Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1466 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 1466 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6365636 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #512867 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #512863 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #489351 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #153633 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #153617 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #153539 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #153462 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #153457 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #61891 | — | 2 | 1 | no | — |
| 11 | #61682 | — | 2 | 1 | no | — |
| 12 | #61110 | C22 | 1 | 1 | yes | characteristic |
| 13 | #33688 | — | 2 | 1 | no | — |
| 14 | #33559 | — | 2 | 1 | no | — |
| 15 | C2×#2198 | — | 2 | 1 | no | — |
| 16 | #20310 | C22 | 1 | 2 | yes | complemented |
| 17 | #20294 | — | 2 | 1 | no | — |
| 18 | #20260 | — | 2 | 2 | no | — |
| 19 | #20192 | — | 2 | 2 | no | — |
| 20 | #20138 | — | 2 | 1 | no | — |
| 21 | #20067 | C22 | 1 | 2 | yes | complemented |
| 22 | #19727 | C22 | 1 | 1 | yes | characteristic |
| 23 | #19506 | — | 2 | 1 | no | — |
| 24 | #19437 | — | 2 | 1 | no | — |
| 25 | #18714 | C22 | 1 | 1 | yes | characteristic |
| 26 | #18610 | — | 2 | 1 | no | — |
| 27 | #18526 | C22 | 1 | 1 | yes | characteristic |
| 28 | #17951 | — | 2 | 1 | no | — |
| 29 | #13676 | — | 2 | 2 | no | — |
| 30 | #13675 | C22 | 1 | 4 | yes | — |
| 31 | #13673 | — | 2 | 2 | no | — |
| 32 | #13673 | C22 | 1 | 4 | yes | — |
| 33 | #13585 | C22 | 1 | 1 | yes | characteristic |
| 34 | #13584 | C22 | 1 | 1 | yes | characteristic |
| 35 | #13561 | — | 2 | 1 | no | — |
| 36 | #13560 | — | 2 | 1 | no | — |
| 37 | #12366 | C22 | 1 | 2 | yes | — |
| 38 | #12365 | — | 2 | 1 | no | — |
| 39 | #12314 | — | 2 | 1 | no | — |
| 40 | #12310 | C22 | 1 | 2 | yes | — |
| 41 | #11992 | C22 | 1 | 1 | yes | characteristic |
| 42 | #11670 | — | 2 | 1 | no | — |
| 43 | #7533 | C22 | 1 | 2 | yes | complemented |
| 44 | #7529 | C22 | 1 | 2 | yes | complemented |
| 45 | #7516 | C22 | 1 | 4 | yes | complemented |
| 46 | #7515 | C22 | 1 | 4 | yes | complemented |
| 47 | #3585 | — | 4 | 1 | no | — |
| 48 | #3549 | D4 | 1 | 1 | yes | characteristic |
| 49 | #3497 | — | 2 | 1 | no | — |
| 50 | C2×#559 | D4 | 1 | 1 | yes | characteristic, complemented |
| 51 | #3399 | — | 2 | 2 | no | — |
| 52 | #3399 | — | 2 | 2 | no | — |
| 53 | #3399 | — | 4 | 2 | no | — |
| 54 | #3373 | — | 2 | 2 | no | — |
| 55 | #3373 | — | 2 | 2 | no | — |
| 56 | #3373 | — | 4 | 2 | no | — |
| 57 | #3329 | — | 2 | 2 | no | — |
| 58 | #3321 | — | 4 | 2 | no | — |
| 59 | #3305 | — | 2 | 2 | no | — |
| 60 | #3292 | — | 2 | 1 | no | — |
| 61 | #3292 | C23 | 1 | 2 | yes | — |
| 62 | #3291 | — | 2 | 1 | no | — |
| 63 | #3291 | — | 2 | 1 | no | — |
| 64 | #3288 | — | 4 | 2 | no | — |
| 65 | D4×SD16 | — | 2 | 2 | no | — |
| 66 | #3274 | — | 2 | 2 | no | — |
| 67 | #3265 | — | 4 | 2 | no | — |
| 68 | #3214 | — | 2 | 1 | no | — |
| 69 | #3213 | — | 4 | 2 | no | — |
| 70 | #3207 | — | 2 | 1 | no | — |
| 71 | #3205 | — | 2 | 1 | no | — |
| 72 | #3205 | — | 2 | 1 | no | — |
| 73 | #3198 | — | 4 | 2 | no | — |
| 74 | #3184 | D4 | 1 | 1 | yes | characteristic, complemented |
| 75 | #3151 | C23 | 1 | 1 | yes | characteristic |
| 76 | #3112 | — | 2 | 1 | no | — |
| 77 | #3109 | — | 4 | 2 | no | — |
| 78 | #3103 | — | 2 | 1 | no | — |
| 79 | #3103 | — | 2 | 1 | no | — |
| 80 | #3068 | — | 4 | 1 | no | — |
| 81 | #3027 | — | 4 | 1 | no | — |
| 82 | C2×#458 | — | 4 | 1 | no | — |
| 83 | #3018 | — | 2 | 1 | no | — |
| 84 | C2×#453 | — | 2 | 1 | no | — |
| 85 | #3010 | — | 4 | 2 | no | — |
| 86 | #2983 | — | 2 | 1 | no | — |
| 87 | #2981 | — | 2 | 1 | no | — |
| 88 | #2956 | — | 2 | 1 | no | — |
| 89 | #2238 | — | 4 | 1 | no | — |
| 90 | #2230 | — | 2 | 2 | no | — |
| 91 | #2213 | — | 2 | 2 | no | — |
| 92 | #2199 | — | 4 | 2 | no | — |
| 93 | #2198 | — | 2 | 4 | no | — |
| 94 | #2198 | — | 4 | 2 | no | — |
| 95 | #2196 | — | 2 | 4 | no | — |
| 96 | #2190 | — | 4 | 1 | no | — |
| 97 | AGL(1,ℤ/16) | — | 4 | 2 | no | — |
| 98 | #2165 | — | 2 | 1 | no | — |
| 99 | #2126 | — | 2 | 1 | no | — |
| 100 | C2×#353 | — | 2 | 1 | no | — |
| 101 | #2122 | — | 4 | 1 | no | — |
| 102 | C2×#352 | — | 4 | 1 | no | — |
| 103 | #1721 | — | 2 | 1 | no | — |
| 104 | #1721 | D4 | 1 | 1 | yes | characteristic, complemented |
| 105 | #1717 | — | 2 | 1 | no | — |
| 106 | #1715 | C23 | 1 | 1 | yes | characteristic |
| 107 | #1712 | C23 | 1 | 1 | yes | characteristic |
| 108 | #1708 | D4 | 1 | 1 | yes | characteristic, complemented |
| 109 | #1704 | — | 2 | 2 | no | — |
| 110 | #1701 | — | 2 | 2 | no | — |
| 111 | #1698 | — | 2 | 2 | no | — |
| 112 | #1688 | — | 2 | 2 | no | — |
| 113 | #1687 | — | 2 | 2 | no | — |
| 114 | #1686 | — | 2 | 2 | no | — |
| 115 | #1681 | — | 2 | 2 | no | — |
| 116 | #1667 | — | 2 | 2 | no | — |
| 117 | #1651 | — | 2 | 2 | no | — |
| 118 | #1642 | — | 2 | 2 | no | — |
| 119 | #1630 | — | 2 | 1 | no | — |
| 120 | #1630 | D4 | 1 | 2 | yes | complemented |
| 121 | #1627 | — | 2 | 2 | no | — |
| 122 | #1624 | — | 2 | 1 | no | — |
| 123 | #1624 | — | 2 | 1 | no | — |
| 124 | #1621 | — | 2 | 2 | no | — |
| 125 | #1620 | — | 2 | 1 | no | — |
| 126 | #1620 | C23 | 1 | 2 | yes | — |
| 127 | #1619 | D4 | 1 | 2 | yes | — |
| 128 | #1619 | C23 | 1 | 2 | yes | — |
| 129 | #1592 | — | 2 | 2 | no | — |
| 130 | #1590 | — | 2 | 2 | no | — |
| 131 | #1585 | — | 2 | 2 | no | — |
| 132 | #1582 | — | 2 | 2 | no | — |
| 133 | #1572 | — | 2 | 1 | no | — |
| 134 | #1555 | D4 | 1 | 1 | yes | characteristic, complemented |
| 135 | #1553 | — | 2 | 1 | no | — |
| 136 | #1543 | D4 | 1 | 1 | yes | characteristic |
| 137 | #1491 | — | 2 | 1 | no | — |
| 138 | #1484 | — | 2 | 1 | no | — |
| 139 | #1453 | D4 | 1 | 1 | yes | characteristic, complemented |
| 140 | #1409 | — | 2 | 1 | no | — |
| 141 | #1408 | — | 2 | 1 | no | — |
| 142 | #1408 | C23 | 1 | 2 | yes | — |
| 143 | #1408 | C23 | 1 | 2 | yes | — |
| 144 | #1402 | — | 2 | 4 | no | — |
| 145 | #1402 | — | 2 | 4 | no | — |
| 146 | #1359 | — | 2 | 1 | no | — |
| 147 | #1357 | C23 | 1 | 2 | yes | — |
| 148 | #1336 | — | 2 | 2 | no | — |
| 149 | #1335 | — | 2 | 2 | no | — |
| 150 | #585 | — | 2 | 1 | no | — |
| 151 | C2×2−1+4 | — | 4 | 1 | no | — |
| 152 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 153 | #577 | — | 4 | 2 | no | — |
| 154 | #577 | — | 4 | 2 | no | — |
| 155 | #577 | — | 8 | 2 | no | — |
| 156 | #576 | — | 4 | 2 | no | — |
| 157 | #576 | — | 4 | 2 | no | — |
| 158 | #576 | — | 8 | 2 | no | — |
| 159 | #575 | — | 2 | 1 | no | — |
| 160 | #575 | — | 4 | 1 | no | — |
| 161 | #575 | — | 8 | 2 | no | — |
| 162 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 163 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 164 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 165 | C2×AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 166 | C22×SD16 | — | 4 | 2 | no | — |
| 167 | #568 | — | 4 | 1 | no | — |
| 168 | H(3,𝔽4) | — | 4 | 1 | no | — |
| 169 | #559 | — | 2 | 1 | no | — |
| 170 | #559 | — | 4 | 2 | no | — |
| 171 | #559 | — | 4 | 1 | no | — |
| 172 | #559 | C2×D4 | 1 | 2 | yes | — |
| 173 | #555 | — | 2 | 1 | no | — |
| 174 | #555 | — | 4 | 1 | no | — |
| 175 | #550 | — | 2 | 2 | no | — |
| 176 | #550 | — | 4 | 1 | no | — |
| 177 | D4×Q8 | — | 2 | 2 | no | — |
| 178 | D4×Q8 | — | 4 | 1 | no | — |
| 179 | #548 | — | 4 | 2 | no | — |
| 180 | #548 | — | 8 | 1 | no | — |
| 181 | D42 | — | 4 | 1 | no | — |
| 182 | D42 | C2×D4 | 1 | 2 | yes | — |
| 183 | #537 | — | 4 | 1 | no | — |
| 184 | #537 | — | 8 | 1 | no | — |
| 185 | #535 | — | 4 | 1 | no | — |
| 186 | #535 | — | 4 | 2 | no | — |
| 187 | #535 | — | 8 | 1 | no | — |
| 188 | #532 | — | 2 | 1 | no | — |
| 189 | #532 | — | 2 | 1 | no | — |
| 190 | #532 | — | 4 | 2 | no | — |
| 191 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×#127 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×#124 | — | 4 | 1 | no | — |
| 194 | C2×#123 | — | 4 | 1 | no | — |
| 195 | C2×#123 | — | 8 | 1 | no | — |
| 196 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 197 | C2×C4×D4 | — | 4 | 1 | no | — |
| 198 | #509 | — | 4 | 2 | no | — |
| 199 | #498 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | #496 | — | 4 | 1 | no | — |
| 201 | #496 | — | 4 | 1 | no | — |
| 202 | #496 | — | 4 | 2 | no | — |
| 203 | #496 | — | 4 | 2 | no | — |
| 204 | #493 | — | 2 | 1 | no | — |
| 205 | #493 | — | 2 | 1 | no | — |
| 206 | #493 | — | 2 | 1 | no | — |
| 207 | #493 | — | 4 | 1 | no | — |
| 208 | #493 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | #493 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | #493 | C24 | 1 | 1 | yes | characteristic |
| 211 | #492 | — | 2 | 1 | no | — |
| 212 | #492 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | #492 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | #489 | — | 4 | 2 | no | — |
| 215 | #489 | — | 4 | 2 | no | — |
| 216 | #489 | — | 4 | 1 | no | — |
| 217 | #487 | — | 2 | 1 | no | — |
| 218 | #486 | — | 2 | 1 | no | — |
| 219 | #486 | — | 2 | 1 | no | — |
| 220 | #486 | — | 2 | 1 | no | — |
| 221 | #486 | — | 2 | 1 | no | — |
| 222 | #486 | — | 4 | 1 | no | — |
| 223 | #485 | — | 4 | 2 | no | — |
| 224 | #482 | — | 4 | 2 | no | — |
| 225 | #481 | — | 2 | 2 | no | — |
| 226 | #481 | — | 4 | 1 | no | — |
| 227 | #480 | — | 4 | 1 | no | — |
| 228 | #477 | — | 2 | 2 | no | — |
| 229 | #476 | — | 4 | 2 | no | — |
| 230 | #476 | — | 4 | 2 | no | — |
| 231 | #475 | — | 2 | 2 | no | — |
| 232 | #475 | — | 2 | 2 | no | — |
| 233 | #472 | — | 4 | 2 | no | — |
| 234 | #472 | — | 4 | 2 | no | — |
| 235 | #471 | — | 4 | 2 | no | — |
| 236 | #471 | — | 4 | 2 | no | — |
| 237 | #469 | — | 4 | 2 | no | — |
| 238 | #469 | — | 4 | 1 | no | — |
| 239 | #468 | — | 4 | 2 | no | — |
| 240 | #466 | — | 4 | 2 | no | — |
| 241 | #465 | — | 4 | 2 | no | — |
| 242 | #463 | — | 4 | 2 | no | — |
| 243 | #463 | — | 4 | 2 | no | — |
| 244 | #463 | — | 4 | 2 | no | — |
| 245 | #463 | — | 4 | 2 | no | — |
| 246 | #463 | — | 4 | 2 | no | — |
| 247 | #461 | — | 2 | 2 | no | — |
| 248 | #460 | — | 2 | 2 | no | — |
| 249 | #460 | — | 2 | 2 | no | — |
| 250 | #460 | — | 2 | 2 | no | — |
| 251 | #459 | — | 2 | 2 | no | — |
| 252 | #459 | — | 2 | 2 | no | — |
| 253 | #459 | — | 2 | 2 | no | — |
| 254 | #459 | — | 4 | 2 | no | — |
| 255 | #459 | — | 4 | 2 | no | — |
| 256 | #459 | — | 4 | 2 | no | — |
| 257 | #458 | — | 4 | 4 | no | — |
| 258 | #458 | — | 8 | 2 | no | — |
| 259 | B(4,𝔽2) | — | 4 | 4 | no | — |
| 260 | B(4,𝔽2) | — | 8 | 2 | no | — |
| 261 | #456 | — | 4 | 1 | no | — |
| 262 | #455 | — | 2 | 2 | no | — |
| 263 | #454 | — | 4 | 1 | no | — |
| 264 | #453 | — | 2 | 2 | no | — |
| 265 | #453 | — | 2 | 2 | no | — |
| 266 | #453 | — | 2 | 2 | no | — |
| 267 | #453 | — | 4 | 1 | no | — |
| 268 | #453 | — | 4 | 1 | no | — |
| 269 | #450 | — | 4 | 2 | no | — |
| 270 | #449 | — | 4 | 2 | no | — |
| 271 | #449 | — | 4 | 2 | no | — |
| 272 | #449 | — | 4 | 2 | no | — |
| 273 | #449 | — | 4 | 2 | no | — |
| 274 | #448 | — | 2 | 2 | no | — |
| 275 | #448 | — | 4 | 2 | no | — |
| 276 | #448 | — | 4 | 2 | no | — |
| 277 | #448 | — | 4 | 1 | no | — |
| 278 | #448 | — | 4 | 1 | no | — |
| 279 | #447 | — | 4 | 2 | no | — |
| 280 | #447 | — | 4 | 2 | no | — |
| 281 | #447 | — | 4 | 2 | no | — |
| 282 | #446 | — | 2 | 2 | no | — |
| 283 | #446 | — | 2 | 2 | no | — |
| 284 | #446 | — | 4 | 2 | no | — |
| 285 | #444 | — | 2 | 2 | no | — |
| 286 | #444 | — | 4 | 1 | no | — |
| 287 | #443 | — | 2 | 2 | no | — |
| 288 | #443 | — | 4 | 1 | no | — |
| 289 | #442 | — | 4 | 1 | no | — |
| 290 | #442 | — | 4 | 2 | no | — |
| 291 | #442 | — | 4 | 2 | no | — |
| 292 | #442 | — | 4 | 2 | no | — |
| 293 | #442 | — | 4 | 2 | no | — |
| 294 | #440 | — | 4 | 2 | no | — |
| 295 | C4×SD16 | — | 2 | 2 | no | — |
| 296 | C4×SD16 | — | 2 | 2 | no | — |
| 297 | C4×SD16 | — | 4 | 2 | no | — |
| 298 | #436 | — | 2 | 2 | no | — |
| 299 | #435 | — | 4 | 2 | no | — |
| 300 | C8×D4 | — | 2 | 2 | no | — |
| 301 | #432 | — | 2 | 1 | no | — |
| 302 | #432 | — | 4 | 2 | no | — |
| 303 | #431 | — | 2 | 1 | no | — |
| 304 | #431 | — | 2 | 1 | no | — |
| 305 | #430 | — | 2 | 1 | no | — |
| 306 | C2×#104 | — | 4 | 1 | no | — |
| 307 | #419 | — | 4 | 2 | no | — |
| 308 | #416 | — | 4 | 2 | no | — |
| 309 | #413 | — | 2 | 1 | no | — |
| 310 | C2×#100 | — | 2 | 1 | no | — |
| 311 | #410 | — | 4 | 1 | no | — |
| 312 | #410 | — | 8 | 1 | no | — |
| 313 | C2×#99 | — | 4 | 1 | no | — |
| 314 | C2×#99 | — | 8 | 1 | no | — |
| 315 | #408 | — | 4 | 2 | no | — |
| 316 | C4×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 317 | #365 | — | 4 | 2 | no | — |
| 318 | #364 | — | 2 | 2 | no | — |
| 319 | #361 | — | 4 | 2 | no | — |
| 320 | #360 | — | 4 | 2 | no | — |
| 321 | #354 | — | 4 | 1 | no | — |
| 322 | #353 | — | 2 | 2 | no | — |
| 323 | #353 | — | 2 | 2 | no | — |
| 324 | #353 | — | 4 | 1 | no | — |
| 325 | #352 | — | 4 | 4 | no | — |
| 326 | AΣL(1,𝔽16) | — | 4 | 4 | no | — |
| 327 | #349 | — | 4 | 1 | no | — |
| 328 | #347 | — | 4 | 1 | no | — |
| 329 | #335 | — | 2 | 2 | no | — |
| 330 | #334 | — | 2 | 2 | no | — |
| 331 | #333 | — | 2 | 1 | no | — |
| 332 | #332 | — | 2 | 2 | no | — |
| 333 | #331 | — | 2 | 2 | no | — |
| 334 | #331 | — | 2 | 1 | no | — |
| 335 | #331 | C2×D4 | 1 | 2 | yes | — |
| 336 | #331 | C2×D4 | 1 | 2 | yes | — |
| 337 | Q8⋊C8 | — | 2 | 2 | no | — |
| 338 | Q8⋊C8 | — | 2 | 2 | no | — |
| 339 | D4⋊C8 | — | 2 | 2 | no | — |
| 340 | D4⋊C8 | — | 2 | 2 | no | — |
| 341 | #322 | — | 2 | 1 | no | — |
| 342 | #322 | C2×D4 | 1 | 1 | yes | characteristic |
| 343 | C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 344 | 2−1+4 | — | 4 | 1 | no | — |
| 345 | 2−1+4 | — | 8 | 1 | no | — |
| 346 | 2−1+4 | — | 16 | 4 | no | — |
| 347 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 348 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 349 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 350 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 351 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 352 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 353 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 354 | C2×#41 | — | 2 | 1 | no | — |
| 355 | C2×#41 | — | 4 | 1 | no | — |
| 356 | C2×#41 | — | 4 | 1 | no | — |
| 357 | C2×#41 | — | 4 | 2 | no | — |
| 358 | C2×#41 | — | 4 | 1 | no | — |
| 359 | C2×#41 | — | 8 | 2 | no | — |
| 360 | C2×#41 | — | 8 | 1 | no | — |
| 361 | C2×#41 | — | 8 | 1 | no | — |
| 362 | C2×#41 | — | 8 | 1 | no | — |
| 363 | C2×#41 | — | 8 | 2 | no | — |
| 364 | C22×Q8 | — | 2 | 1 | no | — |
| 365 | C22×Q8 | — | 4 | 2 | no | — |
| 366 | C22×Q8 | — | 8 | 1 | no | — |
| 367 | C22×D4 | — | 2 | 1 | no | — |
| 368 | C22×D4 | — | 4 | 1 | no | — |
| 369 | C22×D4 | — | 4 | 2 | no | — |
| 370 | C22×D4 | — | 4 | 1 | no | — |
| 371 | C22×D4 | — | 8 | 1 | no | — |
| 372 | C22×D4 | — | 8 | 1 | no | — |
| 373 | C23×C4 | — | 4 | 1 | no | — |
| 374 | #137 | — | 4 | 2 | no | — |
| 375 | #137 | — | 4 | 2 | no | — |
| 376 | #137 | — | 8 | 2 | no | — |
| 377 | #137 | — | 8 | 2 | no | — |
| 378 | #137 | — | 8 | 1 | no | — |
| 379 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 380 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 381 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 382 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 383 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 384 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 385 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 386 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 387 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 388 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 389 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 390 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 391 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 392 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 393 | AGL(1,ℤ/8) | — | 16 | 4 | no | — |
| 394 | #135 | — | 2 | 2 | no | — |
| 395 | #135 | — | 4 | 1 | no | — |
| 396 | #135 | — | 8 | 2 | no | — |
| 397 | #135 | — | 8 | 2 | no | — |
| 398 | #135 | — | 8 | 2 | no | — |
| 399 | #135 | — | 8 | 2 | no | — |
| 400 | #135 | — | 8 | 2 | no | — |
| 401 | C2×SD16 | — | 2 | 2 | no | — |
| 402 | C2×SD16 | — | 2 | 2 | no | — |
| 403 | C2×SD16 | — | 4 | 1 | no | — |
| 404 | C2×SD16 | — | 4 | 1 | no | — |
| 405 | C2×SD16 | — | 4 | 2 | no | — |
| 406 | C2×SD16 | — | 4 | 2 | no | — |
| 407 | C2×SD16 | — | 4 | 2 | no | — |
| 408 | C2×SD16 | — | 4 | 2 | no | — |
| 409 | C2×SD16 | — | 8 | 2 | no | — |
| 410 | C2×SD16 | — | 8 | 2 | no | — |
| 411 | C2×SD16 | — | 8 | 1 | no | — |
| 412 | C2×SD16 | — | 16 | 4 | no | — |
| 413 | C2×D8 | — | 4 | 1 | no | — |
| 414 | C2×D8 | — | 4 | 1 | no | — |
| 415 | C2×D8 | — | 4 | 1 | no | — |
| 416 | C2×D8 | — | 4 | 2 | no | — |
| 417 | C2×D8 | — | 4 | 2 | no | — |
| 418 | C2×D8 | — | 4 | 2 | no | — |
| 419 | C2×D8 | — | 4 | 2 | no | — |
| 420 | C2×D8 | — | 4 | 2 | no | — |
| 421 | C2×D8 | — | 4 | 2 | no | — |
| 422 | C2×D8 | — | 8 | 2 | no | — |
| 423 | C2×D8 | — | 8 | 2 | no | — |
| 424 | C2×D8 | — | 8 | 1 | no | — |
| 425 | #131 | — | 4 | 2 | no | — |
| 426 | #131 | — | 4 | 2 | no | — |
| 427 | #131 | — | 8 | 2 | no | — |
| 428 | C2×M16 | — | 2 | 1 | no | — |
| 429 | C2×M16 | — | 4 | 2 | no | — |
| 430 | C2×M16 | — | 4 | 1 | no | — |
| 431 | C2×M16 | — | 8 | 2 | no | — |
| 432 | C22×C8 | — | 4 | 2 | no | — |
| 433 | C4⋊Q8 | — | 2 | 1 | no | — |
| 434 | C4⋊Q8 | — | 2 | 1 | no | — |
| 435 | C4⋊Q8 | — | 4 | 2 | no | — |
| 436 | C4⋊Q8 | #120 | 1 | 1 | yes | characteristic |
| 437 | #127 | — | 2 | 1 | no | — |
| 438 | #127 | — | 2 | 1 | no | — |
| 439 | #127 | — | 2 | 1 | no | — |
| 440 | #127 | — | 4 | 1 | no | — |
| 441 | #127 | — | 4 | 2 | no | — |
| 442 | #127 | — | 8 | 1 | no | — |
| 443 | #127 | — | 16 | 1 | no | — |
| 444 | #127 | #120 | 1 | 1 | yes | characteristic |
| 445 | #127 | C22×D4 | 1 | 1 | yes | characteristic |
| 446 | #127 | C22×D4 | 1 | 1 | yes | characteristic |
| 447 | #124 | — | 2 | 1 | no | — |
| 448 | #124 | — | 4 | 1 | no | — |
| 449 | #124 | — | 4 | 2 | no | — |
| 450 | #124 | — | 4 | 2 | no | — |
| 451 | #124 | — | 4 | 1 | no | — |
| 452 | #124 | — | 8 | 2 | no | — |
| 453 | #124 | — | 8 | 2 | no | — |
| 454 | #124 | — | 8 | 1 | no | — |
| 455 | #124 | — | 8 | 2 | no | — |
| 456 | #124 | — | 16 | 1 | no | — |
| 457 | #123 | — | 4 | 2 | no | — |
| 458 | #123 | — | 4 | 2 | no | — |
| 459 | #123 | — | 8 | 1 | no | — |
| 460 | #123 | — | 8 | 1 | no | — |
| 461 | #123 | — | 8 | 4 | no | — |
| 462 | #123 | — | 16 | 2 | no | — |
| 463 | C22⋊Q8 | — | 4 | 2 | no | — |
| 464 | C22⋊Q8 | — | 8 | 2 | no | — |
| 465 | C22⋊Q8 | — | 8 | 2 | no | — |
| 466 | C22⋊Q8 | — | 8 | 1 | no | — |
| 467 | #121 | — | 2 | 2 | no | — |
| 468 | #121 | — | 4 | 1 | no | — |
| 469 | #121 | — | 4 | 2 | no | — |
| 470 | #121 | — | 4 | 2 | no | — |
| 471 | #121 | — | 4 | 1 | no | — |
| 472 | #121 | — | 4 | 1 | no | — |
| 473 | #121 | — | 4 | 2 | no | — |
| 474 | #121 | — | 4 | 1 | no | — |
| 475 | #121 | — | 8 | 2 | no | — |
| 476 | #121 | — | 8 | 1 | no | — |
| 477 | #121 | — | 8 | 1 | no | — |
| 478 | #121 | — | 8 | 2 | no | — |
| 479 | #121 | — | 8 | 2 | no | — |
| 480 | #121 | — | 16 | 2 | no | — |
| 481 | #120 | — | 4 | 2 | no | — |
| 482 | #120 | — | 4 | 2 | no | — |
| 483 | #120 | — | 8 | 2 | no | — |
| 484 | #120 | — | 8 | 4 | no | — |
| 485 | C4×Q8 | — | 2 | 2 | no | — |
| 486 | C4×Q8 | — | 2 | 2 | no | — |
| 487 | C4×Q8 | — | 4 | 1 | no | — |
| 488 | C4×Q8 | — | 4 | 1 | no | — |
| 489 | C4×D4 | — | 2 | 2 | no | — |
| 490 | C4×D4 | — | 4 | 1 | no | — |
| 491 | C4×D4 | — | 4 | 1 | no | — |
| 492 | C4×D4 | — | 4 | 1 | no | — |
| 493 | C4×D4 | — | 4 | 2 | no | — |
| 494 | C4×D4 | — | 4 | 2 | no | — |
| 495 | C4×D4 | — | 4 | 2 | no | — |
| 496 | C4×D4 | — | 4 | 2 | no | — |
| 497 | C4×D4 | — | 4 | 1 | no | — |
| 498 | C4×D4 | — | 8 | 2 | no | — |
| 499 | C4×D4 | — | 8 | 2 | no | — |
| 500 | #117 | — | 4 | 1 | no | — |
| 501 | #117 | — | 4 | 2 | no | — |
| 502 | #117 | — | 8 | 1 | no | — |
| 503 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 504 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 505 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 506 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 507 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 508 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 509 | C2×C22⋊C4 | — | 16 | 1 | no | — |
| 510 | C2×C42 | — | 4 | 1 | no | — |
| 511 | C2×C42 | #120 | 1 | 1 | yes | characteristic |
| 512 | SD32 | — | 8 | 2 | no | — |
| 513 | D16 | — | 8 | 2 | no | — |
| 514 | M32 | — | 4 | 2 | no | — |
| 515 | #108 | — | 2 | 2 | no | — |
| 516 | #108 | — | 4 | 1 | no | — |
| 517 | #107 | — | 4 | 2 | no | — |
| 518 | #106 | — | 2 | 2 | no | — |
| 519 | #106 | — | 2 | 2 | no | — |
| 520 | #106 | — | 4 | 2 | no | — |
| 521 | #106 | — | 4 | 1 | no | — |
| 522 | C4⋊C8 | — | 2 | 2 | no | — |
| 523 | C4⋊C8 | — | 2 | 2 | no | — |
| 524 | C4⋊C8 | — | 2 | 2 | no | — |
| 525 | C4⋊C8 | — | 4 | 2 | no | — |
| 526 | C4⋊C8 | — | 4 | 2 | no | — |
| 527 | #104 | — | 4 | 2 | no | — |
| 528 | #104 | — | 4 | 2 | no | — |
| 529 | #103 | — | 2 | 2 | no | — |
| 530 | #103 | — | 2 | 2 | no | — |
| 531 | #103 | — | 4 | 2 | no | — |
| 532 | #103 | — | 4 | 2 | no | — |
| 533 | #103 | — | 4 | 2 | no | — |
| 534 | #103 | — | 4 | 2 | no | — |
| 535 | #102 | — | 2 | 2 | no | — |
| 536 | #102 | — | 2 | 2 | no | — |
| 537 | #102 | — | 4 | 2 | no | — |
| 538 | #102 | — | 4 | 2 | no | — |
| 539 | #102 | — | 4 | 2 | no | — |
| 540 | #102 | — | 4 | 2 | no | — |
| 541 | #102 | — | 4 | 2 | no | — |
| 542 | #102 | — | 4 | 2 | no | — |
| 543 | #102 | — | 4 | 2 | no | — |
| 544 | #102 | — | 4 | 2 | no | — |
| 545 | #102 | — | 8 | 1 | no | — |
| 546 | #101 | — | 4 | 1 | no | — |
| 547 | #100 | — | 2 | 2 | no | — |
| 548 | #100 | — | 2 | 2 | no | — |
| 549 | #100 | — | 4 | 1 | no | — |
| 550 | #99 | — | 4 | 2 | no | — |
| 551 | #99 | — | 4 | 2 | no | — |
| 552 | #99 | — | 8 | 4 | no | — |
| 553 | #99 | — | 8 | 4 | no | — |
| 554 | #99 | — | 8 | 1 | no | — |
| 555 | #99 | — | 8 | 1 | no | — |
| 556 | C22⋊C8 | — | 2 | 2 | no | — |
| 557 | C22⋊C8 | — | 4 | 2 | no | — |
| 558 | C22⋊C8 | — | 4 | 2 | no | — |
| 559 | C22⋊C8 | — | 4 | 1 | no | — |
| 560 | C22⋊C8 | — | 4 | 1 | no | — |
| 561 | #97 | — | 2 | 1 | no | — |
| 562 | #97 | — | 4 | 1 | no | — |
| 563 | #97 | — | 4 | 2 | no | — |
| 564 | #97 | — | 4 | 2 | no | — |
| 565 | C4×C8 | — | 2 | 1 | no | — |
| 566 | C4×C8 | — | 2 | 1 | no | — |
| 567 | C4×C8 | — | 4 | 1 | no | — |
| 568 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 569 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 570 | C24 | — | 4 | 1 | no | — |
| 571 | C24 | — | 4 | 2 | no | — |
| 572 | C24 | — | 8 | 1 | no | — |
| 573 | #41 | — | 4 | 2 | no | — |
| 574 | #41 | — | 4 | 2 | no | — |
| 575 | #41 | — | 8 | 1 | no | — |
| 576 | #41 | — | 8 | 1 | no | — |
| 577 | #41 | — | 8 | 1 | no | — |
| 578 | #41 | — | 8 | 1 | no | — |
| 579 | #41 | — | 8 | 2 | no | — |
| 580 | #41 | — | 8 | 2 | no | — |
| 581 | #41 | — | 8 | 2 | no | — |
| 582 | #41 | — | 8 | 2 | no | — |
| 583 | #41 | — | 8 | 4 | no | — |
| 584 | #41 | — | 16 | 2 | no | — |
| 585 | #41 | — | 16 | 1 | no | — |
| 586 | #41 | — | 16 | 2 | no | — |
| 587 | #41 | — | 16 | 1 | no | — |
| 588 | #41 | — | 16 | 2 | no | — |
| 589 | #41 | — | 16 | 2 | no | — |
| 590 | #41 | — | 16 | 2 | no | — |
| 591 | #41 | — | 16 | 1 | no | — |
| 592 | #41 | — | 16 | 8 | no | — |
| 593 | #41 | — | 16 | 4 | no | — |
| 594 | C2×Q8 | — | 2 | 2 | no | — |
| 595 | C2×Q8 | — | 2 | 1 | no | — |
| 596 | C2×Q8 | — | 4 | 1 | no | — |
| 597 | C2×Q8 | — | 4 | 1 | no | — |
| 598 | C2×Q8 | — | 4 | 1 | no | — |
| 599 | C2×Q8 | — | 4 | 1 | no | — |
| 600 | C2×Q8 | — | 8 | 2 | no | — |
| 601 | C2×Q8 | — | 8 | 2 | no | — |
| 602 | C2×Q8 | — | 8 | 1 | no | — |
| 603 | C2×Q8 | — | 8 | 2 | no | — |
| 604 | C2×Q8 | — | 8 | 4 | no | — |
| 605 | C2×Q8 | — | 16 | 2 | no | — |
| 606 | C2×Q8 | — | 16 | 4 | no | — |
| 607 | C2×D4 | — | 2 | 2 | no | — |
| 608 | C2×D4 | — | 2 | 1 | no | — |
| 609 | C2×D4 | — | 2 | 1 | no | — |
| 610 | C2×D4 | — | 2 | 1 | no | — |
| 611 | C2×D4 | — | 4 | 1 | no | — |
| 612 | C2×D4 | — | 4 | 1 | no | — |
| 613 | C2×D4 | — | 4 | 1 | no | — |
| 614 | C2×D4 | — | 4 | 1 | no | — |
| 615 | C2×D4 | — | 4 | 1 | no | — |
| 616 | C2×D4 | — | 4 | 1 | no | — |
| 617 | C2×D4 | — | 4 | 1 | no | — |
| 618 | C2×D4 | — | 4 | 1 | no | — |
| 619 | C2×D4 | — | 4 | 2 | no | — |
| 620 | C2×D4 | — | 4 | 1 | no | — |
| 621 | C2×D4 | — | 4 | 1 | no | — |
| 622 | C2×D4 | — | 4 | 1 | no | — |
| 623 | C2×D4 | — | 8 | 1 | no | — |
| 624 | C2×D4 | — | 8 | 1 | no | — |
| 625 | C2×D4 | — | 8 | 1 | no | — |
| 626 | C2×D4 | — | 8 | 2 | no | — |
| 627 | C2×D4 | — | 8 | 2 | no | — |
| 628 | C2×D4 | — | 8 | 1 | no | — |
| 629 | C2×D4 | — | 8 | 2 | no | — |
| 630 | C2×D4 | — | 8 | 2 | no | — |
| 631 | C2×D4 | — | 8 | 2 | no | — |
| 632 | C2×D4 | — | 8 | 2 | no | — |
| 633 | C2×D4 | — | 8 | 1 | no | — |
| 634 | C2×D4 | — | 8 | 2 | no | — |
| 635 | C2×D4 | — | 8 | 2 | no | — |
| 636 | C2×D4 | — | 8 | 2 | no | — |
| 637 | C2×D4 | — | 8 | 1 | no | — |
| 638 | C2×D4 | — | 8 | 1 | no | — |
| 639 | C2×D4 | — | 16 | 2 | no | — |
| 640 | C2×D4 | — | 16 | 2 | no | — |
| 641 | C2×D4 | — | 16 | 2 | no | — |
| 642 | C2×D4 | — | 16 | 2 | no | — |
| 643 | C2×D4 | — | 16 | 1 | no | — |
| 644 | C2×D4 | — | 16 | 1 | no | — |
| 645 | C2×D4 | — | 16 | 1 | no | — |
| 646 | C2×D4 | — | 16 | 1 | no | — |
| 647 | C2×D4 | — | 16 | 1 | no | — |
| 648 | C2×D4 | — | 16 | 2 | no | — |
| 649 | C2×D4 | — | 16 | 4 | no | — |
| 650 | C22×C4 | — | 2 | 1 | no | — |
| 651 | C22×C4 | — | 4 | 2 | no | — |
| 652 | C22×C4 | — | 4 | 1 | no | — |
| 653 | C22×C4 | — | 4 | 1 | no | — |
| 654 | C22×C4 | — | 4 | 1 | no | — |
| 655 | C22×C4 | — | 4 | 2 | no | — |
| 656 | C22×C4 | — | 8 | 1 | no | — |
| 657 | C22×C4 | — | 8 | 2 | no | — |
| 658 | C22×C4 | — | 8 | 1 | no | — |
| 659 | C22×C4 | — | 8 | 1 | no | — |
| 660 | C22×C4 | — | 8 | 2 | no | — |
| 661 | C22×C4 | — | 8 | 1 | no | — |
| 662 | C22×C4 | — | 8 | 2 | no | — |
| 663 | C22×C4 | — | 16 | 1 | no | — |
| 664 | C22×C4 | — | 16 | 1 | no | — |
| 665 | C22×C4 | — | 16 | 1 | no | — |
| 666 | C22×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 667 | Q16 | — | 2 | 2 | no | — |
| 668 | Q16 | — | 4 | 1 | no | — |
| 669 | Q16 | — | 8 | 2 | no | — |
| 670 | SD16 | — | 4 | 2 | no | — |
| 671 | SD16 | — | 4 | 2 | no | — |
| 672 | SD16 | — | 8 | 2 | no | — |
| 673 | SD16 | — | 8 | 2 | no | — |
| 674 | SD16 | — | 8 | 2 | no | — |
| 675 | SD16 | — | 8 | 2 | no | — |
| 676 | SD16 | — | 8 | 2 | no | — |
| 677 | SD16 | — | 8 | 4 | no | — |
| 678 | SD16 | — | 8 | 2 | no | — |
| 679 | SD16 | — | 8 | 2 | no | — |
| 680 | SD16 | — | 8 | 2 | no | — |
| 681 | SD16 | — | 16 | 2 | no | — |
| 682 | SD16 | — | 16 | 2 | no | — |
| 683 | SD16 | — | 16 | 2 | no | — |
| 684 | D8 | — | 2 | 2 | no | — |
| 685 | D8 | — | 4 | 1 | no | — |
| 686 | D8 | — | 8 | 2 | no | — |
| 687 | D8 | — | 8 | 2 | no | — |
| 688 | D8 | — | 8 | 2 | no | — |
| 689 | D8 | — | 8 | 2 | no | — |
| 690 | D8 | — | 8 | 2 | no | — |
| 691 | D8 | — | 8 | 2 | no | — |
| 692 | D8 | — | 16 | 2 | no | — |
| 693 | D8 | — | 16 | 2 | no | — |
| 694 | D8 | — | 16 | 2 | no | — |
| 695 | D8 | — | 16 | 2 | no | — |
| 696 | D8 | — | 16 | 2 | no | — |
| 697 | D8 | — | 16 | 2 | no | — |
| 698 | M16 | — | 4 | 2 | no | — |
| 699 | M16 | — | 4 | 2 | no | — |
| 700 | M16 | — | 8 | 2 | no | — |
| 701 | M16 | — | 8 | 2 | no | — |
| 702 | M16 | — | 8 | 1 | no | — |
| 703 | M16 | — | 16 | 2 | no | — |
| 704 | C2×C8 | — | 2 | 1 | no | — |
| 705 | C2×C8 | — | 2 | 2 | no | — |
| 706 | C2×C8 | — | 2 | 2 | no | — |
| 707 | C2×C8 | — | 2 | 1 | no | — |
| 708 | C2×C8 | — | 4 | 2 | no | — |
| 709 | C2×C8 | — | 4 | 2 | no | — |
| 710 | C2×C8 | — | 8 | 2 | no | — |
| 711 | C2×C8 | — | 8 | 2 | no | — |
| 712 | C2×C8 | — | 8 | 1 | no | — |
| 713 | C2×C8 | — | 16 | 2 | no | — |
| 714 | C4⋊C4 | — | 2 | 2 | no | — |
| 715 | C4⋊C4 | — | 2 | 2 | no | — |
| 716 | C4⋊C4 | — | 4 | 1 | no | — |
| 717 | C4⋊C4 | — | 4 | 1 | no | — |
| 718 | C4⋊C4 | — | 4 | 1 | no | — |
| 719 | C4⋊C4 | — | 4 | 2 | no | — |
| 720 | C4⋊C4 | — | 4 | 1 | no | — |
| 721 | C4⋊C4 | — | 4 | 2 | no | — |
| 722 | C4⋊C4 | — | 4 | 1 | no | — |
| 723 | C4⋊C4 | — | 8 | 2 | no | — |
| 724 | C4⋊C4 | — | 16 | 4 | no | — |
| 725 | C4⋊C4 | — | 16 | 1 | no | — |
| 726 | C22⋊C4 | — | 4 | 2 | no | — |
| 727 | C22⋊C4 | — | 4 | 2 | no | — |
| 728 | C22⋊C4 | — | 4 | 2 | no | — |
| 729 | C22⋊C4 | — | 4 | 2 | no | — |
| 730 | C22⋊C4 | — | 8 | 1 | no | — |
| 731 | C22⋊C4 | — | 8 | 1 | no | — |
| 732 | C22⋊C4 | — | 8 | 1 | no | — |
| 733 | C22⋊C4 | — | 8 | 2 | no | — |
| 734 | C22⋊C4 | — | 8 | 2 | no | — |
| 735 | C22⋊C4 | — | 8 | 2 | no | — |
| 736 | C22⋊C4 | — | 8 | 2 | no | — |
| 737 | C22⋊C4 | — | 8 | 2 | no | — |
| 738 | C22⋊C4 | — | 8 | 1 | no | — |
| 739 | C22⋊C4 | — | 8 | 2 | no | — |
| 740 | C22⋊C4 | — | 8 | 2 | no | — |
| 741 | C22⋊C4 | — | 16 | 4 | no | — |
| 742 | C22⋊C4 | — | 16 | 1 | no | — |
| 743 | C22⋊C4 | — | 16 | 4 | no | — |
| 744 | C42 | — | 2 | 1 | no | — |
| 745 | C42 | — | 4 | 2 | no | — |
| 746 | C42 | — | 4 | 2 | no | — |
| 747 | C42 | — | 8 | 1 | no | — |
| 748 | C42 | — | 16 | 1 | no | — |
| 749 | C42 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 750 | C42 | C2×#120 | 1 | 1 | yes | characteristic |
| 751 | C16 | — | 8 | 2 | no | — |
| 752 | C23 | — | 4 | 2 | no | — |
| 753 | C23 | — | 4 | 1 | no | — |
| 754 | C23 | — | 4 | 1 | no | — |
| 755 | C23 | — | 4 | 1 | no | — |
| 756 | C23 | — | 8 | 1 | no | — |
| 757 | C23 | — | 8 | 1 | no | — |
| 758 | C23 | — | 8 | 1 | no | — |
| 759 | C23 | — | 8 | 2 | no | — |
| 760 | C23 | — | 8 | 2 | no | — |
| 761 | C23 | — | 8 | 1 | no | — |
| 762 | C23 | — | 16 | 2 | no | — |
| 763 | C23 | — | 16 | 1 | no | — |
| 764 | C23 | — | 16 | 2 | no | — |
| 765 | C23 | — | 32 | 2 | no | — |
| 766 | C23 | — | 32 | 2 | no | — |
| 767 | C23 | #2196 | 1 | 1 | yes | characteristic |
| 768 | Q8 | — | 4 | 2 | no | — |
| 769 | Q8 | — | 4 | 2 | no | — |
| 770 | Q8 | — | 4 | 2 | no | — |
| 771 | Q8 | — | 8 | 1 | no | — |
| 772 | Q8 | — | 8 | 1 | no | — |
| 773 | Q8 | — | 8 | 2 | no | — |
| 774 | Q8 | — | 8 | 2 | no | — |
| 775 | Q8 | — | 16 | 1 | no | — |
| 776 | Q8 | — | 16 | 1 | no | — |
| 777 | Q8 | — | 16 | 4 | no | — |
| 778 | D4 | — | 4 | 2 | no | — |
| 779 | D4 | — | 4 | 2 | no | — |
| 780 | D4 | — | 4 | 2 | no | — |
| 781 | D4 | — | 8 | 1 | no | — |
| 782 | D4 | — | 8 | 1 | no | — |
| 783 | D4 | — | 8 | 1 | no | — |
| 784 | D4 | — | 8 | 1 | no | — |
| 785 | D4 | — | 8 | 2 | no | — |
| 786 | D4 | — | 8 | 2 | no | — |
| 787 | D4 | — | 8 | 2 | no | — |
| 788 | D4 | — | 8 | 2 | no | — |
| 789 | D4 | — | 8 | 2 | no | — |
| 790 | D4 | — | 8 | 2 | no | — |
| 791 | D4 | — | 8 | 2 | no | — |
| 792 | D4 | — | 16 | 1 | no | — |
| 793 | D4 | — | 16 | 1 | no | — |
| 794 | D4 | — | 16 | 1 | no | — |
| 795 | D4 | — | 16 | 1 | no | — |
| 796 | D4 | — | 16 | 2 | no | — |
| 797 | D4 | — | 16 | 1 | no | — |
| 798 | D4 | — | 16 | 2 | no | — |
| 799 | D4 | — | 16 | 2 | no | — |
| 800 | D4 | — | 16 | 2 | no | — |
| 801 | D4 | — | 16 | 2 | no | — |
| 802 | D4 | — | 16 | 1 | no | — |
| 803 | D4 | — | 16 | 4 | no | — |
| 804 | D4 | — | 16 | 2 | no | — |
| 805 | D4 | — | 32 | 1 | no | — |
| 806 | D4 | — | 32 | 2 | no | — |
| 807 | D4 | — | 32 | 2 | no | — |
| 808 | D4 | — | 64 | 4 | no | — |
| 809 | C2×C4 | — | 2 | 1 | no | — |
| 810 | C2×C4 | — | 2 | 1 | no | — |
| 811 | C2×C4 | — | 4 | 1 | no | — |
| 812 | C2×C4 | — | 4 | 2 | no | — |
| 813 | C2×C4 | — | 4 | 2 | no | — |
| 814 | C2×C4 | — | 4 | 2 | no | — |
| 815 | C2×C4 | — | 4 | 2 | no | — |
| 816 | C2×C4 | — | 4 | 1 | no | — |
| 817 | C2×C4 | — | 8 | 1 | no | — |
| 818 | C2×C4 | — | 8 | 1 | no | — |
| 819 | C2×C4 | — | 8 | 2 | no | — |
| 820 | C2×C4 | — | 8 | 2 | no | — |
| 821 | C2×C4 | — | 8 | 2 | no | — |
| 822 | C2×C4 | — | 8 | 2 | no | — |
| 823 | C2×C4 | — | 8 | 1 | no | — |
| 824 | C2×C4 | — | 8 | 2 | no | — |
| 825 | C2×C4 | — | 8 | 2 | no | — |
| 826 | C2×C4 | — | 8 | 2 | no | — |
| 827 | C2×C4 | — | 8 | 1 | no | — |
| 828 | C2×C4 | — | 16 | 2 | no | — |
| 829 | C2×C4 | — | 16 | 1 | no | — |
| 830 | C2×C4 | — | 16 | 1 | no | — |
| 831 | C2×C4 | — | 16 | 2 | no | — |
| 832 | C2×C4 | — | 16 | 4 | no | — |
| 833 | C2×C4 | — | 16 | 4 | no | — |
| 834 | C2×C4 | — | 16 | 2 | no | — |
| 835 | C2×C4 | — | 16 | 2 | no | — |
| 836 | C2×C4 | — | 16 | 2 | no | — |
| 837 | C2×C4 | — | 32 | 1 | no | — |
| 838 | C2×C4 | — | 32 | 2 | no | — |
| 839 | C2×C4 | #2196 | 1 | 1 | yes | characteristic |
| 840 | C2×C4 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 841 | C8 | — | 2 | 2 | no | — |
| 842 | C8 | — | 4 | 1 | no | — |
| 843 | C8 | — | 4 | 2 | no | — |
| 844 | C8 | — | 4 | 2 | no | — |
| 845 | C8 | — | 8 | 2 | no | — |
| 846 | C8 | — | 8 | 2 | no | — |
| 847 | C8 | — | 8 | 2 | no | — |
| 848 | C22 | — | 2 | 1 | no | — |
| 849 | C22 | — | 4 | 1 | no | — |
| 850 | C22 | — | 8 | 2 | no | — |
| 851 | C22 | — | 8 | 2 | no | — |
| 852 | C22 | — | 8 | 1 | no | — |
| 853 | C22 | — | 8 | 1 | no | — |
| 854 | C22 | — | 8 | 2 | no | — |
| 855 | C22 | — | 8 | 1 | no | — |
| 856 | C22 | — | 8 | 2 | no | — |
| 857 | C22 | — | 16 | 1 | no | — |
| 858 | C22 | — | 16 | 1 | no | — |
| 859 | C22 | — | 16 | 1 | no | — |
| 860 | C22 | — | 16 | 1 | no | — |
| 861 | C22 | — | 16 | 1 | no | — |
| 862 | C22 | — | 16 | 2 | no | — |
| 863 | C22 | — | 16 | 1 | no | — |
| 864 | C22 | — | 32 | 1 | no | — |
| 865 | C22 | — | 32 | 1 | no | — |
| 866 | C22 | — | 32 | 2 | no | — |
| 867 | C22 | — | 32 | 4 | no | — |
| 868 | C22 | — | 32 | 2 | no | — |
| 869 | C22 | — | 64 | 1 | no | — |
| 870 | C22 | C2×#2196 | 1 | 1 | yes | characteristic |
| 871 | C4 | — | 2 | 2 | no | — |
| 872 | C4 | — | 2 | 1 | no | — |
| 873 | C4 | — | 2 | 1 | no | — |
| 874 | C4 | — | 4 | 1 | no | — |
| 875 | C4 | — | 8 | 2 | no | — |
| 876 | C4 | — | 8 | 2 | no | — |
| 877 | C4 | — | 8 | 1 | no | — |
| 878 | C4 | — | 8 | 2 | no | — |
| 879 | C4 | — | 8 | 2 | no | — |
| 880 | C4 | — | 16 | 1 | no | — |
| 881 | C4 | — | 32 | 2 | no | — |
| 882 | C4 | — | 32 | 2 | no | — |
| 883 | C2 | — | 2 | 1 | no | — |
| 884 | C2 | — | 4 | 1 | no | — |
| 885 | C2 | — | 16 | 1 | no | — |
| 886 | C2 | — | 16 | 1 | no | — |
| 887 | C2 | — | 16 | 2 | no | — |
| 888 | C2 | — | 16 | 1 | no | — |
| 889 | C2 | — | 16 | 2 | no | — |
| 890 | C2 | — | 32 | 1 | no | — |
| 891 | C2 | #512862 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #512862 |
| commutator, Frattini, cosocle | #493 | C24 |
| LCS | G ▷ #493 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #3151 ◁ G | |
| LECS | G ▷ #493 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #6365636 | C2 | semidirect |
| 2. #512867 | C2 | semidirect |
| 3. #512863 | C2 | semidirect |
| 4. #489351 | C2 | semidirect |
| 5. #153633 | C2 | semidirect |
| 6. #153617 | C2 | semidirect |
| 7. #153539 | C2 | semidirect |
| 8. #153462 | C2 | semidirect |
| 9. #153457 | C2 | semidirect |
| 16. #20310 | C22 | semidirect |
| 21. #20067 | C22 | semidirect |
| 43. #7533 | C22 | semidirect |
| 44. #7529 | C22 | semidirect |
| 45. #7516 | C22 | semidirect |
| 46. #7515 | C22 | semidirect |
| 50. C2×#559 | D4 | semidirect |
| 74. #3184 | D4 | semidirect |
| 104. #1721 | D4 | semidirect |
| 108. #1708 | D4 | semidirect |
| 120. #1630 | D4 | semidirect |
| 134. #1555 | D4 | semidirect |
| 139. #1453 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6365636 | 2 |
| #512867 | 2 |
| #512863 | 2 |
| #489351 | 2 |
| #153633 | 2 |
| #153617 | 2 |
| #153539 | 2 |
| #153462 | 2 |
| #153457 | 2 |