Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1666 conjugacy classes of subgroups.
The subgroup lattice has 917 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61374 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61217 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #60881 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #60623 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33220 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #30838 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #30700 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #30280 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #29859 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #28732 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #28669 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #25986 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #25923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #25876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #25830 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #25666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #24926 | C2 | 1 | 4 | yes | maximal, complemented |
| 18 | #22234 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #21137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | #3511 | C22 | 1 | 1 | yes | characteristic |
| 21 | #3503 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3503 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3499 | C22 | 1 | 1 | yes | characteristic |
| 24 | #3387 | — | 2 | 1 | no | — |
| 25 | #3387 | — | 2 | 1 | no | — |
| 26 | #3384 | — | 2 | 1 | no | — |
| 27 | #3384 | — | 2 | 1 | no | — |
| 28 | #3381 | — | 2 | 1 | no | — |
| 29 | #3381 | — | 2 | 1 | no | — |
| 30 | Q8×SD16 | — | 2 | 1 | no | — |
| 31 | Q8×SD16 | — | 2 | 1 | no | — |
| 32 | #3331 | — | 2 | 1 | no | — |
| 33 | #3330 | — | 2 | 1 | no | — |
| 34 | #3329 | — | 2 | 1 | no | — |
| 35 | #3328 | — | 2 | 1 | no | — |
| 36 | #3303 | — | 2 | 1 | no | — |
| 37 | #3302 | — | 2 | 1 | no | — |
| 38 | #3299 | — | 2 | 1 | no | — |
| 39 | #3298 | — | 2 | 1 | no | — |
| 40 | #3244 | — | 2 | 4 | no | — |
| 41 | #3231 | — | 2 | 1 | no | — |
| 42 | #3229 | — | 2 | 1 | no | — |
| 43 | #3228 | — | 2 | 1 | no | — |
| 44 | #3227 | — | 2 | 1 | no | — |
| 45 | #3165 | C22 | 1 | 1 | yes | characteristic |
| 46 | #3163 | C22 | 1 | 2 | yes | — |
| 47 | C2×#498 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#498 | C22 | 1 | 1 | yes | characteristic |
| 49 | #3141 | — | 2 | 1 | no | — |
| 50 | #3141 | C22 | 1 | 1 | yes | characteristic |
| 51 | #3141 | C22 | 1 | 1 | yes | characteristic |
| 52 | #3139 | — | 2 | 1 | no | — |
| 53 | #3139 | C22 | 1 | 1 | yes | characteristic |
| 54 | #3137 | — | 2 | 4 | no | — |
| 55 | #3137 | C22 | 1 | 4 | yes | — |
| 56 | #3131 | — | 2 | 1 | no | — |
| 57 | #3131 | C22 | 1 | 1 | yes | characteristic |
| 58 | C2×#487 | — | 2 | 1 | no | — |
| 59 | C2×#487 | C22 | 1 | 1 | yes | characteristic |
| 60 | C2×#487 | C22 | 1 | 1 | yes | characteristic |
| 61 | #3099 | C22 | 1 | 4 | yes | — |
| 62 | #3097 | C22 | 1 | 2 | yes | — |
| 63 | #3084 | C22 | 1 | 4 | yes | — |
| 64 | #3084 | C22 | 1 | 2 | yes | — |
| 65 | #3084 | C22 | 1 | 2 | yes | — |
| 66 | #3079 | C22 | 1 | 1 | yes | characteristic |
| 67 | #3079 | C22 | 1 | 1 | yes | characteristic |
| 68 | #3079 | C22 | 1 | 1 | yes | characteristic |
| 69 | #3063 | C22 | 1 | 2 | yes | — |
| 70 | #3039 | C22 | 1 | 1 | yes | characteristic |
| 71 | #3013 | C22 | 1 | 2 | yes | — |
| 72 | #2960 | C22 | 1 | 1 | yes | characteristic |
| 73 | #2952 | C22 | 1 | 2 | yes | — |
| 74 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 75 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 76 | #2922 | C22 | 1 | 1 | yes | characteristic |
| 77 | #2898 | C22 | 1 | 2 | yes | — |
| 78 | #2898 | C22 | 1 | 4 | yes | — |
| 79 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 80 | #2868 | C22 | 1 | 1 | yes | characteristic |
| 81 | #2862 | C22 | 1 | 1 | yes | characteristic |
| 82 | #2096 | C22 | 1 | 4 | yes | — |
| 83 | #2096 | C22 | 1 | 4 | yes | — |
| 84 | #2079 | C22 | 1 | 4 | yes | — |
| 85 | #2064 | C22 | 1 | 4 | yes | — |
| 86 | #2064 | C22 | 1 | 4 | yes | — |
| 87 | #2060 | C22 | 1 | 4 | yes | — |
| 88 | #2052 | C22 | 1 | 4 | yes | — |
| 89 | #2039 | C22 | 1 | 4 | yes | — |
| 90 | #2038 | C22 | 1 | 4 | yes | — |
| 91 | #2028 | C22 | 1 | 4 | yes | — |
| 92 | #1997 | C22 | 1 | 1 | yes | characteristic |
| 93 | #1997 | C22 | 1 | 1 | yes | characteristic |
| 94 | #1997 | C22 | 1 | 1 | yes | characteristic |
| 95 | #1994 | C22 | 1 | 1 | yes | characteristic |
| 96 | #1966 | C22 | 1 | 1 | yes | characteristic |
| 97 | #1962 | C22 | 1 | 1 | yes | characteristic |
| 98 | #1951 | C22 | 1 | 4 | yes | — |
| 99 | #1930 | C22 | 1 | 4 | yes | — |
| 100 | #1929 | C22 | 1 | 4 | yes | — |
| 101 | #1929 | C22 | 1 | 2 | yes | — |
| 102 | #1922 | C22 | 1 | 2 | yes | — |
| 103 | #1882 | C22 | 1 | 4 | yes | — |
| 104 | #1876 | C22 | 1 | 2 | yes | — |
| 105 | #1866 | C22 | 1 | 2 | yes | — |
| 106 | #1866 | C22 | 1 | 4 | yes | — |
| 107 | #1859 | C22 | 1 | 4 | yes | — |
| 108 | #1859 | C22 | 1 | 4 | yes | — |
| 109 | #1848 | C22 | 1 | 1 | yes | characteristic |
| 110 | #1815 | C22 | 1 | 4 | yes | — |
| 111 | #1815 | C22 | 1 | 4 | yes | — |
| 112 | #1793 | C22 | 1 | 4 | yes | — |
| 113 | C4×#108 | C22 | 1 | 1 | yes | characteristic |
| 114 | C4×#104 | C22 | 1 | 1 | yes | characteristic |
| 115 | C4×#104 | C22 | 1 | 1 | yes | characteristic |
| 116 | #1744 | C22 | 1 | 1 | yes | characteristic |
| 117 | C2×2−1+4 | C23 | 1 | 2 | yes | — |
| 118 | C2×#137 | C23 | 1 | 2 | yes | — |
| 119 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 120 | C2×#131 | C23 | 1 | 2 | yes | — |
| 121 | C2×#131 | C23 | 1 | 2 | yes | — |
| 122 | Q82 | — | 2 | 1 | no | — |
| 123 | Q82 | — | 2 | 1 | no | — |
| 124 | #557 | — | 2 | 1 | no | — |
| 125 | #557 | — | 2 | 1 | no | — |
| 126 | #556 | — | 2 | 1 | no | — |
| 127 | #555 | — | 2 | 1 | no | — |
| 128 | #554 | — | 2 | 1 | no | — |
| 129 | #554 | — | 2 | 1 | no | — |
| 130 | #554 | — | 2 | 1 | no | — |
| 131 | #554 | — | 4 | 1 | no | — |
| 132 | #554 | — | 4 | 1 | no | — |
| 133 | #553 | — | 4 | 1 | no | — |
| 134 | D4×Q8 | — | 2 | 1 | no | — |
| 135 | D4×Q8 | — | 2 | 1 | no | — |
| 136 | D4×Q8 | — | 2 | 1 | no | — |
| 137 | D4×Q8 | — | 2 | 1 | no | — |
| 138 | D4×Q8 | — | 4 | 1 | no | — |
| 139 | D4×Q8 | — | 4 | 1 | no | — |
| 140 | #548 | — | 4 | 1 | no | — |
| 141 | #547 | — | 2 | 1 | no | — |
| 142 | #547 | — | 2 | 1 | no | — |
| 143 | #547 | — | 2 | 1 | no | — |
| 144 | #547 | — | 4 | 1 | no | — |
| 145 | #547 | — | 4 | 1 | no | — |
| 146 | #544 | — | 2 | 2 | no | — |
| 147 | #544 | — | 2 | 2 | no | — |
| 148 | #544 | C23 | 1 | 2 | yes | — |
| 149 | #544 | C23 | 1 | 2 | yes | — |
| 150 | #542 | — | 2 | 2 | no | — |
| 151 | #537 | C23 | 1 | 2 | yes | — |
| 152 | #536 | — | 2 | 2 | no | — |
| 153 | #536 | C23 | 1 | 2 | yes | — |
| 154 | #533 | — | 2 | 1 | no | — |
| 155 | #533 | — | 2 | 1 | no | — |
| 156 | #533 | — | 2 | 1 | no | — |
| 157 | #533 | C23 | 1 | 1 | yes | characteristic |
| 158 | #532 | — | 2 | 1 | no | — |
| 159 | #532 | — | 2 | 1 | no | — |
| 160 | #532 | C23 | 1 | 1 | yes | characteristic |
| 161 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 162 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 163 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 164 | C2×C4⋊Q8 | — | 4 | 1 | no | — |
| 165 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 166 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 167 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 168 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 169 | #520 | C23 | 1 | 2 | yes | — |
| 170 | #520 | C23 | 1 | 2 | yes | — |
| 171 | #520 | C23 | 1 | 2 | yes | — |
| 172 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 173 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 174 | #501 | — | 2 | 2 | no | — |
| 175 | #501 | — | 2 | 2 | no | — |
| 176 | #501 | — | 2 | 2 | no | — |
| 177 | #500 | — | 2 | 1 | no | — |
| 178 | #499 | — | 2 | 2 | no | — |
| 179 | #498 | — | 2 | 1 | no | — |
| 180 | #498 | — | 2 | 2 | no | — |
| 181 | #498 | — | 2 | 1 | no | — |
| 182 | #498 | — | 2 | 1 | no | — |
| 183 | #498 | — | 2 | 1 | no | — |
| 184 | #498 | — | 2 | 1 | no | — |
| 185 | #498 | — | 2 | 1 | no | — |
| 186 | #498 | — | 2 | 1 | no | — |
| 187 | #498 | — | 2 | 2 | no | — |
| 188 | #491 | — | 2 | 2 | no | — |
| 189 | #491 | — | 2 | 4 | no | — |
| 190 | #489 | — | 2 | 2 | no | — |
| 191 | #489 | — | 2 | 2 | no | — |
| 192 | #489 | — | 2 | 4 | no | — |
| 193 | #488 | — | 2 | 4 | no | — |
| 194 | #488 | D4 | 1 | 4 | yes | — |
| 195 | #487 | — | 2 | 1 | no | — |
| 196 | #487 | — | 2 | 1 | no | — |
| 197 | #487 | — | 2 | 1 | no | — |
| 198 | #487 | — | 2 | 1 | no | — |
| 199 | #487 | — | 2 | 4 | no | — |
| 200 | #487 | — | 2 | 1 | no | — |
| 201 | #487 | — | 2 | 1 | no | — |
| 202 | #487 | — | 2 | 1 | no | — |
| 203 | #487 | — | 2 | 2 | no | — |
| 204 | #487 | — | 2 | 1 | no | — |
| 205 | #487 | — | 2 | 1 | no | — |
| 206 | #487 | — | 2 | 1 | no | — |
| 207 | #487 | D4 | 1 | 1 | yes | characteristic |
| 208 | #487 | D4 | 1 | 1 | yes | characteristic |
| 209 | #486 | — | 2 | 1 | no | — |
| 210 | #486 | — | 2 | 1 | no | — |
| 211 | #486 | D4 | 1 | 1 | yes | characteristic |
| 212 | #486 | D4 | 1 | 1 | yes | characteristic |
| 213 | #485 | — | 2 | 2 | no | — |
| 214 | #485 | — | 2 | 2 | no | — |
| 215 | #485 | — | 2 | 4 | no | — |
| 216 | #484 | — | 2 | 2 | no | — |
| 217 | #483 | — | 2 | 2 | no | — |
| 218 | #483 | — | 2 | 4 | no | — |
| 219 | #482 | — | 2 | 4 | no | — |
| 220 | #481 | — | 2 | 4 | no | — |
| 221 | #479 | — | 2 | 2 | no | — |
| 222 | #479 | — | 2 | 2 | no | — |
| 223 | #479 | — | 2 | 4 | no | — |
| 224 | #478 | — | 2 | 2 | no | — |
| 225 | #478 | — | 2 | 2 | no | — |
| 226 | #478 | — | 2 | 4 | no | — |
| 227 | #477 | — | 2 | 1 | no | — |
| 228 | #477 | — | 2 | 1 | no | — |
| 229 | #477 | — | 2 | 1 | no | — |
| 230 | #476 | — | 2 | 1 | no | — |
| 231 | #476 | — | 2 | 1 | no | — |
| 232 | #476 | — | 2 | 1 | no | — |
| 233 | #476 | — | 2 | 2 | no | — |
| 234 | #476 | — | 2 | 2 | no | — |
| 235 | #476 | — | 2 | 4 | no | — |
| 236 | #475 | — | 2 | 1 | no | — |
| 237 | #475 | — | 2 | 1 | no | — |
| 238 | #475 | — | 2 | 1 | no | — |
| 239 | #475 | — | 2 | 2 | no | — |
| 240 | #475 | — | 2 | 2 | no | — |
| 241 | #475 | — | 2 | 4 | no | — |
| 242 | #474 | — | 2 | 1 | no | — |
| 243 | #474 | — | 2 | 1 | no | — |
| 244 | #474 | — | 2 | 1 | no | — |
| 245 | #470 | — | 2 | 2 | no | — |
| 246 | #468 | — | 2 | 2 | no | — |
| 247 | #467 | — | 2 | 2 | no | — |
| 248 | #465 | — | 2 | 2 | no | — |
| 249 | #462 | — | 2 | 1 | no | — |
| 250 | #462 | — | 2 | 1 | no | — |
| 251 | #461 | — | 2 | 1 | no | — |
| 252 | #461 | — | 2 | 1 | no | — |
| 253 | #452 | — | 2 | 2 | no | — |
| 254 | #451 | — | 2 | 2 | no | — |
| 255 | #449 | — | 2 | 2 | no | — |
| 256 | #448 | — | 2 | 2 | no | — |
| 257 | #446 | — | 2 | 1 | no | — |
| 258 | #446 | — | 2 | 1 | no | — |
| 259 | C8×Q8 | — | 2 | 1 | no | — |
| 260 | C8×Q8 | — | 2 | 1 | no | — |
| 261 | #442 | — | 2 | 2 | no | — |
| 262 | #441 | — | 2 | 2 | no | — |
| 263 | C4×Q16 | D4 | 1 | 1 | yes | characteristic |
| 264 | C4×Q16 | D4 | 1 | 1 | yes | characteristic |
| 265 | C4×SD16 | — | 2 | 2 | no | — |
| 266 | C4×SD16 | — | 2 | 2 | no | — |
| 267 | C4×SD16 | D4 | 1 | 1 | yes | characteristic |
| 268 | C4×SD16 | D4 | 1 | 1 | yes | characteristic |
| 269 | C4×SD16 | D4 | 1 | 1 | yes | characteristic |
| 270 | C4×SD16 | D4 | 1 | 1 | yes | characteristic |
| 271 | C4×D8 | D4 | 1 | 1 | yes | characteristic |
| 272 | C4×D8 | D4 | 1 | 1 | yes | characteristic |
| 273 | #436 | — | 2 | 1 | no | — |
| 274 | #436 | — | 2 | 1 | no | — |
| 275 | C8×D4 | — | 2 | 1 | no | — |
| 276 | C8×D4 | — | 2 | 1 | no | — |
| 277 | #433 | — | 2 | 2 | no | — |
| 278 | #431 | — | 2 | 1 | no | — |
| 279 | #431 | — | 2 | 1 | no | — |
| 280 | C2×#108 | C23 | 1 | 4 | yes | — |
| 281 | C2×#108 | C23 | 1 | 2 | yes | — |
| 282 | #428 | C23 | 1 | 2 | yes | — |
| 283 | #428 | C23 | 1 | 2 | yes | — |
| 284 | #428 | C23 | 1 | 2 | yes | — |
| 285 | #428 | C23 | 1 | 4 | yes | — |
| 286 | #427 | C23 | 1 | 1 | yes | characteristic |
| 287 | C2×#106 | C23 | 1 | 2 | yes | — |
| 288 | C2×#106 | C23 | 1 | 4 | yes | — |
| 289 | C2×#106 | C23 | 1 | 2 | yes | — |
| 290 | #424 | C23 | 1 | 2 | yes | — |
| 291 | #424 | C23 | 1 | 2 | yes | — |
| 292 | #423 | C23 | 1 | 1 | yes | characteristic |
| 293 | #423 | C23 | 1 | 1 | yes | characteristic |
| 294 | C2×#104 | C23 | 1 | 2 | yes | — |
| 295 | C2×#104 | C23 | 1 | 4 | yes | — |
| 296 | C2×#104 | C23 | 1 | 2 | yes | — |
| 297 | #419 | — | 2 | 2 | no | — |
| 298 | #419 | — | 2 | 4 | no | — |
| 299 | #419 | C23 | 1 | 2 | yes | — |
| 300 | #419 | C23 | 1 | 4 | yes | — |
| 301 | #417 | — | 2 | 2 | no | — |
| 302 | #417 | — | 2 | 4 | no | — |
| 303 | #417 | C23 | 1 | 2 | yes | — |
| 304 | #417 | C23 | 1 | 4 | yes | — |
| 305 | #417 | C23 | 1 | 2 | yes | — |
| 306 | #417 | C23 | 1 | 2 | yes | — |
| 307 | #417 | C23 | 1 | 4 | yes | — |
| 308 | #416 | — | 2 | 4 | no | — |
| 309 | #416 | — | 2 | 2 | no | — |
| 310 | #416 | C23 | 1 | 1 | yes | characteristic |
| 311 | #416 | C23 | 1 | 1 | yes | characteristic |
| 312 | #416 | C23 | 1 | 4 | yes | — |
| 313 | C2×#103 | — | 2 | 4 | no | — |
| 314 | C2×#103 | — | 2 | 2 | no | — |
| 315 | C2×#103 | C23 | 1 | 4 | yes | — |
| 316 | C2×#103 | C23 | 1 | 2 | yes | — |
| 317 | C2×#103 | C23 | 1 | 2 | yes | — |
| 318 | C2×#101 | C23 | 1 | 4 | yes | — |
| 319 | #408 | C23 | 1 | 2 | yes | — |
| 320 | #408 | C23 | 1 | 2 | yes | — |
| 321 | #405 | — | 2 | 2 | no | — |
| 322 | #405 | C23 | 1 | 2 | yes | — |
| 323 | #405 | C23 | 1 | 2 | yes | — |
| 324 | C4×M16 | — | 2 | 1 | no | — |
| 325 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 326 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 327 | C2×C4×C8 | — | 2 | 1 | no | — |
| 328 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 329 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 330 | #391 | — | 4 | 1 | no | — |
| 331 | #391 | C23 | 1 | 4 | yes | — |
| 332 | #384 | — | 4 | 1 | no | — |
| 333 | #384 | C23 | 1 | 4 | yes | — |
| 334 | #382 | — | 4 | 1 | no | — |
| 335 | C43 | C23 | 1 | 1 | yes | characteristic |
| 336 | #343 | C23 | 1 | 4 | yes | — |
| 337 | #343 | C23 | 1 | 4 | yes | — |
| 338 | #343 | C23 | 1 | 4 | yes | — |
| 339 | #341 | C23 | 1 | 2 | yes | — |
| 340 | #339 | C23 | 1 | 2 | yes | — |
| 341 | #339 | C23 | 1 | 4 | yes | — |
| 342 | #339 | C23 | 1 | 2 | yes | — |
| 343 | #336 | C23 | 1 | 2 | yes | — |
| 344 | #336 | C23 | 1 | 2 | yes | — |
| 345 | 2−1+4 | — | 2 | 8 | no | — |
| 346 | 2−1+4 | — | 4 | 4 | no | — |
| 347 | C2×#41 | — | 2 | 2 | no | — |
| 348 | C2×#41 | — | 2 | 2 | no | — |
| 349 | C2×#41 | — | 4 | 2 | no | — |
| 350 | C2×#41 | — | 4 | 1 | no | — |
| 351 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 352 | C2×#41 | C24 | 1 | 2 | yes | — |
| 353 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 354 | C22×Q8 | — | 2 | 1 | no | — |
| 355 | C22×Q8 | — | 2 | 1 | no | — |
| 356 | C22×Q8 | — | 2 | 1 | no | — |
| 357 | C22×Q8 | — | 2 | 2 | no | — |
| 358 | C22×Q8 | — | 2 | 2 | no | — |
| 359 | C22×Q8 | — | 4 | 1 | no | — |
| 360 | C22×Q8 | — | 4 | 1 | no | — |
| 361 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 362 | #137 | — | 4 | 4 | no | — |
| 363 | #135 | — | 2 | 4 | no | — |
| 364 | C2×Q16 | — | 2 | 2 | no | — |
| 365 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 366 | C2×SD16 | — | 2 | 2 | no | — |
| 367 | C2×SD16 | C2×D4 | 1 | 1 | yes | characteristic |
| 368 | C2×SD16 | C2×D4 | 1 | 1 | yes | characteristic |
| 369 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 370 | #131 | — | 2 | 4 | no | — |
| 371 | #131 | — | 4 | 2 | no | — |
| 372 | #131 | — | 4 | 4 | no | — |
| 373 | C2×M16 | — | 2 | 2 | no | — |
| 374 | C2×M16 | — | 2 | 2 | no | — |
| 375 | C2×M16 | C24 | 1 | 2 | yes | — |
| 376 | C2×M16 | C24 | 1 | 2 | yes | — |
| 377 | C2×M16 | C24 | 1 | 2 | yes | — |
| 378 | C2×M16 | C24 | 1 | 2 | yes | — |
| 379 | C22×C8 | — | 2 | 2 | no | — |
| 380 | C22×C8 | — | 2 | 2 | no | — |
| 381 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 382 | C22×C8 | C24 | 1 | 2 | yes | — |
| 383 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 384 | C4⋊Q8 | — | 2 | 2 | no | — |
| 385 | C4⋊Q8 | — | 2 | 2 | no | — |
| 386 | C4⋊Q8 | — | 2 | 2 | no | — |
| 387 | C4⋊Q8 | — | 2 | 2 | no | — |
| 388 | C4⋊Q8 | — | 2 | 2 | no | — |
| 389 | C4⋊Q8 | — | 2 | 1 | no | — |
| 390 | C4⋊Q8 | — | 2 | 1 | no | — |
| 391 | C4⋊Q8 | — | 2 | 1 | no | — |
| 392 | C4⋊Q8 | — | 2 | 1 | no | — |
| 393 | C4⋊Q8 | — | 2 | 1 | no | — |
| 394 | C4⋊Q8 | — | 2 | 1 | no | — |
| 395 | C4⋊Q8 | — | 2 | 1 | no | — |
| 396 | C4⋊Q8 | — | 2 | 1 | no | — |
| 397 | C4⋊Q8 | — | 2 | 1 | no | — |
| 398 | C4⋊Q8 | — | 2 | 1 | no | — |
| 399 | C4⋊Q8 | — | 2 | 1 | no | — |
| 400 | C4⋊Q8 | — | 2 | 1 | no | — |
| 401 | C4⋊Q8 | — | 2 | 1 | no | — |
| 402 | C4⋊Q8 | — | 2 | 1 | no | — |
| 403 | C4⋊Q8 | — | 2 | 1 | no | — |
| 404 | C4⋊Q8 | — | 2 | 1 | no | — |
| 405 | C4⋊Q8 | — | 4 | 1 | no | — |
| 406 | C4⋊Q8 | — | 4 | 1 | no | — |
| 407 | C4⋊Q8 | — | 4 | 1 | no | — |
| 408 | C4⋊Q8 | — | 4 | 1 | no | — |
| 409 | C4⋊Q8 | — | 4 | 1 | no | — |
| 410 | C4⋊Q8 | — | 4 | 1 | no | — |
| 411 | C4⋊Q8 | — | 4 | 2 | no | — |
| 412 | C4⋊Q8 | — | 4 | 2 | no | — |
| 413 | C4⋊Q8 | — | 8 | 4 | no | — |
| 414 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 415 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 416 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 417 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 418 | #126 | — | 4 | 2 | no | — |
| 419 | #125 | — | 2 | 2 | no | — |
| 420 | #125 | — | 2 | 2 | no | — |
| 421 | #125 | — | 2 | 2 | no | — |
| 422 | #125 | — | 2 | 2 | no | — |
| 423 | #125 | — | 4 | 1 | no | — |
| 424 | #125 | — | 4 | 2 | no | — |
| 425 | #125 | — | 4 | 2 | no | — |
| 426 | #125 | C2×D4 | 1 | 2 | yes | — |
| 427 | #124 | — | 2 | 2 | no | — |
| 428 | #124 | — | 4 | 1 | no | — |
| 429 | #124 | — | 4 | 2 | no | — |
| 430 | #124 | C2×D4 | 1 | 2 | yes | — |
| 431 | #123 | — | 4 | 2 | no | — |
| 432 | #123 | — | 4 | 2 | no | — |
| 433 | #123 | — | 4 | 2 | no | — |
| 434 | #123 | — | 4 | 2 | no | — |
| 435 | C22⋊Q8 | — | 2 | 1 | no | — |
| 436 | C22⋊Q8 | — | 2 | 1 | no | — |
| 437 | C22⋊Q8 | — | 2 | 2 | no | — |
| 438 | C22⋊Q8 | — | 2 | 2 | no | — |
| 439 | C22⋊Q8 | — | 2 | 2 | no | — |
| 440 | C22⋊Q8 | — | 2 | 2 | no | — |
| 441 | C22⋊Q8 | — | 4 | 2 | no | — |
| 442 | C22⋊Q8 | — | 4 | 2 | no | — |
| 443 | C22⋊Q8 | — | 4 | 2 | no | — |
| 444 | C22⋊Q8 | — | 4 | 2 | no | — |
| 445 | C22⋊Q8 | — | 4 | 2 | no | — |
| 446 | C22⋊Q8 | — | 4 | 2 | no | — |
| 447 | C22⋊Q8 | — | 4 | 2 | no | — |
| 448 | C22⋊Q8 | — | 4 | 2 | no | — |
| 449 | C22⋊Q8 | — | 4 | 2 | no | — |
| 450 | C22⋊Q8 | — | 4 | 1 | no | — |
| 451 | C22⋊Q8 | — | 4 | 1 | no | — |
| 452 | C22⋊Q8 | — | 4 | 1 | no | — |
| 453 | C22⋊Q8 | — | 4 | 1 | no | — |
| 454 | C22⋊Q8 | — | 4 | 1 | no | — |
| 455 | #121 | — | 2 | 1 | no | — |
| 456 | #121 | — | 2 | 1 | no | — |
| 457 | #121 | — | 2 | 2 | no | — |
| 458 | #121 | — | 2 | 2 | no | — |
| 459 | #121 | — | 4 | 2 | no | — |
| 460 | #121 | — | 4 | 1 | no | — |
| 461 | #121 | — | 4 | 1 | no | — |
| 462 | #121 | — | 4 | 1 | no | — |
| 463 | C4×Q8 | — | 2 | 1 | no | — |
| 464 | C4×Q8 | — | 2 | 1 | no | — |
| 465 | C4×Q8 | — | 2 | 2 | no | — |
| 466 | C4×Q8 | — | 2 | 2 | no | — |
| 467 | C4×Q8 | — | 2 | 2 | no | — |
| 468 | C4×Q8 | — | 4 | 1 | no | — |
| 469 | C4×Q8 | — | 4 | 1 | no | — |
| 470 | C4×Q8 | — | 4 | 1 | no | — |
| 471 | C4×Q8 | — | 4 | 1 | no | — |
| 472 | C4×Q8 | — | 4 | 1 | no | — |
| 473 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 474 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 475 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 476 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 477 | C4×D4 | — | 2 | 1 | no | — |
| 478 | C4×D4 | — | 2 | 1 | no | — |
| 479 | C4×D4 | — | 2 | 1 | no | — |
| 480 | C4×D4 | — | 2 | 1 | no | — |
| 481 | C4×D4 | — | 2 | 2 | no | — |
| 482 | C4×D4 | — | 2 | 2 | no | — |
| 483 | C4×D4 | — | 2 | 2 | no | — |
| 484 | C4×D4 | — | 2 | 1 | no | — |
| 485 | C4×D4 | — | 2 | 1 | no | — |
| 486 | C4×D4 | — | 4 | 1 | no | — |
| 487 | C4×D4 | — | 4 | 1 | no | — |
| 488 | C4×D4 | — | 4 | 1 | no | — |
| 489 | C4×D4 | — | 4 | 2 | no | — |
| 490 | C4×D4 | — | 4 | 2 | no | — |
| 491 | C4×D4 | — | 4 | 2 | no | — |
| 492 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 493 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 494 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 495 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 496 | #117 | — | 2 | 1 | no | — |
| 497 | #117 | — | 2 | 1 | no | — |
| 498 | #117 | — | 2 | 2 | no | — |
| 499 | #117 | — | 2 | 2 | no | — |
| 500 | #117 | — | 2 | 2 | no | — |
| 501 | #117 | — | 4 | 1 | no | — |
| 502 | #117 | C24 | 1 | 1 | yes | characteristic |
| 503 | #117 | C24 | 1 | 1 | yes | characteristic |
| 504 | #117 | C24 | 1 | 2 | yes | — |
| 505 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 506 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 507 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 508 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 509 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 510 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 511 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 512 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 513 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 514 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 515 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 516 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 517 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 518 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 519 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 520 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 521 | C2×C42 | — | 2 | 1 | no | — |
| 522 | C2×C42 | — | 2 | 1 | no | — |
| 523 | C2×C42 | — | 2 | 1 | no | — |
| 524 | C2×C42 | — | 2 | 1 | no | — |
| 525 | C2×C42 | C24 | 1 | 2 | yes | — |
| 526 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 527 | #108 | — | 4 | 4 | no | — |
| 528 | #108 | — | 4 | 2 | no | — |
| 529 | #107 | — | 2 | 2 | no | — |
| 530 | #107 | — | 2 | 2 | no | — |
| 531 | #107 | — | 2 | 2 | no | — |
| 532 | #107 | — | 2 | 4 | no | — |
| 533 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 534 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 535 | #106 | — | 2 | 2 | no | — |
| 536 | #106 | — | 2 | 2 | no | — |
| 537 | #106 | — | 2 | 2 | no | — |
| 538 | #106 | — | 2 | 2 | no | — |
| 539 | #106 | — | 2 | 4 | no | — |
| 540 | #106 | — | 2 | 4 | no | — |
| 541 | #106 | — | 2 | 2 | no | — |
| 542 | #106 | — | 2 | 2 | no | — |
| 543 | #106 | — | 2 | 2 | no | — |
| 544 | #106 | — | 2 | 4 | no | — |
| 545 | #106 | C2×D4 | 1 | 1 | yes | characteristic |
| 546 | #106 | C2×D4 | 1 | 1 | yes | characteristic |
| 547 | C4⋊C8 | — | 2 | 2 | no | — |
| 548 | C4⋊C8 | — | 2 | 2 | no | — |
| 549 | C4⋊C8 | — | 2 | 2 | no | — |
| 550 | C4⋊C8 | — | 2 | 2 | no | — |
| 551 | C4⋊C8 | — | 2 | 1 | no | — |
| 552 | C4⋊C8 | — | 2 | 1 | no | — |
| 553 | C4⋊C8 | — | 2 | 1 | no | — |
| 554 | C4⋊C8 | — | 2 | 1 | no | — |
| 555 | #104 | — | 2 | 4 | no | — |
| 556 | #104 | — | 4 | 4 | no | — |
| 557 | #104 | — | 4 | 2 | no | — |
| 558 | #103 | — | 2 | 2 | no | — |
| 559 | #103 | — | 2 | 4 | no | — |
| 560 | #103 | — | 2 | 2 | no | — |
| 561 | #103 | — | 2 | 2 | no | — |
| 562 | #103 | — | 2 | 4 | no | — |
| 563 | #103 | — | 2 | 2 | no | — |
| 564 | #103 | — | 2 | 4 | no | — |
| 565 | #103 | — | 2 | 2 | no | — |
| 566 | #103 | — | 2 | 4 | no | — |
| 567 | #103 | — | 2 | 2 | no | — |
| 568 | #103 | — | 2 | 2 | no | — |
| 569 | #103 | — | 2 | 2 | no | — |
| 570 | #103 | — | 2 | 4 | no | — |
| 571 | #103 | — | 2 | 2 | no | — |
| 572 | #103 | — | 2 | 4 | no | — |
| 573 | #103 | C2×D4 | 1 | 1 | yes | characteristic |
| 574 | #103 | C2×D4 | 1 | 4 | yes | — |
| 575 | #103 | C2×D4 | 1 | 1 | yes | characteristic |
| 576 | #103 | C2×D4 | 1 | 4 | yes | — |
| 577 | #103 | C2×D4 | 1 | 1 | yes | characteristic |
| 578 | #103 | C2×D4 | 1 | 1 | yes | characteristic |
| 579 | #102 | — | 2 | 2 | no | — |
| 580 | #102 | — | 2 | 4 | no | — |
| 581 | #102 | — | 2 | 2 | no | — |
| 582 | #102 | — | 2 | 2 | no | — |
| 583 | #102 | — | 2 | 4 | no | — |
| 584 | #102 | C2×D4 | 1 | 1 | yes | characteristic |
| 585 | #102 | C2×D4 | 1 | 4 | yes | — |
| 586 | #102 | C2×D4 | 1 | 1 | yes | characteristic |
| 587 | #102 | C2×D4 | 1 | 4 | yes | — |
| 588 | #102 | C2×D4 | 1 | 1 | yes | characteristic |
| 589 | #102 | C2×D4 | 1 | 1 | yes | characteristic |
| 590 | #101 | — | 4 | 4 | no | — |
| 591 | C22⋊C8 | — | 2 | 2 | no | — |
| 592 | C22⋊C8 | — | 2 | 2 | no | — |
| 593 | C22⋊C8 | — | 2 | 2 | no | — |
| 594 | C22⋊C8 | — | 2 | 2 | no | — |
| 595 | #97 | — | 2 | 2 | no | — |
| 596 | #97 | — | 2 | 2 | no | — |
| 597 | #97 | — | 2 | 1 | no | — |
| 598 | #97 | — | 2 | 1 | no | — |
| 599 | C4×C8 | — | 2 | 2 | no | — |
| 600 | C4×C8 | — | 2 | 2 | no | — |
| 601 | C4×C8 | — | 2 | 1 | no | — |
| 602 | C4×C8 | — | 2 | 1 | no | — |
| 603 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 604 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 605 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 606 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 607 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 608 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 609 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 610 | #95 | — | 4 | 4 | no | — |
| 611 | #41 | — | 2 | 2 | no | — |
| 612 | #41 | — | 2 | 2 | no | — |
| 613 | #41 | — | 2 | 4 | no | — |
| 614 | #41 | — | 2 | 4 | no | — |
| 615 | #41 | — | 2 | 2 | no | — |
| 616 | #41 | — | 4 | 8 | no | — |
| 617 | #41 | — | 4 | 4 | no | — |
| 618 | #41 | — | 8 | 8 | no | — |
| 619 | #41 | — | 8 | 2 | no | — |
| 620 | #41 | — | 16 | 2 | no | — |
| 621 | #41 | 2−1+4 | 1 | 4 | yes | — |
| 622 | C2×Q8 | — | 2 | 1 | no | — |
| 623 | C2×Q8 | — | 2 | 1 | no | — |
| 624 | C2×Q8 | — | 2 | 2 | no | — |
| 625 | C2×Q8 | — | 2 | 2 | no | — |
| 626 | C2×Q8 | — | 2 | 4 | no | — |
| 627 | C2×Q8 | — | 2 | 4 | no | — |
| 628 | C2×Q8 | — | 4 | 2 | no | — |
| 629 | C2×Q8 | — | 4 | 2 | no | — |
| 630 | C2×Q8 | — | 4 | 2 | no | — |
| 631 | C2×Q8 | — | 4 | 8 | no | — |
| 632 | C2×Q8 | — | 4 | 1 | no | — |
| 633 | C2×Q8 | — | 4 | 1 | no | — |
| 634 | C2×Q8 | — | 4 | 1 | no | — |
| 635 | C2×Q8 | — | 4 | 1 | no | — |
| 636 | C2×Q8 | — | 4 | 1 | no | — |
| 637 | C2×Q8 | — | 4 | 1 | no | — |
| 638 | C2×Q8 | — | 4 | 4 | no | — |
| 639 | C2×Q8 | — | 8 | 2 | no | — |
| 640 | C2×Q8 | — | 8 | 2 | no | — |
| 641 | C2×Q8 | — | 8 | 2 | no | — |
| 642 | C2×Q8 | — | 8 | 2 | no | — |
| 643 | C2×Q8 | — | 16 | 2 | no | — |
| 644 | C2×Q8 | — | 16 | 2 | no | — |
| 645 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 646 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 647 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 648 | C2×D4 | — | 2 | 1 | no | — |
| 649 | C2×D4 | — | 2 | 1 | no | — |
| 650 | C2×D4 | — | 2 | 2 | no | — |
| 651 | C2×D4 | — | 2 | 1 | no | — |
| 652 | C2×D4 | — | 2 | 1 | no | — |
| 653 | C2×D4 | — | 4 | 2 | no | — |
| 654 | C2×D4 | — | 4 | 2 | no | — |
| 655 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 656 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 657 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 658 | C22×C4 | — | 2 | 1 | no | — |
| 659 | C22×C4 | — | 2 | 2 | no | — |
| 660 | C22×C4 | — | 2 | 1 | no | — |
| 661 | C22×C4 | — | 2 | 1 | no | — |
| 662 | C22×C4 | — | 2 | 1 | no | — |
| 663 | C22×C4 | — | 2 | 1 | no | — |
| 664 | C22×C4 | — | 2 | 1 | no | — |
| 665 | C22×C4 | — | 2 | 2 | no | — |
| 666 | C22×C4 | — | 2 | 2 | no | — |
| 667 | C22×C4 | — | 2 | 2 | no | — |
| 668 | C22×C4 | — | 2 | 2 | no | — |
| 669 | C22×C4 | — | 2 | 2 | no | — |
| 670 | C22×C4 | — | 4 | 2 | no | — |
| 671 | C22×C4 | — | 4 | 2 | no | — |
| 672 | C22×C4 | — | 4 | 2 | no | — |
| 673 | C22×C4 | — | 4 | 2 | no | — |
| 674 | C22×C4 | — | 4 | 2 | no | — |
| 675 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 676 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 677 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 678 | Q16 | — | 2 | 2 | no | — |
| 679 | Q16 | — | 8 | 2 | no | — |
| 680 | SD16 | — | 2 | 2 | no | — |
| 681 | SD16 | — | 2 | 2 | no | — |
| 682 | SD16 | — | 8 | 2 | no | — |
| 683 | D8 | — | 2 | 2 | no | — |
| 684 | M16 | — | 2 | 2 | no | — |
| 685 | M16 | — | 2 | 2 | no | — |
| 686 | M16 | — | 2 | 2 | no | — |
| 687 | M16 | — | 2 | 4 | no | — |
| 688 | M16 | — | 2 | 2 | no | — |
| 689 | M16 | — | 2 | 4 | no | — |
| 690 | M16 | — | 4 | 4 | no | — |
| 691 | M16 | — | 8 | 2 | no | — |
| 692 | C2×C8 | — | 2 | 2 | no | — |
| 693 | C2×C8 | — | 2 | 2 | no | — |
| 694 | C2×C8 | — | 2 | 2 | no | — |
| 695 | C2×C8 | — | 2 | 2 | no | — |
| 696 | C2×C8 | — | 2 | 2 | no | — |
| 697 | C2×C8 | — | 2 | 2 | no | — |
| 698 | C2×C8 | — | 2 | 2 | no | — |
| 699 | C2×C8 | — | 2 | 2 | no | — |
| 700 | C2×C8 | — | 4 | 4 | no | — |
| 701 | C2×C8 | — | 8 | 2 | no | — |
| 702 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 703 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 704 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 705 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 706 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 707 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 708 | C4⋊C4 | — | 2 | 1 | no | — |
| 709 | C4⋊C4 | — | 2 | 1 | no | — |
| 710 | C4⋊C4 | — | 2 | 1 | no | — |
| 711 | C4⋊C4 | — | 2 | 1 | no | — |
| 712 | C4⋊C4 | — | 2 | 1 | no | — |
| 713 | C4⋊C4 | — | 2 | 1 | no | — |
| 714 | C4⋊C4 | — | 2 | 1 | no | — |
| 715 | C4⋊C4 | — | 2 | 1 | no | — |
| 716 | C4⋊C4 | — | 2 | 2 | no | — |
| 717 | C4⋊C4 | — | 2 | 2 | no | — |
| 718 | C4⋊C4 | — | 2 | 2 | no | — |
| 719 | C4⋊C4 | — | 2 | 2 | no | — |
| 720 | C4⋊C4 | — | 2 | 2 | no | — |
| 721 | C4⋊C4 | — | 2 | 2 | no | — |
| 722 | C4⋊C4 | — | 2 | 2 | no | — |
| 723 | C4⋊C4 | — | 2 | 2 | no | — |
| 724 | C4⋊C4 | — | 4 | 2 | no | — |
| 725 | C4⋊C4 | — | 4 | 2 | no | — |
| 726 | C4⋊C4 | — | 4 | 2 | no | — |
| 727 | C4⋊C4 | — | 4 | 2 | no | — |
| 728 | C4⋊C4 | — | 4 | 2 | no | — |
| 729 | C4⋊C4 | — | 4 | 2 | no | — |
| 730 | C4⋊C4 | — | 4 | 2 | no | — |
| 731 | C4⋊C4 | — | 4 | 2 | no | — |
| 732 | C4⋊C4 | — | 4 | 2 | no | — |
| 733 | C4⋊C4 | — | 4 | 2 | no | — |
| 734 | C4⋊C4 | — | 4 | 2 | no | — |
| 735 | C4⋊C4 | — | 4 | 2 | no | — |
| 736 | C4⋊C4 | — | 4 | 1 | no | — |
| 737 | C4⋊C4 | — | 4 | 1 | no | — |
| 738 | C4⋊C4 | — | 4 | 1 | no | — |
| 739 | C4⋊C4 | — | 4 | 1 | no | — |
| 740 | C4⋊C4 | — | 4 | 1 | no | — |
| 741 | C4⋊C4 | — | 4 | 1 | no | — |
| 742 | C4⋊C4 | — | 4 | 1 | no | — |
| 743 | C4⋊C4 | — | 4 | 1 | no | — |
| 744 | C4⋊C4 | — | 4 | 1 | no | — |
| 745 | C4⋊C4 | — | 4 | 1 | no | — |
| 746 | C4⋊C4 | — | 8 | 8 | no | — |
| 747 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 748 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 749 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 750 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 751 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 752 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 753 | C22⋊C4 | — | 2 | 1 | no | — |
| 754 | C22⋊C4 | — | 2 | 1 | no | — |
| 755 | C22⋊C4 | — | 2 | 2 | no | — |
| 756 | C22⋊C4 | — | 2 | 1 | no | — |
| 757 | C22⋊C4 | — | 2 | 1 | no | — |
| 758 | C22⋊C4 | — | 2 | 1 | no | — |
| 759 | C22⋊C4 | — | 2 | 1 | no | — |
| 760 | C22⋊C4 | — | 2 | 2 | no | — |
| 761 | C22⋊C4 | — | 2 | 2 | no | — |
| 762 | C22⋊C4 | — | 4 | 2 | no | — |
| 763 | C22⋊C4 | — | 4 | 2 | no | — |
| 764 | C22⋊C4 | — | 4 | 2 | no | — |
| 765 | C22⋊C4 | — | 4 | 2 | no | — |
| 766 | C22⋊C4 | — | 4 | 2 | no | — |
| 767 | C22⋊C4 | — | 4 | 2 | no | — |
| 768 | C22⋊C4 | — | 4 | 2 | no | — |
| 769 | C42 | — | 2 | 4 | no | — |
| 770 | C42 | — | 2 | 1 | no | — |
| 771 | C42 | — | 2 | 1 | no | — |
| 772 | C42 | — | 2 | 1 | no | — |
| 773 | C42 | — | 2 | 1 | no | — |
| 774 | C42 | — | 2 | 1 | no | — |
| 775 | C42 | — | 2 | 2 | no | — |
| 776 | C42 | — | 2 | 1 | no | — |
| 777 | C42 | — | 2 | 2 | no | — |
| 778 | C42 | — | 2 | 2 | no | — |
| 779 | C42 | — | 4 | 2 | no | — |
| 780 | C42 | — | 4 | 2 | no | — |
| 781 | C42 | — | 4 | 2 | no | — |
| 782 | C42 | — | 4 | 2 | no | — |
| 783 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 784 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 785 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 786 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 787 | C23 | — | 2 | 1 | no | — |
| 788 | C23 | — | 2 | 1 | no | — |
| 789 | C23 | — | 2 | 2 | no | — |
| 790 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 791 | Q8 | — | 2 | 1 | no | — |
| 792 | Q8 | — | 2 | 1 | no | — |
| 793 | Q8 | — | 2 | 4 | no | — |
| 794 | Q8 | — | 2 | 1 | no | — |
| 795 | Q8 | — | 4 | 2 | no | — |
| 796 | Q8 | — | 4 | 2 | no | — |
| 797 | Q8 | — | 4 | 2 | no | — |
| 798 | Q8 | — | 4 | 4 | no | — |
| 799 | Q8 | — | 4 | 2 | no | — |
| 800 | Q8 | — | 8 | 4 | no | — |
| 801 | Q8 | — | 8 | 2 | no | — |
| 802 | Q8 | — | 8 | 2 | no | — |
| 803 | Q8 | — | 8 | 2 | no | — |
| 804 | Q8 | — | 16 | 1 | no | — |
| 805 | Q8 | — | 16 | 1 | no | — |
| 806 | Q8 | — | 16 | 1 | no | — |
| 807 | Q8 | — | 16 | 2 | no | — |
| 808 | Q8 | — | 16 | 2 | no | — |
| 809 | Q8 | #536 | 1 | 2 | yes | — |
| 810 | D4 | — | 2 | 4 | no | — |
| 811 | D4 | — | 2 | 1 | no | — |
| 812 | D4 | — | 2 | 4 | no | — |
| 813 | D4 | — | 2 | 1 | no | — |
| 814 | D4 | — | 2 | 1 | no | — |
| 815 | D4 | — | 4 | 2 | no | — |
| 816 | D4 | — | 4 | 4 | no | — |
| 817 | D4 | — | 4 | 2 | no | — |
| 818 | D4 | — | 4 | 2 | no | — |
| 819 | D4 | — | 8 | 4 | no | — |
| 820 | D4 | — | 16 | 2 | no | — |
| 821 | D4 | #536 | 1 | 2 | yes | — |
| 822 | C2×C4 | — | 2 | 1 | no | — |
| 823 | C2×C4 | — | 2 | 4 | no | — |
| 824 | C2×C4 | — | 2 | 2 | no | — |
| 825 | C2×C4 | — | 2 | 2 | no | — |
| 826 | C2×C4 | — | 2 | 4 | no | — |
| 827 | C2×C4 | — | 2 | 1 | no | — |
| 828 | C2×C4 | — | 2 | 1 | no | — |
| 829 | C2×C4 | — | 2 | 1 | no | — |
| 830 | C2×C4 | — | 2 | 1 | no | — |
| 831 | C2×C4 | — | 2 | 1 | no | — |
| 832 | C2×C4 | — | 2 | 2 | no | — |
| 833 | C2×C4 | — | 2 | 2 | no | — |
| 834 | C2×C4 | — | 2 | 2 | no | — |
| 835 | C2×C4 | — | 4 | 2 | no | — |
| 836 | C2×C4 | — | 4 | 2 | no | — |
| 837 | C2×C4 | — | 4 | 2 | no | — |
| 838 | C2×C4 | — | 4 | 2 | no | — |
| 839 | C2×C4 | — | 4 | 2 | no | — |
| 840 | C2×C4 | — | 4 | 2 | no | — |
| 841 | C2×C4 | — | 4 | 2 | no | — |
| 842 | C2×C4 | — | 4 | 2 | no | — |
| 843 | C2×C4 | — | 4 | 2 | no | — |
| 844 | C2×C4 | — | 4 | 2 | no | — |
| 845 | C2×C4 | — | 4 | 2 | no | — |
| 846 | C2×C4 | — | 4 | 2 | no | — |
| 847 | C2×C4 | — | 4 | 2 | no | — |
| 848 | C2×C4 | — | 4 | 4 | no | — |
| 849 | C2×C4 | — | 8 | 4 | no | — |
| 850 | C2×C4 | — | 8 | 4 | no | — |
| 851 | C2×C4 | — | 8 | 2 | no | — |
| 852 | C2×C4 | — | 8 | 2 | no | — |
| 853 | C2×C4 | — | 8 | 2 | no | — |
| 854 | C2×C4 | — | 16 | 2 | no | — |
| 855 | C2×C4 | — | 16 | 2 | no | — |
| 856 | C2×C4 | — | 16 | 2 | no | — |
| 857 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 858 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 859 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 860 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 861 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 862 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 863 | C2×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 864 | C2×C4 | #585 | 1 | 2 | yes | — |
| 865 | C8 | — | 2 | 1 | no | — |
| 866 | C8 | — | 2 | 1 | no | — |
| 867 | C8 | — | 2 | 2 | no | — |
| 868 | C8 | — | 2 | 2 | no | — |
| 869 | C8 | — | 2 | 1 | no | — |
| 870 | C8 | — | 2 | 1 | no | — |
| 871 | C8 | — | 4 | 2 | no | — |
| 872 | C8 | — | 4 | 2 | no | — |
| 873 | C8 | — | 4 | 2 | no | — |
| 874 | C8 | — | 4 | 2 | no | — |
| 875 | C22 | — | 2 | 1 | no | — |
| 876 | C22 | — | 2 | 1 | no | — |
| 877 | C22 | — | 2 | 2 | no | — |
| 878 | C22 | — | 4 | 1 | no | — |
| 879 | C22 | — | 4 | 1 | no | — |
| 880 | C22 | — | 4 | 2 | no | — |
| 881 | C22 | — | 4 | 1 | no | — |
| 882 | C22 | — | 4 | 1 | no | — |
| 883 | C22 | — | 4 | 2 | no | — |
| 884 | C22 | — | 4 | 1 | no | — |
| 885 | C22 | — | 4 | 2 | no | — |
| 886 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 887 | C22 | #3561 | 1 | 2 | yes | — |
| 888 | C4 | — | 2 | 2 | no | — |
| 889 | C4 | — | 2 | 1 | no | — |
| 890 | C4 | — | 2 | 1 | no | — |
| 891 | C4 | — | 4 | 4 | no | — |
| 892 | C4 | — | 4 | 2 | no | — |
| 893 | C4 | — | 4 | 1 | no | — |
| 894 | C4 | — | 4 | 1 | no | — |
| 895 | C4 | — | 4 | 1 | no | — |
| 896 | C4 | — | 4 | 2 | no | — |
| 897 | C4 | — | 4 | 1 | no | — |
| 898 | C4 | — | 4 | 1 | no | — |
| 899 | C4 | — | 4 | 2 | no | — |
| 900 | C4 | — | 8 | 2 | no | — |
| 901 | C4 | — | 8 | 2 | no | — |
| 902 | C4 | — | 8 | 2 | no | — |
| 903 | C4 | — | 8 | 2 | no | — |
| 904 | C4 | #3289 | 1 | 2 | yes | — |
| 905 | C4 | #3291 | 1 | 2 | yes | — |
| 906 | C4 | C2×#536 | 1 | 1 | yes | characteristic |
| 907 | C4 | #3489 | 1 | 2 | yes | — |
| 908 | C4 | #3500 | 1 | 1 | yes | characteristic |
| 909 | C2 | — | 2 | 2 | no | — |
| 910 | C2 | — | 4 | 2 | no | — |
| 911 | C2 | — | 8 | 2 | no | — |
| 912 | C2 | — | 8 | 1 | no | — |
| 913 | C2 | #37676 | 1 | 1 | yes | characteristic |
| 914 | C2 | C2×#3289 | 1 | 1 | yes | characteristic |
| 915 | C2 | C2×#3291 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | #61217 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61374 | C2 | semidirect |
| 3. #60881 | C2 | semidirect |
| 4. #60623 | C2 | semidirect |
| 5. #33220 | C2 | semidirect |
| 6. #30838 | C2 | semidirect |
| 7. #30700 | C2 | semidirect |
| 8. #30280 | C2 | semidirect |
| 9. #29859 | C2 | semidirect |
| 10. #28732 | C2 | semidirect |
| 11. #28669 | C2 | semidirect |
| 12. #25986 | C2 | semidirect |
| 13. #25923 | C2 | semidirect |
| 14. #25876 | C2 | semidirect |
| 15. #25830 | C2 | semidirect |
| 16. #25666 | C2 | semidirect |
| 17. #24926 | C2 | semidirect |
| 18. #22234 | C2 | semidirect |
| 19. #21137 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61374 | 2 |
| #61217 | 2 |
| #60881 | 2 |
| #60623 | 2 |
| #33220 | 2 |
| #30838 | 2 |
| #30700 | 2 |
| #30280 | 2 |
| #29859 | 2 |
| #28732 | 2 |
| #28669 | 2 |
| #25986 | 2 |
| #25923 | 2 |
| #25876 | 2 |
| #25830 | 2 |
| #25666 | 2 |
| #24926 | 2 |
| #22234 | 2 |
| #21137 | 2 |