Finite Group DatabasebetaFinite Group DatabasebetaOrder 8192.
1196 conjugacy classes of subgroups.
The subgroup lattice has 848 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72227046 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72227007 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72226996 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72226990 | C4 | 1 | 2 | yes | complemented |
| 5 | #72226989 | C4 | 1 | 2 | yes | complemented |
| 6 | #72226838 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72226834 | — | 2 | 1 | no | — |
| 8 | #72225607 | — | 2 | 1 | no | — |
| 9 | #72225606 | — | 2 | 1 | no | — |
| 10 | #72225604 | — | 4 | 1 | no | — |
| 11 | #72225603 | — | 4 | 1 | no | — |
| 12 | #72225602 | — | 4 | 1 | no | — |
| 13 | #72225601 | — | 2 | 1 | no | — |
| 14 | #72225599 | — | 2 | 1 | no | — |
| 15 | #72225598 | — | 2 | 1 | no | — |
| 16 | #72225596 | — | 4 | 1 | no | — |
| 17 | #72225595 | — | 4 | 1 | no | — |
| 18 | #72225594 | — | 4 | 1 | no | — |
| 19 | #72225564 | — | 4 | 1 | no | — |
| 20 | #72225556 | — | 4 | 1 | no | — |
| 21 | #72225495 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 22 | #72225490 | — | 2 | 1 | no | — |
| 23 | #72225487 | — | 2 | 1 | no | — |
| 24 | #72225485 | — | 4 | 1 | no | — |
| 25 | #72225484 | — | 4 | 1 | no | — |
| 26 | #72225464 | C2 | 1 | 1 | yes | maximal, characteristic |
| 27 | #72225457 | — | 2 | 1 | no | — |
| 28 | #72225455 | — | 2 | 1 | no | — |
| 29 | #72225453 | — | 4 | 1 | no | — |
| 30 | #72225452 | — | 4 | 1 | no | — |
| 31 | #72225402 | C22 | 1 | 1 | yes | characteristic |
| 32 | #72225402 | C22 | 1 | 1 | yes | characteristic |
| 33 | #72225401 | — | 2 | 1 | no | — |
| 34 | #72225398 | — | 2 | 1 | no | — |
| 35 | #72225398 | — | 2 | 1 | no | — |
| 36 | #72225397 | — | 2 | 1 | no | — |
| 37 | #72225397 | C2×C4 | 1 | 2 | yes | complemented |
| 38 | #72225395 | — | 2 | 1 | no | — |
| 39 | #72225395 | — | 2 | 1 | no | — |
| 40 | #72225366 | C22 | 1 | 1 | yes | characteristic |
| 41 | #72225363 | — | 2 | 1 | no | — |
| 42 | #72225362 | D4 | 1 | 1 | yes | characteristic |
| 43 | #72225360 | C22 | 1 | 1 | yes | characteristic |
| 44 | #72225356 | — | 2 | 1 | no | — |
| 45 | #72225356 | Q8 | 1 | 2 | yes | — |
| 46 | #72225355 | — | 2 | 1 | no | — |
| 47 | #72225355 | C2×C4 | 1 | 2 | yes | — |
| 48 | #72225353 | — | 2 | 1 | no | — |
| 49 | #72225352 | D4 | 1 | 1 | yes | characteristic |
| 50 | #72225342 | — | 2 | 1 | no | — |
| 51 | #72225341 | — | 2 | 1 | no | — |
| 52 | #72225313 | D4 | 1 | 1 | yes | characteristic |
| 53 | #72225308 | D4 | 1 | 1 | yes | characteristic |
| 54 | #72225194 | — | 2 | 1 | no | — |
| 55 | #72225123 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 56 | #72225067 | C22 | 1 | 1 | yes | characteristic |
| 57 | #72225038 | — | 2 | 1 | no | — |
| 58 | #72225038 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 59 | #72216560 | — | 2 | 1 | no | — |
| 60 | #72216534 | — | 2 | 1 | no | — |
| 61 | C2×#93751 | — | 2 | 1 | no | — |
| 62 | #72216413 | — | 2 | 1 | no | — |
| 63 | #72216379 | — | 2 | 1 | no | — |
| 64 | #72216379 | C22 | 1 | 1 | yes | characteristic |
| 65 | #72216301 | — | 2 | 1 | no | — |
| 66 | #72216301 | C22 | 1 | 1 | yes | characteristic |
| 67 | #72216298 | — | 2 | 1 | no | — |
| 68 | #72216298 | — | 2 | 1 | no | — |
| 69 | #72216298 | — | 4 | 2 | no | — |
| 70 | #72216296 | — | 2 | 1 | no | — |
| 71 | #72216296 | — | 2 | 1 | no | — |
| 72 | #72216296 | — | 4 | 2 | no | — |
| 73 | #72216273 | — | 2 | 1 | no | — |
| 74 | #72216267 | — | 2 | 1 | no | — |
| 75 | #72216239 | — | 2 | 1 | no | — |
| 76 | #72216239 | D4 | 1 | 1 | yes | characteristic |
| 77 | C16×M64 | — | 2 | 1 | no | — |
| 78 | C16×M64 | C23 | 1 | 1 | yes | characteristic |
| 79 | #72216197 | D4 | 1 | 1 | yes | characteristic |
| 80 | C322 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 81 | #512779 | — | 8 | 1 | no | — |
| 82 | #512773 | D8 | 1 | 1 | yes | characteristic |
| 83 | #512751 | — | 4 | 1 | no | — |
| 84 | #512724 | — | 8 | 1 | no | — |
| 85 | #497894 | — | 4 | 1 | no | — |
| 86 | #497891 | — | 4 | 1 | no | — |
| 87 | #497857 | — | 4 | 1 | no | — |
| 88 | #497855 | — | 4 | 1 | no | — |
| 89 | C2×#12046 | — | 2 | 1 | no | — |
| 90 | #153582 | — | 4 | 1 | no | — |
| 91 | #153582 | — | 4 | 1 | no | — |
| 92 | #152874 | — | 4 | 1 | no | — |
| 93 | #152873 | — | 4 | 1 | no | — |
| 94 | #152861 | — | 8 | 1 | no | — |
| 95 | #152447 | — | 8 | 1 | no | — |
| 96 | #152446 | — | 8 | 1 | no | — |
| 97 | #152432 | — | 8 | 1 | no | — |
| 98 | #152431 | — | 8 | 1 | no | — |
| 99 | #152407 | — | 4 | 1 | no | — |
| 100 | #152407 | — | 4 | 1 | no | — |
| 101 | #152407 | — | 4 | 1 | no | — |
| 102 | #152407 | — | 4 | 1 | no | — |
| 103 | #152407 | — | 8 | 4 | no | — |
| 104 | #152301 | — | 8 | 1 | no | — |
| 105 | #152283 | — | 4 | 1 | no | — |
| 106 | #152282 | — | 4 | 1 | no | — |
| 107 | #151998 | D8 | 1 | 1 | yes | characteristic |
| 108 | #151989 | — | 4 | 1 | no | — |
| 109 | #151082 | — | 2 | 1 | no | — |
| 110 | #151082 | Q16 | 1 | 2 | yes | — |
| 111 | #151081 | — | 2 | 1 | no | — |
| 112 | #151081 | C4⋊C4 | 1 | 2 | yes | — |
| 113 | #151073 | — | 4 | 1 | no | — |
| 114 | #151073 | — | 4 | 1 | no | — |
| 115 | #151072 | — | 2 | 2 | no | — |
| 116 | #151072 | — | 2 | 2 | no | — |
| 117 | #151055 | — | 4 | 1 | no | — |
| 118 | #151055 | — | 4 | 1 | no | — |
| 119 | #151055 | — | 4 | 1 | no | — |
| 120 | #151055 | — | 4 | 1 | no | — |
| 121 | #151055 | — | 8 | 4 | no | — |
| 122 | #151040 | D8 | 1 | 1 | yes | characteristic |
| 123 | #151035 | D8 | 1 | 1 | yes | characteristic |
| 124 | C2×#7459 | — | 2 | 1 | no | — |
| 125 | C2×#7459 | — | 2 | 1 | no | — |
| 126 | #150067 | — | 2 | 1 | no | — |
| 127 | #150051 | — | 4 | 1 | no | — |
| 128 | C8×M64 | — | 2 | 2 | no | — |
| 129 | C8×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C8×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | #140438 | — | 4 | 1 | no | — |
| 132 | #140437 | — | 4 | 1 | no | — |
| 133 | #136326 | — | 8 | 1 | no | — |
| 134 | #136324 | — | 8 | 1 | no | — |
| 135 | #135796 | — | 4 | 1 | no | — |
| 136 | #135796 | — | 4 | 1 | no | — |
| 137 | #135796 | — | 4 | 1 | no | — |
| 138 | #135781 | — | 2 | 1 | no | — |
| 139 | #135781 | — | 4 | 1 | no | — |
| 140 | #135778 | — | 2 | 1 | no | — |
| 141 | #135778 | — | 4 | 1 | no | — |
| 142 | #134971 | — | 4 | 1 | no | — |
| 143 | #134970 | — | 4 | 1 | no | — |
| 144 | #129142 | — | 2 | 1 | no | — |
| 145 | C2×C162 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | #94754 | — | 8 | 2 | no | — |
| 147 | #94748 | — | 2 | 2 | no | — |
| 148 | #94748 | — | 4 | 1 | no | — |
| 149 | #94746 | — | 4 | 1 | no | — |
| 150 | #94746 | — | 4 | 1 | no | — |
| 151 | #94613 | — | 8 | 2 | no | — |
| 152 | #94366 | — | 4 | 1 | no | — |
| 153 | #94365 | — | 4 | 1 | no | — |
| 154 | #94364 | — | 4 | 1 | no | — |
| 155 | #94364 | — | 4 | 1 | no | — |
| 156 | #94053 | — | 2 | 1 | no | — |
| 157 | #94041 | — | 4 | 1 | no | — |
| 158 | #93885 | — | 2 | 1 | no | — |
| 159 | #93885 | — | 2 | 1 | no | — |
| 160 | #93882 | — | 2 | 1 | no | — |
| 161 | #93882 | C4⋊C4 | 1 | 2 | yes | — |
| 162 | #93751 | — | 2 | 2 | no | — |
| 163 | #93751 | — | 2 | 2 | no | — |
| 164 | #93664 | — | 2 | 2 | no | — |
| 165 | #93664 | C2×Q8 | 1 | 1 | yes | characteristic |
| 166 | #93664 | #41 | 1 | 1 | yes | characteristic |
| 167 | C16×C32 | — | 2 | 1 | no | — |
| 168 | C16×C32 | — | 2 | 1 | no | — |
| 169 | C16×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 170 | C16×C32 | #41 | 1 | 1 | yes | characteristic |
| 171 | #33981 | SD32 | 1 | 1 | yes | characteristic |
| 172 | #33974 | — | 8 | 1 | no | — |
| 173 | #33465 | — | 8 | 1 | no | — |
| 174 | C2×#2178 | — | 2 | 1 | no | — |
| 175 | #33460 | — | 8 | 1 | no | — |
| 176 | C2×#2170 | — | 4 | 1 | no | — |
| 177 | #33414 | — | 8 | 1 | no | — |
| 178 | #33411 | — | 8 | 1 | no | — |
| 179 | #22694 | — | 8 | 1 | no | — |
| 180 | #22692 | — | 8 | 1 | no | — |
| 181 | #13658 | — | 16 | 2 | no | — |
| 182 | #13657 | — | 16 | 2 | no | — |
| 183 | #13656 | — | 2 | 1 | no | — |
| 184 | #13656 | SD32 | 1 | 2 | yes | — |
| 185 | #13655 | — | 2 | 1 | no | — |
| 186 | #13655 | #107 | 1 | 2 | yes | — |
| 187 | #13648 | — | 8 | 1 | no | — |
| 188 | #13648 | — | 8 | 1 | no | — |
| 189 | #13647 | — | 4 | 2 | no | — |
| 190 | #13647 | — | 4 | 2 | no | — |
| 191 | #13638 | — | 2 | 1 | no | — |
| 192 | #13638 | — | 8 | 1 | no | — |
| 193 | #13638 | — | 16 | 2 | no | — |
| 194 | C2×#1426 | — | 8 | 1 | no | — |
| 195 | C2×#1426 | — | 8 | 1 | no | — |
| 196 | C2×#1426 | — | 8 | 1 | no | — |
| 197 | C2×#1426 | — | 8 | 1 | no | — |
| 198 | C2×#1426 | — | 8 | 1 | no | — |
| 199 | C2×#1426 | — | 16 | 1 | no | — |
| 200 | C2×#1426 | — | 16 | 1 | no | — |
| 201 | C2×#1426 | — | 16 | 2 | no | — |
| 202 | C2×#1426 | — | 16 | 8 | no | — |
| 203 | #13636 | SD32 | 1 | 1 | yes | characteristic |
| 204 | C2×#1422 | — | 4 | 1 | no | — |
| 205 | C2×#1422 | — | 4 | 1 | no | — |
| 206 | #13625 | — | 8 | 1 | no | — |
| 207 | C2×#1418 | — | 8 | 1 | no | — |
| 208 | #13620 | — | 2 | 1 | no | — |
| 209 | #13558 | — | 8 | 1 | no | — |
| 210 | #13551 | — | 8 | 1 | no | — |
| 211 | C4×M64 | — | 2 | 4 | no | — |
| 212 | C4×M64 | C2×D8 | 1 | 1 | yes | characteristic |
| 213 | C4×M64 | C2×D8 | 1 | 1 | yes | characteristic |
| 214 | C4×M64 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 215 | C4×M64 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 216 | #13182 | — | 8 | 1 | no | — |
| 217 | #13181 | — | 8 | 1 | no | — |
| 218 | #13173 | — | 8 | 1 | no | — |
| 219 | #13172 | — | 8 | 1 | no | — |
| 220 | #12947 | — | 16 | 1 | no | — |
| 221 | #12946 | — | 16 | 1 | no | — |
| 222 | #12927 | — | 16 | 1 | no | — |
| 223 | #12926 | — | 16 | 1 | no | — |
| 224 | #12909 | — | 4 | 1 | no | — |
| 225 | #12909 | — | 4 | 1 | no | — |
| 226 | #12909 | — | 8 | 2 | no | — |
| 227 | #12906 | — | 4 | 1 | no | — |
| 228 | #12906 | — | 4 | 1 | no | — |
| 229 | #12906 | — | 8 | 2 | no | — |
| 230 | #12843 | — | 8 | 1 | no | — |
| 231 | #12841 | — | 8 | 1 | no | — |
| 232 | #12822 | — | 8 | 1 | no | — |
| 233 | #12821 | — | 8 | 1 | no | — |
| 234 | #12670 | — | 2 | 1 | no | — |
| 235 | #12664 | — | 4 | 1 | no | — |
| 236 | #12046 | — | 2 | 2 | no | — |
| 237 | #12046 | — | 2 | 2 | no | — |
| 238 | #12046 | — | 4 | 1 | no | — |
| 239 | #12046 | — | 4 | 1 | no | — |
| 240 | #12023 | — | 8 | 2 | no | — |
| 241 | #12023 | — | 8 | 2 | no | — |
| 242 | #12023 | — | 8 | 1 | no | — |
| 243 | #12023 | — | 8 | 1 | no | — |
| 244 | C2×#1373 | — | 2 | 1 | no | — |
| 245 | C2×#1373 | — | 2 | 1 | no | — |
| 246 | C2×#1335 | — | 4 | 1 | no | — |
| 247 | C2×C8×C16 | — | 2 | 1 | no | — |
| 248 | C2×C8×C16 | #120 | 1 | 1 | yes | characteristic |
| 249 | #8823 | — | 4 | 1 | no | — |
| 250 | #8823 | — | 8 | 1 | no | — |
| 251 | #8818 | — | 4 | 1 | no | — |
| 252 | #7544 | — | 4 | 2 | no | — |
| 253 | #7544 | — | 8 | 1 | no | — |
| 254 | #7513 | — | 8 | 1 | no | — |
| 255 | #7513 | — | 8 | 1 | no | — |
| 256 | #7511 | — | 8 | 1 | no | — |
| 257 | #7511 | — | 8 | 1 | no | — |
| 258 | #7479 | — | 8 | 1 | no | — |
| 259 | #7477 | — | 8 | 1 | no | — |
| 260 | #7476 | — | 8 | 1 | no | — |
| 261 | #7476 | SD32 | 1 | 1 | yes | characteristic |
| 262 | #7475 | SD32 | 1 | 1 | yes | characteristic |
| 263 | #7474 | — | 8 | 1 | no | — |
| 264 | #7469 | — | 8 | 1 | no | — |
| 265 | #7464 | — | 2 | 1 | no | — |
| 266 | #7464 | — | 2 | 1 | no | — |
| 267 | #7463 | — | 8 | 1 | no | — |
| 268 | #7463 | — | 8 | 1 | no | — |
| 269 | #7463 | — | 8 | 1 | no | — |
| 270 | #7463 | — | 8 | 1 | no | — |
| 271 | #7463 | — | 16 | 8 | no | — |
| 272 | #7463 | — | 16 | 1 | no | — |
| 273 | #7463 | — | 16 | 1 | no | — |
| 274 | #7462 | — | 2 | 1 | no | — |
| 275 | #7462 | #107 | 1 | 2 | yes | — |
| 276 | #7459 | — | 2 | 2 | no | — |
| 277 | #7459 | — | 4 | 1 | no | — |
| 278 | #7459 | — | 4 | 1 | no | — |
| 279 | #7459 | — | 4 | 1 | no | — |
| 280 | #7387 | — | 2 | 2 | no | — |
| 281 | #7387 | — | 2 | 2 | no | — |
| 282 | #7381 | — | 4 | 2 | no | — |
| 283 | #7381 | — | 4 | 2 | no | — |
| 284 | #7329 | — | 2 | 4 | no | — |
| 285 | #7329 | C2×Q16 | 1 | 1 | yes | characteristic |
| 286 | #7329 | #135 | 1 | 1 | yes | characteristic |
| 287 | #7329 | #137 | 1 | 1 | yes | characteristic |
| 288 | #7329 | #137 | 1 | 1 | yes | characteristic |
| 289 | C8×C32 | — | 2 | 2 | no | — |
| 290 | C8×C32 | — | 2 | 2 | no | — |
| 291 | C8×C32 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 292 | C8×C32 | C4×D4 | 1 | 1 | yes | characteristic |
| 293 | C8×C32 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 294 | C8×C32 | #123 | 1 | 1 | yes | characteristic |
| 295 | #7270 | — | 8 | 1 | no | — |
| 296 | #7269 | — | 8 | 1 | no | — |
| 297 | #7179 | — | 4 | 1 | no | — |
| 298 | C162 | — | 2 | 1 | no | — |
| 299 | C162 | C4×D4 | 1 | 1 | yes | characteristic |
| 300 | C162 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 301 | C2×#508 | — | 2 | 1 | no | — |
| 302 | C2×#504 | — | 8 | 1 | no | — |
| 303 | #2957 | — | 16 | 1 | no | — |
| 304 | C2×#443 | — | 4 | 1 | no | — |
| 305 | #2951 | — | 16 | 1 | no | — |
| 306 | #2916 | — | 16 | 1 | no | — |
| 307 | #2913 | — | 16 | 1 | no | — |
| 308 | #2264 | — | 2 | 2 | no | — |
| 309 | #2263 | — | 2 | 2 | no | — |
| 310 | #2262 | — | 2 | 1 | no | — |
| 311 | #2262 | #367 | 1 | 2 | yes | — |
| 312 | #2258 | — | 8 | 2 | no | — |
| 313 | #2258 | — | 8 | 2 | no | — |
| 314 | #2258 | — | 16 | 2 | no | — |
| 315 | C2×M64 | — | 2 | 8 | no | — |
| 316 | C2×M64 | — | 2 | 1 | no | — |
| 317 | C2×M64 | — | 2 | 1 | no | — |
| 318 | C2×M64 | — | 8 | 1 | no | — |
| 319 | C2×M64 | — | 8 | 1 | no | — |
| 320 | C2×M64 | — | 16 | 2 | no | — |
| 321 | C2×M64 | C2×SD32 | 1 | 1 | yes | characteristic |
| 322 | C2×M64 | C2×SD32 | 1 | 1 | yes | characteristic |
| 323 | C2×M64 | #509 | 1 | 1 | yes | characteristic |
| 324 | C2×M64 | #509 | 1 | 1 | yes | characteristic |
| 325 | #2179 | — | 16 | 2 | no | — |
| 326 | #2178 | — | 2 | 2 | no | — |
| 327 | #2178 | — | 2 | 2 | no | — |
| 328 | #2178 | — | 4 | 1 | no | — |
| 329 | #2178 | — | 4 | 1 | no | — |
| 330 | #2178 | — | 32 | 1 | no | — |
| 331 | #2177 | — | 16 | 1 | no | — |
| 332 | #2176 | — | 16 | 1 | no | — |
| 333 | C4×SD32 | — | 32 | 1 | no | — |
| 334 | #2170 | — | 4 | 2 | no | — |
| 335 | #2170 | — | 4 | 2 | no | — |
| 336 | #2170 | — | 8 | 1 | no | — |
| 337 | #2170 | — | 8 | 1 | no | — |
| 338 | #2161 | — | 16 | 1 | no | — |
| 339 | #2161 | — | 32 | 1 | no | — |
| 340 | C2×#368 | — | 2 | 1 | no | — |
| 341 | C2×#368 | — | 2 | 1 | no | — |
| 342 | C2×#368 | — | 8 | 1 | no | — |
| 343 | C2×#368 | — | 8 | 1 | no | — |
| 344 | C2×#368 | — | 8 | 1 | no | — |
| 345 | C2×#368 | — | 8 | 1 | no | — |
| 346 | C2×#368 | — | 16 | 2 | no | — |
| 347 | C2×#368 | — | 16 | 4 | no | — |
| 348 | #2159 | — | 16 | 1 | no | — |
| 349 | #2159 | — | 32 | 1 | no | — |
| 350 | #2158 | — | 2 | 1 | no | — |
| 351 | #2158 | — | 16 | 1 | no | — |
| 352 | C2×#367 | — | 8 | 1 | no | — |
| 353 | C2×#367 | — | 8 | 1 | no | — |
| 354 | C2×#367 | — | 8 | 1 | no | — |
| 355 | C2×#367 | — | 8 | 1 | no | — |
| 356 | C2×#367 | — | 16 | 1 | no | — |
| 357 | C2×#367 | — | 16 | 4 | no | — |
| 358 | C2×#364 | — | 4 | 1 | no | — |
| 359 | C2×#364 | — | 4 | 1 | no | — |
| 360 | #2143 | — | 16 | 1 | no | — |
| 361 | C2×#359 | — | 4 | 1 | no | — |
| 362 | #2139 | — | 16 | 1 | no | — |
| 363 | C2×#350 | — | 8 | 1 | no | — |
| 364 | #2108 | — | 8 | 1 | no | — |
| 365 | C2×C4×C16 | — | 2 | 2 | no | — |
| 366 | C2×C4×C16 | #447 | 1 | 1 | yes | characteristic |
| 367 | C2×C4×C16 | #447 | 1 | 1 | yes | characteristic |
| 368 | #1953 | — | 16 | 1 | no | — |
| 369 | #1952 | — | 16 | 1 | no | — |
| 370 | #1861 | — | 32 | 1 | no | — |
| 371 | #1859 | — | 32 | 1 | no | — |
| 372 | #1848 | — | 8 | 1 | no | — |
| 373 | #1848 | — | 16 | 1 | no | — |
| 374 | #1845 | — | 8 | 1 | no | — |
| 375 | #1845 | — | 16 | 1 | no | — |
| 376 | #1816 | — | 16 | 1 | no | — |
| 377 | #1814 | — | 16 | 1 | no | — |
| 378 | #1772 | — | 4 | 1 | no | — |
| 379 | #1567 | — | 16 | 1 | no | — |
| 380 | #1567 | — | 16 | 1 | no | — |
| 381 | #1567 | — | 16 | 1 | no | — |
| 382 | C2×C82 | #453 | 1 | 1 | yes | characteristic |
| 383 | M128 | — | 8 | 2 | no | — |
| 384 | M128 | — | 16 | 1 | no | — |
| 385 | #1426 | — | 4 | 2 | no | — |
| 386 | #1426 | — | 16 | 1 | no | — |
| 387 | #1426 | — | 16 | 1 | no | — |
| 388 | #1426 | — | 16 | 2 | no | — |
| 389 | #1426 | — | 16 | 2 | no | — |
| 390 | #1426 | — | 16 | 2 | no | — |
| 391 | #1426 | — | 32 | 1 | no | — |
| 392 | #1426 | — | 32 | 1 | no | — |
| 393 | #1426 | — | 32 | 2 | no | — |
| 394 | #1426 | — | 32 | 2 | no | — |
| 395 | #1426 | — | 32 | 16 | no | — |
| 396 | #1425 | — | 2 | 1 | no | — |
| 397 | #1425 | #367 | 1 | 2 | yes | — |
| 398 | #1422 | — | 4 | 2 | no | — |
| 399 | #1422 | — | 8 | 1 | no | — |
| 400 | #1422 | — | 8 | 1 | no | — |
| 401 | #1422 | — | 8 | 1 | no | — |
| 402 | #1420 | — | 16 | 1 | no | — |
| 403 | #1419 | — | 16 | 1 | no | — |
| 404 | #1418 | — | 16 | 2 | no | — |
| 405 | #1417 | — | 2 | 2 | no | — |
| 406 | #1417 | — | 2 | 2 | no | — |
| 407 | #1401 | — | 8 | 2 | no | — |
| 408 | #1401 | — | 8 | 2 | no | — |
| 409 | #1398 | — | 16 | 2 | no | — |
| 410 | #1397 | — | 2 | 8 | no | — |
| 411 | #1397 | — | 2 | 1 | no | — |
| 412 | #1397 | — | 2 | 1 | no | — |
| 413 | #1397 | C2×SD32 | 1 | 1 | yes | characteristic |
| 414 | #1397 | #508 | 1 | 1 | yes | characteristic |
| 415 | #1397 | #509 | 1 | 1 | yes | characteristic |
| 416 | #1397 | #510 | 1 | 1 | yes | characteristic |
| 417 | C4×C32 | — | 2 | 4 | no | — |
| 418 | C4×C32 | — | 2 | 4 | no | — |
| 419 | C4×C32 | C2×#107 | 1 | 1 | yes | characteristic |
| 420 | C4×C32 | #428 | 1 | 1 | yes | characteristic |
| 421 | C4×C32 | C4×D8 | 1 | 1 | yes | characteristic |
| 422 | C4×C32 | #440 | 1 | 1 | yes | characteristic |
| 423 | C4×C32 | #474 | 1 | 1 | yes | characteristic |
| 424 | C4×C32 | #478 | 1 | 1 | yes | characteristic |
| 425 | C4×C32 | #480 | 1 | 1 | yes | characteristic |
| 426 | C4×C32 | #484 | 1 | 1 | yes | characteristic |
| 427 | #1389 | — | 16 | 1 | no | — |
| 428 | #1388 | — | 16 | 1 | no | — |
| 429 | #1387 | — | 16 | 1 | no | — |
| 430 | #1387 | — | 16 | 1 | no | — |
| 431 | #1382 | — | 4 | 1 | no | — |
| 432 | #1379 | — | 8 | 1 | no | — |
| 433 | #1373 | — | 2 | 2 | no | — |
| 434 | #1373 | — | 4 | 1 | no | — |
| 435 | #1373 | — | 4 | 1 | no | — |
| 436 | #1373 | — | 4 | 1 | no | — |
| 437 | #1372 | — | 16 | 4 | no | — |
| 438 | #1372 | — | 16 | 4 | no | — |
| 439 | #1372 | — | 16 | 1 | no | — |
| 440 | #1372 | — | 16 | 1 | no | — |
| 441 | #1372 | — | 16 | 1 | no | — |
| 442 | #1372 | — | 16 | 1 | no | — |
| 443 | #1335 | — | 4 | 2 | no | — |
| 444 | #1335 | — | 4 | 2 | no | — |
| 445 | C8×C16 | — | 2 | 2 | no | — |
| 446 | C8×C16 | — | 2 | 1 | no | — |
| 447 | C8×C16 | — | 2 | 1 | no | — |
| 448 | C8×C16 | #385 | 1 | 1 | yes | characteristic |
| 449 | C8×C16 | #451 | 1 | 1 | yes | characteristic |
| 450 | C8×C16 | #452 | 1 | 1 | yes | characteristic |
| 451 | C8×C16 | #456 | 1 | 1 | yes | characteristic |
| 452 | C2×#135 | — | 4 | 1 | no | — |
| 453 | #568 | — | 32 | 1 | no | — |
| 454 | C2×#131 | — | 8 | 1 | no | — |
| 455 | #520 | — | 32 | 1 | no | — |
| 456 | #508 | — | 2 | 2 | no | — |
| 457 | #508 | — | 2 | 2 | no | — |
| 458 | #508 | — | 4 | 1 | no | — |
| 459 | #508 | — | 4 | 1 | no | — |
| 460 | C2×Q32 | — | 2 | 1 | no | — |
| 461 | C2×SD32 | — | 4 | 1 | no | — |
| 462 | C2×D16 | — | 2 | 1 | no | — |
| 463 | #504 | — | 8 | 2 | no | — |
| 464 | #504 | — | 8 | 2 | no | — |
| 465 | #504 | — | 16 | 1 | no | — |
| 466 | #504 | — | 16 | 1 | no | — |
| 467 | C2×M32 | — | 8 | 1 | no | — |
| 468 | C2×M32 | — | 8 | 1 | no | — |
| 469 | C2×M32 | — | 16 | 1 | no | — |
| 470 | C22×C16 | — | 2 | 4 | no | — |
| 471 | C22×C16 | — | 16 | 1 | no | — |
| 472 | C22×C16 | #2187 | 1 | 1 | yes | characteristic |
| 473 | C22×C16 | #2187 | 1 | 1 | yes | characteristic |
| 474 | C22×C16 | #2194 | 1 | 1 | yes | characteristic |
| 475 | C22×C16 | #2194 | 1 | 1 | yes | characteristic |
| 476 | #444 | — | 64 | 1 | no | — |
| 477 | #443 | — | 4 | 2 | no | — |
| 478 | #443 | — | 4 | 2 | no | — |
| 479 | #443 | — | 8 | 1 | no | — |
| 480 | #443 | — | 8 | 1 | no | — |
| 481 | #443 | — | 32 | 2 | no | — |
| 482 | #440 | — | 64 | 1 | no | — |
| 483 | C4×Q16 | — | 32 | 1 | no | — |
| 484 | C4×D8 | — | 32 | 1 | no | — |
| 485 | #430 | — | 32 | 1 | no | — |
| 486 | #430 | — | 64 | 1 | no | — |
| 487 | C2×#108 | — | 4 | 1 | no | — |
| 488 | C2×#108 | — | 4 | 1 | no | — |
| 489 | C2×#108 | — | 16 | 1 | no | — |
| 490 | C2×#108 | — | 16 | 1 | no | — |
| 491 | C2×#108 | — | 32 | 2 | no | — |
| 492 | C2×#108 | — | 32 | 2 | no | — |
| 493 | #428 | — | 32 | 1 | no | — |
| 494 | #428 | — | 64 | 1 | no | — |
| 495 | #427 | — | 4 | 1 | no | — |
| 496 | #427 | — | 32 | 1 | no | — |
| 497 | C2×#107 | — | 16 | 1 | no | — |
| 498 | C2×#107 | — | 16 | 1 | no | — |
| 499 | C2×#107 | — | 32 | 1 | no | — |
| 500 | C2×#107 | — | 32 | 2 | no | — |
| 501 | #423 | — | 16 | 1 | no | — |
| 502 | #423 | — | 32 | 1 | no | — |
| 503 | #421 | — | 32 | 1 | no | — |
| 504 | C2×#104 | — | 8 | 1 | no | — |
| 505 | #417 | — | 32 | 1 | no | — |
| 506 | #405 | — | 8 | 1 | no | — |
| 507 | C2×C4×C8 | — | 2 | 1 | no | — |
| 508 | C2×C4×C8 | #1619 | 1 | 1 | yes | characteristic |
| 509 | #384 | — | 16 | 1 | no | — |
| 510 | Q64 | — | 2 | 1 | no | — |
| 511 | Q64 | #1426 | 1 | 2 | yes | complemented |
| 512 | SD64 | — | 2 | 2 | no | — |
| 513 | SD64 | — | 2 | 2 | no | — |
| 514 | D32 | — | 2 | 1 | no | — |
| 515 | D32 | #1426 | 1 | 2 | yes | complemented |
| 516 | M64 | — | 2 | 2 | no | — |
| 517 | M64 | — | 2 | 2 | no | — |
| 518 | M64 | — | 4 | 1 | no | — |
| 519 | M64 | — | 4 | 1 | no | — |
| 520 | M64 | — | 4 | 2 | no | — |
| 521 | M64 | — | 4 | 2 | no | — |
| 522 | M64 | — | 4 | 16 | no | — |
| 523 | M64 | — | 8 | 2 | no | — |
| 524 | M64 | — | 16 | 2 | no | — |
| 525 | M64 | — | 16 | 1 | no | — |
| 526 | M64 | — | 16 | 2 | no | — |
| 527 | M64 | — | 16 | 1 | no | — |
| 528 | M64 | — | 16 | 1 | no | — |
| 529 | C2×C32 | — | 2 | 8 | no | — |
| 530 | C2×C32 | — | 2 | 1 | no | — |
| 531 | C2×C32 | — | 2 | 1 | no | — |
| 532 | C2×C32 | — | 2 | 8 | no | — |
| 533 | C2×C32 | — | 2 | 1 | no | — |
| 534 | C2×C32 | — | 2 | 1 | no | — |
| 535 | C2×C32 | — | 16 | 2 | no | — |
| 536 | C2×C32 | — | 16 | 1 | no | — |
| 537 | C2×C32 | — | 16 | 2 | no | — |
| 538 | C2×C32 | — | 16 | 1 | no | — |
| 539 | C2×C32 | C2×#367 | 1 | 1 | yes | characteristic |
| 540 | C2×C32 | #2159 | 1 | 1 | yes | characteristic |
| 541 | C2×C32 | C4×SD32 | 1 | 1 | yes | characteristic |
| 542 | C2×C32 | #2177 | 1 | 1 | yes | characteristic |
| 543 | C2×C32 | #2226 | 1 | 1 | yes | characteristic |
| 544 | C2×C32 | #2228 | 1 | 1 | yes | characteristic |
| 545 | C2×C32 | #2233 | 1 | 1 | yes | characteristic |
| 546 | C2×C32 | #2235 | 1 | 1 | yes | characteristic |
| 547 | #368 | — | 2 | 2 | no | — |
| 548 | #368 | — | 4 | 1 | no | — |
| 549 | #368 | — | 4 | 1 | no | — |
| 550 | #368 | — | 4 | 1 | no | — |
| 551 | #368 | — | 16 | 1 | no | — |
| 552 | #368 | — | 16 | 1 | no | — |
| 553 | #368 | — | 16 | 1 | no | — |
| 554 | #368 | — | 16 | 1 | no | — |
| 555 | #368 | — | 32 | 2 | no | — |
| 556 | #368 | — | 32 | 1 | no | — |
| 557 | #368 | — | 32 | 1 | no | — |
| 558 | #368 | — | 32 | 8 | no | — |
| 559 | #367 | — | 4 | 1 | no | — |
| 560 | #367 | — | 16 | 1 | no | — |
| 561 | #367 | — | 16 | 1 | no | — |
| 562 | #367 | — | 16 | 1 | no | — |
| 563 | #367 | — | 16 | 1 | no | — |
| 564 | #367 | — | 32 | 1 | no | — |
| 565 | #367 | — | 32 | 1 | no | — |
| 566 | #367 | — | 32 | 1 | no | — |
| 567 | #367 | — | 32 | 8 | no | — |
| 568 | #366 | — | 4 | 1 | no | — |
| 569 | #366 | — | 32 | 1 | no | — |
| 570 | #364 | — | 4 | 2 | no | — |
| 571 | #364 | — | 8 | 1 | no | — |
| 572 | #364 | — | 8 | 1 | no | — |
| 573 | #364 | — | 8 | 1 | no | — |
| 574 | #359 | — | 4 | 2 | no | — |
| 575 | #359 | — | 4 | 2 | no | — |
| 576 | #359 | — | 32 | 2 | no | — |
| 577 | #358 | — | 32 | 1 | no | — |
| 578 | #357 | — | 32 | 1 | no | — |
| 579 | #350 | — | 8 | 2 | no | — |
| 580 | #350 | — | 8 | 2 | no | — |
| 581 | #346 | — | 16 | 1 | no | — |
| 582 | C4×C16 | — | 2 | 2 | no | — |
| 583 | C4×C16 | — | 2 | 2 | no | — |
| 584 | C4×C16 | — | 2 | 4 | no | — |
| 585 | C4×C16 | — | 16 | 1 | no | — |
| 586 | C4×C16 | #1647 | 1 | 1 | yes | characteristic |
| 587 | C4×C16 | #1649 | 1 | 1 | yes | characteristic |
| 588 | C4×C16 | #1852 | 1 | 1 | yes | characteristic |
| 589 | C4×C16 | #1862 | 1 | 1 | yes | characteristic |
| 590 | C4×C16 | #2185 | 1 | 1 | yes | characteristic |
| 591 | C4×C16 | #2186 | 1 | 1 | yes | characteristic |
| 592 | C4×C16 | #2193 | 1 | 1 | yes | characteristic |
| 593 | C4×C16 | #2193 | 1 | 1 | yes | characteristic |
| 594 | #344 | — | 32 | 1 | no | — |
| 595 | #343 | — | 32 | 1 | no | — |
| 596 | #339 | — | 8 | 1 | no | — |
| 597 | #335 | — | 32 | 2 | no | — |
| 598 | #335 | — | 32 | 2 | no | — |
| 599 | #335 | — | 32 | 1 | no | — |
| 600 | #335 | — | 32 | 1 | no | — |
| 601 | C82 | — | 2 | 1 | no | — |
| 602 | C82 | #1632 | 1 | 1 | yes | characteristic |
| 603 | C82 | #1859 | 1 | 1 | yes | characteristic |
| 604 | C64 | — | 16 | 2 | no | — |
| 605 | C64 | — | 32 | 1 | no | — |
| 606 | C2×#41 | — | 8 | 1 | no | — |
| 607 | #135 | — | 4 | 2 | no | — |
| 608 | #135 | — | 4 | 2 | no | — |
| 609 | #135 | — | 8 | 1 | no | — |
| 610 | #135 | — | 8 | 1 | no | — |
| 611 | C2×Q16 | — | 4 | 1 | no | — |
| 612 | C2×SD16 | — | 8 | 1 | no | — |
| 613 | C2×D8 | — | 4 | 1 | no | — |
| 614 | #131 | — | 8 | 2 | no | — |
| 615 | #131 | — | 8 | 2 | no | — |
| 616 | #131 | — | 16 | 1 | no | — |
| 617 | #131 | — | 16 | 1 | no | — |
| 618 | #131 | — | 64 | 2 | no | — |
| 619 | #131 | — | 128 | 1 | no | — |
| 620 | C2×M16 | — | 8 | 1 | no | — |
| 621 | C2×M16 | — | 8 | 1 | no | — |
| 622 | C2×M16 | — | 16 | 1 | no | — |
| 623 | C2×M16 | — | 32 | 1 | no | — |
| 624 | C2×M16 | — | 64 | 2 | no | — |
| 625 | C2×M16 | — | 64 | 1 | no | — |
| 626 | C22×C8 | — | 2 | 2 | no | — |
| 627 | C22×C8 | — | 16 | 1 | no | — |
| 628 | C22×C8 | #12320 | 1 | 1 | yes | characteristic |
| 629 | C22×C8 | #12320 | 1 | 1 | yes | characteristic |
| 630 | C4×Q8 | — | 64 | 1 | no | — |
| 631 | C4×D4 | — | 64 | 1 | no | — |
| 632 | C4×D4 | — | 128 | 1 | no | — |
| 633 | #117 | — | 8 | 1 | no | — |
| 634 | #117 | — | 64 | 1 | no | — |
| 635 | C2×C4⋊C4 | — | 32 | 1 | no | — |
| 636 | C2×C4⋊C4 | — | 64 | 1 | no | — |
| 637 | C2×C4⋊C4 | — | 64 | 1 | no | — |
| 638 | C2×C42 | #12310 | 1 | 1 | yes | characteristic |
| 639 | Q32 | — | 2 | 2 | no | — |
| 640 | Q32 | — | 4 | 1 | no | — |
| 641 | SD32 | — | 4 | 2 | no | — |
| 642 | SD32 | — | 4 | 2 | no | — |
| 643 | D16 | — | 2 | 2 | no | — |
| 644 | D16 | — | 4 | 1 | no | — |
| 645 | M32 | — | 8 | 2 | no | — |
| 646 | M32 | — | 16 | 2 | no | — |
| 647 | M32 | — | 16 | 1 | no | — |
| 648 | M32 | — | 16 | 2 | no | — |
| 649 | M32 | — | 16 | 1 | no | — |
| 650 | M32 | — | 16 | 1 | no | — |
| 651 | C2×C16 | — | 2 | 4 | no | — |
| 652 | C2×C16 | — | 2 | 1 | no | — |
| 653 | C2×C16 | — | 2 | 1 | no | — |
| 654 | C2×C16 | — | 2 | 1 | no | — |
| 655 | C2×C16 | — | 2 | 1 | no | — |
| 656 | C2×C16 | — | 2 | 4 | no | — |
| 657 | C2×C16 | — | 4 | 1 | no | — |
| 658 | C2×C16 | — | 4 | 1 | no | — |
| 659 | C2×C16 | — | 4 | 8 | no | — |
| 660 | C2×C16 | — | 16 | 2 | no | — |
| 661 | C2×C16 | — | 16 | 1 | no | — |
| 662 | C2×C16 | — | 16 | 2 | no | — |
| 663 | C2×C16 | — | 16 | 1 | no | — |
| 664 | C2×C16 | #12394 | 1 | 1 | yes | characteristic |
| 665 | C2×C16 | #12396 | 1 | 1 | yes | characteristic |
| 666 | C2×C16 | #12407 | 1 | 1 | yes | characteristic |
| 667 | C2×C16 | #12408 | 1 | 1 | yes | characteristic |
| 668 | C2×C16 | #12920 | 1 | 1 | yes | characteristic |
| 669 | C2×C16 | #12926 | 1 | 1 | yes | characteristic |
| 670 | C2×C16 | #12937 | 1 | 1 | yes | characteristic |
| 671 | C2×C16 | #12946 | 1 | 1 | yes | characteristic |
| 672 | #108 | — | 4 | 2 | no | — |
| 673 | #108 | — | 8 | 1 | no | — |
| 674 | #108 | — | 8 | 1 | no | — |
| 675 | #108 | — | 8 | 1 | no | — |
| 676 | #108 | — | 32 | 1 | no | — |
| 677 | #108 | — | 32 | 1 | no | — |
| 678 | #108 | — | 32 | 1 | no | — |
| 679 | #108 | — | 32 | 1 | no | — |
| 680 | #108 | — | 64 | 4 | no | — |
| 681 | #108 | — | 64 | 2 | no | — |
| 682 | #107 | — | 8 | 1 | no | — |
| 683 | #107 | — | 32 | 1 | no | — |
| 684 | #107 | — | 32 | 1 | no | — |
| 685 | #107 | — | 32 | 1 | no | — |
| 686 | #107 | — | 32 | 1 | no | — |
| 687 | #107 | — | 64 | 1 | no | — |
| 688 | #107 | — | 64 | 4 | no | — |
| 689 | #106 | — | 8 | 1 | no | — |
| 690 | #106 | — | 64 | 1 | no | — |
| 691 | C4⋊C8 | — | 64 | 1 | no | — |
| 692 | C4⋊C8 | — | 64 | 1 | no | — |
| 693 | C4⋊C8 | — | 64 | 1 | no | — |
| 694 | #104 | — | 8 | 2 | no | — |
| 695 | #104 | — | 8 | 2 | no | — |
| 696 | #104 | — | 64 | 2 | no | — |
| 697 | #103 | — | 64 | 1 | no | — |
| 698 | #102 | — | 64 | 1 | no | — |
| 699 | #97 | — | 16 | 1 | no | — |
| 700 | C4×C8 | — | 2 | 2 | no | — |
| 701 | C4×C8 | — | 2 | 1 | no | — |
| 702 | C4×C8 | — | 2 | 1 | no | — |
| 703 | C4×C8 | — | 16 | 1 | no | — |
| 704 | C4×C8 | #8882 | 1 | 1 | yes | characteristic |
| 705 | C4×C8 | #12313 | 1 | 1 | yes | characteristic |
| 706 | C4×C8 | #12318 | 1 | 1 | yes | characteristic |
| 707 | C4×C8 | #12319 | 1 | 1 | yes | characteristic |
| 708 | C32 | — | 2 | 16 | no | — |
| 709 | C32 | — | 2 | 2 | no | — |
| 710 | C32 | — | 2 | 2 | no | — |
| 711 | C32 | — | 2 | 1 | no | — |
| 712 | C32 | — | 2 | 1 | no | — |
| 713 | C32 | — | 2 | 1 | no | — |
| 714 | C32 | — | 2 | 1 | no | — |
| 715 | C32 | — | 2 | 1 | no | — |
| 716 | C32 | — | 2 | 1 | no | — |
| 717 | C32 | — | 4 | 8 | no | — |
| 718 | C32 | — | 4 | 1 | no | — |
| 719 | C32 | — | 4 | 1 | no | — |
| 720 | C32 | — | 16 | 2 | no | — |
| 721 | C32 | — | 32 | 1 | no | — |
| 722 | C32 | C2×#1426 | 1 | 2 | yes | — |
| 723 | C32 | #13658 | 1 | 2 | yes | — |
| 724 | #41 | — | 8 | 2 | no | — |
| 725 | #41 | — | 8 | 2 | no | — |
| 726 | #41 | — | 16 | 1 | no | — |
| 727 | #41 | — | 16 | 1 | no | — |
| 728 | C2×Q8 | — | 8 | 1 | no | — |
| 729 | C2×D4 | — | 8 | 1 | no | — |
| 730 | C2×D4 | — | 16 | 1 | no | — |
| 731 | C22×C4 | — | 2 | 1 | no | — |
| 732 | C22×C4 | — | 16 | 1 | no | — |
| 733 | C22×C4 | — | 64 | 1 | no | — |
| 734 | C22×C4 | — | 128 | 1 | no | — |
| 735 | C22×C4 | #123285 | 1 | 1 | yes | characteristic |
| 736 | Q16 | — | 4 | 2 | no | — |
| 737 | Q16 | — | 8 | 1 | no | — |
| 738 | SD16 | — | 8 | 2 | no | — |
| 739 | SD16 | — | 8 | 2 | no | — |
| 740 | D8 | — | 4 | 2 | no | — |
| 741 | D8 | — | 8 | 1 | no | — |
| 742 | M16 | — | 8 | 2 | no | — |
| 743 | M16 | — | 16 | 2 | no | — |
| 744 | M16 | — | 16 | 1 | no | — |
| 745 | M16 | — | 16 | 2 | no | — |
| 746 | M16 | — | 16 | 1 | no | — |
| 747 | M16 | — | 16 | 1 | no | — |
| 748 | M16 | — | 64 | 1 | no | — |
| 749 | M16 | — | 64 | 1 | no | — |
| 750 | M16 | — | 128 | 2 | no | — |
| 751 | M16 | — | 128 | 2 | no | — |
| 752 | C2×C8 | — | 2 | 2 | no | — |
| 753 | C2×C8 | — | 2 | 1 | no | — |
| 754 | C2×C8 | — | 2 | 1 | no | — |
| 755 | C2×C8 | — | 2 | 1 | no | — |
| 756 | C2×C8 | — | 2 | 1 | no | — |
| 757 | C2×C8 | — | 2 | 2 | no | — |
| 758 | C2×C8 | — | 4 | 4 | no | — |
| 759 | C2×C8 | — | 16 | 2 | no | — |
| 760 | C2×C8 | — | 16 | 1 | no | — |
| 761 | C2×C8 | — | 16 | 2 | no | — |
| 762 | C2×C8 | — | 16 | 1 | no | — |
| 763 | C2×C8 | — | 64 | 1 | no | — |
| 764 | C2×C8 | — | 128 | 1 | no | — |
| 765 | C2×C8 | — | 128 | 2 | no | — |
| 766 | C2×C8 | #123307 | 1 | 1 | yes | characteristic |
| 767 | C2×C8 | #123310 | 1 | 1 | yes | characteristic |
| 768 | C2×C8 | #136331 | 1 | 1 | yes | characteristic |
| 769 | C2×C8 | #136339 | 1 | 1 | yes | characteristic |
| 770 | C4⋊C4 | — | 16 | 1 | no | — |
| 771 | C4⋊C4 | — | 64 | 1 | no | — |
| 772 | C4⋊C4 | — | 64 | 1 | no | — |
| 773 | C4⋊C4 | — | 128 | 2 | no | — |
| 774 | C4⋊C4 | — | 128 | 1 | no | — |
| 775 | C22⋊C4 | — | 16 | 1 | no | — |
| 776 | C22⋊C4 | — | 128 | 1 | no | — |
| 777 | C42 | — | 2 | 1 | no | — |
| 778 | C42 | — | 16 | 1 | no | — |
| 779 | C42 | — | 128 | 1 | no | — |
| 780 | C42 | #123278 | 1 | 1 | yes | characteristic |
| 781 | C42 | #136324 | 1 | 1 | yes | characteristic |
| 782 | C16 | — | 2 | 8 | no | — |
| 783 | C16 | — | 2 | 1 | no | — |
| 784 | C16 | — | 2 | 1 | no | — |
| 785 | C16 | — | 2 | 1 | no | — |
| 786 | C16 | — | 2 | 1 | no | — |
| 787 | C16 | — | 2 | 1 | no | — |
| 788 | C16 | — | 2 | 1 | no | — |
| 789 | C16 | — | 4 | 4 | no | — |
| 790 | C16 | — | 16 | 2 | no | — |
| 791 | C16 | — | 32 | 1 | no | — |
| 792 | C16 | #152427 | 1 | 1 | yes | characteristic |
| 793 | C16 | #152432 | 1 | 1 | yes | characteristic |
| 794 | C16 | #152447 | 1 | 1 | yes | characteristic |
| 795 | C16 | #152454 | 1 | 1 | yes | characteristic |
| 796 | C23 | — | 16 | 1 | no | — |
| 797 | C23 | #72214234 | 1 | 1 | yes | characteristic |
| 798 | Q8 | — | 8 | 2 | no | — |
| 799 | Q8 | — | 16 | 1 | no | — |
| 800 | D4 | — | 8 | 2 | no | — |
| 801 | D4 | — | 16 | 1 | no | — |
| 802 | D4 | — | 16 | 2 | no | — |
| 803 | D4 | — | 16 | 2 | no | — |
| 804 | C2×C4 | — | 256 | 1 | no | — |
| 805 | C2×C4 | — | 512 | 1 | no | — |
| 806 | C2×C4 | — | 2 | 1 | no | — |
| 807 | C2×C4 | — | 2 | 1 | no | — |
| 808 | C2×C4 | — | 2 | 1 | no | — |
| 809 | C2×C4 | — | 2 | 1 | no | — |
| 810 | C2×C4 | — | 4 | 2 | no | — |
| 811 | C2×C4 | — | 16 | 2 | no | — |
| 812 | C2×C4 | — | 16 | 1 | no | — |
| 813 | C2×C4 | — | 16 | 2 | no | — |
| 814 | C2×C4 | — | 32 | 1 | no | — |
| 815 | C2×C4 | — | 128 | 1 | no | — |
| 816 | C2×C4 | #72214234 | 1 | 1 | yes | characteristic |
| 817 | C2×C4 | #72225193 | 1 | 1 | yes | characteristic |
| 818 | C8 | — | 256 | 1 | no | — |
| 819 | C8 | — | 2 | 4 | no | — |
| 820 | C8 | — | 2 | 1 | no | — |
| 821 | C8 | — | 2 | 1 | no | — |
| 822 | C8 | — | 4 | 2 | no | — |
| 823 | C8 | — | 16 | 2 | no | — |
| 824 | C8 | — | 32 | 1 | no | — |
| 825 | C8 | — | 128 | 1 | no | — |
| 826 | C8 | #72225594 | 1 | 1 | yes | characteristic |
| 827 | C8 | #72225602 | 1 | 1 | yes | characteristic |
| 828 | C8 | #72227129 | 1 | 1 | yes | characteristic |
| 829 | C8 | #72227133 | 1 | 1 | yes | characteristic |
| 830 | C22 | — | 2 | 1 | no | — |
| 831 | C22 | — | 4 | 1 | no | — |
| 832 | C22 | — | 16 | 2 | no | — |
| 833 | C22 | — | 64 | 1 | no | — |
| 834 | C22 | #72225194 | 1 | 1 | yes | characteristic |
| 835 | C4 | — | 256 | 1 | no | — |
| 836 | C4 | — | 2 | 2 | no | — |
| 837 | C4 | — | 2 | 1 | no | — |
| 838 | C4 | — | 4 | 1 | no | — |
| 839 | C4 | — | 16 | 2 | no | — |
| 840 | C4 | — | 64 | 1 | no | — |
| 841 | C4 | #72227131 | 1 | 1 | yes | characteristic |
| 842 | C4 | #72227134 | 1 | 1 | yes | characteristic |
| 843 | C2 | — | 2 | 1 | no | — |
| 844 | C2 | — | 4 | 1 | no | — |
| 845 | C2 | — | 32 | 2 | no | — |
| 846 | C2 | #72227135 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72227135 |
| commutator | C16×C32 | C22×C4 |
| Frattini, cosocle | C16×M64 | C23 |
| prime radical | #33981 | SD32 |
| LCS | G ▷ C16×C32 ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C4×C8 ◁ C2×C8×C16 ◁ C16×M64 ◁ G | |
| LECS | G ▷ C16×M64 ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72227046 | C2 | semidirect |
| 2. #72227007 | C2 | semidirect |
| 4. #72226990 | C4 | semidirect |
| 5. #72226989 | C4 | semidirect |
| 21. #72225495 | C2 | semidirect |
| 37. #72225397 | C2×C4 | semidirect |
| 55. #72225123 | C2 | semidirect |
| 58. #72225038 | C2×C4 | semidirect |
| 80. C322 | C2×C4 | semidirect |
| 511. Q64 | #1426 | semidirect |
| 515. D32 | #1426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72227046 | 2 |
| #72227007 | 2 |
| #72226996 | 2 |
| #72226838 | 2 |
| #72225495 | 2 |
| #72225464 | 2 |
| #72225123 | 2 |