 186 | #7381 | — | 2 | 8 | no | — |
| 187 | #7329 | C2×Q8 | 1 | 2 | yes | — |
| 188 | #7329 | #41 | 1 | 2 | yes | — |
| 189 | C8×C32 | C22×C4 | 1 | 2 | yes | — |
| 190 | C8×C32 | C22×C4 | 1 | 2 | yes | — |
| 191 | #7270 | — | 4 | 2 | no | — |
| 192 | #7269 | — | 4 | 2 | no | — |
| 193 | #7179 | — | 2 | 2 | no | — |
| 194 | C162 | — | 2 | 1 | no | — |
| 195 | C162 | C22×C4 | 1 | 1 | yes | characteristic |
| 196 | C162 | C22×C4 | 1 | 1 | yes | characteristic |
| 197 | C2×#508 | C2×D8 | 1 | 2 | yes | — |
| 198 | C2×#504 | — | 4 | 2 | no | — |
| 199 | #2957 | — | 8 | 2 | no | — |
| 200 | C2×#443 | — | 2 | 2 | no | — |
| 201 | #2951 | — | 8 | 2 | no | — |
| 202 | #2916 | — | 8 | 2 | no | — |
| 203 | #2913 | — | 8 | 2 | no | — |
| 204 | #2264 | SD32 | 1 | 4 | yes | — |
| 205 | #2263 | SD32 | 1 | 4 | yes | — |
| 206 | #2262 | #107 | 1 | 4 | yes | — |
| 207 | #2258 | — | 4 | 8 | no | — |
| 208 | #2258 | — | 8 | 4 | no | — |
| 209 | C2×M64 | — | 2 | 1 | no | — |
| 210 | C2×M64 | — | 2 | 1 | no | — |
| 211 | C2×M64 | — | 4 | 2 | no | — |
| 212 | C2×M64 | — | 4 | 2 | no | — |
| 213 | C2×M64 | — | 8 | 4 | no | — |
| 214 | C2×M64 | C2×D8 | 1 | 1 | yes | characteristic |
| 215 | C2×M64 | C2×D8 | 1 | 1 | yes | characteristic |
| 216 | C2×M64 | C2×D8 | 1 | 1 | yes | characteristic |
| 217 | C2×M64 | C2×D8 | 1 | 1 | yes | characteristic |
| 218 | #2179 | — | 8 | 4 | no | — |
| 219 | #2178 | — | 2 | 2 | no | — |
| 220 | #2178 | — | 2 | 2 | no | — |
| 221 | #2178 | — | 16 | 2 | no | — |
| 222 | #2178 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 223 | #2178 | C2×Q16 | 1 | 4 | yes | — |
| 224 | #2177 | — | 8 | 2 | no | — |
| 225 | #2176 | — | 8 | 2 | no | — |
| 226 | C4×SD32 | — | 16 | 2 | no | — |
| 227 | #2170 | — | 2 | 4 | no | — |
| 228 | #2170 | — | 2 | 4 | no | — |
| 229 | #2170 | — | 4 | 2 | no | — |
| 230 | #2170 | — | 4 | 2 | no | — |
| 231 | #2161 | — | 8 | 2 | no | — |
| 232 | #2161 | — | 16 | 2 | no | — |
| 233 | C2×#368 | — | 4 | 2 | no | — |
| 234 | C2×#368 | — | 4 | 2 | no | — |
| 235 | C2×#368 | — | 4 | 2 | no | — |
| 236 | C2×#368 | — | 4 | 2 | no | — |
| 237 | C2×#368 | — | 8 | 4 | no | — |
| 238 | C2×#368 | C2×D8 | 1 | 2 | yes | — |
| 239 | C2×#368 | C2×D8 | 1 | 2 | yes | — |
| 240 | #2159 | — | 8 | 2 | no | — |
| 241 | #2159 | — | 16 | 2 | no | — |
| 242 | #2158 | — | 8 | 2 | no | — |
| 243 | #2158 | C2×D8 | 1 | 2 | yes | — |
| 244 | C2×#367 | — | 4 | 2 | no | — |
| 245 | C2×#367 | — | 4 | 2 | no | — |
| 246 | C2×#367 | — | 4 | 2 | no | — |
| 247 | C2×#367 | — | 4 | 2 | no | — |
| 248 | C2×#367 | — | 8 | 2 | no | — |
| 249 | C2×#367 | — | 16 | 4 | no | — |
| 250 | C2×#364 | — | 2 | 2 | no | — |
| 251 | C2×#364 | — | 2 | 2 | no | — |
| 252 | #2143 | — | 8 | 2 | no | — |
| 253 | C2×#359 | — | 2 | 2 | no | — |
| 254 | #2139 | — | 8 | 2 | no | — |
| 255 | C2×#350 | — | 4 | 2 | no | — |
| 256 | #2108 | — | 4 | 2 | no | — |
| 257 | C2×C4×C16 | — | 2 | 2 | no | — |
| 258 | C2×C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | #1953 | — | 8 | 2 | no | — |
| 261 | #1952 | — | 8 | 2 | no | — |
| 262 | #1861 | — | 16 | 2 | no | — |
| 263 | #1859 | — | 16 | 2 | no | — |
| 264 | #1848 | — | 4 | 2 | no | — |
| 265 | #1845 | — | 4 | 2 | no | — |
| 266 | #1845 | — | 8 | 2 | no | — |
| 267 | #1816 | — | 8 | 2 | no | — |
| 268 | #1814 | — | 8 | 2 | no | — |
| 269 | #1772 | — | 2 | 2 | no | — |
| 270 | #1567 | — | 8 | 2 | no | — |
| 271 | C2×C82 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 272 | #1426 | — | 2 | 4 | no | — |
| 273 | #1426 | — | 8 | 2 | no | — |
| 274 | #1426 | — | 8 | 2 | no | — |
| 275 | #1426 | — | 8 | 4 | no | — |
| 276 | #1426 | — | 8 | 4 | no | — |
| 277 | #1426 | — | 8 | 4 | no | — |
| 278 | #1426 | — | 16 | 2 | no | — |
| 279 | #1426 | — | 16 | 2 | no | — |
| 280 | #1426 | — | 16 | 4 | no | — |
| 281 | #1426 | — | 16 | 4 | no | — |
| 282 | #1425 | #107 | 1 | 4 | yes | — |
| 283 | #1422 | — | 2 | 4 | no | — |
| 284 | #1422 | — | 4 | 2 | no | — |
| 285 | #1422 | — | 4 | 2 | no | — |
| 286 | #1422 | — | 4 | 2 | no | — |
| 287 | #1420 | — | 8 | 2 | no | — |
| 288 | #1419 | — | 8 | 2 | no | — |
| 289 | #1418 | — | 8 | 4 | no | — |
| 290 | #1417 | #107 | 1 | 8 | yes | — |
| 291 | #1401 | — | 4 | 8 | no | — |
| 292 | #1398 | — | 8 | 4 | no | — |
| 293 | #1397 | — | 2 | 1 | no | — |
| 294 | #1397 | — | 2 | 1 | no | — |
| 295 | #1397 | C2×Q16 | 1 | 2 | yes | — |
| 296 | #1397 | #135 | 1 | 2 | yes | — |
| 297 | C4×C32 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 298 | C4×C32 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 299 | C4×C32 | C4×D4 | 1 | 2 | yes | — |
| 300 | C4×C32 | C4×D4 | 1 | 2 | yes | — |
| 301 | #1389 | — | 8 | 2 | no | — |
| 302 | #1388 | — | 8 | 2 | no | — |
| 303 | #1387 | — | 8 | 2 | no | — |
| 304 | #1387 | — | 8 | 2 | no | — |
| 305 | #1382 | — | 2 | 2 | no | — |
| 306 | #1379 | — | 4 | 2 | no | — |
| 307 | #1373 | — | 2 | 2 | no | — |
| 308 | #1373 | — | 2 | 2 | no | — |
| 309 | #1373 | — | 2 | 2 | no | — |
| 310 | #1373 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 311 | #1372 | — | 16 | 4 | no | — |
| 312 | #1335 | — | 2 | 4 | no | — |
| 313 | #1335 | — | 2 | 4 | no | — |
| 314 | C8×C16 | — | 2 | 2 | no | — |
| 315 | C8×C16 | — | 2 | 1 | no | — |
| 316 | C8×C16 | — | 2 | 1 | no | — |
| 317 | C8×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 318 | C8×C16 | C22×Q8 | 1 | 1 | yes | characteristic |
| 319 | C8×C16 | C2×#41 | 1 | 1 | yes | characteristic |
| 320 | C8×C16 | 2−1+4 | 1 | 1 | yes | characteristic |
| 321 | C2×#135 | — | 2 | 2 | no | — |
| 322 | #568 | — | 16 | 2 | no | — |
| 323 | C2×#131 | — | 4 | 2 | no | — |
| 324 | #520 | — | 16 | 2 | no | — |
| 325 | #508 | — | 2 | 2 | no | — |
| 326 | #508 | — | 2 | 2 | no | — |
| 327 | #508 | C2×#107 | 1 | 4 | yes | — |
| 328 | #508 | C2×SD32 | 1 | 4 | yes | — |
| 329 | C2×Q32 | C2×SD32 | 1 | 2 | yes | — |
| 330 | C2×SD32 | — | 2 | 2 | no | — |
| 331 | C2×D16 | C2×SD32 | 1 | 2 | yes | — |
| 332 | #504 | — | 4 | 4 | no | — |
| 333 | #504 | — | 4 | 4 | no | — |
| 334 | #504 | — | 8 | 2 | no | — |
| 335 | #504 | — | 8 | 2 | no | — |
| 336 | C2×M32 | — | 4 | 2 | no | — |
| 337 | C2×M32 | — | 4 | 2 | no | — |
| 338 | C2×M32 | — | 8 | 2 | no | — |
| 339 | C22×C16 | — | 2 | 4 | no | — |
| 340 | C22×C16 | — | 8 | 2 | no | — |
| 341 | C22×C16 | C22×D8 | 1 | 1 | yes | characteristic |
| 342 | C22×C16 | C22×D8 | 1 | 1 | yes | characteristic |
| 343 | C22×C16 | #576 | 1 | 1 | yes | characteristic |
| 344 | C22×C16 | #576 | 1 | 1 | yes | characteristic |
| 345 | #444 | — | 32 | 2 | no | — |
| 346 | #443 | — | 2 | 4 | no | — |
| 347 | #443 | — | 2 | 4 | no | — |
| 348 | #443 | — | 4 | 2 | no | — |
| 349 | #443 | — | 4 | 2 | no | — |
| 350 | #443 | — | 16 | 4 | no | — |
| 351 | #440 | — | 32 | 2 | no | — |
| 352 | C4×Q16 | — | 16 | 2 | no | — |
| 353 | C4×D8 | — | 16 | 2 | no | — |
| 354 | #430 | — | 16 | 2 | no | — |
| 355 | #430 | — | 32 | 2 | no | — |
| 356 | C2×#108 | — | 2 | 2 | no | — |
| 357 | C2×#108 | — | 2 | 2 | no | — |
| 358 | C2×#108 | — | 8 | 2 | no | — |
| 359 | C2×#108 | — | 8 | 2 | no | — |
| 360 | C2×#108 | — | 16 | 4 | no | — |
| 361 | #428 | — | 16 | 2 | no | — |
| 362 | #428 | — | 32 | 2 | no | — |
| 363 | #427 | — | 2 | 2 | no | — |
| 364 | #427 | — | 16 | 2 | no | — |
| 365 | C2×#107 | — | 8 | 2 | no | — |
| 366 | C2×#107 | — | 8 | 2 | no | — |
| 367 | C2×#107 | — | 16 | 2 | no | — |
| 368 | C2×#107 | — | 16 | 4 | no | — |
| 369 | #423 | — | 8 | 2 | no | — |
| 370 | #421 | — | 16 | 2 | no | — |
| 371 | C2×#104 | — | 4 | 2 | no | — |
| 372 | #417 | — | 16 | 2 | no | — |
| 373 | #405 | — | 4 | 2 | no | — |
| 374 | C2×C4×C8 | — | 2 | 1 | no | — |
| 375 | C2×C4×C8 | D42 | 1 | 1 | yes | characteristic |
| 376 | #384 | — | 8 | 2 | no | — |
| 377 | Q64 | #367 | 1 | 4 | yes | complemented |
| 378 | SD64 | #367 | 1 | 8 | yes | complemented |
| 379 | D32 | #367 | 1 | 4 | yes | complemented |
| 380 | M64 | — | 2 | 4 | no | — |
| 381 | M64 | — | 2 | 4 | no | — |
| 382 | M64 | — | 2 | 2 | no | — |
| 383 | M64 | — | 2 | 2 | no | — |
| 384 | M64 | — | 4 | 4 | no | — |
| 385 | M64 | — | 8 | 2 | no | — |
| 386 | M64 | — | 8 | 8 | no | — |
| 387 | M64 | — | 8 | 2 | no | — |
| 388 | M64 | — | 8 | 2 | no | — |
| 389 | M64 | C2×SD32 | 1 | 4 | yes | — |
| 390 | M64 | #509 | 1 | 4 | yes | — |
| 391 | C2×C32 | — | 2 | 2 | no | — |
| 392 | C2×C32 | — | 2 | 2 | no | — |
| 393 | C2×C32 | — | 8 | 2 | no | — |
| 394 | C2×C32 | — | 8 | 8 | no | — |
| 395 | C2×C32 | — | 8 | 2 | no | — |
| 396 | C2×C32 | C2×#107 | 1 | 2 | yes | — |
| 397 | C2×C32 | C2×#107 | 1 | 2 | yes | — |
| 398 | C2×C32 | C4×D8 | 1 | 2 | yes | — |
| 399 | C2×C32 | C4×D8 | 1 | 2 | yes | — |
| 400 | #368 | — | 2 | 2 | no | — |
| 401 | #368 | — | 2 | 2 | no | — |
| 402 | #368 | — | 2 | 2 | no | — |
| 403 | #368 | — | 8 | 2 | no | — |
| 404 | #368 | — | 8 | 2 | no | — |
| 405 | #368 | — | 8 | 2 | no | — |
| 406 | #368 | — | 8 | 2 | no | — |
| 407 | #368 | — | 16 | 4 | no | — |
| 408 | #368 | — | 16 | 2 | no | — |
| 409 | #368 | — | 16 | 2 | no | — |
| 410 | #368 | C2×#107 | 1 | 4 | yes | — |
| 411 | #367 | — | 2 | 2 | no | — |
| 412 | #367 | — | 8 | 2 | no | — |
| 413 | #367 | — | 8 | 2 | no | — |
| 414 | #367 | — | 8 | 2 | no | — |
| 415 | #367 | — | 8 | 2 | no | — |
| 416 | #367 | — | 16 | 2 | no | — |
| 417 | #367 | — | 16 | 2 | no | — |
| 418 | #367 | — | 16 | 2 | no | — |
| 419 | #367 | — | 32 | 8 | no | — |
| 420 | #366 | — | 2 | 2 | no | — |
| 421 | #366 | — | 16 | 2 | no | — |
| 422 | #364 | — | 2 | 4 | no | — |
| 423 | #364 | — | 4 | 2 | no | — |
| 424 | #364 | — | 4 | 2 | no | — |
| 425 | #364 | — | 4 | 2 | no | — |
| 426 | #359 | — | 2 | 4 | no | — |
| 427 | #359 | — | 2 | 4 | no | — |
| 428 | #359 | — | 16 | 4 | no | — |
| 429 | #358 | — | 16 | 2 | no | — |
| 430 | #357 | — | 16 | 2 | no | — |
| 431 | #350 | — | 4 | 4 | no | — |
| 432 | #350 | — | 4 | 4 | no | — |
| 433 | #346 | — | 8 | 2 | no | — |
| 434 | C4×C16 | — | 2 | 2 | no | — |
| 435 | C4×C16 | — | 2 | 2 | no | — |
| 436 | C4×C16 | — | 2 | 4 | no | — |
| 437 | C4×C16 | — | 8 | 2 | no | — |
| 438 | C4×C16 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 439 | C4×C16 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 440 | C4×C16 | #547 | 1 | 1 | yes | characteristic |
| 441 | C4×C16 | D4×Q8 | 1 | 1 | yes | characteristic |
| 442 | C4×C16 | C22×Q16 | 1 | 1 | yes | characteristic |
| 443 | C4×C16 | C2×#135 | 1 | 1 | yes | characteristic |
| 444 | C4×C16 | #578 | 1 | 1 | yes | characteristic |
| 445 | C4×C16 | #578 | 1 | 1 | yes | characteristic |
| 446 | #344 | — | 16 | 2 | no | — |
| 447 | #343 | — | 16 | 2 | no | — |
| 448 | #339 | — | 4 | 2 | no | — |
| 449 | #335 | — | 16 | 4 | no | — |
| 450 | C82 | — | 2 | 1 | no | — |
| 451 | C82 | #520 | 1 | 1 | yes | characteristic |
| 452 | C82 | #554 | 1 | 1 | yes | characteristic |
| 453 | C2×#41 | — | 4 | 2 | no | — |
| 454 | #135 | — | 2 | 4 | no | — |
| 455 | #135 | — | 2 | 4 | no | — |
| 456 | #135 | — | 4 | 2 | no | — |
| 457 | #135 | — | 4 | 2 | no | — |
| 458 | C2×Q16 | — | 2 | 2 | no | — |
| 459 | C2×SD16 | — | 4 | 2 | no | — |
| 460 | C2×D8 | — | 2 | 2 | no | — |
| 461 | #131 | — | 4 | 4 | no | — |
| 462 | #131 | — | 4 | 4 | no | — |
| 463 | #131 | — | 8 | 2 | no | — |
| 464 | #131 | — | 8 | 2 | no | — |
| 465 | #131 | — | 32 | 4 | no | — |
| 466 | #131 | — | 64 | 2 | no | — |
| 467 | C2×M16 | — | 4 | 2 | no | — |
| 468 | C2×M16 | — | 4 | 2 | no | — |
| 469 | C2×M16 | — | 8 | 2 | no | — |
| 470 | C2×M16 | — | 16 | 2 | no | — |
| 471 | C2×M16 | — | 32 | 4 | no | — |
| 472 | C22×C8 | — | 2 | 2 | no | — |
| 473 | C22×C8 | — | 8 | 2 | no | — |
| 474 | C22×C8 | D4×D8 | 1 | 1 | yes | characteristic |
| 475 | C22×C8 | D4×D8 | 1 | 1 | yes | characteristic |
| 476 | C4×Q8 | — | 32 | 2 | no | — |
| 477 | C4×D4 | — | 32 | 2 | no | — |
| 478 | C4×D4 | — | 64 | 2 | no | — |
| 479 | #117 | — | 4 | 2 | no | — |
| 480 | #117 | — | 32 | 2 | no | — |
| 481 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 482 | C2×C4⋊C4 | — | 32 | 2 | no | — |
| 483 | C2×C4⋊C4 | — | 32 | 2 | no | — |
| 484 | C2×C42 | #3292 | 1 | 1 | yes | characteristic |
| 485 | Q32 | — | 2 | 2 | no | — |
| 486 | Q32 | C2×#367 | 1 | 4 | yes | — |
| 487 | SD32 | — | 2 | 4 | no | — |
| 488 | SD32 | — | 2 | 4 | no | — |
| 489 | D16 | — | 2 | 2 | no | — |
| 490 | D16 | C2×#367 | 1 | 4 | yes | — |
| 491 | M32 | — | 4 | 4 | no | — |
| 492 | M32 | — | 8 | 2 | no | — |
| 493 | M32 | — | 8 | 4 | no | — |
| 494 | M32 | — | 8 | 4 | no | — |
| 495 | M32 | — | 8 | 2 | no | — |
| 496 | M32 | — | 8 | 2 | no | — |
| 497 | C2×C16 | — | 2 | 4 | no | — |
| 498 | C2×C16 | — | 2 | 2 | no | — |
| 499 | C2×C16 | — | 2 | 2 | no | — |
| 500 | C2×C16 | — | 2 | 4 | no | — |
| 501 | C2×C16 | — | 4 | 8 | no | — |
| 502 | C2×C16 | — | 8 | 2 | no | — |
| 503 | C2×C16 | — | 8 | 4 | no | — |
| 504 | C2×C16 | — | 8 | 4 | no | — |
| 505 | C2×C16 | — | 8 | 2 | no | — |
| 506 | C2×C16 | C22×#107 | 1 | 1 | yes | characteristic |
| 507 | C2×C16 | #2913 | 1 | 1 | yes | characteristic |
| 508 | C2×C16 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 509 | C2×C16 | #2951 | 1 | 1 | yes | characteristic |
| 510 | C2×C16 | #3334 | 1 | 1 | yes | characteristic |
| 511 | C2×C16 | #3338 | 1 | 1 | yes | characteristic |
| 512 | C2×C16 | Q8×D8 | 1 | 1 | yes | characteristic |
| 513 | C2×C16 | #3380 | 1 | 1 | yes | characteristic |
| 514 | C2×C16 | C22×SD32 | 1 | 2 | yes | — |
| 515 | C2×C16 | C2×#509 | 1 | 2 | yes | — |
| 516 | C2×C16 | #3416 | 1 | 2 | yes | — |
| 517 | C2×C16 | #3416 | 1 | 2 | yes | — |
| 518 | #108 | — | 2 | 4 | no | — |
| 519 | #108 | — | 4 | 2 | no | — |
| 520 | #108 | — | 4 | 2 | no | — |
| 521 | #108 | — | 4 | 2 | no | — |
| 522 | #108 | — | 16 | 2 | no | — |
| 523 | #108 | — | 16 | 2 | no | — |
| 524 | #108 | — | 16 | 2 | no | — |
| 525 | #108 | — | 16 | 2 | no | — |
| 526 | #108 | — | 32 | 4 | no | — |
| 527 | #107 | — | 4 | 2 | no | — |
| 528 | #107 | — | 16 | 2 | no | — |
| 529 | #107 | — | 16 | 2 | no | — |
| 530 | #107 | — | 16 | 2 | no | — |
| 531 | #107 | — | 16 | 2 | no | — |
| 532 | #107 | — | 32 | 2 | no | — |
| 533 | #107 | — | 32 | 8 | no | — |
| 534 | #106 | — | 4 | 2 | no | — |
| 535 | #106 | — | 32 | 2 | no | — |
| 536 | C4⋊C8 | — | 32 | 2 | no | — |
| 537 | #104 | — | 4 | 4 | no | — |
| 538 | #104 | — | 4 | 4 | no | — |
| 539 | #104 | — | 32 | 4 | no | — |
| 540 | #103 | — | 32 | 2 | no | — |
| 541 | #102 | — | 32 | 2 | no | — |
| 542 | #97 | — | 8 | 2 | no | — |
| 543 | C4×C8 | — | 2 | 2 | no | — |
| 544 | C4×C8 | — | 2 | 1 | no | — |
| 545 | C4×C8 | — | 2 | 1 | no | — |
| 546 | C4×C8 | — | 8 | 2 | no | — |
| 547 | C4×C8 | D4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 548 | C4×C8 | #3283 | 1 | 1 | yes | characteristic |
| 549 | C4×C8 | D4×Q16 | 1 | 1 | yes | characteristic |
| 550 | C4×C8 | #3293 | 1 | 1 | yes | characteristic |
| 551 | C32 | — | 2 | 4 | no | — |
| 552 | C32 | — | 2 | 4 | no | — |
| 553 | C32 | — | 2 | 2 | no | — |
| 554 | C32 | — | 2 | 2 | no | — |
| 555 | C32 | — | 8 | 4 | no | — |
| 556 | C32 | — | 16 | 2 | no | — |
| 557 | C32 | C2×#367 | 1 | 4 | yes | — |
| 558 | C32 | #2177 | 1 | 4 | yes | — |
| 559 | #41 | — | 4 | 4 | no | — |
| 560 | #41 | — | 4 | 4 | no | — |
| 561 | #41 | — | 8 | 2 | no | — |
| 562 | #41 | — | 8 | 2 | no | — |
| 563 | C2×Q8 | — | 4 | 2 | no | — |
| 564 | C2×D4 | — | 4 | 2 | no | — |
| 565 | C2×D4 | — | 8 | 2 | no | — |
| 566 | C22×C4 | — | 2 | 1 | no | — |
| 567 | C22×C4 | — | 8 | 2 | no | — |
| 568 | C22×C4 | — | 32 | 2 | no | — |
| 569 | C22×C4 | — | 64 | 2 | no | — |
| 570 | C22×C4 | D82 | 1 | 1 | yes | characteristic |
| 571 | Q16 | — | 2 | 4 | no | — |
| 572 | Q16 | — | 4 | 2 | no | — |
| 573 | SD16 | — | 4 | 4 | no | — |
| 574 | SD16 | — | 4 | 4 | no | — |
| 575 | D8 | — | 2 | 4 | no | — |
| 576 | D8 | — | 4 | 2 | no | — |
| 577 | M16 | — | 4 | 4 | no | — |
| 578 | M16 | — | 8 | 2 | no | — |
| 579 | M16 | — | 8 | 4 | no | — |
| 580 | M16 | — | 8 | 4 | no | — |
| 581 | M16 | — | 8 | 2 | no | — |
| 582 | M16 | — | 8 | 2 | no | — |
| 583 | M16 | — | 32 | 2 | no | — |
| 584 | M16 | — | 32 | 2 | no | — |
| 585 | M16 | — | 64 | 4 | no | — |
| 586 | C2×C8 | — | 2 | 2 | no | — |
| 587 | C2×C8 | — | 2 | 2 | no | — |
| 588 | C2×C8 | — | 4 | 4 | no | — |
| 589 | C2×C8 | — | 8 | 2 | no | — |
| 590 | C2×C8 | — | 8 | 4 | no | — |
| 591 | C2×C8 | — | 8 | 4 | no | — |
| 592 | C2×C8 | — | 8 | 2 | no | — |
| 593 | C2×C8 | — | 32 | 2 | no | — |
| 594 | C2×C8 | — | 64 | 4 | no | — |
| 595 | C2×C8 | #19971 | 1 | 1 | yes | characteristic |
| 596 | C2×C8 | D8×Q16 | 1 | 1 | yes | characteristic |
| 597 | C2×C8 | D4×#107 | 1 | 1 | yes | characteristic |
| 598 | C2×C8 | C4⋊C4×D8 | 1 | 1 | yes | characteristic |
| 599 | C2×C8 | #33838 | 1 | 2 | yes | — |
| 600 | C2×C8 | D4×SD32 | 1 | 2 | yes | — |
| 601 | C2×C8 | #33856 | 1 | 2 | yes | — |
| 602 | C2×C8 | #33856 | 1 | 2 | yes | — |
| 603 | C4⋊C4 | — | 8 | 2 | no | — |
| 604 | C4⋊C4 | — | 32 | 2 | no | — |
| 605 | C4⋊C4 | — | 32 | 2 | no | — |
| 606 | C4⋊C4 | — | 64 | 4 | no | — |
| 607 | C4⋊C4 | — | 64 | 2 | no | — |
| 608 | C22⋊C4 | — | 8 | 2 | no | — |
| 609 | C22⋊C4 | — | 64 | 2 | no | — |
| 610 | C42 | — | 2 | 1 | no | — |
| 611 | C42 | — | 8 | 2 | no | — |
| 612 | C42 | — | 64 | 2 | no | — |
| 613 | C42 | #20006 | 1 | 1 | yes | characteristic |
| 614 | C42 | #22692 | 1 | 1 | yes | characteristic |
| 615 | C16 | — | 2 | 8 | no | — |
| 616 | C16 | — | 2 | 1 | no | — |
| 617 | C16 | — | 2 | 1 | no | — |
| 618 | C16 | — | 2 | 1 | no | — |
| 619 | C16 | — | 2 | 1 | no | — |
| 620 | C16 | — | 4 | 4 | no | — |
| 621 | C16 | — | 8 | 4 | no | — |
| 622 | C16 | — | 16 | 2 | no | — |
| 623 | C16 | C22×#367 | 1 | 1 | yes | characteristic |
| 624 | C16 | #33411 | 1 | 1 | yes | characteristic |
| 625 | C16 | C2×#2177 | 1 | 1 | yes | characteristic |
| 626 | C16 | #33460 | 1 | 1 | yes | characteristic |
| 627 | C16 | #33902 | 1 | 2 | yes | — |
| 628 | C16 | #33951 | 1 | 2 | yes | — |
| 629 | C23 | — | 8 | 2 | no | — |
| 630 | C23 | #492531 | 1 | 1 | yes | characteristic |
| 631 | Q8 | — | 4 | 4 | no | — |
| 632 | Q8 | — | 8 | 2 | no | — |
| 633 | D4 | — | 4 | 4 | no | — |
| 634 | D4 | — | 8 | 4 | no | — |
| 635 | D4 | — | 8 | 4 | no | — |
| 636 | D4 | — | 8 | 2 | no | — |
| 637 | C2×C4 | — | 256 | 2 | no | — |
| 638 | C2×C4 | — | 2 | 1 | no | — |
| 639 | C2×C4 | — | 2 | 1 | no | — |
| 640 | C2×C4 | — | 4 | 2 | no | — |
| 641 | C2×C4 | — | 8 | 2 | no | — |
| 642 | C2×C4 | — | 8 | 4 | no | — |
| 643 | C2×C4 | — | 8 | 4 | no | — |
| 644 | C2×C4 | — | 16 | 2 | no | — |
| 645 | C2×C4 | — | 64 | 2 | no | — |
| 646 | C2×C4 | — | 128 | 2 | no | — |
| 647 | C2×C4 | D8×#107 | 1 | 1 | yes | characteristic |
| 648 | C2×C4 | #492512 | 1 | 2 | yes | — |
| 649 | C2×C4 | D8×SD32 | 1 | 2 | yes | — |
| 650 | C2×C4 | #492531 | 1 | 1 | yes | characteristic |
| 651 | C8 | — | 2 | 4 | no | — |
| 652 | C8 | — | 4 | 2 | no | — |
| 653 | C8 | — | 8 | 4 | no | — |
| 654 | C8 | — | 16 | 2 | no | — |
| 655 | C8 | — | 64 | 2 | no | — |
| 656 | C8 | #492675 | 1 | 2 | yes | — |
| 657 | C8 | #492794 | 1 | 2 | yes | — |
| 658 | C8 | D4×#367 | 1 | 1 | yes | characteristic |
| 659 | C8 | #497855 | 1 | 1 | yes | characteristic |
| 660 | C8 | #497870 | 1 | 1 | yes | characteristic |
| 661 | C8 | #497891 | 1 | 1 | yes | characteristic |
| 662 | C22 | — | 4 | 1 | no | — |
| 663 | C22 | — | 8 | 4 | no | — |
| 664 | C22 | — | 32 | 2 | no | — |
| 665 | C22 | #72216413 | 1 | 1 | yes | characteristic |
| 666 | C22 | #72226835 | 1 | 2 | yes | — |
| 667 | C4 | — | 2 | 2 | no | — |
| 668 | C4 | — | 4 | 1 | no | — |
| 669 | C4 | — | 8 | 4 | no | — |
| 670 | C4 | — | 32 | 2 | no | — |
| 671 | C4 | — | 128 | 2 | no | — |
| 672 | C4 | #72225597 | 1 | 1 | yes | characteristic |
| 673 | C4 | D8×#367 | 1 | 1 | yes | characteristic |
| 674 | C4 | #72226835 | 1 | 2 | yes | — |
| 675 | C2 | — | 2 | 1 | no | — |
| 676 | C2 | — | 2 | 2 | no | — |
| 677 | C2 | — | 16 | 4 | no | — |
| 678 | C2 | #72226836 | 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