Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1010 conjugacy classes of subgroups.
The subgroup lattice has 817 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61959 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #29824 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #25744 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22507 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #19163 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #18804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10294 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10206 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #9320 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #9253 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #9237 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #8841 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #8420 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3498 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3475 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3397 | — | 2 | 1 | no | — |
| 19 | #3366 | — | 2 | 1 | no | — |
| 20 | #3325 | — | 2 | 1 | no | — |
| 21 | #3310 | — | 2 | 2 | no | — |
| 22 | #3272 | — | 2 | 1 | no | — |
| 23 | #3264 | — | 2 | 2 | no | — |
| 24 | #3251 | — | 2 | 1 | no | — |
| 25 | #3246 | C22 | 1 | 1 | yes | characteristic |
| 26 | #3229 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #3217 | — | 2 | 1 | no | — |
| 28 | #3208 | C22 | 1 | 1 | yes | characteristic |
| 29 | #3152 | C22 | 1 | 1 | yes | characteristic |
| 30 | #3115 | — | 2 | 1 | no | — |
| 31 | #3100 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#474 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #3039 | C22 | 1 | 1 | yes | characteristic |
| 34 | #3038 | — | 2 | 1 | no | — |
| 35 | C2×#459 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#455 | — | 2 | 1 | no | — |
| 37 | C2×#455 | — | 2 | 1 | no | — |
| 38 | #2989 | C22 | 1 | 1 | yes | characteristic |
| 39 | D4×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #2858 | C22 | 1 | 1 | yes | characteristic |
| 41 | #2293 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #2067 | — | 2 | 2 | no | — |
| 43 | #2054 | — | 2 | 2 | no | — |
| 44 | #2004 | — | 2 | 1 | no | — |
| 45 | #2004 | — | 2 | 1 | no | — |
| 46 | #1994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #1988 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #1986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #1982 | C22 | 1 | 1 | yes | characteristic |
| 50 | #1965 | C22 | 1 | 1 | yes | characteristic |
| 51 | #1962 | C22 | 1 | 1 | yes | characteristic |
| 52 | #1897 | — | 2 | 1 | no | — |
| 53 | #1871 | — | 2 | 1 | no | — |
| 54 | #1842 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #1826 | — | 2 | 1 | no | — |
| 56 | #1806 | C22 | 1 | 1 | yes | characteristic |
| 57 | C4×#104 | C22 | 1 | 1 | yes | characteristic |
| 58 | #1733 | — | 2 | 1 | no | — |
| 59 | #1689 | — | 2 | 1 | no | — |
| 60 | #1685 | — | 2 | 1 | no | — |
| 61 | #1669 | — | 2 | 1 | no | — |
| 62 | #1665 | — | 2 | 1 | no | — |
| 63 | #1654 | — | 2 | 1 | no | — |
| 64 | #1652 | — | 2 | 1 | no | — |
| 65 | #1646 | — | 2 | 1 | no | — |
| 66 | #1644 | — | 2 | 1 | no | — |
| 67 | #1565 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #1550 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #1547 | C22 | 1 | 1 | yes | characteristic |
| 70 | #1546 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #1545 | C22 | 1 | 1 | yes | characteristic |
| 72 | #1502 | C22 | 1 | 1 | yes | characteristic |
| 73 | #1486 | C22 | 1 | 1 | yes | characteristic, complemented |
| 74 | #1477 | C22 | 1 | 1 | yes | characteristic |
| 75 | #1303 | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | #1292 | C22 | 1 | 1 | yes | characteristic, complemented |
| 77 | #1283 | C22 | 1 | 1 | yes | characteristic, complemented |
| 78 | #1276 | C22 | 1 | 1 | yes | characteristic, complemented |
| 79 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 80 | C2×#137 | — | 2 | 1 | no | — |
| 81 | C2×#137 | — | 2 | 1 | no | — |
| 82 | C2×#137 | — | 2 | 1 | no | — |
| 83 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 84 | C22×D8 | D4 | 1 | 2 | yes | — |
| 85 | C22×M16 | — | 2 | 1 | no | — |
| 86 | #556 | D4 | 1 | 1 | yes | characteristic |
| 87 | #555 | D4 | 1 | 1 | yes | characteristic |
| 88 | #554 | D4 | 1 | 1 | yes | characteristic |
| 89 | #553 | — | 2 | 1 | no | — |
| 90 | #552 | — | 2 | 1 | no | — |
| 91 | #552 | — | 2 | 1 | no | — |
| 92 | #551 | — | 4 | 1 | no | — |
| 93 | #550 | — | 2 | 1 | no | — |
| 94 | #550 | — | 2 | 1 | no | — |
| 95 | #547 | D4 | 1 | 1 | yes | characteristic |
| 96 | #546 | — | 2 | 1 | no | — |
| 97 | D42 | — | 2 | 2 | no | — |
| 98 | D42 | — | 2 | 1 | no | — |
| 99 | D42 | — | 2 | 1 | no | — |
| 100 | D42 | — | 4 | 1 | no | — |
| 101 | #535 | — | 2 | 1 | no | — |
| 102 | #535 | — | 4 | 1 | no | — |
| 103 | #533 | C23 | 1 | 1 | yes | characteristic |
| 104 | #532 | — | 2 | 1 | no | — |
| 105 | #532 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 107 | C2×#127 | — | 2 | 1 | no | — |
| 108 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 109 | #529 | — | 2 | 1 | no | — |
| 110 | #529 | — | 4 | 1 | no | — |
| 111 | C2×#124 | — | 2 | 1 | no | — |
| 112 | C2×#124 | — | 2 | 1 | no | — |
| 113 | #525 | — | 2 | 1 | no | — |
| 114 | C4×#41 | — | 2 | 1 | no | — |
| 115 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 117 | C2×#117 | — | 2 | 1 | no | — |
| 118 | C2×#117 | — | 2 | 1 | no | — |
| 119 | #498 | — | 2 | 1 | no | — |
| 120 | #497 | — | 4 | 1 | no | — |
| 121 | #496 | — | 2 | 2 | no | — |
| 122 | #494 | — | 2 | 1 | no | — |
| 123 | #492 | — | 2 | 1 | no | — |
| 124 | #492 | — | 2 | 1 | no | — |
| 125 | #490 | — | 2 | 2 | no | — |
| 126 | #487 | — | 2 | 1 | no | — |
| 127 | #486 | — | 2 | 1 | no | — |
| 128 | #483 | — | 4 | 1 | no | — |
| 129 | #482 | — | 2 | 2 | no | — |
| 130 | #480 | — | 2 | 1 | no | — |
| 131 | #478 | — | 2 | 2 | no | — |
| 132 | #476 | — | 2 | 1 | no | — |
| 133 | #475 | — | 2 | 1 | no | — |
| 134 | #475 | — | 4 | 1 | no | — |
| 135 | #474 | — | 2 | 1 | no | — |
| 136 | #474 | — | 2 | 1 | no | — |
| 137 | #474 | — | 2 | 1 | no | — |
| 138 | #474 | — | 2 | 1 | no | — |
| 139 | #474 | D4 | 1 | 1 | yes | characteristic |
| 140 | #474 | D4 | 1 | 1 | yes | characteristic |
| 141 | #469 | — | 2 | 2 | no | — |
| 142 | #468 | — | 2 | 2 | no | — |
| 143 | #465 | — | 2 | 2 | no | — |
| 144 | #463 | — | 2 | 2 | no | — |
| 145 | #462 | — | 2 | 1 | no | — |
| 146 | #462 | — | 2 | 1 | no | — |
| 147 | #461 | — | 2 | 1 | no | — |
| 148 | #461 | — | 2 | 1 | no | — |
| 149 | #461 | — | 2 | 1 | no | — |
| 150 | #460 | — | 2 | 2 | no | — |
| 151 | #460 | — | 2 | 1 | no | — |
| 152 | #460 | — | 2 | 1 | no | — |
| 153 | #460 | — | 2 | 1 | no | — |
| 154 | #459 | — | 2 | 2 | no | — |
| 155 | #459 | — | 2 | 1 | no | — |
| 156 | #459 | — | 2 | 1 | no | — |
| 157 | #459 | — | 2 | 1 | no | — |
| 158 | #459 | — | 2 | 1 | no | — |
| 159 | #459 | D4 | 1 | 1 | yes | characteristic |
| 160 | #459 | D4 | 1 | 1 | yes | characteristic |
| 161 | #455 | — | 4 | 4 | no | — |
| 162 | #455 | — | 4 | 4 | no | — |
| 163 | #450 | — | 2 | 2 | no | — |
| 164 | #450 | — | 2 | 2 | no | — |
| 165 | #449 | — | 2 | 2 | no | — |
| 166 | #447 | — | 2 | 2 | no | — |
| 167 | #447 | — | 2 | 1 | no | — |
| 168 | #446 | — | 2 | 1 | no | — |
| 169 | #442 | — | 2 | 2 | no | — |
| 170 | #440 | — | 2 | 2 | no | — |
| 171 | C4×D8 | — | 2 | 1 | no | — |
| 172 | C4×D8 | — | 2 | 1 | no | — |
| 173 | #436 | — | 2 | 1 | no | — |
| 174 | #436 | — | 2 | 1 | no | — |
| 175 | #435 | — | 2 | 2 | no | — |
| 176 | #435 | — | 4 | 1 | no | — |
| 177 | C8×D4 | — | 2 | 1 | no | — |
| 178 | #432 | — | 2 | 1 | no | — |
| 179 | #431 | C23 | 1 | 1 | yes | characteristic |
| 180 | #431 | C23 | 1 | 1 | yes | characteristic |
| 181 | C2×#107 | — | 2 | 1 | no | — |
| 182 | #423 | — | 2 | 1 | no | — |
| 183 | #423 | C23 | 1 | 1 | yes | characteristic |
| 184 | #423 | C23 | 1 | 1 | yes | characteristic |
| 185 | C2×C4⋊C8 | — | 2 | 2 | no | — |
| 186 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 187 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 188 | C2×#104 | — | 2 | 1 | no | — |
| 189 | C2×#104 | — | 2 | 1 | no | — |
| 190 | C2×#104 | — | 2 | 1 | no | — |
| 191 | C2×#104 | D4 | 1 | 1 | yes | characteristic |
| 192 | C2×#104 | D4 | 1 | 1 | yes | characteristic |
| 193 | #419 | — | 2 | 1 | no | — |
| 194 | #418 | — | 2 | 2 | no | — |
| 195 | C2×#102 | — | 2 | 1 | no | — |
| 196 | C2×#102 | — | 2 | 2 | no | — |
| 197 | C2×#102 | D4 | 1 | 2 | yes | — |
| 198 | C2×#100 | — | 2 | 1 | no | — |
| 199 | C2×#100 | — | 2 | 1 | no | — |
| 200 | #407 | — | 2 | 1 | no | — |
| 201 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 202 | #390 | — | 2 | 1 | no | — |
| 203 | #390 | — | 2 | 2 | no | — |
| 204 | #390 | — | 4 | 1 | no | — |
| 205 | #389 | — | 2 | 1 | no | — |
| 206 | #388 | — | 4 | 1 | no | — |
| 207 | C4×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 208 | C4×C22⋊C4 | — | 2 | 1 | no | — |
| 209 | C43 | C23 | 1 | 1 | yes | characteristic |
| 210 | #340 | — | 2 | 2 | no | — |
| 211 | #339 | — | 2 | 1 | no | — |
| 212 | #339 | — | 2 | 1 | no | — |
| 213 | #339 | — | 2 | 1 | no | — |
| 214 | #339 | — | 2 | 1 | no | — |
| 215 | #339 | — | 2 | 1 | no | — |
| 216 | #339 | D4 | 1 | 1 | yes | characteristic |
| 217 | #339 | D4 | 1 | 1 | yes | characteristic |
| 218 | #335 | — | 2 | 1 | no | — |
| 219 | #334 | — | 2 | 1 | no | — |
| 220 | #333 | — | 2 | 1 | no | — |
| 221 | #332 | — | 2 | 1 | no | — |
| 222 | #332 | — | 2 | 1 | no | — |
| 223 | #332 | — | 2 | 1 | no | — |
| 224 | #332 | — | 2 | 1 | no | — |
| 225 | #331 | — | 2 | 1 | no | — |
| 226 | #331 | — | 4 | 1 | no | — |
| 227 | #327 | — | 4 | 1 | no | — |
| 228 | Q8⋊C8 | — | 2 | 1 | no | — |
| 229 | D4⋊C8 | — | 2 | 1 | no | — |
| 230 | D4⋊C8 | — | 2 | 1 | no | — |
| 231 | D4⋊C8 | — | 2 | 1 | no | — |
| 232 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 233 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 234 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 235 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 236 | C2×#41 | — | 2 | 1 | no | — |
| 237 | C2×#41 | — | 2 | 1 | no | — |
| 238 | C2×#41 | — | 4 | 1 | no | — |
| 239 | C2×#41 | — | 4 | 1 | no | — |
| 240 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C22×Q8 | — | 2 | 1 | no | — |
| 242 | C22×D4 | — | 2 | 2 | no | — |
| 243 | C22×D4 | — | 2 | 1 | no | — |
| 244 | C22×D4 | — | 2 | 1 | no | — |
| 245 | C22×D4 | — | 4 | 1 | no | — |
| 246 | C22×D4 | — | 4 | 1 | no | — |
| 247 | C22×D4 | — | 4 | 2 | no | — |
| 248 | C22×D4 | — | 4 | 1 | no | — |
| 249 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 250 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C23×C4 | — | 2 | 1 | no | — |
| 252 | #137 | — | 4 | 2 | no | — |
| 253 | #137 | — | 4 | 2 | no | — |
| 254 | #137 | — | 4 | 2 | no | — |
| 255 | #137 | — | 4 | 2 | no | — |
| 256 | #137 | — | 8 | 1 | no | — |
| 257 | #137 | — | 8 | 1 | no | — |
| 258 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 259 | C2×Q16 | — | 4 | 1 | no | — |
| 260 | C2×Q16 | — | 4 | 1 | no | — |
| 261 | C2×Q16 | — | 4 | 1 | no | — |
| 262 | C2×SD16 | — | 2 | 2 | no | — |
| 263 | C2×SD16 | — | 2 | 2 | no | — |
| 264 | C2×SD16 | — | 2 | 2 | no | — |
| 265 | C2×SD16 | — | 4 | 1 | no | — |
| 266 | C2×SD16 | — | 4 | 1 | no | — |
| 267 | C2×SD16 | — | 4 | 1 | no | — |
| 268 | C2×D8 | — | 2 | 2 | no | — |
| 269 | C2×D8 | — | 2 | 1 | no | — |
| 270 | C2×D8 | — | 2 | 2 | no | — |
| 271 | C2×D8 | — | 2 | 1 | no | — |
| 272 | C2×D8 | — | 8 | 2 | no | — |
| 273 | C2×M16 | — | 2 | 2 | no | — |
| 274 | C2×M16 | — | 2 | 1 | no | — |
| 275 | C2×M16 | — | 2 | 1 | no | — |
| 276 | C2×M16 | — | 4 | 1 | no | — |
| 277 | C2×M16 | — | 4 | 2 | no | — |
| 278 | C2×M16 | — | 8 | 1 | no | — |
| 279 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C22×C8 | — | 2 | 1 | no | — |
| 282 | C22×C8 | — | 4 | 1 | no | — |
| 283 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 284 | C4⋊Q8 | — | 2 | 1 | no | — |
| 285 | C4⋊Q8 | — | 2 | 1 | no | — |
| 286 | C4⋊Q8 | — | 2 | 1 | no | — |
| 287 | C4⋊Q8 | — | 2 | 1 | no | — |
| 288 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 289 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 290 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | #127 | — | 2 | 2 | no | — |
| 292 | #127 | — | 2 | 1 | no | — |
| 293 | #127 | — | 2 | 1 | no | — |
| 294 | #127 | — | 2 | 1 | no | — |
| 295 | #127 | — | 2 | 1 | no | — |
| 296 | #127 | — | 4 | 1 | no | — |
| 297 | #127 | — | 4 | 1 | no | — |
| 298 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | #126 | — | 4 | 1 | no | — |
| 300 | #126 | — | 4 | 1 | no | — |
| 301 | #126 | — | 4 | 1 | no | — |
| 302 | #125 | — | 2 | 1 | no | — |
| 303 | #125 | — | 2 | 1 | no | — |
| 304 | #125 | — | 4 | 1 | no | — |
| 305 | #124 | — | 2 | 1 | no | — |
| 306 | #124 | — | 2 | 1 | no | — |
| 307 | #124 | — | 4 | 1 | no | — |
| 308 | #124 | — | 4 | 2 | no | — |
| 309 | #124 | — | 4 | 1 | no | — |
| 310 | #124 | — | 4 | 2 | no | — |
| 311 | #124 | — | 8 | 1 | no | — |
| 312 | #124 | — | 8 | 1 | no | — |
| 313 | #123 | — | 4 | 1 | no | — |
| 314 | #123 | — | 4 | 1 | no | — |
| 315 | #123 | — | 4 | 1 | no | — |
| 316 | #123 | — | 4 | 1 | no | — |
| 317 | C22⋊Q8 | — | 2 | 1 | no | — |
| 318 | C22⋊Q8 | — | 2 | 1 | no | — |
| 319 | C22⋊Q8 | — | 2 | 1 | no | — |
| 320 | C22⋊Q8 | — | 2 | 1 | no | — |
| 321 | C22⋊Q8 | — | 2 | 1 | no | — |
| 322 | C22⋊Q8 | — | 4 | 1 | no | — |
| 323 | #121 | — | 2 | 2 | no | — |
| 324 | #121 | — | 2 | 1 | no | — |
| 325 | #121 | — | 2 | 1 | no | — |
| 326 | #121 | — | 2 | 1 | no | — |
| 327 | #121 | — | 2 | 1 | no | — |
| 328 | #121 | — | 2 | 1 | no | — |
| 329 | #121 | — | 4 | 1 | no | — |
| 330 | #121 | — | 4 | 1 | no | — |
| 331 | #121 | — | 4 | 2 | no | — |
| 332 | #121 | — | 4 | 2 | no | — |
| 333 | #121 | — | 4 | 1 | no | — |
| 334 | #121 | — | 4 | 1 | no | — |
| 335 | #120 | — | 4 | 2 | no | — |
| 336 | #120 | — | 4 | 2 | no | — |
| 337 | #120 | — | 4 | 2 | no | — |
| 338 | #120 | — | 4 | 1 | no | — |
| 339 | C4×Q8 | — | 2 | 1 | no | — |
| 340 | C4×Q8 | — | 2 | 1 | no | — |
| 341 | C4×Q8 | — | 2 | 1 | no | — |
| 342 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 343 | C4×Q8 | #41 | 1 | 1 | yes | characteristic |
| 344 | C4×D4 | — | 2 | 1 | no | — |
| 345 | C4×D4 | — | 2 | 1 | no | — |
| 346 | C4×D4 | — | 2 | 2 | no | — |
| 347 | C4×D4 | — | 2 | 1 | no | — |
| 348 | C4×D4 | — | 2 | 1 | no | — |
| 349 | C4×D4 | — | 2 | 1 | no | — |
| 350 | C4×D4 | — | 2 | 1 | no | — |
| 351 | C4×D4 | — | 2 | 1 | no | — |
| 352 | C4×D4 | — | 4 | 1 | no | — |
| 353 | C4×D4 | — | 4 | 1 | no | — |
| 354 | C4×D4 | — | 4 | 1 | no | — |
| 355 | C4×D4 | — | 4 | 1 | no | — |
| 356 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 357 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 358 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 359 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 360 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 361 | C4×D4 | #41 | 1 | 1 | yes | characteristic |
| 362 | #117 | — | 2 | 1 | no | — |
| 363 | #117 | — | 2 | 1 | no | — |
| 364 | #117 | — | 2 | 1 | no | — |
| 365 | #117 | — | 2 | 1 | no | — |
| 366 | #117 | — | 2 | 1 | no | — |
| 367 | #117 | — | 4 | 1 | no | — |
| 368 | #117 | — | 4 | 1 | no | — |
| 369 | #117 | — | 4 | 1 | no | — |
| 370 | #117 | — | 4 | 2 | no | — |
| 371 | #117 | — | 8 | 1 | no | — |
| 372 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 373 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 374 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 375 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 376 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 377 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 378 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 379 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 380 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 381 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 382 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 383 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 384 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 385 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 386 | C2×C42 | — | 2 | 1 | no | — |
| 387 | C2×C42 | — | 2 | 1 | no | — |
| 388 | C2×C42 | — | 2 | 1 | no | — |
| 389 | C2×C42 | — | 2 | 1 | no | — |
| 390 | C2×C42 | — | 4 | 1 | no | — |
| 391 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 392 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 393 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 394 | #107 | — | 2 | 1 | no | — |
| 395 | #107 | — | 2 | 1 | no | — |
| 396 | #107 | — | 4 | 1 | no | — |
| 397 | #107 | — | 4 | 1 | no | — |
| 398 | #106 | — | 2 | 2 | no | — |
| 399 | #106 | — | 4 | 2 | no | — |
| 400 | C4⋊C8 | — | 2 | 2 | no | — |
| 401 | C4⋊C8 | — | 2 | 1 | no | — |
| 402 | C4⋊C8 | — | 2 | 1 | no | — |
| 403 | C4⋊C8 | — | 2 | 1 | no | — |
| 404 | C4⋊C8 | — | 2 | 1 | no | — |
| 405 | C4⋊C8 | — | 2 | 1 | no | — |
| 406 | C4⋊C8 | — | 2 | 1 | no | — |
| 407 | C4⋊C8 | — | 2 | 1 | no | — |
| 408 | C4⋊C8 | — | 2 | 1 | no | — |
| 409 | C4⋊C8 | — | 2 | 1 | no | — |
| 410 | C4⋊C8 | — | 8 | 2 | no | — |
| 411 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 412 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 413 | #104 | — | 2 | 2 | no | — |
| 414 | #104 | — | 2 | 2 | no | — |
| 415 | #104 | — | 4 | 2 | no | — |
| 416 | #104 | — | 4 | 2 | no | — |
| 417 | #104 | — | 8 | 1 | no | — |
| 418 | #103 | — | 2 | 2 | no | — |
| 419 | #103 | — | 4 | 2 | no | — |
| 420 | #103 | — | 4 | 1 | no | — |
| 421 | #103 | — | 4 | 1 | no | — |
| 422 | #102 | — | 2 | 2 | no | — |
| 423 | #102 | — | 2 | 2 | no | — |
| 424 | #102 | — | 2 | 2 | no | — |
| 425 | #102 | — | 2 | 1 | no | — |
| 426 | #102 | — | 2 | 1 | no | — |
| 427 | #102 | — | 2 | 2 | no | — |
| 428 | #102 | — | 2 | 2 | no | — |
| 429 | #102 | — | 2 | 1 | no | — |
| 430 | #102 | — | 2 | 1 | no | — |
| 431 | #102 | — | 4 | 1 | no | — |
| 432 | #102 | — | 4 | 1 | no | — |
| 433 | #102 | — | 8 | 2 | no | — |
| 434 | #100 | — | 4 | 2 | no | — |
| 435 | #100 | — | 4 | 2 | no | — |
| 436 | C22⋊C8 | — | 2 | 2 | no | — |
| 437 | C22⋊C8 | — | 2 | 1 | no | — |
| 438 | C22⋊C8 | — | 2 | 1 | no | — |
| 439 | C22⋊C8 | — | 4 | 1 | no | — |
| 440 | C22⋊C8 | — | 4 | 1 | no | — |
| 441 | #97 | — | 2 | 2 | no | — |
| 442 | #97 | — | 2 | 1 | no | — |
| 443 | C4×C8 | — | 2 | 1 | no | — |
| 444 | C4×C8 | — | 2 | 1 | no | — |
| 445 | C4×C8 | — | 2 | 1 | no | — |
| 446 | #95 | — | 2 | 1 | no | — |
| 447 | #95 | — | 4 | 1 | no | — |
| 448 | C24 | — | 2 | 1 | no | — |
| 449 | C24 | — | 2 | 2 | no | — |
| 450 | C24 | — | 4 | 2 | no | — |
| 451 | #41 | — | 2 | 1 | no | — |
| 452 | #41 | — | 2 | 1 | no | — |
| 453 | #41 | — | 2 | 1 | no | — |
| 454 | #41 | — | 2 | 1 | no | — |
| 455 | #41 | — | 4 | 2 | no | — |
| 456 | #41 | — | 4 | 1 | no | — |
| 457 | #41 | — | 4 | 1 | no | — |
| 458 | #41 | — | 4 | 1 | no | — |
| 459 | #41 | — | 4 | 1 | no | — |
| 460 | #41 | — | 8 | 1 | no | — |
| 461 | #41 | — | 8 | 2 | no | — |
| 462 | #41 | — | 8 | 2 | no | — |
| 463 | #41 | — | 8 | 2 | no | — |
| 464 | #41 | — | 8 | 2 | no | — |
| 465 | C2×Q8 | — | 2 | 1 | no | — |
| 466 | C2×Q8 | — | 2 | 1 | no | — |
| 467 | C2×Q8 | — | 2 | 1 | no | — |
| 468 | C2×Q8 | — | 4 | 1 | no | — |
| 469 | C2×Q8 | — | 4 | 1 | no | — |
| 470 | C2×Q8 | — | 4 | 1 | no | — |
| 471 | C2×Q8 | — | 4 | 1 | no | — |
| 472 | C2×Q8 | — | 4 | 1 | no | — |
| 473 | C2×Q8 | — | 4 | 1 | no | — |
| 474 | C2×Q8 | #121 | 1 | 1 | yes | characteristic |
| 475 | C2×D4 | — | 2 | 1 | no | — |
| 476 | C2×D4 | — | 2 | 2 | no | — |
| 477 | C2×D4 | — | 2 | 1 | no | — |
| 478 | C2×D4 | — | 2 | 1 | no | — |
| 479 | C2×D4 | — | 2 | 1 | no | — |
| 480 | C2×D4 | — | 2 | 1 | no | — |
| 481 | C2×D4 | — | 2 | 2 | no | — |
| 482 | C2×D4 | — | 4 | 1 | no | — |
| 483 | C2×D4 | — | 4 | 1 | no | — |
| 484 | C2×D4 | — | 4 | 2 | no | — |
| 485 | C2×D4 | — | 4 | 2 | no | — |
| 486 | C2×D4 | — | 4 | 2 | no | — |
| 487 | C2×D4 | — | 4 | 2 | no | — |
| 488 | C2×D4 | — | 4 | 2 | no | — |
| 489 | C2×D4 | — | 4 | 1 | no | — |
| 490 | C2×D4 | — | 4 | 2 | no | — |
| 491 | C2×D4 | — | 4 | 1 | no | — |
| 492 | C2×D4 | — | 4 | 1 | no | — |
| 493 | C2×D4 | — | 4 | 1 | no | — |
| 494 | C2×D4 | — | 4 | 1 | no | — |
| 495 | C2×D4 | — | 4 | 1 | no | — |
| 496 | C2×D4 | — | 4 | 1 | no | — |
| 497 | C2×D4 | — | 4 | 1 | no | — |
| 498 | C2×D4 | — | 4 | 1 | no | — |
| 499 | C2×D4 | — | 4 | 1 | no | — |
| 500 | C2×D4 | — | 4 | 1 | no | — |
| 501 | C2×D4 | — | 8 | 2 | no | — |
| 502 | C2×D4 | — | 8 | 2 | no | — |
| 503 | C2×D4 | — | 8 | 2 | no | — |
| 504 | C2×D4 | — | 8 | 2 | no | — |
| 505 | C2×D4 | — | 8 | 2 | no | — |
| 506 | C2×D4 | — | 8 | 2 | no | — |
| 507 | C2×D4 | — | 8 | 2 | no | — |
| 508 | C2×D4 | — | 8 | 4 | no | — |
| 509 | C2×D4 | — | 8 | 4 | no | — |
| 510 | C2×D4 | — | 16 | 2 | no | — |
| 511 | C2×D4 | #120 | 1 | 1 | yes | characteristic |
| 512 | C2×D4 | #120 | 1 | 1 | yes | characteristic |
| 513 | C2×D4 | #121 | 1 | 1 | yes | characteristic |
| 514 | C22×C4 | — | 2 | 1 | no | — |
| 515 | C22×C4 | — | 2 | 1 | no | — |
| 516 | C22×C4 | — | 2 | 1 | no | — |
| 517 | C22×C4 | — | 2 | 1 | no | — |
| 518 | C22×C4 | — | 2 | 1 | no | — |
| 519 | C22×C4 | — | 2 | 1 | no | — |
| 520 | C22×C4 | — | 2 | 1 | no | — |
| 521 | C22×C4 | — | 2 | 1 | no | — |
| 522 | C22×C4 | — | 2 | 1 | no | — |
| 523 | C22×C4 | — | 2 | 1 | no | — |
| 524 | C22×C4 | — | 4 | 1 | no | — |
| 525 | C22×C4 | — | 4 | 2 | no | — |
| 526 | C22×C4 | — | 4 | 1 | no | — |
| 527 | C22×C4 | — | 4 | 1 | no | — |
| 528 | C22×C4 | — | 4 | 1 | no | — |
| 529 | C22×C4 | — | 4 | 1 | no | — |
| 530 | C22×C4 | — | 4 | 1 | no | — |
| 531 | C22×C4 | — | 4 | 1 | no | — |
| 532 | C22×C4 | — | 4 | 1 | no | — |
| 533 | C22×C4 | — | 4 | 1 | no | — |
| 534 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 535 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 536 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 537 | Q16 | — | 8 | 2 | no | — |
| 538 | Q16 | — | 8 | 2 | no | — |
| 539 | Q16 | — | 8 | 2 | no | — |
| 540 | SD16 | — | 8 | 2 | no | — |
| 541 | SD16 | — | 8 | 2 | no | — |
| 542 | SD16 | — | 8 | 2 | no | — |
| 543 | SD16 | — | 8 | 2 | no | — |
| 544 | SD16 | — | 8 | 2 | no | — |
| 545 | SD16 | — | 8 | 2 | no | — |
| 546 | D8 | — | 4 | 4 | no | — |
| 547 | D8 | — | 4 | 2 | no | — |
| 548 | D8 | — | 8 | 1 | no | — |
| 549 | D8 | — | 8 | 2 | no | — |
| 550 | M16 | — | 2 | 1 | no | — |
| 551 | M16 | — | 2 | 1 | no | — |
| 552 | M16 | — | 2 | 1 | no | — |
| 553 | M16 | — | 4 | 1 | no | — |
| 554 | M16 | — | 4 | 1 | no | — |
| 555 | M16 | — | 4 | 1 | no | — |
| 556 | M16 | — | 4 | 1 | no | — |
| 557 | M16 | — | 8 | 2 | no | — |
| 558 | M16 | — | 8 | 2 | no | — |
| 559 | M16 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 560 | C2×C8 | — | 2 | 1 | no | — |
| 561 | C2×C8 | — | 2 | 1 | no | — |
| 562 | C2×C8 | — | 2 | 1 | no | — |
| 563 | C2×C8 | — | 2 | 2 | no | — |
| 564 | C2×C8 | — | 2 | 1 | no | — |
| 565 | C2×C8 | — | 4 | 2 | no | — |
| 566 | C2×C8 | — | 4 | 2 | no | — |
| 567 | C2×C8 | — | 4 | 1 | no | — |
| 568 | C2×C8 | — | 4 | 1 | no | — |
| 569 | C2×C8 | — | 4 | 1 | no | — |
| 570 | C2×C8 | — | 4 | 1 | no | — |
| 571 | C2×C8 | — | 8 | 2 | no | — |
| 572 | C4⋊C4 | — | 2 | 1 | no | — |
| 573 | C4⋊C4 | — | 2 | 1 | no | — |
| 574 | C4⋊C4 | — | 2 | 1 | no | — |
| 575 | C4⋊C4 | — | 2 | 1 | no | — |
| 576 | C4⋊C4 | — | 2 | 1 | no | — |
| 577 | C4⋊C4 | — | 2 | 1 | no | — |
| 578 | C4⋊C4 | — | 2 | 1 | no | — |
| 579 | C4⋊C4 | — | 2 | 1 | no | — |
| 580 | C4⋊C4 | — | 2 | 1 | no | — |
| 581 | C4⋊C4 | — | 4 | 1 | no | — |
| 582 | C4⋊C4 | — | 4 | 1 | no | — |
| 583 | C4⋊C4 | — | 4 | 1 | no | — |
| 584 | C4⋊C4 | — | 4 | 1 | no | — |
| 585 | C4⋊C4 | — | 4 | 1 | no | — |
| 586 | C4⋊C4 | — | 4 | 1 | no | — |
| 587 | C4⋊C4 | — | 4 | 1 | no | — |
| 588 | C4⋊C4 | — | 4 | 1 | no | — |
| 589 | C4⋊C4 | — | 4 | 1 | no | — |
| 590 | C4⋊C4 | — | 4 | 1 | no | — |
| 591 | C4⋊C4 | — | 4 | 1 | no | — |
| 592 | C4⋊C4 | — | 4 | 1 | no | — |
| 593 | C4⋊C4 | — | 8 | 2 | no | — |
| 594 | C4⋊C4 | #120 | 1 | 1 | yes | characteristic |
| 595 | C4⋊C4 | #120 | 1 | 1 | yes | characteristic |
| 596 | C4⋊C4 | #121 | 1 | 1 | yes | characteristic |
| 597 | C4⋊C4 | #121 | 1 | 1 | yes | characteristic |
| 598 | C22⋊C4 | — | 2 | 1 | no | — |
| 599 | C22⋊C4 | — | 2 | 1 | no | — |
| 600 | C22⋊C4 | — | 2 | 1 | no | — |
| 601 | C22⋊C4 | — | 2 | 1 | no | — |
| 602 | C22⋊C4 | — | 2 | 1 | no | — |
| 603 | C22⋊C4 | — | 2 | 1 | no | — |
| 604 | C22⋊C4 | — | 2 | 1 | no | — |
| 605 | C22⋊C4 | — | 4 | 1 | no | — |
| 606 | C22⋊C4 | — | 4 | 1 | no | — |
| 607 | C22⋊C4 | — | 4 | 1 | no | — |
| 608 | C22⋊C4 | — | 4 | 1 | no | — |
| 609 | C22⋊C4 | — | 4 | 1 | no | — |
| 610 | C22⋊C4 | — | 4 | 1 | no | — |
| 611 | C22⋊C4 | — | 4 | 2 | no | — |
| 612 | C22⋊C4 | — | 4 | 2 | no | — |
| 613 | C22⋊C4 | — | 4 | 1 | no | — |
| 614 | C22⋊C4 | — | 4 | 1 | no | — |
| 615 | C22⋊C4 | — | 4 | 1 | no | — |
| 616 | C22⋊C4 | — | 8 | 2 | no | — |
| 617 | C22⋊C4 | — | 8 | 4 | no | — |
| 618 | C22⋊C4 | — | 8 | 4 | no | — |
| 619 | C22⋊C4 | — | 8 | 2 | no | — |
| 620 | C42 | — | 2 | 1 | no | — |
| 621 | C42 | — | 2 | 1 | no | — |
| 622 | C42 | — | 2 | 1 | no | — |
| 623 | C42 | — | 2 | 1 | no | — |
| 624 | C42 | — | 2 | 1 | no | — |
| 625 | C42 | — | 2 | 1 | no | — |
| 626 | C42 | — | 4 | 1 | no | — |
| 627 | C42 | — | 4 | 1 | no | — |
| 628 | C42 | — | 4 | 1 | no | — |
| 629 | C42 | — | 4 | 1 | no | — |
| 630 | C42 | — | 4 | 1 | no | — |
| 631 | C42 | — | 4 | 1 | no | — |
| 632 | C42 | — | 4 | 1 | no | — |
| 633 | C42 | — | 8 | 1 | no | — |
| 634 | C42 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 635 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 636 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 637 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 638 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 639 | C23 | — | 2 | 1 | no | — |
| 640 | C23 | — | 2 | 1 | no | — |
| 641 | C23 | — | 2 | 1 | no | — |
| 642 | C23 | — | 4 | 1 | no | — |
| 643 | C23 | — | 4 | 1 | no | — |
| 644 | C23 | — | 4 | 1 | no | — |
| 645 | C23 | — | 4 | 2 | no | — |
| 646 | C23 | — | 4 | 2 | no | — |
| 647 | C23 | — | 4 | 2 | no | — |
| 648 | C23 | — | 8 | 1 | no | — |
| 649 | C23 | — | 8 | 1 | no | — |
| 650 | C23 | — | 8 | 2 | no | — |
| 651 | C23 | — | 8 | 2 | no | — |
| 652 | C23 | — | 8 | 4 | no | — |
| 653 | C23 | — | 16 | 2 | no | — |
| 654 | C23 | — | 16 | 2 | no | — |
| 655 | C23 | D42 | 1 | 1 | yes | characteristic |
| 656 | Q8 | — | 2 | 1 | no | — |
| 657 | Q8 | — | 2 | 1 | no | — |
| 658 | Q8 | — | 4 | 1 | no | — |
| 659 | Q8 | — | 4 | 1 | no | — |
| 660 | Q8 | — | 4 | 1 | no | — |
| 661 | Q8 | — | 4 | 1 | no | — |
| 662 | Q8 | — | 8 | 1 | no | — |
| 663 | Q8 | — | 8 | 1 | no | — |
| 664 | Q8 | — | 8 | 1 | no | — |
| 665 | Q8 | — | 8 | 1 | no | — |
| 666 | Q8 | — | 8 | 1 | no | — |
| 667 | D4 | — | 2 | 1 | no | — |
| 668 | D4 | — | 2 | 1 | no | — |
| 669 | D4 | — | 2 | 1 | no | — |
| 670 | D4 | — | 2 | 1 | no | — |
| 671 | D4 | — | 2 | 1 | no | — |
| 672 | D4 | — | 2 | 1 | no | — |
| 673 | D4 | — | 4 | 1 | no | — |
| 674 | D4 | — | 4 | 1 | no | — |
| 675 | D4 | — | 4 | 1 | no | — |
| 676 | D4 | — | 4 | 1 | no | — |
| 677 | D4 | — | 4 | 2 | no | — |
| 678 | D4 | — | 4 | 1 | no | — |
| 679 | D4 | — | 4 | 1 | no | — |
| 680 | D4 | — | 4 | 2 | no | — |
| 681 | D4 | — | 8 | 1 | no | — |
| 682 | D4 | — | 8 | 2 | no | — |
| 683 | D4 | — | 8 | 1 | no | — |
| 684 | D4 | — | 8 | 2 | no | — |
| 685 | D4 | — | 8 | 4 | no | — |
| 686 | D4 | — | 8 | 2 | no | — |
| 687 | D4 | — | 8 | 4 | no | — |
| 688 | D4 | — | 8 | 1 | no | — |
| 689 | D4 | — | 8 | 1 | no | — |
| 690 | D4 | — | 8 | 1 | no | — |
| 691 | D4 | — | 8 | 1 | no | — |
| 692 | D4 | — | 8 | 1 | no | — |
| 693 | D4 | — | 8 | 1 | no | — |
| 694 | D4 | — | 16 | 1 | no | — |
| 695 | D4 | — | 16 | 2 | no | — |
| 696 | D4 | — | 16 | 2 | no | — |
| 697 | D4 | — | 16 | 1 | no | — |
| 698 | C2×C4 | — | 2 | 1 | no | — |
| 699 | C2×C4 | — | 2 | 1 | no | — |
| 700 | C2×C4 | — | 2 | 1 | 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 | — | 4 | 1 | no | — |
| 707 | C2×C4 | — | 4 | 1 | no | — |
| 708 | C2×C4 | — | 4 | 1 | no | — |
| 709 | C2×C4 | — | 4 | 1 | no | — |
| 710 | C2×C4 | — | 4 | 1 | no | — |
| 711 | C2×C4 | — | 4 | 1 | no | — |
| 712 | C2×C4 | — | 4 | 1 | no | — |
| 713 | C2×C4 | — | 4 | 1 | no | — |
| 714 | C2×C4 | — | 4 | 1 | no | — |
| 715 | C2×C4 | — | 4 | 1 | no | — |
| 716 | C2×C4 | — | 4 | 1 | no | — |
| 717 | C2×C4 | — | 4 | 1 | no | — |
| 718 | C2×C4 | — | 4 | 1 | no | — |
| 719 | C2×C4 | — | 4 | 1 | no | — |
| 720 | C2×C4 | — | 4 | 1 | no | — |
| 721 | C2×C4 | — | 4 | 1 | no | — |
| 722 | C2×C4 | — | 4 | 1 | no | — |
| 723 | C2×C4 | — | 4 | 1 | no | — |
| 724 | C2×C4 | — | 4 | 1 | no | — |
| 725 | C2×C4 | — | 4 | 1 | no | — |
| 726 | C2×C4 | — | 4 | 1 | no | — |
| 727 | C2×C4 | — | 4 | 1 | no | — |
| 728 | C2×C4 | — | 4 | 1 | no | — |
| 729 | C2×C4 | — | 8 | 1 | no | — |
| 730 | C2×C4 | — | 8 | 2 | no | — |
| 731 | C2×C4 | — | 8 | 4 | no | — |
| 732 | C2×C4 | — | 8 | 1 | no | — |
| 733 | C2×C4 | — | 8 | 1 | no | — |
| 734 | C2×C4 | — | 8 | 1 | no | — |
| 735 | C2×C4 | — | 8 | 1 | no | — |
| 736 | C2×C4 | — | 8 | 1 | no | — |
| 737 | C2×C4 | — | 8 | 1 | no | — |
| 738 | C2×C4 | — | 8 | 1 | no | — |
| 739 | C2×C4 | — | 8 | 1 | no | — |
| 740 | C2×C4 | — | 16 | 1 | no | — |
| 741 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 742 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 743 | C2×C4 | #534 | 1 | 1 | yes | characteristic |
| 744 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 745 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 746 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 747 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 748 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 749 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 750 | C2×C4 | #577 | 1 | 1 | yes | characteristic |
| 751 | C8 | — | 2 | 2 | no | — |
| 752 | C8 | — | 4 | 1 | no | — |
| 753 | C8 | — | 4 | 2 | no | — |
| 754 | C8 | — | 4 | 1 | no | — |
| 755 | C8 | — | 4 | 1 | no | — |
| 756 | C8 | — | 8 | 1 | no | — |
| 757 | C8 | — | 8 | 1 | no | — |
| 758 | C8 | — | 8 | 1 | no | — |
| 759 | C8 | — | 8 | 1 | no | — |
| 760 | C22 | — | 2 | 1 | no | — |
| 761 | C22 | — | 2 | 1 | no | — |
| 762 | C22 | — | 4 | 1 | no | — |
| 763 | C22 | — | 4 | 1 | no | — |
| 764 | C22 | — | 4 | 1 | no | — |
| 765 | C22 | — | 4 | 1 | no | — |
| 766 | C22 | — | 4 | 1 | no | — |
| 767 | C22 | — | 4 | 1 | no | — |
| 768 | C22 | — | 4 | 1 | no | — |
| 769 | C22 | — | 4 | 1 | no | — |
| 770 | C22 | — | 4 | 1 | no | — |
| 771 | C22 | — | 8 | 1 | no | — |
| 772 | C22 | — | 8 | 2 | no | — |
| 773 | C22 | — | 8 | 2 | no | — |
| 774 | C22 | — | 8 | 1 | no | — |
| 775 | C22 | — | 8 | 2 | no | — |
| 776 | C22 | — | 8 | 1 | no | — |
| 777 | C22 | — | 16 | 1 | no | — |
| 778 | C22 | — | 16 | 1 | no | — |
| 779 | C22 | — | 16 | 2 | no | — |
| 780 | C22 | — | 16 | 2 | no | — |
| 781 | C22 | — | 32 | 4 | no | — |
| 782 | C22 | #2410 | 1 | 1 | yes | characteristic |
| 783 | C22 | #3264 | 1 | 1 | yes | characteristic |
| 784 | C22 | #3272 | 1 | 1 | yes | characteristic |
| 785 | C4 | — | 2 | 1 | no | — |
| 786 | C4 | — | 2 | 1 | no | — |
| 787 | C4 | — | 2 | 1 | no | — |
| 788 | C4 | — | 4 | 2 | no | — |
| 789 | C4 | — | 4 | 1 | no | — |
| 790 | C4 | — | 4 | 1 | no | — |
| 791 | C4 | — | 4 | 1 | no | — |
| 792 | C4 | — | 4 | 1 | no | — |
| 793 | C4 | — | 4 | 1 | no | — |
| 794 | C4 | — | 8 | 1 | no | — |
| 795 | C4 | — | 8 | 1 | no | — |
| 796 | C4 | — | 8 | 1 | no | — |
| 797 | C4 | — | 8 | 1 | no | — |
| 798 | C4 | — | 16 | 1 | no | — |
| 799 | C4 | — | 16 | 1 | no | — |
| 800 | C4 | #3019 | 1 | 1 | yes | characteristic |
| 801 | C4 | #3022 | 1 | 1 | yes | characteristic |
| 802 | C4 | #3038 | 1 | 1 | yes | characteristic |
| 803 | C4 | #3045 | 1 | 1 | yes | characteristic |
| 804 | C4 | #3264 | 1 | 1 | yes | characteristic |
| 805 | C4 | #3272 | 1 | 1 | yes | characteristic |
| 806 | C2 | — | 2 | 1 | no | — |
| 807 | C2 | — | 2 | 1 | no | — |
| 808 | C2 | — | 8 | 1 | no | — |
| 809 | C2 | — | 8 | 1 | no | — |
| 810 | C2 | — | 8 | 1 | no | — |
| 811 | C2 | — | 16 | 2 | no | — |
| 812 | C2 | — | 16 | 1 | no | — |
| 813 | C2 | #24372 | 1 | 1 | yes | characteristic |
| 814 | C2 | #24471 | 1 | 1 | yes | characteristic |
| 815 | C2 | #24475 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #2410 |
| commutator, Frattini, cosocle | C2×C42 | C24 |
| prime radical | #61959 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #29824 | C2 | semidirect |
| 3. #25744 | C2 | semidirect |
| 4. #22507 | C2 | semidirect |
| 5. #19163 | C2 | semidirect |
| 6. #18804 | C2 | semidirect |
| 7. #10520 | C2 | semidirect |
| 8. #10504 | C2 | semidirect |
| 9. #10294 | C2 | semidirect |
| 10. #10206 | C2 | semidirect |
| 11. #9320 | C2 | semidirect |
| 12. #9253 | C2 | semidirect |
| 13. #9237 | C2 | semidirect |
| 14. #8841 | C2 | semidirect |
| 15. #8420 | C2 | semidirect |
| 26. #3229 | C22 | semidirect |
| 32. C2×#474 | C22 | semidirect |
| 39. D4×M16 | C22 | semidirect |
| 41. #2293 | C22 | semidirect |
| 46. #1994 | C22 | semidirect |
| 47. #1988 | C22 | semidirect |
| 48. #1986 | C22 | semidirect |
| 54. #1842 | C22 | semidirect |
| 67. #1565 | C22 | semidirect |
| 68. #1550 | C22 | semidirect |
| 70. #1546 | C22 | semidirect |
| 73. #1486 | C22 | semidirect |
| 75. #1303 | C22 | semidirect |
| 76. #1292 | C22 | semidirect |
| 77. #1283 | C22 | semidirect |
| 78. #1276 | C22 | semidirect |
| 559. M16 | AGL(1,ℤ/8) | semidirect |
| 634. C42 | AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61959 | 2 |
| #29824 | 2 |
| #25744 | 2 |
| #22507 | 2 |
| #19163 | 2 |
| #18804 | 2 |
| #10520 | 2 |
| #10504 | 2 |
| #10294 | 2 |
| #10206 | 2 |
| #9320 | 2 |
| #9253 | 2 |
| #9237 | 2 |
| #8841 | 2 |
| #8420 | 2 |