Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1699 conjugacy classes of subgroups.
The subgroup lattice has 1034 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #62342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #61686 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #61682 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20064 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20059 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20035 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20030 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #19783 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #19780 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #19759 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #19757 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #19708 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #19511 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #19510 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #19329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #19263 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #18946 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #18934 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | #18862 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 21 | #18854 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 22 | #17989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 23 | #17908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 24 | #3549 | C22 | 1 | 1 | yes | characteristic |
| 25 | #3548 | C22 | 1 | 1 | yes | characteristic |
| 26 | #3497 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3497 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #3391 | — | 2 | 1 | no | — |
| 29 | #3391 | C22 | 1 | 2 | yes | complemented |
| 30 | Q8×D8 | — | 2 | 1 | no | — |
| 31 | Q8×D8 | C22 | 1 | 2 | yes | complemented |
| 32 | #3358 | — | 2 | 1 | no | — |
| 33 | #3358 | — | 2 | 1 | no | — |
| 34 | #3358 | C22 | 1 | 2 | yes | complemented |
| 35 | #3358 | C22 | 1 | 2 | yes | complemented |
| 36 | #3357 | — | 2 | 1 | no | — |
| 37 | #3354 | C22 | 1 | 2 | yes | — |
| 38 | #3332 | C22 | 1 | 2 | yes | complemented |
| 39 | #3329 | C22 | 1 | 2 | yes | — |
| 40 | #3321 | — | 2 | 2 | no | — |
| 41 | #3316 | — | 2 | 2 | no | — |
| 42 | #3305 | — | 2 | 1 | no | — |
| 43 | #3305 | C22 | 1 | 2 | yes | — |
| 44 | #3303 | C22 | 1 | 2 | yes | — |
| 45 | #3298 | C22 | 1 | 2 | yes | complemented |
| 46 | #3295 | — | 2 | 1 | no | — |
| 47 | #3294 | C22 | 1 | 2 | yes | — |
| 48 | #3284 | C22 | 1 | 2 | yes | complemented |
| 49 | D4×SD16 | C22 | 1 | 2 | yes | — |
| 50 | #3276 | C22 | 1 | 2 | yes | complemented |
| 51 | #3274 | — | 2 | 1 | no | — |
| 52 | #3274 | C22 | 1 | 2 | yes | — |
| 53 | #3272 | C22 | 1 | 2 | yes | — |
| 54 | #3271 | — | 2 | 2 | no | — |
| 55 | #3265 | — | 2 | 2 | no | — |
| 56 | #3254 | C22 | 1 | 1 | yes | characteristic |
| 57 | #3253 | C22 | 1 | 1 | yes | characteristic |
| 58 | #3245 | — | 2 | 2 | no | — |
| 59 | #3245 | C22 | 1 | 1 | yes | characteristic |
| 60 | #3245 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #3228 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #3214 | C22 | 1 | 1 | yes | characteristic |
| 63 | #3214 | C22 | 1 | 1 | yes | characteristic |
| 64 | #3210 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #3207 | C22 | 1 | 1 | yes | characteristic |
| 66 | #3207 | C22 | 1 | 1 | yes | characteristic |
| 67 | #3204 | — | 2 | 2 | no | — |
| 68 | #3198 | — | 2 | 2 | no | — |
| 69 | #3198 | — | 2 | 2 | no | — |
| 70 | #3169 | — | 2 | 2 | no | — |
| 71 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 72 | #3169 | C22 | 1 | 1 | yes | characteristic, complemented |
| 73 | #3167 | C22 | 1 | 1 | yes | characteristic |
| 74 | #3113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 75 | #3112 | C22 | 1 | 1 | yes | characteristic |
| 76 | #3103 | C22 | 1 | 1 | yes | characteristic |
| 77 | #3062 | — | 2 | 2 | no | — |
| 78 | #3013 | — | 2 | 2 | no | — |
| 79 | #3010 | — | 2 | 2 | no | — |
| 80 | #2981 | C22 | 1 | 1 | yes | characteristic |
| 81 | #2981 | C22 | 1 | 1 | yes | characteristic, complemented |
| 82 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 83 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 84 | #1722 | C22 | 1 | 1 | yes | characteristic |
| 85 | #1721 | C22 | 1 | 1 | yes | characteristic |
| 86 | #1720 | C22 | 1 | 1 | yes | characteristic, complemented |
| 87 | #1718 | C22 | 1 | 1 | yes | characteristic, complemented |
| 88 | #1717 | C22 | 1 | 1 | yes | characteristic |
| 89 | #1717 | C22 | 1 | 1 | yes | characteristic, complemented |
| 90 | #1715 | C22 | 1 | 1 | yes | characteristic |
| 91 | #1714 | C22 | 1 | 1 | yes | characteristic, complemented |
| 92 | #1701 | C22 | 1 | 2 | yes | complemented |
| 93 | #1701 | C22 | 1 | 2 | yes | complemented |
| 94 | #1699 | C22 | 1 | 2 | yes | complemented |
| 95 | #1697 | C22 | 1 | 2 | yes | complemented |
| 96 | #1685 | C22 | 1 | 2 | yes | — |
| 97 | #1685 | C22 | 1 | 2 | yes | complemented |
| 98 | #1684 | C22 | 1 | 2 | yes | complemented |
| 99 | #1683 | C22 | 1 | 2 | yes | complemented |
| 100 | #1682 | C22 | 1 | 2 | yes | — |
| 101 | #1681 | C22 | 1 | 2 | yes | complemented |
| 102 | #1673 | C22 | 1 | 2 | yes | complemented |
| 103 | #1672 | C22 | 1 | 2 | yes | complemented |
| 104 | #1669 | C22 | 1 | 2 | yes | complemented |
| 105 | #1667 | C22 | 1 | 2 | yes | — |
| 106 | #1667 | C22 | 1 | 2 | yes | complemented |
| 107 | #1666 | C22 | 1 | 2 | yes | — |
| 108 | #1654 | C22 | 1 | 2 | yes | complemented |
| 109 | #1651 | C22 | 1 | 2 | yes | complemented |
| 110 | #1649 | C22 | 1 | 2 | yes | complemented |
| 111 | #1647 | C22 | 1 | 2 | yes | complemented |
| 112 | #1646 | C22 | 1 | 2 | yes | — |
| 113 | #1642 | C22 | 1 | 2 | yes | complemented |
| 114 | #1641 | C22 | 1 | 2 | yes | complemented |
| 115 | #1639 | C22 | 1 | 2 | yes | — |
| 116 | #1637 | C22 | 1 | 2 | yes | complemented |
| 117 | #1631 | C22 | 1 | 2 | yes | complemented |
| 118 | #1627 | C22 | 1 | 2 | yes | — |
| 119 | #1625 | C22 | 1 | 2 | yes | complemented |
| 120 | #1625 | C22 | 1 | 2 | yes | complemented |
| 121 | #1624 | C22 | 1 | 2 | yes | — |
| 122 | #1621 | C22 | 1 | 2 | yes | — |
| 123 | #1619 | C22 | 1 | 2 | yes | — |
| 124 | #1588 | C22 | 1 | 2 | yes | complemented |
| 125 | #1588 | C22 | 1 | 2 | yes | complemented |
| 126 | #1586 | C22 | 1 | 2 | yes | complemented |
| 127 | #1586 | C22 | 1 | 2 | yes | complemented |
| 128 | #1581 | C22 | 1 | 2 | yes | complemented |
| 129 | #1581 | C22 | 1 | 2 | yes | complemented |
| 130 | SD16⋊C8 | C22 | 1 | 2 | yes | complemented |
| 131 | SD16⋊C8 | C22 | 1 | 2 | yes | complemented |
| 132 | #1571 | C22 | 1 | 1 | yes | characteristic, complemented |
| 133 | #1568 | C22 | 1 | 1 | yes | characteristic, complemented |
| 134 | #1557 | C22 | 1 | 1 | yes | characteristic, complemented |
| 135 | #1557 | C22 | 1 | 1 | yes | characteristic, complemented |
| 136 | #1552 | C22 | 1 | 1 | yes | characteristic, complemented |
| 137 | #1551 | C22 | 1 | 1 | yes | characteristic |
| 138 | #1496 | C22 | 1 | 1 | yes | characteristic |
| 139 | #1496 | C22 | 1 | 1 | yes | characteristic, complemented |
| 140 | #1487 | C22 | 1 | 1 | yes | characteristic, complemented |
| 141 | #1480 | C22 | 1 | 1 | yes | characteristic |
| 142 | #1452 | C22 | 1 | 1 | yes | characteristic, complemented |
| 143 | C2×2−1+4 | — | 2 | 1 | no | — |
| 144 | C2×2−1+4 | — | 2 | 1 | no | — |
| 145 | C2×#137 | — | 2 | 2 | no | — |
| 146 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 147 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 148 | C2×#135 | — | 2 | 2 | no | — |
| 149 | C22×SD16 | — | 2 | 2 | no | — |
| 150 | C2×#131 | — | 2 | 1 | no | — |
| 151 | #562 | — | 4 | 1 | no | — |
| 152 | H(3,𝔽4) | — | 4 | 1 | no | — |
| 153 | #555 | — | 2 | 1 | no | — |
| 154 | #555 | — | 2 | 1 | no | — |
| 155 | #555 | C23 | 1 | 2 | yes | — |
| 156 | #554 | — | 2 | 1 | no | — |
| 157 | #554 | — | 2 | 1 | no | — |
| 158 | #550 | — | 2 | 1 | no | — |
| 159 | #550 | — | 2 | 1 | no | — |
| 160 | #550 | — | 2 | 1 | no | — |
| 161 | #550 | — | 2 | 1 | no | — |
| 162 | #550 | C23 | 1 | 2 | yes | — |
| 163 | #550 | C23 | 1 | 2 | yes | — |
| 164 | D4×Q8 | — | 2 | 1 | no | — |
| 165 | D4×Q8 | — | 2 | 1 | no | — |
| 166 | D4×Q8 | C23 | 1 | 2 | yes | — |
| 167 | D4×Q8 | C23 | 1 | 2 | yes | — |
| 168 | #548 | — | 2 | 2 | no | — |
| 169 | #548 | — | 2 | 2 | no | — |
| 170 | #548 | — | 4 | 1 | no | — |
| 171 | #548 | — | 4 | 1 | no | — |
| 172 | #547 | C23 | 1 | 2 | yes | — |
| 173 | #547 | C23 | 1 | 2 | yes | — |
| 174 | D42 | — | 2 | 1 | no | — |
| 175 | D42 | — | 2 | 1 | no | — |
| 176 | D42 | C23 | 1 | 2 | yes | — |
| 177 | #540 | — | 4 | 1 | no | — |
| 178 | #537 | — | 2 | 2 | no | — |
| 179 | #537 | — | 2 | 2 | no | — |
| 180 | #537 | — | 2 | 1 | no | — |
| 181 | #537 | — | 2 | 1 | no | — |
| 182 | #537 | — | 4 | 1 | no | — |
| 183 | #537 | — | 4 | 1 | no | — |
| 184 | #535 | — | 2 | 2 | no | — |
| 185 | #535 | — | 2 | 2 | no | — |
| 186 | #535 | — | 4 | 1 | no | — |
| 187 | #533 | C23 | 1 | 1 | yes | characteristic |
| 188 | #532 | — | 2 | 2 | no | — |
| 189 | #532 | — | 2 | 2 | no | — |
| 190 | #532 | C23 | 1 | 1 | yes | characteristic |
| 191 | #532 | C23 | 1 | 1 | yes | characteristic |
| 192 | #532 | C23 | 1 | 1 | yes | characteristic |
| 193 | #532 | C23 | 1 | 1 | yes | characteristic |
| 194 | #532 | C23 | 1 | 1 | yes | characteristic |
| 195 | #532 | C23 | 1 | 1 | yes | characteristic |
| 196 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 197 | #500 | — | 2 | 2 | no | — |
| 198 | #500 | D4 | 1 | 1 | yes | characteristic |
| 199 | #500 | C23 | 1 | 1 | yes | characteristic |
| 200 | #500 | C23 | 1 | 1 | yes | characteristic |
| 201 | #498 | C23 | 1 | 1 | yes | characteristic |
| 202 | #498 | C23 | 1 | 1 | yes | characteristic |
| 203 | #496 | — | 2 | 1 | no | — |
| 204 | #496 | — | 2 | 1 | no | — |
| 205 | #494 | C23 | 1 | 1 | yes | characteristic |
| 206 | #493 | — | 2 | 2 | no | — |
| 207 | #493 | D4 | 1 | 1 | yes | characteristic |
| 208 | #493 | C23 | 1 | 1 | yes | characteristic |
| 209 | #493 | C23 | 1 | 1 | yes | characteristic |
| 210 | #493 | C23 | 1 | 1 | yes | characteristic |
| 211 | #492 | C23 | 1 | 1 | yes | characteristic |
| 212 | #492 | C23 | 1 | 1 | yes | characteristic |
| 213 | #492 | C23 | 1 | 1 | yes | characteristic |
| 214 | #492 | C23 | 1 | 1 | yes | characteristic |
| 215 | #489 | — | 2 | 1 | no | — |
| 216 | #489 | — | 2 | 1 | no | — |
| 217 | #487 | C23 | 1 | 1 | yes | characteristic |
| 218 | #487 | C23 | 1 | 1 | yes | characteristic |
| 219 | #487 | C23 | 1 | 1 | yes | characteristic |
| 220 | #487 | C23 | 1 | 1 | yes | characteristic |
| 221 | #486 | — | 2 | 2 | no | — |
| 222 | #486 | — | 2 | 2 | no | — |
| 223 | #486 | D4 | 1 | 1 | yes | characteristic |
| 224 | #486 | D4 | 1 | 1 | yes | characteristic |
| 225 | #486 | C23 | 1 | 1 | yes | characteristic |
| 226 | #486 | C23 | 1 | 1 | yes | characteristic |
| 227 | #486 | C23 | 1 | 1 | yes | characteristic |
| 228 | #486 | C23 | 1 | 1 | yes | characteristic |
| 229 | #486 | C23 | 1 | 1 | yes | characteristic |
| 230 | #486 | C23 | 1 | 1 | yes | characteristic |
| 231 | #486 | C23 | 1 | 1 | yes | characteristic |
| 232 | #486 | C23 | 1 | 1 | yes | characteristic |
| 233 | #485 | — | 2 | 2 | no | — |
| 234 | #485 | — | 2 | 2 | no | — |
| 235 | #483 | — | 2 | 1 | no | — |
| 236 | #483 | — | 2 | 2 | no | — |
| 237 | #482 | — | 2 | 2 | no | — |
| 238 | #482 | — | 2 | 2 | no | — |
| 239 | #482 | — | 4 | 1 | no | — |
| 240 | #481 | — | 2 | 2 | no | — |
| 241 | #481 | — | 2 | 2 | no | — |
| 242 | #481 | D4 | 1 | 2 | yes | — |
| 243 | #480 | — | 2 | 1 | no | — |
| 244 | #480 | — | 2 | 2 | no | — |
| 245 | #478 | — | 4 | 1 | no | — |
| 246 | #477 | — | 2 | 1 | no | — |
| 247 | #477 | C23 | 1 | 2 | yes | — |
| 248 | #476 | — | 2 | 1 | no | — |
| 249 | #476 | C23 | 1 | 2 | yes | — |
| 250 | #475 | D4 | 1 | 2 | yes | — |
| 251 | #475 | C23 | 1 | 2 | yes | — |
| 252 | #474 | — | 2 | 1 | no | — |
| 253 | #474 | — | 2 | 1 | no | — |
| 254 | #474 | — | 2 | 2 | no | — |
| 255 | #474 | — | 2 | 2 | no | — |
| 256 | #474 | — | 2 | 2 | no | — |
| 257 | #474 | — | 2 | 2 | no | — |
| 258 | #474 | C23 | 1 | 2 | yes | — |
| 259 | #474 | C23 | 1 | 2 | yes | — |
| 260 | #474 | C23 | 1 | 2 | yes | — |
| 261 | #470 | — | 2 | 2 | no | — |
| 262 | #469 | — | 2 | 2 | no | — |
| 263 | #469 | — | 2 | 2 | no | — |
| 264 | #469 | — | 2 | 2 | no | — |
| 265 | #469 | — | 2 | 2 | no | — |
| 266 | #468 | — | 2 | 2 | no | — |
| 267 | #468 | — | 2 | 2 | no | — |
| 268 | #468 | — | 2 | 2 | no | — |
| 269 | #466 | — | 2 | 1 | no | — |
| 270 | #466 | — | 2 | 1 | no | — |
| 271 | #466 | — | 2 | 2 | no | — |
| 272 | #466 | — | 2 | 2 | no | — |
| 273 | #466 | — | 2 | 2 | no | — |
| 274 | #466 | — | 2 | 2 | no | — |
| 275 | #466 | D4 | 1 | 2 | yes | — |
| 276 | #466 | D4 | 1 | 2 | yes | — |
| 277 | #465 | — | 2 | 1 | no | — |
| 278 | #465 | — | 2 | 1 | no | — |
| 279 | #465 | — | 2 | 2 | no | — |
| 280 | #465 | — | 2 | 2 | no | — |
| 281 | #465 | — | 2 | 2 | no | — |
| 282 | #465 | — | 2 | 2 | no | — |
| 283 | #464 | — | 2 | 2 | no | — |
| 284 | #463 | — | 2 | 2 | no | — |
| 285 | #463 | — | 4 | 1 | no | — |
| 286 | #462 | C23 | 1 | 2 | yes | — |
| 287 | #461 | C23 | 1 | 2 | yes | — |
| 288 | #461 | C23 | 1 | 2 | yes | — |
| 289 | #461 | C23 | 1 | 2 | yes | — |
| 290 | #460 | — | 2 | 1 | no | — |
| 291 | #460 | D4 | 1 | 2 | yes | — |
| 292 | #460 | C23 | 1 | 2 | yes | — |
| 293 | #459 | — | 2 | 2 | no | — |
| 294 | #459 | — | 2 | 2 | no | — |
| 295 | #459 | — | 2 | 1 | no | — |
| 296 | #459 | — | 2 | 1 | no | — |
| 297 | #459 | — | 2 | 1 | no | — |
| 298 | #459 | — | 2 | 2 | no | — |
| 299 | #459 | — | 2 | 2 | no | — |
| 300 | #459 | C23 | 1 | 2 | yes | — |
| 301 | #459 | C23 | 1 | 2 | yes | — |
| 302 | #459 | C23 | 1 | 2 | yes | — |
| 303 | #459 | C23 | 1 | 2 | yes | — |
| 304 | #459 | C23 | 1 | 2 | yes | — |
| 305 | #452 | — | 2 | 2 | no | — |
| 306 | #452 | — | 2 | 2 | no | — |
| 307 | #452 | — | 2 | 2 | no | — |
| 308 | #451 | — | 2 | 1 | no | — |
| 309 | #451 | — | 2 | 2 | no | — |
| 310 | #450 | — | 2 | 2 | no | — |
| 311 | #450 | — | 2 | 2 | no | — |
| 312 | #449 | — | 2 | 2 | no | — |
| 313 | #449 | — | 2 | 2 | no | — |
| 314 | #449 | — | 2 | 2 | no | — |
| 315 | #449 | — | 2 | 2 | no | — |
| 316 | #449 | — | 2 | 2 | no | — |
| 317 | #449 | — | 2 | 2 | no | — |
| 318 | #449 | — | 2 | 2 | no | — |
| 319 | #449 | — | 2 | 2 | no | — |
| 320 | #449 | — | 2 | 2 | no | — |
| 321 | #449 | — | 4 | 1 | no | — |
| 322 | #448 | — | 2 | 1 | no | — |
| 323 | #448 | — | 2 | 2 | no | — |
| 324 | #448 | — | 2 | 2 | no | — |
| 325 | #448 | — | 2 | 2 | no | — |
| 326 | #448 | D4 | 1 | 2 | yes | — |
| 327 | #447 | — | 2 | 2 | no | — |
| 328 | #447 | — | 2 | 2 | no | — |
| 329 | C8×Q8 | — | 2 | 1 | no | — |
| 330 | C8×Q8 | — | 2 | 1 | no | — |
| 331 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 332 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 333 | #441 | — | 2 | 2 | no | — |
| 334 | #440 | — | 2 | 2 | no | — |
| 335 | C4×SD16 | — | 2 | 1 | no | — |
| 336 | C4×SD16 | — | 2 | 1 | no | — |
| 337 | C4×SD16 | C23 | 1 | 2 | yes | — |
| 338 | C4×SD16 | C23 | 1 | 2 | yes | — |
| 339 | C4×D8 | — | 2 | 2 | no | — |
| 340 | C4×D8 | — | 2 | 2 | no | — |
| 341 | C4×D8 | — | 2 | 2 | no | — |
| 342 | C4×D8 | — | 2 | 2 | no | — |
| 343 | C4×D8 | — | 2 | 1 | no | — |
| 344 | C4×D8 | — | 2 | 1 | no | — |
| 345 | C4×D8 | C23 | 1 | 2 | yes | — |
| 346 | C4×D8 | C23 | 1 | 2 | yes | — |
| 347 | #436 | — | 2 | 1 | no | — |
| 348 | #436 | C23 | 1 | 2 | yes | — |
| 349 | #436 | C23 | 1 | 2 | yes | — |
| 350 | #436 | C23 | 1 | 2 | yes | — |
| 351 | #435 | — | 2 | 2 | no | — |
| 352 | #435 | — | 2 | 2 | no | — |
| 353 | C8×D4 | — | 2 | 1 | no | — |
| 354 | C8×D4 | C23 | 1 | 2 | yes | — |
| 355 | C8×D4 | C23 | 1 | 2 | yes | — |
| 356 | C8×D4 | C23 | 1 | 2 | yes | — |
| 357 | #432 | C23 | 1 | 1 | yes | characteristic |
| 358 | #432 | C23 | 1 | 1 | yes | characteristic |
| 359 | #431 | C23 | 1 | 1 | yes | characteristic |
| 360 | #431 | C23 | 1 | 1 | yes | characteristic |
| 361 | #428 | — | 2 | 2 | no | — |
| 362 | #423 | C23 | 1 | 1 | yes | characteristic |
| 363 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 364 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 365 | #419 | — | 2 | 2 | no | — |
| 366 | #417 | — | 2 | 2 | no | — |
| 367 | #416 | — | 2 | 2 | no | — |
| 368 | #416 | — | 2 | 2 | no | — |
| 369 | C2×#103 | — | 2 | 2 | no | — |
| 370 | C2×#102 | — | 2 | 2 | no | — |
| 371 | #408 | — | 2 | 1 | no | — |
| 372 | #408 | — | 2 | 2 | no | — |
| 373 | #408 | — | 2 | 2 | no | — |
| 374 | C2×C4×C8 | — | 2 | 1 | no | — |
| 375 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 376 | #335 | C23 | 1 | 2 | yes | — |
| 377 | #335 | C23 | 1 | 2 | yes | — |
| 378 | #335 | C23 | 1 | 2 | yes | — |
| 379 | #334 | C23 | 1 | 2 | yes | — |
| 380 | #333 | C23 | 1 | 2 | yes | — |
| 381 | #332 | C23 | 1 | 2 | yes | — |
| 382 | #332 | C23 | 1 | 2 | yes | — |
| 383 | #332 | C23 | 1 | 2 | yes | — |
| 384 | #332 | C23 | 1 | 2 | yes | — |
| 385 | #331 | C23 | 1 | 2 | yes | — |
| 386 | #331 | C23 | 1 | 2 | yes | — |
| 387 | #331 | C23 | 1 | 2 | yes | — |
| 388 | Q8⋊C8 | C23 | 1 | 2 | yes | — |
| 389 | Q8⋊C8 | C23 | 1 | 2 | yes | — |
| 390 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 391 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 392 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 393 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 394 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 395 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 396 | #322 | C23 | 1 | 1 | yes | characteristic |
| 397 | #322 | C23 | 1 | 1 | yes | characteristic |
| 398 | #322 | C23 | 1 | 1 | yes | characteristic |
| 399 | #322 | C23 | 1 | 1 | yes | characteristic |
| 400 | 2−1+4 | — | 8 | 4 | no | — |
| 401 | 2−1+4 | — | 8 | 4 | no | — |
| 402 | C2×#41 | — | 2 | 1 | no | — |
| 403 | C2×#41 | — | 2 | 1 | no | — |
| 404 | C2×#41 | — | 2 | 1 | no | — |
| 405 | C2×#41 | — | 2 | 2 | no | — |
| 406 | C2×#41 | — | 2 | 2 | no | — |
| 407 | C2×#41 | — | 2 | 2 | no | — |
| 408 | C2×#41 | — | 2 | 2 | no | — |
| 409 | C2×#41 | — | 2 | 1 | no | — |
| 410 | C2×#41 | — | 2 | 1 | no | — |
| 411 | C2×#41 | — | 2 | 1 | no | — |
| 412 | C2×#41 | — | 4 | 2 | no | — |
| 413 | C2×#41 | — | 4 | 2 | no | — |
| 414 | C2×#41 | — | 4 | 1 | no | — |
| 415 | C2×#41 | — | 4 | 1 | no | — |
| 416 | C22×Q8 | — | 2 | 2 | no | — |
| 417 | C22×Q8 | — | 2 | 2 | no | — |
| 418 | C22×Q8 | — | 4 | 1 | no | — |
| 419 | C22×Q8 | — | 4 | 1 | no | — |
| 420 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 421 | C22×D4 | — | 2 | 2 | no | — |
| 422 | C22×D4 | — | 2 | 2 | no | — |
| 423 | C22×D4 | — | 4 | 1 | no | — |
| 424 | #137 | — | 8 | 4 | no | — |
| 425 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 426 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 427 | #135 | — | 8 | 4 | no | — |
| 428 | C2×Q16 | — | 2 | 2 | no | — |
| 429 | C2×Q16 | — | 2 | 2 | no | — |
| 430 | C2×SD16 | — | 2 | 2 | no | — |
| 431 | C2×SD16 | — | 2 | 2 | no | — |
| 432 | C2×SD16 | — | 2 | 2 | no | — |
| 433 | C2×SD16 | — | 2 | 2 | no | — |
| 434 | C2×SD16 | — | 2 | 1 | no | — |
| 435 | C2×SD16 | — | 2 | 2 | no | — |
| 436 | C2×SD16 | — | 2 | 2 | no | — |
| 437 | C2×SD16 | — | 2 | 1 | no | — |
| 438 | C2×SD16 | — | 4 | 1 | no | — |
| 439 | C2×SD16 | — | 8 | 4 | no | — |
| 440 | C2×SD16 | C2×D4 | 1 | 2 | yes | — |
| 441 | C2×SD16 | C2×D4 | 1 | 2 | yes | — |
| 442 | C2×D8 | — | 2 | 2 | no | — |
| 443 | C2×D8 | — | 2 | 2 | no | — |
| 444 | C2×D8 | — | 2 | 2 | no | — |
| 445 | C2×D8 | — | 2 | 2 | no | — |
| 446 | C2×D8 | — | 2 | 2 | no | — |
| 447 | C2×D8 | — | 2 | 1 | no | — |
| 448 | C2×D8 | — | 2 | 2 | no | — |
| 449 | C2×D8 | — | 2 | 1 | no | — |
| 450 | C2×D8 | — | 4 | 1 | no | — |
| 451 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 452 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 453 | #131 | — | 8 | 2 | no | — |
| 454 | C2×M16 | — | 2 | 1 | no | — |
| 455 | C2×M16 | — | 2 | 2 | no | — |
| 456 | C2×M16 | — | 2 | 2 | no | — |
| 457 | C2×M16 | — | 2 | 2 | no | — |
| 458 | C22×C8 | — | 2 | 1 | no | — |
| 459 | C22×C8 | — | 2 | 2 | no | — |
| 460 | C22×C8 | — | 2 | 2 | no | — |
| 461 | C22×C8 | — | 2 | 2 | no | — |
| 462 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 463 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 464 | C4⋊Q8 | — | 2 | 2 | no | — |
| 465 | C4⋊Q8 | — | 2 | 2 | no | — |
| 466 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 467 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 468 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 469 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 470 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 471 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 472 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 473 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 474 | #127 | — | 2 | 2 | no | — |
| 475 | #127 | — | 2 | 2 | no | — |
| 476 | #127 | — | 4 | 2 | no | — |
| 477 | #127 | — | 4 | 1 | no | — |
| 478 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 479 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 480 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 481 | #127 | C24 | 1 | 1 | yes | characteristic |
| 482 | #127 | C24 | 1 | 1 | yes | characteristic |
| 483 | #127 | C24 | 1 | 1 | yes | characteristic |
| 484 | #125 | — | 2 | 1 | no | — |
| 485 | #125 | — | 4 | 1 | no | — |
| 486 | #124 | — | 2 | 1 | no | — |
| 487 | #124 | — | 2 | 1 | no | — |
| 488 | #124 | — | 2 | 1 | no | — |
| 489 | #124 | — | 2 | 1 | no | — |
| 490 | #124 | — | 2 | 1 | no | — |
| 491 | #124 | — | 2 | 1 | no | — |
| 492 | #124 | — | 4 | 2 | no | — |
| 493 | #124 | — | 4 | 2 | no | — |
| 494 | #124 | — | 4 | 2 | no | — |
| 495 | #124 | — | 4 | 2 | no | — |
| 496 | #124 | — | 4 | 2 | no | — |
| 497 | #123 | — | 4 | 2 | no | — |
| 498 | #123 | — | 4 | 2 | no | — |
| 499 | C22⋊Q8 | — | 2 | 1 | no | — |
| 500 | C22⋊Q8 | — | 2 | 1 | no | — |
| 501 | C22⋊Q8 | — | 2 | 2 | no | — |
| 502 | C22⋊Q8 | — | 2 | 2 | no | — |
| 503 | C22⋊Q8 | — | 2 | 2 | no | — |
| 504 | C22⋊Q8 | — | 2 | 2 | no | — |
| 505 | C22⋊Q8 | — | 4 | 2 | no | — |
| 506 | C22⋊Q8 | — | 4 | 2 | no | — |
| 507 | C22⋊Q8 | — | 4 | 2 | no | — |
| 508 | C22⋊Q8 | — | 4 | 2 | no | — |
| 509 | C22⋊Q8 | — | 4 | 2 | no | — |
| 510 | C22⋊Q8 | — | 4 | 2 | no | — |
| 511 | C22⋊Q8 | — | 4 | 1 | no | — |
| 512 | C22⋊Q8 | — | 4 | 1 | no | — |
| 513 | #121 | — | 2 | 1 | no | — |
| 514 | #121 | — | 2 | 1 | no | — |
| 515 | #121 | — | 2 | 1 | no | — |
| 516 | #121 | — | 2 | 2 | no | — |
| 517 | #121 | — | 2 | 2 | no | — |
| 518 | #121 | — | 2 | 2 | no | — |
| 519 | #121 | — | 2 | 2 | no | — |
| 520 | #121 | — | 2 | 1 | no | — |
| 521 | #121 | — | 2 | 1 | no | — |
| 522 | #121 | — | 2 | 1 | no | — |
| 523 | #121 | — | 2 | 1 | no | — |
| 524 | #121 | — | 2 | 1 | no | — |
| 525 | #121 | — | 2 | 1 | no | — |
| 526 | #121 | — | 2 | 2 | no | — |
| 527 | #121 | — | 2 | 2 | no | — |
| 528 | #121 | — | 2 | 2 | no | — |
| 529 | #121 | — | 2 | 2 | no | — |
| 530 | #121 | — | 4 | 2 | no | — |
| 531 | #121 | — | 4 | 2 | no | — |
| 532 | #121 | — | 4 | 2 | no | — |
| 533 | #121 | — | 4 | 2 | no | — |
| 534 | #121 | — | 4 | 1 | no | — |
| 535 | #121 | — | 4 | 1 | no | — |
| 536 | #121 | — | 4 | 1 | no | — |
| 537 | #121 | — | 4 | 1 | no | — |
| 538 | #121 | — | 4 | 2 | no | — |
| 539 | #121 | — | 4 | 2 | no | — |
| 540 | #121 | — | 4 | 2 | no | — |
| 541 | #121 | — | 4 | 2 | no | — |
| 542 | #121 | — | 4 | 2 | no | — |
| 543 | #121 | — | 4 | 2 | no | — |
| 544 | #121 | C2×D4 | 1 | 2 | yes | — |
| 545 | #121 | C2×D4 | 1 | 2 | yes | — |
| 546 | #121 | C2×D4 | 1 | 2 | yes | — |
| 547 | #120 | — | 4 | 2 | no | — |
| 548 | #120 | — | 4 | 2 | no | — |
| 549 | #120 | — | 4 | 2 | no | — |
| 550 | #120 | — | 4 | 2 | no | — |
| 551 | C4×Q8 | — | 2 | 1 | no | — |
| 552 | C4×Q8 | — | 2 | 1 | no | — |
| 553 | C4×Q8 | — | 2 | 1 | no | — |
| 554 | C4×Q8 | — | 2 | 1 | no | — |
| 555 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 556 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 557 | C4×D4 | — | 2 | 2 | no | — |
| 558 | C4×D4 | — | 2 | 2 | no | — |
| 559 | C4×D4 | — | 2 | 2 | no | — |
| 560 | C4×D4 | — | 2 | 2 | no | — |
| 561 | C4×D4 | — | 2 | 1 | no | — |
| 562 | C4×D4 | — | 2 | 1 | no | — |
| 563 | C4×D4 | — | 2 | 1 | no | — |
| 564 | C4×D4 | — | 2 | 1 | no | — |
| 565 | C4×D4 | — | 2 | 1 | no | — |
| 566 | C4×D4 | — | 2 | 1 | no | — |
| 567 | C4×D4 | — | 2 | 1 | no | — |
| 568 | C4×D4 | — | 2 | 1 | no | — |
| 569 | C4×D4 | — | 2 | 1 | no | — |
| 570 | C4×D4 | — | 4 | 2 | no | — |
| 571 | C4×D4 | — | 4 | 2 | no | — |
| 572 | C4×D4 | — | 4 | 1 | no | — |
| 573 | C4×D4 | — | 4 | 1 | no | — |
| 574 | C4×D4 | C24 | 1 | 2 | yes | — |
| 575 | C4×D4 | C24 | 1 | 2 | yes | — |
| 576 | C4×D4 | C24 | 1 | 2 | yes | — |
| 577 | #117 | — | 2 | 1 | no | — |
| 578 | #117 | — | 2 | 2 | no | — |
| 579 | #117 | — | 2 | 2 | no | — |
| 580 | #117 | — | 4 | 1 | no | — |
| 581 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 582 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 583 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 584 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 585 | C2×C42 | — | 2 | 1 | no | — |
| 586 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 587 | #107 | — | 2 | 1 | no | — |
| 588 | #107 | — | 2 | 1 | no | — |
| 589 | #107 | — | 2 | 2 | no | — |
| 590 | #107 | — | 2 | 2 | no | — |
| 591 | #107 | — | 2 | 2 | no | — |
| 592 | #107 | — | 2 | 2 | no | — |
| 593 | #107 | — | 4 | 1 | no | — |
| 594 | #107 | C2×D4 | 1 | 2 | yes | — |
| 595 | #107 | C2×D4 | 1 | 2 | yes | — |
| 596 | #106 | — | 2 | 1 | no | — |
| 597 | #106 | — | 2 | 1 | no | — |
| 598 | #106 | — | 2 | 2 | no | — |
| 599 | #106 | — | 2 | 2 | no | — |
| 600 | #106 | — | 4 | 1 | no | — |
| 601 | #106 | C2×D4 | 1 | 2 | yes | — |
| 602 | #106 | C2×D4 | 1 | 2 | yes | — |
| 603 | C4⋊C8 | — | 2 | 2 | no | — |
| 604 | C4⋊C8 | — | 2 | 2 | no | — |
| 605 | C4⋊C8 | — | 2 | 1 | no | — |
| 606 | C4⋊C8 | — | 2 | 1 | no | — |
| 607 | C4⋊C8 | — | 2 | 1 | no | — |
| 608 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 609 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 610 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 611 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 612 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 613 | #103 | — | 2 | 2 | no | — |
| 614 | #103 | — | 2 | 2 | no | — |
| 615 | #103 | — | 2 | 2 | no | — |
| 616 | #103 | — | 2 | 1 | no | — |
| 617 | #103 | — | 2 | 2 | no | — |
| 618 | #103 | — | 2 | 1 | no | — |
| 619 | #103 | — | 2 | 2 | no | — |
| 620 | #103 | — | 2 | 2 | no | — |
| 621 | #103 | — | 2 | 2 | no | — |
| 622 | #103 | — | 2 | 2 | no | — |
| 623 | #103 | — | 4 | 1 | no | — |
| 624 | #103 | C2×D4 | 1 | 2 | yes | — |
| 625 | #103 | C2×D4 | 1 | 2 | yes | — |
| 626 | #102 | — | 2 | 2 | no | — |
| 627 | #102 | — | 2 | 2 | no | — |
| 628 | #102 | — | 2 | 2 | no | — |
| 629 | #102 | — | 2 | 2 | no | — |
| 630 | #102 | — | 2 | 1 | no | — |
| 631 | #102 | — | 2 | 2 | no | — |
| 632 | #102 | — | 2 | 2 | no | — |
| 633 | #102 | — | 2 | 1 | no | — |
| 634 | #102 | — | 2 | 1 | no | — |
| 635 | #102 | — | 2 | 1 | no | — |
| 636 | #102 | — | 2 | 1 | no | — |
| 637 | #102 | — | 2 | 1 | no | — |
| 638 | #102 | — | 2 | 2 | no | — |
| 639 | #102 | — | 2 | 2 | no | — |
| 640 | #102 | — | 2 | 2 | no | — |
| 641 | #102 | — | 2 | 2 | no | — |
| 642 | #102 | — | 2 | 2 | no | — |
| 643 | #102 | — | 2 | 2 | no | — |
| 644 | #102 | — | 4 | 1 | no | — |
| 645 | #102 | — | 4 | 1 | no | — |
| 646 | #102 | — | 4 | 1 | no | — |
| 647 | #102 | C2×D4 | 1 | 2 | yes | — |
| 648 | #102 | C2×D4 | 1 | 2 | yes | — |
| 649 | #102 | C2×D4 | 1 | 2 | yes | — |
| 650 | #102 | C2×D4 | 1 | 2 | yes | — |
| 651 | #102 | C2×D4 | 1 | 2 | yes | — |
| 652 | #102 | C2×D4 | 1 | 2 | yes | — |
| 653 | C22⋊C8 | — | 2 | 1 | no | — |
| 654 | C22⋊C8 | — | 2 | 1 | no | — |
| 655 | C22⋊C8 | — | 2 | 1 | no | — |
| 656 | C22⋊C8 | — | 2 | 2 | no | — |
| 657 | C22⋊C8 | — | 2 | 2 | no | — |
| 658 | C22⋊C8 | — | 2 | 2 | no | — |
| 659 | C22⋊C8 | — | 2 | 2 | no | — |
| 660 | C22⋊C8 | — | 2 | 2 | no | — |
| 661 | C22⋊C8 | — | 2 | 2 | no | — |
| 662 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 663 | #97 | — | 2 | 1 | no | — |
| 664 | #97 | — | 2 | 1 | no | — |
| 665 | C4×C8 | — | 2 | 2 | no | — |
| 666 | C4×C8 | — | 2 | 2 | no | — |
| 667 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 668 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 669 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 670 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 671 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 672 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 673 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 674 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 675 | C24 | — | 4 | 2 | no | — |
| 676 | #41 | — | 4 | 4 | no | — |
| 677 | #41 | — | 4 | 4 | no | — |
| 678 | #41 | — | 8 | 1 | no | — |
| 679 | #41 | — | 8 | 1 | no | — |
| 680 | #41 | — | 8 | 2 | no | — |
| 681 | #41 | — | 8 | 2 | no | — |
| 682 | #41 | — | 8 | 2 | no | — |
| 683 | #41 | — | 8 | 2 | no | — |
| 684 | #41 | — | 8 | 8 | no | — |
| 685 | #41 | — | 8 | 8 | no | — |
| 686 | #41 | — | 8 | 2 | no | — |
| 687 | #41 | — | 8 | 2 | no | — |
| 688 | #41 | — | 8 | 2 | no | — |
| 689 | #41 | — | 8 | 2 | no | — |
| 690 | #41 | — | 8 | 2 | no | — |
| 691 | #41 | — | 8 | 2 | no | — |
| 692 | #41 | — | 8 | 4 | no | — |
| 693 | #41 | — | 8 | 4 | no | — |
| 694 | #41 | — | 16 | 1 | no | — |
| 695 | C2×Q8 | — | 2 | 4 | no | — |
| 696 | C2×Q8 | — | 2 | 1 | no | — |
| 697 | C2×Q8 | — | 2 | 1 | no | — |
| 698 | C2×Q8 | — | 2 | 1 | no | — |
| 699 | C2×Q8 | — | 2 | 1 | no | — |
| 700 | C2×Q8 | — | 2 | 1 | no | — |
| 701 | C2×Q8 | — | 2 | 1 | no | — |
| 702 | C2×Q8 | — | 2 | 1 | no | — |
| 703 | C2×Q8 | — | 2 | 1 | no | — |
| 704 | C2×Q8 | — | 2 | 1 | no | — |
| 705 | C2×Q8 | — | 4 | 2 | no | — |
| 706 | C2×Q8 | — | 4 | 2 | no | — |
| 707 | C2×Q8 | — | 4 | 4 | no | — |
| 708 | C2×Q8 | — | 4 | 4 | no | — |
| 709 | C2×Q8 | — | 8 | 2 | no | — |
| 710 | C2×Q8 | — | 8 | 2 | no | — |
| 711 | C2×Q8 | — | 8 | 4 | no | — |
| 712 | C2×Q8 | — | 8 | 4 | no | — |
| 713 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 714 | C2×D4 | — | 2 | 2 | no | — |
| 715 | C2×D4 | — | 2 | 2 | no | — |
| 716 | C2×D4 | — | 2 | 2 | no | — |
| 717 | C2×D4 | — | 2 | 1 | no | — |
| 718 | C2×D4 | — | 2 | 1 | no | — |
| 719 | C2×D4 | — | 2 | 1 | no | — |
| 720 | C2×D4 | — | 2 | 1 | no | — |
| 721 | C2×D4 | — | 2 | 1 | no | — |
| 722 | C2×D4 | — | 2 | 1 | no | — |
| 723 | C2×D4 | — | 2 | 1 | no | — |
| 724 | C2×D4 | — | 2 | 1 | no | — |
| 725 | C2×D4 | — | 2 | 1 | no | — |
| 726 | C2×D4 | — | 2 | 1 | no | — |
| 727 | C2×D4 | — | 2 | 1 | no | — |
| 728 | C2×D4 | — | 2 | 1 | no | — |
| 729 | C2×D4 | — | 2 | 1 | no | — |
| 730 | C2×D4 | — | 2 | 1 | no | — |
| 731 | C2×D4 | — | 2 | 1 | no | — |
| 732 | C2×D4 | — | 4 | 2 | no | — |
| 733 | C2×D4 | — | 4 | 2 | no | — |
| 734 | C2×D4 | — | 4 | 2 | no | — |
| 735 | C2×D4 | — | 4 | 2 | no | — |
| 736 | C2×D4 | — | 4 | 2 | no | — |
| 737 | C2×D4 | — | 4 | 2 | no | — |
| 738 | C2×D4 | — | 4 | 1 | no | — |
| 739 | C2×D4 | — | 4 | 1 | no | — |
| 740 | C2×D4 | — | 4 | 2 | no | — |
| 741 | C2×D4 | — | 4 | 2 | no | — |
| 742 | C2×D4 | — | 4 | 2 | no | — |
| 743 | C2×D4 | — | 4 | 1 | no | — |
| 744 | C2×D4 | — | 8 | 2 | no | — |
| 745 | C2×D4 | — | 8 | 2 | no | — |
| 746 | C2×D4 | — | 8 | 2 | no | — |
| 747 | C2×D4 | — | 8 | 2 | no | — |
| 748 | C2×D4 | — | 16 | 2 | no | — |
| 749 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 750 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 751 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 752 | C22×C4 | — | 2 | 1 | no | — |
| 753 | C22×C4 | — | 2 | 1 | no | — |
| 754 | C22×C4 | — | 2 | 2 | no | — |
| 755 | C22×C4 | — | 2 | 2 | no | — |
| 756 | C22×C4 | — | 2 | 2 | no | — |
| 757 | C22×C4 | — | 4 | 2 | no | — |
| 758 | C22×C4 | — | 4 | 2 | no | — |
| 759 | C22×C4 | — | 4 | 2 | no | — |
| 760 | C22×C4 | — | 4 | 2 | no | — |
| 761 | C22×C4 | — | 4 | 2 | no | — |
| 762 | C22×C4 | — | 4 | 2 | no | — |
| 763 | C22×C4 | — | 4 | 1 | no | — |
| 764 | C22×C4 | — | 4 | 1 | no | — |
| 765 | C22×C4 | — | 4 | 1 | no | — |
| 766 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 767 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 768 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 769 | Q16 | — | 4 | 4 | no | — |
| 770 | Q16 | — | 8 | 2 | no | — |
| 771 | SD16 | — | 2 | 4 | no | — |
| 772 | SD16 | — | 2 | 4 | no | — |
| 773 | SD16 | — | 4 | 2 | no | — |
| 774 | SD16 | — | 4 | 4 | no | — |
| 775 | SD16 | — | 8 | 1 | no | — |
| 776 | SD16 | — | 8 | 2 | no | — |
| 777 | SD16 | — | 8 | 2 | no | — |
| 778 | SD16 | — | 8 | 2 | no | — |
| 779 | SD16 | — | 8 | 2 | no | — |
| 780 | SD16 | — | 8 | 2 | no | — |
| 781 | SD16 | — | 16 | 1 | no | — |
| 782 | D8 | — | 4 | 2 | no | — |
| 783 | D8 | — | 4 | 2 | no | — |
| 784 | D8 | — | 4 | 2 | no | — |
| 785 | D8 | — | 8 | 1 | no | — |
| 786 | D8 | — | 8 | 2 | no | — |
| 787 | D8 | — | 8 | 2 | no | — |
| 788 | D8 | — | 8 | 2 | no | — |
| 789 | D8 | — | 8 | 2 | no | — |
| 790 | D8 | — | 8 | 2 | no | — |
| 791 | D8 | — | 8 | 2 | no | — |
| 792 | D8 | — | 16 | 1 | no | — |
| 793 | M16 | — | 4 | 4 | no | — |
| 794 | M16 | — | 8 | 2 | no | — |
| 795 | M16 | — | 8 | 2 | no | — |
| 796 | M16 | — | 8 | 1 | no | — |
| 797 | C2×C8 | — | 2 | 2 | no | — |
| 798 | C2×C8 | — | 2 | 2 | no | — |
| 799 | C2×C8 | — | 2 | 2 | no | — |
| 800 | C2×C8 | — | 2 | 2 | no | — |
| 801 | C2×C8 | — | 2 | 1 | no | — |
| 802 | C2×C8 | — | 2 | 1 | no | — |
| 803 | C2×C8 | — | 4 | 1 | no | — |
| 804 | C2×C8 | — | 4 | 1 | no | — |
| 805 | C2×C8 | — | 8 | 2 | no | — |
| 806 | C2×C8 | — | 8 | 2 | no | — |
| 807 | C2×C8 | — | 8 | 2 | no | — |
| 808 | C2×C8 | — | 8 | 1 | no | — |
| 809 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 810 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 811 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 812 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 813 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 814 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 815 | C4⋊C4 | — | 2 | 2 | no | — |
| 816 | C4⋊C4 | — | 2 | 1 | no | — |
| 817 | C4⋊C4 | — | 2 | 1 | no | — |
| 818 | C4⋊C4 | — | 2 | 1 | no | — |
| 819 | C4⋊C4 | — | 2 | 1 | no | — |
| 820 | C4⋊C4 | — | 2 | 2 | no | — |
| 821 | C4⋊C4 | — | 2 | 1 | no | — |
| 822 | C4⋊C4 | — | 2 | 1 | no | — |
| 823 | C4⋊C4 | — | 2 | 1 | no | — |
| 824 | C4⋊C4 | — | 2 | 1 | no | — |
| 825 | C4⋊C4 | — | 2 | 1 | no | — |
| 826 | C4⋊C4 | — | 2 | 1 | no | — |
| 827 | C4⋊C4 | — | 2 | 1 | no | — |
| 828 | C4⋊C4 | — | 2 | 1 | no | — |
| 829 | C4⋊C4 | — | 2 | 1 | no | — |
| 830 | C4⋊C4 | — | 2 | 1 | no | — |
| 831 | C4⋊C4 | — | 4 | 2 | no | — |
| 832 | C4⋊C4 | — | 4 | 2 | no | — |
| 833 | C4⋊C4 | — | 4 | 2 | no | — |
| 834 | C4⋊C4 | — | 4 | 2 | no | — |
| 835 | C4⋊C4 | — | 4 | 1 | no | — |
| 836 | C4⋊C4 | — | 4 | 1 | no | — |
| 837 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 838 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 839 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 840 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 841 | C22⋊C4 | — | 2 | 2 | no | — |
| 842 | C22⋊C4 | — | 2 | 2 | no | — |
| 843 | C22⋊C4 | — | 2 | 2 | no | — |
| 844 | C22⋊C4 | — | 2 | 2 | no | — |
| 845 | C22⋊C4 | — | 2 | 2 | no | — |
| 846 | C22⋊C4 | — | 2 | 2 | no | — |
| 847 | C22⋊C4 | — | 4 | 2 | no | — |
| 848 | C22⋊C4 | — | 4 | 2 | no | — |
| 849 | C22⋊C4 | — | 4 | 2 | no | — |
| 850 | C22⋊C4 | — | 4 | 2 | no | — |
| 851 | C22⋊C4 | — | 4 | 2 | no | — |
| 852 | C22⋊C4 | — | 4 | 2 | no | — |
| 853 | C22⋊C4 | — | 4 | 2 | no | — |
| 854 | C22⋊C4 | — | 4 | 2 | no | — |
| 855 | C22⋊C4 | — | 4 | 2 | no | — |
| 856 | C22⋊C4 | — | 4 | 1 | no | — |
| 857 | C22⋊C4 | — | 4 | 1 | no | — |
| 858 | C22⋊C4 | — | 4 | 1 | no | — |
| 859 | C22⋊C4 | — | 4 | 1 | no | — |
| 860 | C22⋊C4 | — | 4 | 1 | no | — |
| 861 | C22⋊C4 | — | 4 | 1 | no | — |
| 862 | C22⋊C4 | — | 4 | 1 | no | — |
| 863 | C42 | — | 2 | 2 | no | — |
| 864 | C42 | — | 2 | 2 | no | — |
| 865 | C42 | — | 4 | 2 | no | — |
| 866 | C42 | — | 4 | 1 | no | — |
| 867 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 868 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 869 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 870 | C42 | C25 | 1 | 1 | yes | characteristic |
| 871 | C23 | — | 2 | 2 | no | — |
| 872 | C23 | — | 2 | 2 | no | — |
| 873 | C23 | — | 2 | 2 | no | — |
| 874 | C23 | — | 4 | 1 | no | — |
| 875 | C23 | — | 4 | 1 | no | — |
| 876 | C23 | — | 4 | 1 | no | — |
| 877 | C23 | — | 16 | 2 | no | — |
| 878 | C23 | — | 16 | 2 | no | — |
| 879 | C23 | — | 16 | 2 | no | — |
| 880 | C23 | D42 | 1 | 1 | yes | characteristic |
| 881 | Q8 | — | 2 | 4 | no | — |
| 882 | Q8 | — | 2 | 2 | no | — |
| 883 | Q8 | — | 4 | 1 | no | — |
| 884 | Q8 | — | 4 | 1 | no | — |
| 885 | Q8 | — | 4 | 2 | no | — |
| 886 | Q8 | — | 4 | 2 | no | — |
| 887 | Q8 | — | 4 | 2 | no | — |
| 888 | Q8 | — | 8 | 1 | no | — |
| 889 | Q8 | — | 8 | 1 | no | — |
| 890 | Q8 | — | 8 | 1 | no | — |
| 891 | Q8 | — | 8 | 4 | no | — |
| 892 | Q8 | — | 8 | 4 | no | — |
| 893 | Q8 | — | 8 | 1 | no | — |
| 894 | Q8 | #576 | 1 | 4 | yes | — |
| 895 | D4 | — | 2 | 2 | no | — |
| 896 | D4 | — | 2 | 2 | no | — |
| 897 | D4 | — | 2 | 2 | no | — |
| 898 | D4 | — | 2 | 2 | no | — |
| 899 | D4 | — | 2 | 2 | no | — |
| 900 | D4 | — | 2 | 2 | no | — |
| 901 | D4 | — | 4 | 2 | no | — |
| 902 | D4 | — | 4 | 1 | no | — |
| 903 | D4 | — | 4 | 1 | no | — |
| 904 | D4 | — | 4 | 1 | no | — |
| 905 | D4 | — | 4 | 1 | no | — |
| 906 | D4 | — | 4 | 1 | no | — |
| 907 | D4 | — | 4 | 1 | no | — |
| 908 | D4 | — | 4 | 2 | no | — |
| 909 | D4 | — | 4 | 2 | no | — |
| 910 | D4 | — | 4 | 2 | no | — |
| 911 | D4 | — | 8 | 1 | no | — |
| 912 | D4 | — | 8 | 1 | no | — |
| 913 | D4 | — | 8 | 1 | no | — |
| 914 | D4 | — | 8 | 1 | no | — |
| 915 | D4 | — | 8 | 1 | no | — |
| 916 | D4 | — | 8 | 4 | no | — |
| 917 | D4 | — | 8 | 4 | no | — |
| 918 | D4 | — | 8 | 1 | no | — |
| 919 | D4 | — | 8 | 1 | no | — |
| 920 | D4 | — | 8 | 1 | no | — |
| 921 | D4 | — | 8 | 2 | no | — |
| 922 | D4 | — | 8 | 2 | no | — |
| 923 | D4 | — | 8 | 2 | no | — |
| 924 | D4 | — | 8 | 2 | no | — |
| 925 | D4 | — | 8 | 2 | no | — |
| 926 | D4 | — | 16 | 2 | no | — |
| 927 | D4 | — | 16 | 2 | no | — |
| 928 | D4 | — | 16 | 2 | no | — |
| 929 | D4 | — | 16 | 2 | no | — |
| 930 | D4 | — | 16 | 1 | no | — |
| 931 | D4 | — | 16 | 2 | no | — |
| 932 | D4 | — | 16 | 2 | no | — |
| 933 | D4 | — | 16 | 2 | no | — |
| 934 | C2×C4 | — | 2 | 4 | no | — |
| 935 | C2×C4 | — | 2 | 2 | no | — |
| 936 | C2×C4 | — | 2 | 1 | no | — |
| 937 | C2×C4 | — | 2 | 1 | no | — |
| 938 | C2×C4 | — | 2 | 2 | no | — |
| 939 | C2×C4 | — | 2 | 2 | no | — |
| 940 | C2×C4 | — | 2 | 2 | no | — |
| 941 | C2×C4 | — | 2 | 2 | no | — |
| 942 | C2×C4 | — | 2 | 2 | no | — |
| 943 | C2×C4 | — | 4 | 1 | no | — |
| 944 | C2×C4 | — | 4 | 2 | no | — |
| 945 | C2×C4 | — | 4 | 2 | no | — |
| 946 | C2×C4 | — | 4 | 2 | no | — |
| 947 | C2×C4 | — | 4 | 2 | no | — |
| 948 | C2×C4 | — | 4 | 2 | no | — |
| 949 | C2×C4 | — | 4 | 2 | no | — |
| 950 | C2×C4 | — | 4 | 1 | no | — |
| 951 | C2×C4 | — | 4 | 1 | no | — |
| 952 | C2×C4 | — | 4 | 1 | no | — |
| 953 | C2×C4 | — | 4 | 1 | no | — |
| 954 | C2×C4 | — | 4 | 1 | no | — |
| 955 | C2×C4 | — | 8 | 4 | no | — |
| 956 | C2×C4 | — | 8 | 4 | no | — |
| 957 | C2×C4 | — | 8 | 4 | no | — |
| 958 | C2×C4 | — | 8 | 4 | no | — |
| 959 | C2×C4 | — | 8 | 2 | no | — |
| 960 | C2×C4 | — | 8 | 2 | no | — |
| 961 | C2×C4 | — | 8 | 2 | no | — |
| 962 | C2×C4 | — | 8 | 1 | no | — |
| 963 | C2×C4 | — | 16 | 2 | no | — |
| 964 | C2×C4 | — | 16 | 2 | no | — |
| 965 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 966 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 967 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 968 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 969 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 970 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 971 | C8 | — | 2 | 1 | no | — |
| 972 | C8 | — | 2 | 1 | no | — |
| 973 | C8 | — | 2 | 1 | no | — |
| 974 | C8 | — | 2 | 1 | no | — |
| 975 | C8 | — | 2 | 2 | no | — |
| 976 | C8 | — | 2 | 2 | no | — |
| 977 | C8 | — | 4 | 1 | no | — |
| 978 | C8 | — | 4 | 1 | no | — |
| 979 | C8 | — | 4 | 2 | no | — |
| 980 | C8 | — | 4 | 2 | no | — |
| 981 | C8 | — | 4 | 2 | no | — |
| 982 | C8 | — | 4 | 2 | no | — |
| 983 | C22 | — | 2 | 1 | no | — |
| 984 | C22 | — | 2 | 1 | no | — |
| 985 | C22 | — | 2 | 1 | no | — |
| 986 | C22 | — | 4 | 2 | no | — |
| 987 | C22 | — | 4 | 2 | no | — |
| 988 | C22 | — | 4 | 2 | no | — |
| 989 | C22 | — | 4 | 2 | no | — |
| 990 | C22 | — | 4 | 2 | no | — |
| 991 | C22 | — | 4 | 2 | no | — |
| 992 | C22 | — | 4 | 2 | no | — |
| 993 | C22 | — | 4 | 2 | no | — |
| 994 | C22 | — | 4 | 2 | no | — |
| 995 | C22 | — | 8 | 1 | no | — |
| 996 | C22 | — | 8 | 1 | no | — |
| 997 | C22 | — | 8 | 1 | no | — |
| 998 | C22 | — | 8 | 1 | no | — |
| 999 | C22 | — | 8 | 1 | no | — |
| 1000 | C22 | — | 8 | 1 | no | — |
| 1001 | C22 | — | 8 | 1 | no | — |
| 1002 | C22 | — | 8 | 1 | no | — |
| 1003 | C22 | — | 8 | 1 | no | — |
| 1004 | C22 | — | 32 | 4 | no | — |
| 1005 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 1006 | C4 | — | 2 | 4 | no | — |
| 1007 | C4 | — | 2 | 1 | no | — |
| 1008 | C4 | — | 2 | 1 | no | — |
| 1009 | C4 | — | 2 | 1 | no | — |
| 1010 | C4 | — | 2 | 1 | no | — |
| 1011 | C4 | — | 4 | 2 | no | — |
| 1012 | C4 | — | 4 | 2 | no | — |
| 1013 | C4 | — | 4 | 2 | no | — |
| 1014 | C4 | — | 4 | 2 | no | — |
| 1015 | C4 | — | 8 | 1 | no | — |
| 1016 | C4 | — | 8 | 1 | no | — |
| 1017 | C4 | — | 8 | 1 | no | — |
| 1018 | C4 | — | 8 | 1 | no | — |
| 1019 | C4 | — | 8 | 1 | no | — |
| 1020 | C4 | C2×#576 | 1 | 2 | yes | — |
| 1021 | C4 | #3585 | 1 | 1 | yes | characteristic |
| 1022 | C4 | #3586 | 1 | 1 | yes | characteristic |
| 1023 | C2 | — | 4 | 1 | no | — |
| 1024 | C2 | — | 8 | 2 | no | — |
| 1025 | C2 | — | 8 | 2 | no | — |
| 1026 | C2 | — | 8 | 2 | no | — |
| 1027 | C2 | — | 16 | 1 | no | — |
| 1028 | C2 | — | 16 | 1 | no | — |
| 1029 | C2 | — | 16 | 1 | no | — |
| 1030 | C2 | #61049 | 1 | 1 | yes | characteristic |
| 1031 | C2 | #61080 | 1 | 1 | yes | characteristic |
| 1032 | C2 | #61107 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C42 | C25 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62359 | C2 | semidirect |
| 2. #62342 | C2 | semidirect |
| 3. #61686 | C2 | semidirect |
| 4. #61682 | C2 | semidirect |
| 5. #20064 | C2 | semidirect |
| 6. #20059 | C2 | semidirect |
| 7. #20035 | C2 | semidirect |
| 8. #20030 | C2 | semidirect |
| 9. #19783 | C2 | semidirect |
| 10. #19780 | C2 | semidirect |
| 11. #19759 | C2 | semidirect |
| 12. #19757 | C2 | semidirect |
| 13. #19708 | C2 | semidirect |
| 14. #19511 | C2 | semidirect |
| 15. #19510 | C2 | semidirect |
| 16. #19329 | C2 | semidirect |
| 17. #19263 | C2 | semidirect |
| 18. #18946 | C2 | semidirect |
| 19. #18934 | C2 | semidirect |
| 20. #18862 | C2 | semidirect |
| 21. #18854 | C2 | semidirect |
| 22. #17989 | C2 | semidirect |
| 23. #17908 | C2 | semidirect |
| 27. #3497 | C22 | semidirect |
| 29. #3391 | C22 | semidirect |
| 31. Q8×D8 | C22 | semidirect |
| 34. #3358 | C22 | semidirect |
| 35. #3358 | C22 | semidirect |
| 38. #3332 | C22 | semidirect |
| 45. #3298 | C22 | semidirect |
| 48. #3284 | C22 | semidirect |
| 50. #3276 | C22 | semidirect |
| 60. #3245 | C22 | semidirect |
| 61. #3228 | C22 | semidirect |
| 64. #3210 | C22 | semidirect |
| 72. #3169 | C22 | semidirect |
| 74. #3113 | C22 | semidirect |
| 81. #2981 | C22 | semidirect |
| 82. C2×C8×Q8 | C22 | semidirect |
| 86. #1720 | C22 | semidirect |
| 87. #1718 | C22 | semidirect |
| 89. #1717 | C22 | semidirect |
| 91. #1714 | C22 | semidirect |
| 92. #1701 | C22 | semidirect |
| 93. #1701 | C22 | semidirect |
| 94. #1699 | C22 | semidirect |
| 95. #1697 | C22 | semidirect |
| 97. #1685 | C22 | semidirect |
| 98. #1684 | C22 | semidirect |
| 99. #1683 | C22 | semidirect |
| 101. #1681 | C22 | semidirect |
| 102. #1673 | C22 | semidirect |
| 103. #1672 | C22 | semidirect |
| 104. #1669 | C22 | semidirect |
| 106. #1667 | C22 | semidirect |
| 108. #1654 | C22 | semidirect |
| 109. #1651 | C22 | semidirect |
| 110. #1649 | C22 | semidirect |
| 111. #1647 | C22 | semidirect |
| 113. #1642 | C22 | semidirect |
| 114. #1641 | C22 | semidirect |
| 116. #1637 | C22 | semidirect |
| 117. #1631 | C22 | semidirect |
| 119. #1625 | C22 | semidirect |
| 120. #1625 | C22 | semidirect |
| 124. #1588 | C22 | semidirect |
| 125. #1588 | C22 | semidirect |
| 126. #1586 | C22 | semidirect |
| 127. #1586 | C22 | semidirect |
| 128. #1581 | C22 | semidirect |
| 129. #1581 | C22 | semidirect |
| 130. SD16⋊C8 | C22 | semidirect |
| 131. SD16⋊C8 | C22 | semidirect |
| 132. #1571 | C22 | semidirect |
| 133. #1568 | C22 | semidirect |
| 134. #1557 | C22 | semidirect |
| 135. #1557 | C22 | semidirect |
| 136. #1552 | C22 | semidirect |
| 139. #1496 | C22 | semidirect |
| 140. #1487 | C22 | semidirect |
| 142. #1452 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62359 | 2 |
| #62342 | 2 |
| #61686 | 2 |
| #61682 | 2 |
| #20064 | 2 |
| #20059 | 2 |
| #20035 | 2 |
| #20030 | 2 |
| #19783 | 2 |
| #19780 | 2 |
| #19759 | 2 |
| #19757 | 2 |
| #19708 | 2 |
| #19511 | 2 |
| #19510 | 2 |
| #19329 | 2 |
| #19263 | 2 |
| #18946 | 2 |
| #18934 | 2 |
| #18862 | 2 |
| #18854 | 2 |
| #17989 | 2 |
| #17908 | 2 |