Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1886 conjugacy classes of subgroups.
The subgroup lattice has 790 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61430 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61402 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#3287 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #19985 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #19975 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #19962 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #19960 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #19868 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #19867 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #19629 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #19267 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #19255 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #19170 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #18790 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #18770 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | M16×Q16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | C8×AGL(1,ℤ/8) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | C22×#135 | — | 2 | 1 | no | — |
| 19 | #3480 | C22 | 1 | 2 | yes | — |
| 20 | C2×#550 | C22 | 1 | 2 | yes | — |
| 21 | #3399 | — | 2 | 4 | no | — |
| 22 | #3399 | C22 | 1 | 4 | yes | complemented |
| 23 | #3397 | — | 2 | 4 | no | — |
| 24 | #3397 | C22 | 1 | 4 | yes | complemented |
| 25 | #3396 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #3392 | C22 | 1 | 4 | yes | complemented |
| 27 | #3391 | C22 | 1 | 4 | yes | complemented |
| 28 | #3383 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #3365 | C22 | 1 | 2 | yes | complemented |
| 30 | #3342 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #3339 | — | 2 | 1 | no | — |
| 32 | #3304 | C22 | 1 | 2 | yes | complemented |
| 33 | #3301 | — | 2 | 2 | no | — |
| 34 | #3287 | — | 2 | 2 | no | — |
| 35 | #3287 | — | 2 | 1 | no | — |
| 36 | #3287 | — | 2 | 1 | no | — |
| 37 | #3287 | C22 | 1 | 2 | yes | — |
| 38 | #3287 | C22 | 1 | 4 | yes | — |
| 39 | #3287 | C22 | 1 | 2 | yes | — |
| 40 | #3287 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #3285 | — | 2 | 1 | no | — |
| 42 | #3205 | C22 | 1 | 2 | yes | — |
| 43 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 44 | #3168 | — | 2 | 1 | no | — |
| 45 | #3151 | — | 2 | 2 | no | — |
| 46 | #3151 | C22 | 1 | 2 | yes | — |
| 47 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 48 | #3103 | C22 | 1 | 2 | yes | — |
| 49 | #3102 | — | 2 | 2 | no | — |
| 50 | C2×#466 | — | 2 | 1 | no | — |
| 51 | #3038 | — | 2 | 2 | no | — |
| 52 | #3038 | C22 | 1 | 2 | yes | — |
| 53 | #3036 | — | 2 | 2 | no | — |
| 54 | #3036 | C22 | 1 | 2 | yes | — |
| 55 | C2×#460 | C22 | 1 | 2 | yes | — |
| 56 | C2×#449 | — | 2 | 2 | no | — |
| 57 | C8×#41 | C22 | 1 | 1 | yes | characteristic |
| 58 | Q8×M16 | C22 | 1 | 2 | yes | — |
| 59 | C4×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 60 | C4×AGL(1,ℤ/8) | C22 | 1 | 1 | yes | characteristic |
| 61 | C4×#135 | — | 2 | 1 | no | — |
| 62 | C2×C4×Q16 | C22 | 1 | 1 | yes | characteristic |
| 63 | C2×C8×D4 | C22 | 1 | 1 | yes | characteristic |
| 64 | #1721 | C22 | 1 | 4 | yes | complemented |
| 65 | #1712 | C22 | 1 | 2 | yes | complemented |
| 66 | #1706 | C22 | 1 | 2 | yes | complemented |
| 67 | #1688 | C22 | 1 | 4 | yes | complemented |
| 68 | #1686 | C22 | 1 | 4 | yes | complemented |
| 69 | #1681 | C22 | 1 | 4 | yes | complemented |
| 70 | #1673 | C22 | 1 | 2 | yes | complemented |
| 71 | #1668 | C22 | 1 | 4 | yes | complemented |
| 72 | #1668 | C22 | 1 | 2 | yes | complemented |
| 73 | #1668 | C22 | 1 | 2 | yes | complemented |
| 74 | #1667 | C22 | 1 | 2 | yes | complemented |
| 75 | #1667 | C22 | 1 | 2 | yes | complemented |
| 76 | #1667 | C22 | 1 | 2 | yes | complemented |
| 77 | #1666 | C22 | 1 | 4 | yes | complemented |
| 78 | #1642 | C22 | 1 | 4 | yes | complemented |
| 79 | #1642 | C22 | 1 | 4 | yes | complemented |
| 80 | #1628 | C22 | 1 | 4 | yes | complemented |
| 81 | #1626 | C22 | 1 | 4 | yes | complemented |
| 82 | #1621 | C22 | 1 | 4 | yes | complemented |
| 83 | #1621 | C22 | 1 | 4 | yes | complemented |
| 84 | #1621 | C22 | 1 | 4 | yes | complemented |
| 85 | #1620 | C22 | 1 | 4 | yes | complemented |
| 86 | #1591 | C22 | 1 | 2 | yes | complemented |
| 87 | #1584 | C22 | 1 | 4 | yes | complemented |
| 88 | #1580 | C22 | 1 | 2 | yes | complemented |
| 89 | SD16⋊C8 | C22 | 1 | 2 | yes | complemented |
| 90 | C8×Q16 | C22 | 1 | 2 | yes | complemented |
| 91 | C8×SD16 | C22 | 1 | 2 | yes | complemented |
| 92 | C8×D8 | C22 | 1 | 2 | yes | complemented |
| 93 | #1567 | C22 | 1 | 1 | yes | characteristic |
| 94 | #1565 | C22 | 1 | 1 | yes | characteristic |
| 95 | #1547 | C22 | 1 | 2 | yes | — |
| 96 | #1545 | C22 | 1 | 2 | yes | — |
| 97 | #1487 | C22 | 1 | 2 | yes | — |
| 98 | #1478 | C22 | 1 | 1 | yes | characteristic |
| 99 | #1477 | C22 | 1 | 1 | yes | characteristic |
| 100 | C8×M16 | C22 | 1 | 1 | yes | characteristic |
| 101 | C22×#41 | — | 2 | 2 | no | — |
| 102 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 103 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 104 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 105 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 106 | C2×AGL(1,ℤ/8) | D4 | 1 | 1 | yes | characteristic |
| 107 | C2×#135 | — | 2 | 1 | no | — |
| 108 | C2×#135 | — | 2 | 4 | no | — |
| 109 | C2×#135 | — | 2 | 2 | no | — |
| 110 | C2×#135 | — | 2 | 2 | no | — |
| 111 | C2×#135 | — | 4 | 8 | no | — |
| 112 | C22×Q16 | D4 | 1 | 1 | yes | characteristic |
| 113 | C22×SD16 | — | 2 | 2 | no | — |
| 114 | C22×D8 | — | 2 | 1 | no | — |
| 115 | C22×D8 | — | 2 | 1 | no | — |
| 116 | C23×C8 | — | 2 | 1 | no | — |
| 117 | #559 | — | 2 | 2 | no | — |
| 118 | #559 | C23 | 1 | 2 | yes | — |
| 119 | #557 | C23 | 1 | 2 | yes | — |
| 120 | #556 | — | 2 | 2 | no | — |
| 121 | #556 | C23 | 1 | 2 | yes | — |
| 122 | #553 | — | 2 | 2 | no | — |
| 123 | #553 | — | 4 | 2 | no | — |
| 124 | #550 | — | 2 | 4 | no | — |
| 125 | #550 | — | 2 | 2 | no | — |
| 126 | #550 | — | 2 | 2 | no | — |
| 127 | #550 | — | 4 | 2 | no | — |
| 128 | #550 | C23 | 1 | 2 | yes | — |
| 129 | #550 | C23 | 1 | 4 | yes | — |
| 130 | #550 | C23 | 1 | 4 | yes | — |
| 131 | #548 | — | 2 | 2 | no | — |
| 132 | #532 | — | 2 | 2 | no | — |
| 133 | #532 | C23 | 1 | 2 | yes | — |
| 134 | C2×#127 | — | 2 | 2 | no | — |
| 135 | C2×#127 | C23 | 1 | 2 | yes | — |
| 136 | #529 | — | 2 | 2 | no | — |
| 137 | #529 | — | 4 | 2 | no | — |
| 138 | C2×#121 | — | 2 | 2 | no | — |
| 139 | C2×#121 | — | 4 | 2 | no | — |
| 140 | C4×#41 | — | 2 | 2 | no | — |
| 141 | C4×#41 | — | 2 | 2 | no | — |
| 142 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 144 | C2×C4×D4 | — | 2 | 2 | no | — |
| 145 | C2×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 146 | #500 | C23 | 1 | 1 | yes | characteristic |
| 147 | #499 | — | 2 | 1 | no | — |
| 148 | #496 | — | 2 | 4 | no | — |
| 149 | #496 | — | 2 | 4 | no | — |
| 150 | #496 | — | 2 | 4 | no | — |
| 151 | #495 | — | 2 | 1 | no | — |
| 152 | #493 | — | 2 | 4 | no | — |
| 153 | #493 | — | 2 | 1 | no | — |
| 154 | #493 | — | 2 | 1 | no | — |
| 155 | #493 | C23 | 1 | 4 | yes | — |
| 156 | #493 | C23 | 1 | 1 | yes | characteristic |
| 157 | #493 | C23 | 1 | 2 | yes | — |
| 158 | #493 | C23 | 1 | 2 | yes | — |
| 159 | #493 | C23 | 1 | 4 | yes | — |
| 160 | #492 | — | 2 | 4 | no | — |
| 161 | #492 | C23 | 1 | 4 | yes | — |
| 162 | #488 | — | 2 | 2 | no | — |
| 163 | #486 | C23 | 1 | 2 | yes | — |
| 164 | #486 | C23 | 1 | 4 | yes | — |
| 165 | #485 | — | 2 | 2 | no | — |
| 166 | #482 | — | 2 | 2 | no | — |
| 167 | #481 | — | 2 | 2 | no | — |
| 168 | #479 | — | 2 | 2 | no | — |
| 169 | #478 | — | 2 | 2 | no | — |
| 170 | #475 | C23 | 1 | 2 | yes | — |
| 171 | #475 | C23 | 1 | 2 | yes | — |
| 172 | #467 | — | 2 | 1 | no | — |
| 173 | #466 | — | 2 | 1 | no | — |
| 174 | #466 | — | 2 | 1 | no | — |
| 175 | #466 | — | 2 | 1 | no | — |
| 176 | #466 | — | 2 | 2 | no | — |
| 177 | #466 | — | 2 | 2 | no | — |
| 178 | #466 | — | 2 | 4 | no | — |
| 179 | #465 | — | 2 | 2 | no | — |
| 180 | #464 | — | 2 | 2 | no | — |
| 181 | #463 | — | 2 | 4 | no | — |
| 182 | #463 | — | 2 | 2 | no | — |
| 183 | #463 | — | 2 | 4 | no | — |
| 184 | #463 | — | 2 | 4 | no | — |
| 185 | #461 | — | 2 | 4 | no | — |
| 186 | #461 | C23 | 1 | 4 | yes | — |
| 187 | #460 | — | 2 | 2 | no | — |
| 188 | #460 | — | 2 | 2 | no | — |
| 189 | #460 | — | 2 | 2 | no | — |
| 190 | #460 | — | 2 | 4 | no | — |
| 191 | #460 | — | 2 | 4 | no | — |
| 192 | #460 | C23 | 1 | 2 | yes | — |
| 193 | #460 | C23 | 1 | 2 | yes | — |
| 194 | #460 | C23 | 1 | 4 | yes | — |
| 195 | #460 | C23 | 1 | 4 | yes | — |
| 196 | #460 | C23 | 1 | 4 | yes | — |
| 197 | #459 | — | 2 | 2 | no | — |
| 198 | #459 | — | 2 | 4 | no | — |
| 199 | #459 | — | 2 | 4 | no | — |
| 200 | #459 | — | 2 | 4 | no | — |
| 201 | #459 | — | 4 | 2 | no | — |
| 202 | #459 | C23 | 1 | 4 | yes | — |
| 203 | #459 | C23 | 1 | 4 | yes | — |
| 204 | #452 | — | 2 | 2 | no | — |
| 205 | #449 | — | 2 | 2 | no | — |
| 206 | #449 | — | 2 | 4 | no | — |
| 207 | #449 | — | 2 | 4 | no | — |
| 208 | #449 | — | 2 | 4 | no | — |
| 209 | #449 | — | 2 | 4 | no | — |
| 210 | #448 | — | 2 | 2 | no | — |
| 211 | #447 | — | 4 | 2 | no | — |
| 212 | #446 | — | 2 | 4 | no | — |
| 213 | #446 | C23 | 1 | 4 | yes | — |
| 214 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 215 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 216 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 217 | #442 | — | 2 | 4 | no | — |
| 218 | #442 | D4 | 1 | 2 | yes | — |
| 219 | #440 | — | 2 | 4 | no | — |
| 220 | #440 | D4 | 1 | 2 | yes | — |
| 221 | C4×Q16 | — | 2 | 1 | no | — |
| 222 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 223 | C4×Q16 | D4 | 1 | 1 | yes | characteristic |
| 224 | C4×Q16 | D4 | 1 | 1 | yes | characteristic |
| 225 | C4×Q16 | C23 | 1 | 1 | yes | characteristic |
| 226 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 227 | C4×Q16 | C23 | 1 | 1 | yes | characteristic |
| 228 | C4×SD16 | — | 2 | 2 | no | — |
| 229 | C4×SD16 | — | 2 | 2 | no | — |
| 230 | C4×SD16 | — | 2 | 4 | no | — |
| 231 | C4×SD16 | — | 2 | 2 | no | — |
| 232 | C4×SD16 | C23 | 1 | 2 | yes | — |
| 233 | C4×D8 | — | 2 | 1 | no | — |
| 234 | C4×D8 | — | 2 | 4 | no | — |
| 235 | C4×D8 | — | 2 | 1 | no | — |
| 236 | C4×D8 | — | 2 | 1 | no | — |
| 237 | C4×D8 | C23 | 1 | 2 | yes | — |
| 238 | C8×D4 | — | 2 | 1 | no | — |
| 239 | C8×D4 | — | 2 | 1 | no | — |
| 240 | C8×D4 | — | 2 | 1 | no | — |
| 241 | C8×D4 | — | 2 | 1 | no | — |
| 242 | C8×D4 | C23 | 1 | 1 | yes | characteristic |
| 243 | C8×D4 | C23 | 1 | 2 | yes | — |
| 244 | C8×D4 | C23 | 1 | 2 | yes | — |
| 245 | C8×D4 | C23 | 1 | 1 | yes | characteristic |
| 246 | #431 | — | 2 | 1 | no | — |
| 247 | #431 | C23 | 1 | 1 | yes | characteristic |
| 248 | #431 | C23 | 1 | 1 | yes | characteristic |
| 249 | #428 | D4 | 1 | 1 | yes | characteristic |
| 250 | #427 | — | 2 | 1 | no | — |
| 251 | C2×#107 | D4 | 1 | 1 | yes | characteristic |
| 252 | #423 | — | 2 | 2 | no | — |
| 253 | #423 | C23 | 1 | 2 | yes | — |
| 254 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 255 | #418 | — | 2 | 2 | no | — |
| 256 | #418 | D4 | 1 | 1 | yes | characteristic |
| 257 | #417 | — | 2 | 2 | no | — |
| 258 | #417 | D4 | 1 | 1 | yes | characteristic |
| 259 | #416 | — | 2 | 2 | no | — |
| 260 | C2×#103 | D4 | 1 | 2 | yes | — |
| 261 | C2×#102 | — | 2 | 2 | no | — |
| 262 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 263 | C4×M16 | — | 2 | 2 | no | — |
| 264 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×C8 | — | 2 | 1 | no | — |
| 266 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 267 | #335 | C23 | 1 | 2 | yes | — |
| 268 | #335 | C23 | 1 | 2 | yes | — |
| 269 | #335 | C23 | 1 | 2 | yes | — |
| 270 | #334 | C23 | 1 | 2 | yes | — |
| 271 | #332 | C23 | 1 | 4 | yes | — |
| 272 | #331 | C23 | 1 | 4 | yes | — |
| 273 | #331 | C23 | 1 | 4 | yes | — |
| 274 | #331 | C23 | 1 | 4 | yes | — |
| 275 | Q8⋊C8 | C23 | 1 | 2 | yes | — |
| 276 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 277 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 278 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 279 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 280 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 281 | #322 | C23 | 1 | 2 | yes | — |
| 282 | C82 | C23 | 1 | 2 | yes | — |
| 283 | C2×#41 | — | 2 | 2 | no | — |
| 284 | C2×#41 | — | 2 | 4 | no | — |
| 285 | C2×#41 | — | 2 | 4 | no | — |
| 286 | C2×#41 | — | 2 | 2 | no | — |
| 287 | C2×#41 | — | 4 | 4 | no | — |
| 288 | C2×#41 | — | 4 | 8 | no | — |
| 289 | C2×#41 | — | 8 | 4 | no | — |
| 290 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 292 | C22×D4 | — | 2 | 2 | no | — |
| 293 | C22×D4 | — | 2 | 2 | no | — |
| 294 | C22×D4 | — | 2 | 2 | no | — |
| 295 | C22×D4 | — | 4 | 2 | no | — |
| 296 | C22×D4 | — | 4 | 2 | no | — |
| 297 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C23×C4 | — | 2 | 1 | no | — |
| 299 | C23×C4 | — | 4 | 2 | no | — |
| 300 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 301 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 302 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 303 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 304 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 305 | #135 | — | 4 | 16 | no | — |
| 306 | #135 | — | 4 | 8 | no | — |
| 307 | #135 | — | 4 | 4 | no | — |
| 308 | #135 | — | 4 | 8 | no | — |
| 309 | C2×Q16 | — | 2 | 4 | no | — |
| 310 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 311 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 312 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 313 | C2×SD16 | — | 2 | 4 | no | — |
| 314 | C2×SD16 | — | 2 | 4 | no | — |
| 315 | C2×SD16 | — | 2 | 2 | no | — |
| 316 | C2×SD16 | — | 2 | 4 | no | — |
| 317 | C2×SD16 | — | 2 | 2 | no | — |
| 318 | C2×SD16 | — | 2 | 4 | no | — |
| 319 | C2×SD16 | — | 2 | 4 | no | — |
| 320 | C2×SD16 | — | 2 | 4 | no | — |
| 321 | C2×SD16 | — | 4 | 8 | no | — |
| 322 | C2×SD16 | C2×D4 | 1 | 2 | yes | — |
| 323 | C2×D8 | — | 2 | 4 | no | — |
| 324 | C2×D8 | — | 2 | 4 | no | — |
| 325 | C2×D8 | — | 2 | 2 | no | — |
| 326 | C2×D8 | — | 2 | 2 | no | — |
| 327 | C2×D8 | — | 2 | 1 | no | — |
| 328 | C2×D8 | — | 2 | 4 | no | — |
| 329 | C2×D8 | — | 2 | 2 | no | — |
| 330 | C2×D8 | — | 2 | 2 | no | — |
| 331 | C2×D8 | — | 2 | 4 | no | — |
| 332 | C2×D8 | — | 2 | 1 | no | — |
| 333 | C2×D8 | — | 4 | 4 | no | — |
| 334 | C2×D8 | — | 4 | 4 | no | — |
| 335 | C2×D8 | — | 8 | 2 | no | — |
| 336 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 337 | C2×M16 | — | 2 | 2 | no | — |
| 338 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 339 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 340 | C22×C8 | — | 2 | 1 | no | — |
| 341 | C22×C8 | — | 2 | 2 | no | — |
| 342 | C22×C8 | — | 2 | 2 | no | — |
| 343 | C22×C8 | — | 2 | 1 | no | — |
| 344 | C22×C8 | — | 2 | 1 | no | — |
| 345 | C22×C8 | — | 4 | 4 | no | — |
| 346 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 347 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 348 | C4⋊Q8 | — | 2 | 2 | no | — |
| 349 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 350 | #127 | — | 2 | 4 | no | — |
| 351 | #127 | — | 2 | 4 | no | — |
| 352 | #127 | — | 2 | 2 | no | — |
| 353 | #127 | — | 2 | 2 | no | — |
| 354 | #127 | — | 2 | 2 | no | — |
| 355 | #127 | — | 2 | 2 | no | — |
| 356 | #127 | — | 4 | 2 | no | — |
| 357 | #127 | — | 4 | 2 | no | — |
| 358 | #127 | C24 | 1 | 4 | yes | — |
| 359 | #127 | C24 | 1 | 2 | yes | — |
| 360 | #126 | — | 4 | 2 | no | — |
| 361 | #126 | — | 4 | 2 | no | — |
| 362 | #126 | — | 4 | 2 | no | — |
| 363 | #125 | — | 2 | 2 | no | — |
| 364 | #125 | — | 4 | 2 | no | — |
| 365 | #124 | — | 2 | 2 | no | — |
| 366 | #124 | — | 2 | 2 | no | — |
| 367 | #124 | — | 2 | 2 | no | — |
| 368 | #124 | — | 2 | 2 | no | — |
| 369 | #124 | — | 4 | 2 | no | — |
| 370 | #123 | — | 4 | 2 | no | — |
| 371 | #123 | — | 4 | 2 | no | — |
| 372 | #123 | — | 4 | 2 | no | — |
| 373 | C22⋊Q8 | — | 2 | 2 | no | — |
| 374 | C22⋊Q8 | — | 4 | 2 | no | — |
| 375 | #121 | — | 2 | 2 | no | — |
| 376 | #121 | — | 2 | 2 | no | — |
| 377 | #121 | — | 2 | 4 | no | — |
| 378 | #121 | — | 2 | 4 | no | — |
| 379 | #121 | — | 2 | 2 | no | — |
| 380 | #121 | — | 4 | 4 | no | — |
| 381 | #121 | — | 4 | 4 | no | — |
| 382 | #121 | — | 4 | 2 | no | — |
| 383 | #121 | — | 4 | 4 | no | — |
| 384 | #121 | — | 4 | 4 | no | — |
| 385 | #121 | — | 4 | 4 | no | — |
| 386 | #121 | — | 4 | 2 | no | — |
| 387 | #121 | — | 4 | 2 | no | — |
| 388 | C4×Q8 | — | 2 | 2 | no | — |
| 389 | C4×Q8 | — | 2 | 2 | no | — |
| 390 | C4×Q8 | — | 2 | 2 | no | — |
| 391 | C4×Q8 | — | 2 | 2 | no | — |
| 392 | C4×Q8 | — | 2 | 2 | no | — |
| 393 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 394 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 395 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 396 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 397 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 398 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 399 | C4×D4 | — | 2 | 1 | no | — |
| 400 | C4×D4 | — | 2 | 1 | no | — |
| 401 | C4×D4 | — | 2 | 4 | no | — |
| 402 | C4×D4 | — | 2 | 4 | no | — |
| 403 | C4×D4 | — | 2 | 2 | no | — |
| 404 | C4×D4 | — | 2 | 2 | no | — |
| 405 | C4×D4 | — | 2 | 2 | no | — |
| 406 | C4×D4 | — | 2 | 1 | no | — |
| 407 | C4×D4 | — | 2 | 2 | no | — |
| 408 | C4×D4 | — | 2 | 1 | no | — |
| 409 | C4×D4 | — | 2 | 2 | no | — |
| 410 | C4×D4 | — | 4 | 2 | no | — |
| 411 | C4×D4 | — | 4 | 2 | no | — |
| 412 | C4×D4 | — | 4 | 2 | no | — |
| 413 | C4×D4 | — | 4 | 2 | no | — |
| 414 | C4×D4 | — | 4 | 2 | no | — |
| 415 | C4×D4 | — | 4 | 2 | no | — |
| 416 | C4×D4 | — | 4 | 2 | no | — |
| 417 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 418 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 419 | C4×D4 | C24 | 1 | 2 | yes | — |
| 420 | C4×D4 | C24 | 1 | 1 | yes | characteristic |
| 421 | #117 | — | 2 | 1 | no | — |
| 422 | #117 | — | 2 | 2 | no | — |
| 423 | #117 | — | 4 | 2 | no | — |
| 424 | #117 | — | 4 | 2 | no | — |
| 425 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 426 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 427 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 428 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 429 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 430 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 431 | C2×C42 | — | 2 | 2 | no | — |
| 432 | C2×C42 | — | 2 | 1 | no | — |
| 433 | C2×C42 | — | 4 | 2 | no | — |
| 434 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 435 | #107 | — | 2 | 1 | no | — |
| 436 | #107 | — | 2 | 1 | no | — |
| 437 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 438 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 439 | #107 | C2×D4 | 1 | 2 | yes | — |
| 440 | #107 | C2×D4 | 1 | 2 | yes | — |
| 441 | #106 | — | 2 | 2 | no | — |
| 442 | #106 | — | 2 | 2 | no | — |
| 443 | #106 | C2×D4 | 1 | 2 | yes | — |
| 444 | C4⋊C8 | — | 2 | 4 | no | — |
| 445 | C4⋊C8 | — | 2 | 4 | no | — |
| 446 | C4⋊C8 | — | 2 | 1 | no | — |
| 447 | C4⋊C8 | — | 2 | 1 | no | — |
| 448 | C4⋊C8 | — | 2 | 1 | no | — |
| 449 | C4⋊C8 | — | 2 | 2 | no | — |
| 450 | C4⋊C8 | — | 2 | 1 | no | — |
| 451 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 452 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 453 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 454 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 455 | #103 | — | 2 | 2 | no | — |
| 456 | #103 | — | 2 | 2 | no | — |
| 457 | #103 | — | 2 | 4 | no | — |
| 458 | #103 | C2×D4 | 1 | 2 | yes | — |
| 459 | #103 | C2×D4 | 1 | 2 | yes | — |
| 460 | #103 | C2×D4 | 1 | 2 | yes | — |
| 461 | #103 | C2×D4 | 1 | 2 | yes | — |
| 462 | #103 | C2×D4 | 1 | 2 | yes | — |
| 463 | #102 | — | 2 | 2 | no | — |
| 464 | #102 | — | 2 | 2 | no | — |
| 465 | #102 | — | 2 | 4 | no | — |
| 466 | #102 | — | 2 | 4 | no | — |
| 467 | #102 | — | 2 | 2 | no | — |
| 468 | #102 | — | 2 | 4 | no | — |
| 469 | #102 | — | 2 | 4 | no | — |
| 470 | #102 | — | 2 | 4 | no | — |
| 471 | #102 | — | 2 | 2 | no | — |
| 472 | #102 | — | 4 | 4 | no | — |
| 473 | #102 | C2×D4 | 1 | 2 | yes | — |
| 474 | #102 | C2×D4 | 1 | 2 | yes | — |
| 475 | #102 | C2×D4 | 1 | 2 | yes | — |
| 476 | C22⋊C8 | — | 2 | 1 | no | — |
| 477 | C22⋊C8 | — | 2 | 1 | no | — |
| 478 | C22⋊C8 | — | 2 | 2 | no | — |
| 479 | C22⋊C8 | — | 2 | 2 | no | — |
| 480 | C22⋊C8 | — | 2 | 1 | no | — |
| 481 | C22⋊C8 | — | 2 | 1 | no | — |
| 482 | #97 | — | 2 | 4 | no | — |
| 483 | #97 | C2×D4 | 1 | 2 | yes | — |
| 484 | C4×C8 | — | 2 | 1 | no | — |
| 485 | C4×C8 | — | 2 | 1 | no | — |
| 486 | C4×C8 | — | 2 | 4 | no | — |
| 487 | C4×C8 | — | 2 | 1 | no | — |
| 488 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 489 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 490 | C4×C8 | C24 | 1 | 2 | yes | — |
| 491 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 492 | C4×C8 | C24 | 1 | 2 | yes | — |
| 493 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 494 | C24 | — | 2 | 1 | no | — |
| 495 | C24 | — | 4 | 2 | no | — |
| 496 | #41 | — | 2 | 2 | no | — |
| 497 | #41 | — | 2 | 2 | no | — |
| 498 | #41 | — | 4 | 8 | no | — |
| 499 | #41 | — | 4 | 8 | no | — |
| 500 | #41 | — | 4 | 4 | no | — |
| 501 | #41 | — | 4 | 4 | no | — |
| 502 | #41 | — | 4 | 4 | no | — |
| 503 | #41 | — | 8 | 2 | no | — |
| 504 | #41 | — | 8 | 4 | no | — |
| 505 | #41 | — | 8 | 4 | no | — |
| 506 | #41 | — | 8 | 16 | no | — |
| 507 | C2×Q8 | — | 2 | 2 | no | — |
| 508 | C2×Q8 | — | 2 | 4 | no | — |
| 509 | C2×Q8 | — | 2 | 2 | no | — |
| 510 | C2×Q8 | — | 4 | 2 | no | — |
| 511 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 512 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 513 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 514 | C2×D4 | — | 2 | 1 | no | — |
| 515 | C2×D4 | — | 2 | 1 | no | — |
| 516 | C2×D4 | — | 2 | 2 | no | — |
| 517 | C2×D4 | — | 2 | 2 | no | — |
| 518 | C2×D4 | — | 2 | 2 | no | — |
| 519 | C2×D4 | — | 2 | 2 | no | — |
| 520 | C2×D4 | — | 2 | 4 | no | — |
| 521 | C2×D4 | — | 2 | 4 | no | — |
| 522 | C2×D4 | — | 2 | 4 | no | — |
| 523 | C2×D4 | — | 2 | 2 | no | — |
| 524 | C2×D4 | — | 4 | 4 | no | — |
| 525 | C2×D4 | — | 4 | 4 | no | — |
| 526 | C2×D4 | — | 4 | 2 | no | — |
| 527 | C2×D4 | — | 4 | 4 | no | — |
| 528 | C2×D4 | — | 4 | 4 | no | — |
| 529 | C2×D4 | — | 4 | 2 | no | — |
| 530 | C2×D4 | — | 4 | 4 | no | — |
| 531 | C2×D4 | — | 4 | 4 | no | — |
| 532 | C2×D4 | — | 4 | 2 | no | — |
| 533 | C2×D4 | — | 4 | 2 | no | — |
| 534 | C2×D4 | — | 4 | 2 | no | — |
| 535 | C2×D4 | — | 4 | 2 | no | — |
| 536 | C2×D4 | — | 4 | 4 | no | — |
| 537 | C2×D4 | — | 4 | 4 | no | — |
| 538 | C2×D4 | — | 8 | 8 | no | — |
| 539 | C2×D4 | — | 16 | 2 | no | — |
| 540 | C2×D4 | — | 16 | 4 | no | — |
| 541 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 542 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 543 | C22×C4 | — | 2 | 2 | no | — |
| 544 | C22×C4 | — | 2 | 1 | no | — |
| 545 | C22×C4 | — | 2 | 2 | no | — |
| 546 | C22×C4 | — | 2 | 1 | no | — |
| 547 | C22×C4 | — | 2 | 2 | no | — |
| 548 | C22×C4 | — | 2 | 1 | no | — |
| 549 | C22×C4 | — | 2 | 2 | no | — |
| 550 | C22×C4 | — | 2 | 1 | no | — |
| 551 | C22×C4 | — | 4 | 2 | no | — |
| 552 | C22×C4 | — | 4 | 4 | no | — |
| 553 | C22×C4 | — | 4 | 4 | no | — |
| 554 | C22×C4 | — | 4 | 2 | no | — |
| 555 | C22×C4 | — | 4 | 2 | no | — |
| 556 | C22×C4 | — | 4 | 2 | no | — |
| 557 | C22×C4 | — | 4 | 2 | no | — |
| 558 | C22×C4 | — | 8 | 8 | no | — |
| 559 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 560 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 561 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 562 | Q16 | — | 2 | 4 | no | — |
| 563 | Q16 | — | 2 | 2 | no | — |
| 564 | Q16 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 565 | SD16 | — | 2 | 4 | no | — |
| 566 | SD16 | — | 4 | 8 | no | — |
| 567 | SD16 | — | 4 | 8 | no | — |
| 568 | SD16 | — | 4 | 4 | no | — |
| 569 | SD16 | — | 4 | 8 | no | — |
| 570 | SD16 | — | 8 | 4 | no | — |
| 571 | SD16 | — | 8 | 4 | no | — |
| 572 | SD16 | — | 8 | 2 | no | — |
| 573 | SD16 | — | 8 | 4 | no | — |
| 574 | D8 | — | 2 | 4 | no | — |
| 575 | D8 | — | 4 | 4 | no | — |
| 576 | D8 | — | 4 | 8 | no | — |
| 577 | D8 | — | 4 | 4 | no | — |
| 578 | D8 | — | 4 | 2 | no | — |
| 579 | D8 | — | 8 | 1 | no | — |
| 580 | D8 | — | 8 | 2 | no | — |
| 581 | D8 | — | 8 | 2 | no | — |
| 582 | D8 | — | 8 | 4 | no | — |
| 583 | D8 | — | 8 | 4 | no | — |
| 584 | D8 | — | 8 | 4 | no | — |
| 585 | D8 | — | 16 | 4 | no | — |
| 586 | M16 | — | 2 | 2 | no | — |
| 587 | M16 | — | 4 | 4 | no | — |
| 588 | M16 | #135 | 1 | 4 | yes | complemented |
| 589 | C2×C8 | — | 2 | 2 | no | — |
| 590 | C2×C8 | — | 2 | 1 | no | — |
| 591 | C2×C8 | — | 2 | 1 | no | — |
| 592 | C2×C8 | — | 2 | 4 | no | — |
| 593 | C2×C8 | — | 2 | 2 | no | — |
| 594 | C2×C8 | — | 2 | 2 | no | — |
| 595 | C2×C8 | — | 4 | 1 | no | — |
| 596 | C2×C8 | — | 4 | 4 | no | — |
| 597 | C2×C8 | — | 4 | 2 | no | — |
| 598 | C2×C8 | — | 4 | 4 | no | — |
| 599 | C2×C8 | — | 4 | 2 | no | — |
| 600 | C2×C8 | — | 8 | 1 | no | — |
| 601 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 602 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 603 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 604 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 605 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 606 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 607 | C4⋊C4 | — | 2 | 2 | no | — |
| 608 | C4⋊C4 | — | 2 | 2 | no | — |
| 609 | C4⋊C4 | — | 2 | 1 | no | — |
| 610 | C4⋊C4 | — | 2 | 2 | no | — |
| 611 | C4⋊C4 | — | 2 | 1 | no | — |
| 612 | C4⋊C4 | — | 2 | 2 | no | — |
| 613 | C4⋊C4 | — | 2 | 2 | no | — |
| 614 | C4⋊C4 | — | 2 | 1 | no | — |
| 615 | C4⋊C4 | — | 2 | 2 | no | — |
| 616 | C4⋊C4 | — | 2 | 2 | no | — |
| 617 | C4⋊C4 | — | 4 | 2 | no | — |
| 618 | C4⋊C4 | — | 4 | 2 | no | — |
| 619 | C4⋊C4 | — | 4 | 2 | no | — |
| 620 | C4⋊C4 | — | 4 | 2 | no | — |
| 621 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 622 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 623 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 624 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 625 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 626 | C22⋊C4 | — | 2 | 1 | no | — |
| 627 | C22⋊C4 | — | 2 | 2 | no | — |
| 628 | C22⋊C4 | — | 2 | 1 | no | — |
| 629 | C22⋊C4 | — | 2 | 2 | no | — |
| 630 | C22⋊C4 | — | 2 | 1 | no | — |
| 631 | C22⋊C4 | — | 4 | 4 | no | — |
| 632 | C22⋊C4 | — | 4 | 4 | no | — |
| 633 | C22⋊C4 | — | 4 | 2 | no | — |
| 634 | C22⋊C4 | — | 4 | 2 | no | — |
| 635 | C22⋊C4 | — | 4 | 2 | no | — |
| 636 | C22⋊C4 | — | 4 | 2 | no | — |
| 637 | C22⋊C4 | — | 4 | 2 | no | — |
| 638 | C22⋊C4 | — | 4 | 2 | no | — |
| 639 | C22⋊C4 | — | 4 | 2 | no | — |
| 640 | C22⋊C4 | — | 4 | 2 | no | — |
| 641 | C42 | — | 2 | 1 | no | — |
| 642 | C42 | — | 2 | 2 | no | — |
| 643 | C42 | — | 2 | 1 | no | — |
| 644 | C42 | — | 2 | 2 | no | — |
| 645 | C42 | — | 2 | 1 | no | — |
| 646 | C42 | — | 2 | 2 | no | — |
| 647 | C42 | — | 2 | 2 | no | — |
| 648 | C42 | — | 4 | 2 | no | — |
| 649 | C42 | — | 4 | 2 | no | — |
| 650 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 651 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 652 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 653 | C42 | C25 | 1 | 1 | yes | characteristic |
| 654 | C23 | — | 2 | 1 | no | — |
| 655 | C23 | — | 2 | 2 | no | — |
| 656 | C23 | — | 4 | 2 | no | — |
| 657 | C23 | — | 4 | 2 | no | — |
| 658 | C23 | — | 4 | 2 | no | — |
| 659 | C23 | — | 4 | 2 | no | — |
| 660 | C23 | — | 4 | 4 | no | — |
| 661 | C23 | — | 8 | 4 | no | — |
| 662 | C23 | — | 8 | 4 | no | — |
| 663 | C23 | — | 8 | 4 | no | — |
| 664 | C23 | D42 | 1 | 1 | yes | characteristic |
| 665 | Q8 | — | 2 | 2 | no | — |
| 666 | Q8 | — | 2 | 2 | no | — |
| 667 | Q8 | — | 2 | 1 | no | — |
| 668 | Q8 | — | 2 | 2 | no | — |
| 669 | Q8 | — | 2 | 1 | no | — |
| 670 | Q8 | — | 4 | 4 | no | — |
| 671 | Q8 | — | 4 | 2 | no | — |
| 672 | Q8 | — | 4 | 2 | no | — |
| 673 | Q8 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 674 | D4 | — | 2 | 1 | no | — |
| 675 | D4 | — | 2 | 2 | no | — |
| 676 | D4 | — | 2 | 1 | no | — |
| 677 | D4 | — | 2 | 2 | no | — |
| 678 | D4 | — | 4 | 2 | no | — |
| 679 | D4 | — | 4 | 4 | no | — |
| 680 | D4 | — | 4 | 2 | no | — |
| 681 | D4 | — | 4 | 2 | no | — |
| 682 | D4 | — | 4 | 2 | no | — |
| 683 | D4 | — | 4 | 4 | no | — |
| 684 | D4 | — | 4 | 4 | no | — |
| 685 | D4 | — | 4 | 2 | no | — |
| 686 | D4 | — | 4 | 2 | no | — |
| 687 | D4 | — | 4 | 4 | no | — |
| 688 | D4 | — | 8 | 8 | no | — |
| 689 | D4 | — | 8 | 4 | no | — |
| 690 | D4 | — | 8 | 2 | no | — |
| 691 | D4 | — | 8 | 4 | no | — |
| 692 | D4 | — | 8 | 4 | no | — |
| 693 | D4 | — | 8 | 8 | no | — |
| 694 | D4 | — | 8 | 4 | no | — |
| 695 | D4 | — | 8 | 4 | no | — |
| 696 | D4 | — | 16 | 2 | no | — |
| 697 | D4 | — | 16 | 2 | no | — |
| 698 | D4 | — | 16 | 4 | no | — |
| 699 | D4 | — | 16 | 4 | no | — |
| 700 | C2×C4 | — | 2 | 2 | no | — |
| 701 | C2×C4 | — | 2 | 1 | no | — |
| 702 | C2×C4 | — | 2 | 1 | no | — |
| 703 | C2×C4 | — | 2 | 1 | no | — |
| 704 | C2×C4 | — | 2 | 1 | no | — |
| 705 | C2×C4 | — | 2 | 2 | no | — |
| 706 | C2×C4 | — | 2 | 1 | no | — |
| 707 | C2×C4 | — | 2 | 2 | no | — |
| 708 | C2×C4 | — | 2 | 2 | no | — |
| 709 | C2×C4 | — | 2 | 2 | no | — |
| 710 | C2×C4 | — | 4 | 1 | no | — |
| 711 | C2×C4 | — | 4 | 4 | no | — |
| 712 | C2×C4 | — | 4 | 4 | no | — |
| 713 | C2×C4 | — | 4 | 2 | no | — |
| 714 | C2×C4 | — | 4 | 1 | no | — |
| 715 | C2×C4 | — | 4 | 2 | no | — |
| 716 | C2×C4 | — | 4 | 2 | no | — |
| 717 | C2×C4 | — | 4 | 2 | no | — |
| 718 | C2×C4 | — | 4 | 1 | no | — |
| 719 | C2×C4 | — | 4 | 2 | no | — |
| 720 | C2×C4 | — | 8 | 1 | no | — |
| 721 | C2×C4 | — | 8 | 8 | no | — |
| 722 | C2×C4 | — | 8 | 4 | no | — |
| 723 | C2×C4 | — | 8 | 2 | no | — |
| 724 | C2×C4 | — | 8 | 8 | no | — |
| 725 | C2×C4 | — | 8 | 4 | no | — |
| 726 | C2×C4 | — | 16 | 2 | no | — |
| 727 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 728 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 729 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 730 | C2×C4 | C2×#135 | 1 | 2 | yes | — |
| 731 | C2×C4 | #576 | 1 | 2 | yes | — |
| 732 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 733 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 734 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 735 | C8 | — | 2 | 1 | no | — |
| 736 | C8 | — | 2 | 1 | no | — |
| 737 | C8 | — | 2 | 1 | no | — |
| 738 | C8 | — | 2 | 2 | no | — |
| 739 | C8 | — | 4 | 2 | no | — |
| 740 | C8 | — | 4 | 1 | no | — |
| 741 | C8 | — | 4 | 2 | no | — |
| 742 | C8 | — | 4 | 1 | no | — |
| 743 | C8 | — | 4 | 4 | no | — |
| 744 | C8 | C2×#135 | 1 | 4 | yes | complemented |
| 745 | C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 746 | C22 | — | 2 | 1 | no | — |
| 747 | C22 | — | 2 | 1 | no | — |
| 748 | C22 | — | 4 | 1 | no | — |
| 749 | C22 | — | 4 | 2 | no | — |
| 750 | C22 | — | 4 | 2 | no | — |
| 751 | C22 | — | 4 | 1 | no | — |
| 752 | C22 | — | 4 | 1 | no | — |
| 753 | C22 | — | 4 | 2 | no | — |
| 754 | C22 | — | 8 | 4 | no | — |
| 755 | C22 | — | 8 | 2 | no | — |
| 756 | C22 | — | 8 | 4 | no | — |
| 757 | C22 | — | 8 | 4 | no | — |
| 758 | C22 | — | 8 | 2 | no | — |
| 759 | C22 | — | 8 | 2 | no | — |
| 760 | C22 | — | 8 | 4 | no | — |
| 761 | C22 | — | 16 | 8 | no | — |
| 762 | C22 | #3287 | 1 | 2 | yes | — |
| 763 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 764 | C4 | — | 2 | 1 | no | — |
| 765 | C4 | — | 2 | 4 | no | — |
| 766 | C4 | — | 2 | 1 | no | — |
| 767 | C4 | — | 2 | 1 | no | — |
| 768 | C4 | — | 4 | 1 | no | — |
| 769 | C4 | — | 4 | 2 | no | — |
| 770 | C4 | — | 4 | 1 | no | — |
| 771 | C4 | — | 4 | 2 | no | — |
| 772 | C4 | — | 4 | 1 | no | — |
| 773 | C4 | — | 4 | 2 | no | — |
| 774 | C4 | — | 4 | 2 | no | — |
| 775 | C4 | — | 8 | 2 | no | — |
| 776 | C4 | #3287 | 1 | 2 | yes | — |
| 777 | C4 | C22×#135 | 1 | 1 | yes | characteristic |
| 778 | C4 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 779 | C4 | C2×#576 | 1 | 1 | yes | characteristic |
| 780 | C4 | #3585 | 1 | 1 | yes | characteristic |
| 781 | C2 | — | 2 | 2 | no | — |
| 782 | C2 | — | 8 | 1 | no | — |
| 783 | C2 | — | 8 | 2 | no | — |
| 784 | C2 | — | 16 | 2 | no | — |
| 785 | C2 | — | 16 | 4 | no | — |
| 786 | C2 | C2×#3287 | 1 | 1 | yes | characteristic |
| 787 | C2 | D4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 788 | C2 | #61106 | 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. #61430 | C2 | semidirect |
| 2. #61402 | C2 | semidirect |
| 3. C2×#3287 | C2 | semidirect |
| 4. #19985 | C2 | semidirect |
| 5. #19975 | C2 | semidirect |
| 6. #19962 | C2 | semidirect |
| 7. #19960 | C2 | semidirect |
| 8. #19868 | C2 | semidirect |
| 9. #19867 | C2 | semidirect |
| 10. #19629 | C2 | semidirect |
| 11. #19267 | C2 | semidirect |
| 12. #19255 | C2 | semidirect |
| 13. #19170 | C2 | semidirect |
| 14. #18790 | C2 | semidirect |
| 15. #18770 | C2 | semidirect |
| 16. M16×Q16 | C2 | semidirect |
| 17. C8×AGL(1,ℤ/8) | C2 | semidirect |
| 22. #3399 | C22 | semidirect |
| 24. #3397 | C22 | semidirect |
| 25. #3396 | C22 | semidirect |
| 26. #3392 | C22 | semidirect |
| 27. #3391 | C22 | semidirect |
| 28. #3383 | C22 | semidirect |
| 29. #3365 | C22 | semidirect |
| 30. #3342 | C22 | semidirect |
| 32. #3304 | C22 | semidirect |
| 40. #3287 | C22 | semidirect |
| 64. #1721 | C22 | semidirect |
| 65. #1712 | C22 | semidirect |
| 66. #1706 | C22 | semidirect |
| 67. #1688 | C22 | semidirect |
| 68. #1686 | C22 | semidirect |
| 69. #1681 | C22 | semidirect |
| 70. #1673 | C22 | semidirect |
| 71. #1668 | C22 | semidirect |
| 72. #1668 | C22 | semidirect |
| 73. #1668 | C22 | semidirect |
| 74. #1667 | C22 | semidirect |
| 75. #1667 | C22 | semidirect |
| 76. #1667 | C22 | semidirect |
| 77. #1666 | C22 | semidirect |
| 78. #1642 | C22 | semidirect |
| 79. #1642 | C22 | semidirect |
| 80. #1628 | C22 | semidirect |
| 81. #1626 | C22 | semidirect |
| 82. #1621 | C22 | semidirect |
| 83. #1621 | C22 | semidirect |
| 84. #1621 | C22 | semidirect |
| 85. #1620 | C22 | semidirect |
| 86. #1591 | C22 | semidirect |
| 87. #1584 | C22 | semidirect |
| 88. #1580 | C22 | semidirect |
| 89. SD16⋊C8 | C22 | semidirect |
| 90. C8×Q16 | C22 | semidirect |
| 91. C8×SD16 | C22 | semidirect |
| 92. C8×D8 | C22 | semidirect |
| 564. Q16 | AGL(1,ℤ/8) | semidirect |
| 588. M16 | #135 | semidirect |
| 744. C8 | C2×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61430 | 2 |
| #61402 | 2 |
| C2×#3287 | 2 |
| #19985 | 2 |
| #19975 | 2 |
| #19962 | 2 |
| #19960 | 2 |
| #19868 | 2 |
| #19867 | 2 |
| #19629 | 2 |
| #19267 | 2 |
| #19255 | 2 |
| #19170 | 2 |
| #18790 | 2 |
| #18770 | 2 |
| M16×Q16 | 2 |
| C8×AGL(1,ℤ/8) | 2 |