Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1656 conjugacy classes of subgroups.
The subgroup lattice has 1062 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61348 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61347 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #61285 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #60667 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #30840 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #30837 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #28731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #28539 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #27812 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #26193 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #26190 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #26084 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #25695 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #25693 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #25491 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #25490 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #24801 | C2 | 1 | 2 | yes | maximal, complemented |
| 18 | #24323 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #24321 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | #23171 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 21 | #22693 | C2 | 1 | 2 | yes | maximal, complemented |
| 22 | C4×#471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 23 | #21518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 24 | #3507 | C22 | 1 | 1 | yes | characteristic |
| 25 | #3506 | C22 | 1 | 1 | yes | characteristic |
| 26 | #3503 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3503 | C22 | 1 | 1 | yes | characteristic |
| 28 | #3377 | — | 2 | 2 | no | — |
| 29 | #3375 | — | 2 | 1 | no | — |
| 30 | #3373 | — | 2 | 2 | no | — |
| 31 | #3372 | — | 2 | 1 | no | — |
| 32 | #3371 | — | 2 | 2 | no | — |
| 33 | #3369 | — | 2 | 1 | no | — |
| 34 | #3367 | — | 2 | 2 | no | — |
| 35 | #3366 | — | 2 | 1 | no | — |
| 36 | #3363 | — | 2 | 1 | no | — |
| 37 | #3362 | — | 2 | 1 | no | — |
| 38 | #3361 | — | 2 | 1 | no | — |
| 39 | #3360 | — | 2 | 1 | no | — |
| 40 | #3357 | — | 2 | 1 | no | — |
| 41 | #3353 | — | 2 | 1 | no | — |
| 42 | #3351 | — | 2 | 2 | no | — |
| 43 | #3340 | — | 2 | 1 | no | — |
| 44 | #3337 | — | 2 | 2 | no | — |
| 45 | #3335 | — | 2 | 1 | no | — |
| 46 | #3165 | — | 2 | 1 | no | — |
| 47 | #3165 | — | 2 | 1 | no | — |
| 48 | #3165 | C22 | 1 | 1 | yes | characteristic |
| 49 | #3165 | C22 | 1 | 1 | yes | characteristic |
| 50 | #3164 | — | 2 | 2 | no | — |
| 51 | #3164 | — | 2 | 2 | no | — |
| 52 | #3164 | C22 | 1 | 2 | yes | — |
| 53 | #3164 | C22 | 1 | 2 | yes | — |
| 54 | #3160 | — | 2 | 1 | no | — |
| 55 | #3160 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#500 | — | 2 | 1 | no | — |
| 57 | C2×#500 | C22 | 1 | 1 | yes | characteristic |
| 58 | #3141 | C22 | 1 | 1 | yes | characteristic |
| 59 | #3141 | C22 | 1 | 1 | yes | characteristic |
| 60 | #3137 | C22 | 1 | 2 | yes | — |
| 61 | #3136 | C22 | 1 | 2 | yes | — |
| 62 | #3097 | C22 | 1 | 2 | yes | — |
| 63 | #3096 | C22 | 1 | 2 | yes | — |
| 64 | #3084 | C22 | 1 | 2 | yes | — |
| 65 | #3083 | C22 | 1 | 2 | yes | — |
| 66 | #3078 | C22 | 1 | 1 | yes | characteristic |
| 67 | #3077 | C22 | 1 | 1 | yes | characteristic |
| 68 | C2×#477 | C22 | 1 | 1 | yes | characteristic |
| 69 | C2×#476 | C22 | 1 | 1 | yes | characteristic |
| 70 | C2×#471 | C22 | 1 | 1 | yes | characteristic |
| 71 | #3057 | C22 | 1 | 2 | yes | — |
| 72 | #3046 | C22 | 1 | 2 | yes | — |
| 73 | #3045 | C22 | 1 | 2 | yes | — |
| 74 | #3035 | C22 | 1 | 1 | yes | characteristic |
| 75 | #2962 | C22 | 1 | 1 | yes | characteristic |
| 76 | #2962 | C22 | 1 | 1 | yes | characteristic |
| 77 | C2×#444 | C22 | 1 | 2 | yes | — |
| 78 | #2952 | C22 | 1 | 2 | yes | — |
| 79 | #2951 | C22 | 1 | 2 | yes | — |
| 80 | C4×#137 | C22 | 1 | 1 | yes | characteristic |
| 81 | C4×AGL(1,ℤ/8) | C22 | 1 | 1 | yes | characteristic |
| 82 | C2×C4×SD16 | C22 | 1 | 1 | yes | characteristic |
| 83 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 84 | #2913 | C22 | 1 | 2 | yes | — |
| 85 | #2913 | C22 | 1 | 2 | yes | — |
| 86 | #2912 | C22 | 1 | 2 | yes | — |
| 87 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 88 | #2567 | C22 | 1 | 1 | yes | characteristic |
| 89 | #2563 | C22 | 1 | 1 | yes | characteristic |
| 90 | #2097 | C22 | 1 | 2 | yes | — |
| 91 | #2093 | C22 | 1 | 2 | yes | — |
| 92 | #2090 | C22 | 1 | 2 | yes | — |
| 93 | #2089 | C22 | 1 | 2 | yes | — |
| 94 | #2078 | C22 | 1 | 2 | yes | — |
| 95 | #2078 | C22 | 1 | 2 | yes | — |
| 96 | #2064 | C22 | 1 | 2 | yes | — |
| 97 | #2063 | C22 | 1 | 2 | yes | — |
| 98 | #2061 | C22 | 1 | 2 | yes | — |
| 99 | #2060 | C22 | 1 | 2 | yes | — |
| 100 | #2038 | C22 | 1 | 2 | yes | — |
| 101 | #2038 | C22 | 1 | 2 | yes | — |
| 102 | #2037 | C22 | 1 | 2 | yes | — |
| 103 | #2037 | C22 | 1 | 2 | yes | — |
| 104 | #2028 | C22 | 1 | 2 | yes | — |
| 105 | #2027 | C22 | 1 | 2 | yes | — |
| 106 | #1997 | C22 | 1 | 1 | yes | characteristic |
| 107 | #1997 | C22 | 1 | 1 | yes | characteristic |
| 108 | #1986 | C22 | 1 | 1 | yes | characteristic |
| 109 | #1986 | C22 | 1 | 1 | yes | characteristic |
| 110 | #1980 | C22 | 1 | 1 | yes | characteristic |
| 111 | #1977 | C22 | 1 | 1 | yes | characteristic |
| 112 | #1973 | C22 | 1 | 2 | yes | — |
| 113 | #1952 | C22 | 1 | 2 | yes | — |
| 114 | #1951 | C22 | 1 | 1 | yes | characteristic |
| 115 | #1951 | C22 | 1 | 2 | yes | — |
| 116 | #1950 | C22 | 1 | 1 | yes | characteristic |
| 117 | #1946 | C22 | 1 | 2 | yes | — |
| 118 | #1931 | C22 | 1 | 1 | yes | characteristic |
| 119 | #1931 | C22 | 1 | 2 | yes | — |
| 120 | #1930 | C22 | 1 | 1 | yes | characteristic |
| 121 | #1930 | C22 | 1 | 2 | yes | — |
| 122 | #1929 | C22 | 1 | 2 | yes | — |
| 123 | #1922 | C22 | 1 | 2 | yes | — |
| 124 | #1922 | C22 | 1 | 2 | yes | — |
| 125 | #1908 | C22 | 1 | 1 | yes | characteristic |
| 126 | #1907 | C22 | 1 | 1 | yes | characteristic |
| 127 | #1883 | C22 | 1 | 2 | yes | — |
| 128 | #1882 | C22 | 1 | 2 | yes | — |
| 129 | #1876 | C22 | 1 | 2 | yes | — |
| 130 | #1860 | C22 | 1 | 2 | yes | — |
| 131 | #1860 | C22 | 1 | 2 | yes | — |
| 132 | #1860 | C22 | 1 | 2 | yes | — |
| 133 | #1859 | C22 | 1 | 2 | yes | — |
| 134 | #1859 | C22 | 1 | 2 | yes | — |
| 135 | #1859 | C22 | 1 | 2 | yes | — |
| 136 | #1847 | C22 | 1 | 2 | yes | — |
| 137 | #1816 | C22 | 1 | 2 | yes | — |
| 138 | #1816 | C22 | 1 | 2 | yes | — |
| 139 | #1815 | C22 | 1 | 1 | yes | characteristic |
| 140 | #1806 | C22 | 1 | 1 | yes | characteristic |
| 141 | C4×#108 | C22 | 1 | 1 | yes | characteristic |
| 142 | #1773 | C22 | 1 | 2 | yes | — |
| 143 | #1770 | C22 | 1 | 1 | yes | characteristic |
| 144 | #1765 | C22 | 1 | 2 | yes | — |
| 145 | C4×#101 | C22 | 1 | 1 | yes | characteristic |
| 146 | C4×#100 | C22 | 1 | 1 | yes | characteristic |
| 147 | C2×#137 | C23 | 1 | 1 | yes | characteristic |
| 148 | C2×AGL(1,ℤ/8) | C23 | 1 | 1 | yes | characteristic |
| 149 | C2×#135 | C23 | 1 | 2 | yes | — |
| 150 | C22×SD16 | C23 | 1 | 1 | yes | characteristic |
| 151 | C2×#131 | C23 | 1 | 2 | yes | — |
| 152 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 153 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 154 | #559 | — | 2 | 1 | no | — |
| 155 | #559 | — | 2 | 2 | no | — |
| 156 | Q82 | — | 2 | 1 | no | — |
| 157 | Q82 | — | 2 | 1 | no | — |
| 158 | #557 | — | 2 | 1 | no | — |
| 159 | #557 | — | 2 | 1 | no | — |
| 160 | #557 | — | 2 | 1 | no | — |
| 161 | #556 | — | 2 | 1 | no | — |
| 162 | #556 | — | 2 | 1 | no | — |
| 163 | #556 | — | 2 | 2 | no | — |
| 164 | #555 | — | 2 | 1 | no | — |
| 165 | #554 | — | 2 | 1 | no | — |
| 166 | #554 | — | 2 | 1 | no | — |
| 167 | #554 | — | 2 | 1 | no | — |
| 168 | #554 | — | 4 | 1 | no | — |
| 169 | #554 | — | 4 | 1 | no | — |
| 170 | #553 | — | 2 | 2 | no | — |
| 171 | #552 | — | 2 | 2 | no | — |
| 172 | #550 | — | 2 | 1 | no | — |
| 173 | D4×Q8 | — | 2 | 1 | no | — |
| 174 | D4×Q8 | — | 2 | 1 | no | — |
| 175 | D4×Q8 | — | 4 | 1 | no | — |
| 176 | D4×Q8 | — | 4 | 1 | no | — |
| 177 | #547 | — | 2 | 1 | no | — |
| 178 | #544 | — | 2 | 2 | no | — |
| 179 | #544 | — | 2 | 2 | no | — |
| 180 | #544 | C23 | 1 | 2 | yes | — |
| 181 | #544 | C23 | 1 | 2 | yes | — |
| 182 | #539 | — | 4 | 1 | no | — |
| 183 | #538 | — | 4 | 1 | no | — |
| 184 | #536 | C23 | 1 | 2 | yes | — |
| 185 | #535 | C23 | 1 | 2 | yes | — |
| 186 | #533 | — | 2 | 1 | no | — |
| 187 | #533 | — | 2 | 1 | no | — |
| 188 | #533 | C23 | 1 | 1 | yes | characteristic |
| 189 | #533 | C23 | 1 | 1 | yes | characteristic |
| 190 | #532 | C23 | 1 | 1 | yes | characteristic |
| 191 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 192 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 193 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 194 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 195 | #529 | — | 4 | 1 | no | — |
| 196 | #525 | — | 4 | 1 | no | — |
| 197 | #520 | C23 | 1 | 2 | yes | — |
| 198 | #520 | C23 | 1 | 2 | yes | — |
| 199 | #520 | C23 | 1 | 2 | yes | — |
| 200 | #520 | C23 | 1 | 2 | yes | — |
| 201 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 202 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 203 | C2×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 204 | #501 | — | 2 | 2 | no | — |
| 205 | #501 | — | 2 | 2 | no | — |
| 206 | #501 | — | 2 | 2 | no | — |
| 207 | #501 | — | 2 | 2 | no | — |
| 208 | #501 | — | 2 | 2 | no | — |
| 209 | #501 | — | 2 | 2 | no | — |
| 210 | #500 | — | 2 | 1 | no | — |
| 211 | #500 | — | 2 | 1 | no | — |
| 212 | #500 | — | 2 | 2 | no | — |
| 213 | #500 | — | 2 | 2 | no | — |
| 214 | #500 | — | 2 | 1 | no | — |
| 215 | #500 | — | 2 | 1 | no | — |
| 216 | #500 | — | 2 | 1 | no | — |
| 217 | #500 | — | 2 | 1 | no | — |
| 218 | #500 | D4 | 1 | 1 | yes | characteristic |
| 219 | #500 | D4 | 1 | 1 | yes | characteristic |
| 220 | #499 | — | 2 | 2 | no | — |
| 221 | #499 | — | 2 | 2 | no | — |
| 222 | #499 | D4 | 1 | 2 | yes | — |
| 223 | #499 | D4 | 1 | 2 | yes | — |
| 224 | #498 | — | 2 | 1 | no | — |
| 225 | #498 | — | 2 | 1 | no | — |
| 226 | #498 | D4 | 1 | 1 | yes | characteristic |
| 227 | #498 | D4 | 1 | 1 | yes | characteristic |
| 228 | #491 | — | 2 | 2 | no | — |
| 229 | #490 | — | 2 | 2 | no | — |
| 230 | #489 | — | 2 | 2 | no | — |
| 231 | #489 | — | 2 | 2 | no | — |
| 232 | #489 | — | 2 | 2 | no | — |
| 233 | #489 | — | 2 | 2 | no | — |
| 234 | #488 | — | 2 | 2 | no | — |
| 235 | #488 | — | 2 | 2 | no | — |
| 236 | #487 | — | 2 | 1 | no | — |
| 237 | #487 | — | 2 | 1 | no | — |
| 238 | #487 | — | 2 | 2 | no | — |
| 239 | #486 | — | 2 | 1 | no | — |
| 240 | #486 | — | 2 | 1 | no | — |
| 241 | #486 | — | 2 | 2 | no | — |
| 242 | #485 | — | 2 | 2 | no | — |
| 243 | #485 | — | 2 | 2 | no | — |
| 244 | #484 | — | 2 | 2 | no | — |
| 245 | #483 | — | 2 | 2 | no | — |
| 246 | #482 | — | 2 | 2 | no | — |
| 247 | #482 | — | 2 | 2 | no | — |
| 248 | #481 | — | 2 | 2 | no | — |
| 249 | #480 | — | 2 | 2 | no | — |
| 250 | #479 | — | 2 | 2 | no | — |
| 251 | #479 | — | 2 | 2 | no | — |
| 252 | #479 | — | 2 | 2 | no | — |
| 253 | #478 | — | 2 | 2 | no | — |
| 254 | #478 | — | 2 | 2 | no | — |
| 255 | #478 | — | 2 | 2 | no | — |
| 256 | #477 | — | 2 | 1 | no | — |
| 257 | #477 | — | 2 | 1 | no | — |
| 258 | #477 | — | 2 | 2 | no | — |
| 259 | #477 | — | 2 | 1 | no | — |
| 260 | #477 | — | 2 | 2 | no | — |
| 261 | #476 | — | 2 | 1 | no | — |
| 262 | #476 | — | 2 | 1 | no | — |
| 263 | #476 | — | 2 | 1 | no | — |
| 264 | #476 | — | 2 | 2 | no | — |
| 265 | #476 | — | 2 | 2 | no | — |
| 266 | #475 | — | 2 | 1 | no | — |
| 267 | #475 | — | 2 | 2 | no | — |
| 268 | #474 | — | 2 | 1 | no | — |
| 269 | #474 | — | 2 | 2 | no | — |
| 270 | #471 | — | 2 | 4 | no | — |
| 271 | #468 | — | 2 | 2 | no | — |
| 272 | #468 | — | 2 | 2 | no | — |
| 273 | #465 | — | 2 | 2 | no | — |
| 274 | #465 | — | 2 | 2 | no | — |
| 275 | #464 | — | 2 | 2 | no | — |
| 276 | #464 | — | 2 | 2 | no | — |
| 277 | #464 | D4 | 1 | 2 | yes | — |
| 278 | #463 | — | 2 | 2 | no | — |
| 279 | #463 | — | 2 | 2 | no | — |
| 280 | #463 | D4 | 1 | 2 | yes | — |
| 281 | #462 | — | 2 | 2 | no | — |
| 282 | #462 | D4 | 1 | 1 | yes | characteristic |
| 283 | #461 | — | 2 | 2 | no | — |
| 284 | #461 | D4 | 1 | 1 | yes | characteristic |
| 285 | #460 | — | 2 | 2 | no | — |
| 286 | #460 | D4 | 1 | 1 | yes | characteristic |
| 287 | #459 | — | 2 | 2 | no | — |
| 288 | #459 | D4 | 1 | 1 | yes | characteristic |
| 289 | #446 | — | 2 | 1 | no | — |
| 290 | #446 | — | 2 | 2 | no | — |
| 291 | #446 | — | 2 | 2 | no | — |
| 292 | #446 | — | 2 | 1 | no | — |
| 293 | C8×Q8 | — | 2 | 1 | no | — |
| 294 | C8×Q8 | — | 2 | 1 | no | — |
| 295 | #444 | — | 2 | 8 | no | — |
| 296 | #442 | — | 2 | 2 | no | — |
| 297 | #442 | — | 2 | 1 | no | — |
| 298 | #441 | — | 2 | 2 | no | — |
| 299 | #441 | — | 2 | 1 | no | — |
| 300 | #440 | — | 2 | 2 | no | — |
| 301 | #440 | — | 2 | 2 | no | — |
| 302 | #440 | — | 2 | 1 | no | — |
| 303 | #440 | — | 2 | 1 | no | — |
| 304 | C4×Q16 | — | 2 | 2 | no | — |
| 305 | C4×Q16 | — | 2 | 1 | no | — |
| 306 | C4×SD16 | — | 2 | 2 | no | — |
| 307 | C4×SD16 | — | 2 | 2 | no | — |
| 308 | C4×SD16 | — | 2 | 1 | no | — |
| 309 | C4×SD16 | — | 2 | 1 | no | — |
| 310 | C4×SD16 | — | 2 | 1 | no | — |
| 311 | C4×SD16 | — | 2 | 1 | no | — |
| 312 | C4×SD16 | — | 2 | 1 | no | — |
| 313 | C4×SD16 | — | 2 | 1 | no | — |
| 314 | C4×D8 | — | 2 | 2 | no | — |
| 315 | C4×D8 | — | 2 | 1 | no | — |
| 316 | #436 | — | 2 | 1 | no | — |
| 317 | #436 | — | 2 | 1 | no | — |
| 318 | C8×D4 | — | 2 | 1 | no | — |
| 319 | C8×D4 | — | 2 | 1 | no | — |
| 320 | C2×#108 | C23 | 1 | 2 | yes | — |
| 321 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 322 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 323 | #428 | — | 2 | 2 | no | — |
| 324 | #428 | — | 2 | 2 | no | — |
| 325 | #428 | — | 2 | 2 | no | — |
| 326 | #428 | — | 2 | 2 | no | — |
| 327 | #428 | — | 2 | 2 | no | — |
| 328 | #428 | — | 2 | 2 | no | — |
| 329 | #428 | C23 | 1 | 2 | yes | — |
| 330 | #428 | C23 | 1 | 2 | yes | — |
| 331 | #428 | C23 | 1 | 1 | yes | characteristic |
| 332 | #428 | C23 | 1 | 1 | yes | characteristic |
| 333 | #428 | C23 | 1 | 2 | yes | — |
| 334 | #428 | C23 | 1 | 2 | yes | — |
| 335 | #428 | C23 | 1 | 2 | yes | — |
| 336 | #428 | C23 | 1 | 2 | yes | — |
| 337 | #427 | — | 2 | 2 | no | — |
| 338 | #427 | — | 2 | 2 | no | — |
| 339 | #427 | — | 2 | 2 | no | — |
| 340 | #427 | C23 | 1 | 2 | yes | — |
| 341 | #427 | C23 | 1 | 2 | yes | — |
| 342 | C2×#107 | — | 2 | 2 | no | — |
| 343 | C2×#107 | — | 2 | 2 | no | — |
| 344 | C2×#107 | C23 | 1 | 2 | yes | — |
| 345 | C2×#107 | C23 | 1 | 2 | yes | — |
| 346 | C2×#107 | C23 | 1 | 2 | yes | — |
| 347 | C2×#106 | — | 2 | 2 | no | — |
| 348 | C2×#106 | C23 | 1 | 2 | yes | — |
| 349 | C2×#106 | C23 | 1 | 1 | yes | characteristic |
| 350 | #424 | C23 | 1 | 2 | yes | — |
| 351 | #424 | C23 | 1 | 2 | yes | — |
| 352 | #423 | C23 | 1 | 1 | yes | characteristic |
| 353 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 354 | C2×#104 | C23 | 1 | 2 | yes | — |
| 355 | C2×#104 | C23 | 1 | 2 | yes | — |
| 356 | C2×#104 | C23 | 1 | 2 | yes | — |
| 357 | #419 | C23 | 1 | 2 | yes | — |
| 358 | #419 | C23 | 1 | 1 | yes | characteristic |
| 359 | #418 | C23 | 1 | 2 | yes | — |
| 360 | #418 | C23 | 1 | 1 | yes | characteristic |
| 361 | #417 | C23 | 1 | 2 | yes | — |
| 362 | #417 | C23 | 1 | 2 | yes | — |
| 363 | #417 | C23 | 1 | 1 | yes | characteristic |
| 364 | #417 | C23 | 1 | 1 | yes | characteristic |
| 365 | #417 | C23 | 1 | 2 | yes | — |
| 366 | #417 | C23 | 1 | 2 | yes | — |
| 367 | #416 | C23 | 1 | 2 | yes | — |
| 368 | C2×#103 | C23 | 1 | 2 | yes | — |
| 369 | C2×#103 | C23 | 1 | 1 | yes | characteristic |
| 370 | C2×#102 | C23 | 1 | 2 | yes | — |
| 371 | C2×#102 | C23 | 1 | 1 | yes | characteristic |
| 372 | C2×#101 | C23 | 1 | 1 | yes | characteristic |
| 373 | C2×#101 | C23 | 1 | 1 | yes | characteristic |
| 374 | C2×#100 | C23 | 1 | 1 | yes | characteristic |
| 375 | C2×#100 | C23 | 1 | 1 | yes | characteristic |
| 376 | #408 | C23 | 1 | 2 | yes | — |
| 377 | #405 | — | 2 | 1 | no | — |
| 378 | #405 | — | 2 | 1 | no | — |
| 379 | #405 | C23 | 1 | 1 | yes | characteristic |
| 380 | #405 | C23 | 1 | 1 | yes | characteristic |
| 381 | #405 | C23 | 1 | 2 | yes | — |
| 382 | #405 | C23 | 1 | 2 | yes | — |
| 383 | C4×M16 | — | 2 | 1 | no | — |
| 384 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 385 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 386 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 387 | C2×#97 | C23 | 1 | 2 | yes | — |
| 388 | C2×C4×C8 | — | 2 | 1 | no | — |
| 389 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 390 | #395 | — | 4 | 1 | no | — |
| 391 | #393 | — | 4 | 1 | no | — |
| 392 | #391 | C23 | 1 | 2 | yes | — |
| 393 | #390 | C23 | 1 | 2 | yes | — |
| 394 | #389 | — | 4 | 1 | no | — |
| 395 | #384 | C23 | 1 | 2 | yes | — |
| 396 | #382 | C23 | 1 | 2 | yes | — |
| 397 | #380 | — | 4 | 1 | no | — |
| 398 | C4×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 399 | #343 | C23 | 1 | 2 | yes | — |
| 400 | #343 | C23 | 1 | 2 | yes | — |
| 401 | #343 | C23 | 1 | 1 | yes | characteristic |
| 402 | #343 | C23 | 1 | 1 | yes | characteristic |
| 403 | #343 | C23 | 1 | 2 | yes | — |
| 404 | #343 | C23 | 1 | 2 | yes | — |
| 405 | #343 | C23 | 1 | 1 | yes | characteristic |
| 406 | #343 | C23 | 1 | 1 | yes | characteristic |
| 407 | #341 | C23 | 1 | 1 | yes | characteristic |
| 408 | #341 | C23 | 1 | 1 | yes | characteristic |
| 409 | #341 | C23 | 1 | 2 | yes | — |
| 410 | #339 | C23 | 1 | 2 | yes | — |
| 411 | #339 | C23 | 1 | 2 | yes | — |
| 412 | #339 | C23 | 1 | 2 | yes | — |
| 413 | #339 | C23 | 1 | 2 | yes | — |
| 414 | #339 | C23 | 1 | 2 | yes | — |
| 415 | #336 | C23 | 1 | 2 | yes | — |
| 416 | C2×#41 | — | 4 | 1 | no | — |
| 417 | C2×#41 | C24 | 1 | 2 | yes | — |
| 418 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 419 | C22×Q8 | — | 2 | 1 | no | — |
| 420 | C22×Q8 | — | 2 | 1 | no | — |
| 421 | C22×Q8 | — | 4 | 1 | no | — |
| 422 | C22×Q8 | — | 4 | 1 | no | — |
| 423 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 424 | C22×D4 | C24 | 1 | 1 | yes | characteristic |
| 425 | C23×C4 | — | 2 | 1 | no | — |
| 426 | #137 | — | 2 | 2 | no | — |
| 427 | #137 | — | 2 | 2 | no | — |
| 428 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 429 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 430 | #135 | — | 2 | 4 | no | — |
| 431 | #135 | — | 2 | 4 | no | — |
| 432 | C2×Q16 | — | 2 | 1 | no | — |
| 433 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 434 | C2×SD16 | — | 2 | 1 | no | — |
| 435 | C2×SD16 | — | 2 | 1 | no | — |
| 436 | C2×SD16 | — | 2 | 1 | no | — |
| 437 | C2×SD16 | — | 2 | 1 | no | — |
| 438 | C2×SD16 | — | 2 | 2 | no | — |
| 439 | C2×SD16 | — | 2 | 2 | no | — |
| 440 | C2×SD16 | C2×D4 | 1 | 2 | yes | — |
| 441 | C2×SD16 | C2×D4 | 1 | 2 | yes | — |
| 442 | C2×D8 | — | 2 | 1 | no | — |
| 443 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 444 | #131 | — | 2 | 2 | no | — |
| 445 | #131 | — | 2 | 2 | no | — |
| 446 | #131 | — | 2 | 2 | no | — |
| 447 | #131 | — | 2 | 4 | no | — |
| 448 | #131 | — | 2 | 4 | no | — |
| 449 | #131 | #41 | 1 | 4 | yes | complemented |
| 450 | C2×M16 | — | 2 | 1 | no | — |
| 451 | C2×M16 | — | 2 | 1 | no | — |
| 452 | C2×M16 | — | 2 | 2 | no | — |
| 453 | C2×M16 | C24 | 1 | 2 | yes | — |
| 454 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 455 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 456 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 457 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 458 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 459 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 460 | C22×C8 | — | 2 | 1 | no | — |
| 461 | C22×C8 | — | 2 | 1 | no | — |
| 462 | C22×C8 | — | 2 | 2 | no | — |
| 463 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 464 | C22×C8 | C24 | 1 | 2 | yes | — |
| 465 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 466 | C4⋊Q8 | — | 2 | 2 | no | — |
| 467 | C4⋊Q8 | — | 2 | 2 | no | — |
| 468 | C4⋊Q8 | — | 2 | 2 | no | — |
| 469 | C4⋊Q8 | — | 2 | 2 | no | — |
| 470 | C4⋊Q8 | — | 2 | 2 | no | — |
| 471 | C4⋊Q8 | — | 2 | 1 | no | — |
| 472 | C4⋊Q8 | — | 2 | 1 | no | — |
| 473 | C4⋊Q8 | — | 2 | 1 | no | — |
| 474 | C4⋊Q8 | — | 2 | 1 | no | — |
| 475 | C4⋊Q8 | — | 2 | 1 | no | — |
| 476 | C4⋊Q8 | — | 2 | 1 | no | — |
| 477 | C4⋊Q8 | — | 2 | 1 | no | — |
| 478 | C4⋊Q8 | — | 2 | 1 | no | — |
| 479 | C4⋊Q8 | — | 4 | 1 | no | — |
| 480 | C4⋊Q8 | — | 4 | 1 | no | — |
| 481 | C4⋊Q8 | — | 4 | 1 | no | — |
| 482 | C4⋊Q8 | — | 4 | 1 | no | — |
| 483 | C4⋊Q8 | — | 4 | 2 | no | — |
| 484 | C4⋊Q8 | — | 4 | 2 | no | — |
| 485 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 486 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 487 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 488 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 489 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 490 | #127 | — | 2 | 2 | no | — |
| 491 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 492 | #126 | — | 4 | 2 | no | — |
| 493 | #126 | — | 4 | 2 | no | — |
| 494 | #126 | — | 4 | 2 | no | — |
| 495 | #125 | — | 2 | 2 | no | — |
| 496 | #125 | — | 2 | 2 | no | — |
| 497 | #125 | — | 2 | 2 | no | — |
| 498 | #125 | — | 2 | 2 | no | — |
| 499 | #125 | — | 4 | 1 | no | — |
| 500 | #125 | — | 4 | 2 | no | — |
| 501 | #125 | — | 4 | 2 | no | — |
| 502 | #125 | — | 4 | 2 | no | — |
| 503 | #125 | C2×D4 | 1 | 2 | yes | — |
| 504 | #125 | C2×D4 | 1 | 2 | yes | — |
| 505 | #124 | — | 2 | 2 | no | — |
| 506 | #124 | — | 2 | 2 | no | — |
| 507 | #124 | — | 4 | 2 | no | — |
| 508 | #124 | — | 4 | 1 | no | — |
| 509 | #124 | C2×D4 | 1 | 2 | yes | — |
| 510 | #123 | — | 4 | 2 | no | — |
| 511 | #123 | — | 4 | 2 | no | — |
| 512 | #123 | — | 4 | 2 | no | — |
| 513 | #123 | — | 4 | 2 | no | — |
| 514 | C22⋊Q8 | — | 2 | 1 | no | — |
| 515 | C22⋊Q8 | — | 2 | 1 | no | — |
| 516 | C22⋊Q8 | — | 2 | 1 | no | — |
| 517 | C22⋊Q8 | — | 2 | 1 | no | — |
| 518 | C22⋊Q8 | — | 2 | 2 | no | — |
| 519 | C22⋊Q8 | — | 2 | 2 | no | — |
| 520 | C22⋊Q8 | — | 4 | 2 | no | — |
| 521 | C22⋊Q8 | — | 4 | 2 | no | — |
| 522 | C22⋊Q8 | — | 4 | 2 | no | — |
| 523 | C22⋊Q8 | — | 4 | 2 | no | — |
| 524 | C22⋊Q8 | — | 4 | 2 | no | — |
| 525 | C22⋊Q8 | — | 4 | 2 | no | — |
| 526 | C22⋊Q8 | — | 4 | 2 | no | — |
| 527 | C22⋊Q8 | — | 4 | 1 | no | — |
| 528 | C22⋊Q8 | — | 4 | 1 | no | — |
| 529 | C22⋊Q8 | — | 4 | 1 | no | — |
| 530 | C22⋊Q8 | — | 4 | 1 | no | — |
| 531 | C22⋊Q8 | — | 4 | 1 | no | — |
| 532 | #121 | — | 2 | 1 | no | — |
| 533 | #121 | — | 2 | 1 | no | — |
| 534 | #121 | — | 2 | 2 | no | — |
| 535 | #121 | — | 2 | 2 | no | — |
| 536 | #121 | — | 4 | 1 | no | — |
| 537 | #121 | — | 4 | 2 | no | — |
| 538 | #120 | — | 4 | 2 | no | — |
| 539 | C4×Q8 | — | 2 | 1 | no | — |
| 540 | C4×Q8 | — | 2 | 1 | no | — |
| 541 | C4×Q8 | — | 2 | 1 | no | — |
| 542 | C4×Q8 | — | 2 | 1 | no | — |
| 543 | C4×Q8 | — | 2 | 2 | no | — |
| 544 | C4×Q8 | — | 2 | 2 | no | — |
| 545 | C4×Q8 | — | 2 | 2 | no | — |
| 546 | C4×Q8 | — | 2 | 2 | no | — |
| 547 | C4×Q8 | — | 2 | 1 | no | — |
| 548 | C4×Q8 | — | 2 | 1 | no | — |
| 549 | C4×Q8 | — | 2 | 1 | no | — |
| 550 | C4×Q8 | — | 2 | 1 | no | — |
| 551 | C4×Q8 | — | 4 | 1 | no | — |
| 552 | C4×Q8 | — | 4 | 1 | no | — |
| 553 | C4×Q8 | — | 4 | 1 | no | — |
| 554 | C4×Q8 | — | 4 | 1 | no | — |
| 555 | C4×Q8 | — | 4 | 1 | no | — |
| 556 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 557 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 558 | C4×D4 | — | 2 | 1 | no | — |
| 559 | C4×D4 | — | 2 | 1 | no | — |
| 560 | C4×D4 | — | 2 | 2 | no | — |
| 561 | C4×D4 | — | 2 | 2 | no | — |
| 562 | C4×D4 | — | 2 | 2 | no | — |
| 563 | C4×D4 | — | 2 | 2 | no | — |
| 564 | C4×D4 | — | 2 | 1 | no | — |
| 565 | C4×D4 | — | 2 | 1 | no | — |
| 566 | C4×D4 | — | 2 | 1 | no | — |
| 567 | C4×D4 | — | 2 | 1 | no | — |
| 568 | C4×D4 | — | 2 | 1 | no | — |
| 569 | C4×D4 | — | 2 | 1 | no | — |
| 570 | C4×D4 | — | 4 | 2 | no | — |
| 571 | C4×D4 | — | 4 | 2 | no | — |
| 572 | C4×D4 | — | 4 | 2 | no | — |
| 573 | C4×D4 | — | 4 | 2 | no | — |
| 574 | C4×D4 | — | 4 | 2 | no | — |
| 575 | C4×D4 | — | 4 | 1 | no | — |
| 576 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 577 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 578 | #117 | — | 2 | 1 | no | — |
| 579 | #117 | — | 2 | 2 | no | — |
| 580 | #117 | — | 2 | 2 | no | — |
| 581 | #117 | — | 2 | 2 | no | — |
| 582 | #117 | — | 2 | 2 | no | — |
| 583 | #117 | — | 4 | 2 | no | — |
| 584 | #117 | — | 4 | 1 | no | — |
| 585 | #117 | C24 | 1 | 1 | yes | characteristic |
| 586 | #117 | C24 | 1 | 2 | yes | — |
| 587 | #117 | C24 | 1 | 2 | yes | — |
| 588 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 589 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 590 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 591 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 592 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 593 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 594 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 595 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 596 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 597 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 598 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 599 | C2×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 600 | C2×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 601 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 602 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 603 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 604 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 605 | C2×C42 | — | 2 | 1 | no | — |
| 606 | C2×C42 | — | 2 | 1 | no | — |
| 607 | C2×C42 | C24 | 1 | 2 | yes | — |
| 608 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 609 | #108 | — | 2 | 4 | no | — |
| 610 | #108 | — | 2 | 2 | no | — |
| 611 | #108 | — | 2 | 2 | no | — |
| 612 | #107 | — | 2 | 2 | no | — |
| 613 | #107 | — | 2 | 2 | no | — |
| 614 | #107 | — | 2 | 2 | no | — |
| 615 | #107 | — | 2 | 2 | no | — |
| 616 | #107 | — | 2 | 2 | no | — |
| 617 | #107 | — | 2 | 2 | no | — |
| 618 | #107 | — | 2 | 2 | no | — |
| 619 | #107 | — | 2 | 2 | no | — |
| 620 | #107 | — | 2 | 2 | no | — |
| 621 | #107 | — | 2 | 2 | no | — |
| 622 | #107 | — | 2 | 2 | no | — |
| 623 | #107 | — | 2 | 2 | no | — |
| 624 | #107 | — | 2 | 1 | no | — |
| 625 | #107 | — | 2 | 1 | no | — |
| 626 | #107 | C2×D4 | 1 | 2 | yes | — |
| 627 | #107 | C2×D4 | 1 | 2 | yes | — |
| 628 | #107 | C2×D4 | 1 | 2 | yes | — |
| 629 | #107 | C2×D4 | 1 | 2 | yes | — |
| 630 | #106 | — | 2 | 1 | no | — |
| 631 | #106 | — | 2 | 1 | no | — |
| 632 | #106 | — | 2 | 2 | no | — |
| 633 | #106 | — | 2 | 2 | no | — |
| 634 | #106 | — | 2 | 2 | no | — |
| 635 | #106 | — | 2 | 2 | no | — |
| 636 | #106 | — | 2 | 2 | no | — |
| 637 | #106 | — | 2 | 2 | no | — |
| 638 | #106 | — | 2 | 2 | no | — |
| 639 | #106 | — | 2 | 2 | no | — |
| 640 | #106 | — | 2 | 1 | no | — |
| 641 | #106 | — | 2 | 1 | no | — |
| 642 | #106 | C2×D4 | 1 | 2 | yes | — |
| 643 | #106 | C2×D4 | 1 | 2 | yes | — |
| 644 | #106 | C2×D4 | 1 | 2 | yes | — |
| 645 | #106 | C2×D4 | 1 | 2 | yes | — |
| 646 | C4⋊C8 | — | 2 | 2 | no | — |
| 647 | C4⋊C8 | — | 2 | 2 | no | — |
| 648 | C4⋊C8 | — | 2 | 2 | no | — |
| 649 | C4⋊C8 | — | 2 | 2 | no | — |
| 650 | C4⋊C8 | — | 2 | 1 | no | — |
| 651 | C4⋊C8 | — | 2 | 1 | no | — |
| 652 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 653 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 654 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 655 | #104 | — | 2 | 4 | no | — |
| 656 | #104 | — | 2 | 4 | no | — |
| 657 | #104 | — | 2 | 4 | no | — |
| 658 | #103 | — | 2 | 1 | no | — |
| 659 | #103 | — | 2 | 2 | no | — |
| 660 | #103 | — | 2 | 1 | no | — |
| 661 | #103 | — | 2 | 2 | no | — |
| 662 | #103 | — | 2 | 2 | no | — |
| 663 | #103 | — | 2 | 2 | no | — |
| 664 | #103 | — | 2 | 1 | no | — |
| 665 | #103 | — | 2 | 1 | no | — |
| 666 | #103 | — | 2 | 2 | no | — |
| 667 | #103 | — | 2 | 2 | no | — |
| 668 | #103 | — | 2 | 1 | no | — |
| 669 | #103 | — | 2 | 1 | no | — |
| 670 | #103 | — | 2 | 2 | no | — |
| 671 | #103 | — | 2 | 2 | no | — |
| 672 | #103 | C2×D4 | 1 | 2 | yes | — |
| 673 | #103 | C2×D4 | 1 | 2 | yes | — |
| 674 | #102 | — | 2 | 1 | no | — |
| 675 | #102 | — | 2 | 1 | no | — |
| 676 | #102 | — | 2 | 2 | no | — |
| 677 | #102 | — | 2 | 2 | no | — |
| 678 | #102 | — | 2 | 2 | no | — |
| 679 | #102 | — | 2 | 2 | no | — |
| 680 | #102 | — | 2 | 1 | no | — |
| 681 | #102 | — | 2 | 1 | no | — |
| 682 | #102 | — | 2 | 2 | no | — |
| 683 | #102 | — | 2 | 2 | no | — |
| 684 | #102 | — | 2 | 1 | no | — |
| 685 | #102 | — | 2 | 1 | no | — |
| 686 | #102 | — | 2 | 2 | no | — |
| 687 | #102 | — | 2 | 2 | no | — |
| 688 | #102 | C2×D4 | 1 | 2 | yes | — |
| 689 | #102 | C2×D4 | 1 | 2 | yes | — |
| 690 | #101 | — | 2 | 2 | no | — |
| 691 | #101 | — | 2 | 2 | no | — |
| 692 | #100 | — | 2 | 2 | no | — |
| 693 | #100 | — | 2 | 2 | no | — |
| 694 | C22⋊C8 | — | 2 | 2 | no | — |
| 695 | C22⋊C8 | — | 2 | 2 | no | — |
| 696 | #97 | — | 2 | 1 | no | — |
| 697 | #97 | — | 2 | 1 | no | — |
| 698 | #97 | — | 2 | 2 | no | — |
| 699 | #97 | — | 2 | 2 | no | — |
| 700 | #97 | — | 2 | 4 | no | — |
| 701 | #97 | — | 2 | 1 | no | — |
| 702 | #97 | — | 2 | 1 | no | — |
| 703 | #97 | — | 2 | 1 | no | — |
| 704 | C4×C8 | — | 2 | 1 | no | — |
| 705 | C4×C8 | — | 2 | 1 | no | — |
| 706 | C4×C8 | — | 2 | 2 | no | — |
| 707 | C4×C8 | — | 2 | 2 | no | — |
| 708 | C4×C8 | — | 2 | 1 | no | — |
| 709 | C4×C8 | — | 2 | 1 | no | — |
| 710 | C4×C8 | — | 2 | 1 | no | — |
| 711 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 712 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 713 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 714 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 715 | #95 | — | 2 | 1 | no | — |
| 716 | #95 | — | 4 | 2 | no | — |
| 717 | #95 | — | 4 | 2 | no | — |
| 718 | C24 | — | 2 | 1 | no | — |
| 719 | #41 | — | 2 | 1 | no | — |
| 720 | #41 | — | 2 | 1 | no | — |
| 721 | #41 | — | 2 | 2 | no | — |
| 722 | #41 | — | 2 | 2 | no | — |
| 723 | #41 | — | 2 | 2 | no | — |
| 724 | #41 | — | 2 | 2 | no | — |
| 725 | #41 | — | 16 | 2 | no | — |
| 726 | #41 | C2×#41 | 1 | 2 | yes | — |
| 727 | #41 | 2−1+4 | 1 | 2 | yes | — |
| 728 | C2×Q8 | — | 2 | 1 | no | — |
| 729 | C2×Q8 | — | 2 | 1 | no | — |
| 730 | C2×Q8 | — | 2 | 1 | no | — |
| 731 | C2×Q8 | — | 2 | 1 | no | — |
| 732 | C2×Q8 | — | 2 | 1 | no | — |
| 733 | C2×Q8 | — | 2 | 1 | no | — |
| 734 | C2×Q8 | — | 2 | 1 | no | — |
| 735 | C2×Q8 | — | 2 | 1 | no | — |
| 736 | C2×Q8 | — | 2 | 1 | no | — |
| 737 | C2×Q8 | — | 2 | 1 | no | — |
| 738 | C2×Q8 | — | 4 | 2 | no | — |
| 739 | C2×Q8 | — | 4 | 2 | no | — |
| 740 | C2×Q8 | — | 4 | 1 | no | — |
| 741 | C2×Q8 | — | 4 | 1 | no | — |
| 742 | C2×Q8 | — | 4 | 1 | no | — |
| 743 | C2×Q8 | — | 4 | 1 | no | — |
| 744 | C2×Q8 | — | 16 | 1 | no | — |
| 745 | C2×Q8 | — | 16 | 1 | no | — |
| 746 | C2×Q8 | — | 16 | 2 | no | — |
| 747 | C2×Q8 | — | 16 | 2 | no | — |
| 748 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 749 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 750 | C2×D4 | — | 2 | 1 | no | — |
| 751 | C2×D4 | — | 2 | 2 | no | — |
| 752 | C2×D4 | — | 2 | 1 | no | — |
| 753 | C2×D4 | — | 2 | 1 | no | — |
| 754 | C2×D4 | — | 2 | 1 | no | — |
| 755 | C2×D4 | — | 2 | 1 | no | — |
| 756 | C2×D4 | — | 2 | 1 | no | — |
| 757 | C2×D4 | — | 2 | 1 | no | — |
| 758 | C2×D4 | — | 2 | 1 | no | — |
| 759 | C2×D4 | — | 2 | 1 | no | — |
| 760 | C2×D4 | — | 4 | 2 | no | — |
| 761 | C2×D4 | — | 4 | 2 | no | — |
| 762 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 763 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 764 | C22×C4 | — | 2 | 1 | no | — |
| 765 | C22×C4 | — | 2 | 1 | no | — |
| 766 | C22×C4 | — | 2 | 1 | no | — |
| 767 | C22×C4 | — | 2 | 2 | no | — |
| 768 | C22×C4 | — | 2 | 2 | no | — |
| 769 | C22×C4 | — | 2 | 1 | no | — |
| 770 | C22×C4 | — | 2 | 1 | no | — |
| 771 | C22×C4 | — | 2 | 2 | no | — |
| 772 | C22×C4 | — | 2 | 2 | no | — |
| 773 | C22×C4 | — | 2 | 1 | no | — |
| 774 | C22×C4 | — | 4 | 2 | no | — |
| 775 | C22×C4 | — | 4 | 2 | no | — |
| 776 | C22×C4 | — | 4 | 2 | no | — |
| 777 | C22×C4 | — | 4 | 2 | no | — |
| 778 | C22×C4 | — | 4 | 1 | no | — |
| 779 | C22×C4 | — | 4 | 1 | no | — |
| 780 | C22×C4 | — | 8 | 2 | no | — |
| 781 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 782 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 783 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 784 | Q16 | — | 2 | 4 | no | — |
| 785 | Q16 | — | 4 | 2 | no | — |
| 786 | SD16 | — | 2 | 4 | no | — |
| 787 | SD16 | — | 2 | 4 | no | — |
| 788 | SD16 | — | 4 | 2 | no | — |
| 789 | SD16 | — | 4 | 2 | no | — |
| 790 | SD16 | — | 4 | 2 | no | — |
| 791 | SD16 | — | 4 | 2 | no | — |
| 792 | D8 | — | 2 | 4 | no | — |
| 793 | D8 | — | 4 | 2 | no | — |
| 794 | M16 | — | 2 | 4 | no | — |
| 795 | M16 | — | 2 | 1 | no | — |
| 796 | M16 | — | 2 | 1 | no | — |
| 797 | M16 | — | 2 | 4 | no | — |
| 798 | M16 | — | 2 | 1 | no | — |
| 799 | M16 | — | 2 | 1 | no | — |
| 800 | M16 | — | 2 | 2 | no | — |
| 801 | M16 | — | 2 | 1 | no | — |
| 802 | M16 | — | 2 | 1 | no | — |
| 803 | M16 | — | 2 | 1 | no | — |
| 804 | M16 | — | 2 | 1 | no | — |
| 805 | M16 | — | 2 | 2 | no | — |
| 806 | M16 | — | 2 | 1 | no | — |
| 807 | M16 | — | 2 | 1 | no | — |
| 808 | M16 | — | 4 | 4 | no | — |
| 809 | M16 | C2×#41 | 1 | 2 | yes | — |
| 810 | M16 | 2−1+4 | 1 | 2 | yes | — |
| 811 | C2×C8 | — | 2 | 4 | no | — |
| 812 | C2×C8 | — | 2 | 1 | no | — |
| 813 | C2×C8 | — | 2 | 1 | no | — |
| 814 | C2×C8 | — | 2 | 2 | no | — |
| 815 | C2×C8 | — | 2 | 1 | no | — |
| 816 | C2×C8 | — | 2 | 1 | no | — |
| 817 | C2×C8 | — | 2 | 2 | no | — |
| 818 | C2×C8 | — | 2 | 4 | no | — |
| 819 | C2×C8 | — | 2 | 1 | no | — |
| 820 | C2×C8 | — | 2 | 1 | no | — |
| 821 | C2×C8 | — | 2 | 1 | no | — |
| 822 | C2×C8 | — | 2 | 1 | no | — |
| 823 | C2×C8 | — | 2 | 2 | no | — |
| 824 | C2×C8 | — | 4 | 4 | no | — |
| 825 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 826 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 827 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 828 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 829 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 830 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 831 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 832 | C2×C8 | 2−1+4 | 1 | 2 | yes | — |
| 833 | C4⋊C4 | — | 2 | 1 | no | — |
| 834 | C4⋊C4 | — | 2 | 1 | no | — |
| 835 | C4⋊C4 | — | 2 | 1 | no | — |
| 836 | C4⋊C4 | — | 2 | 1 | no | — |
| 837 | C4⋊C4 | — | 2 | 1 | no | — |
| 838 | C4⋊C4 | — | 2 | 2 | no | — |
| 839 | C4⋊C4 | — | 2 | 1 | no | — |
| 840 | C4⋊C4 | — | 2 | 2 | no | — |
| 841 | C4⋊C4 | — | 2 | 1 | no | — |
| 842 | C4⋊C4 | — | 2 | 1 | no | — |
| 843 | C4⋊C4 | — | 2 | 2 | no | — |
| 844 | C4⋊C4 | — | 2 | 2 | no | — |
| 845 | C4⋊C4 | — | 2 | 2 | no | — |
| 846 | C4⋊C4 | — | 2 | 2 | no | — |
| 847 | C4⋊C4 | — | 2 | 1 | no | — |
| 848 | C4⋊C4 | — | 2 | 1 | no | — |
| 849 | C4⋊C4 | — | 2 | 1 | no | — |
| 850 | C4⋊C4 | — | 2 | 1 | no | — |
| 851 | C4⋊C4 | — | 2 | 2 | no | — |
| 852 | C4⋊C4 | — | 2 | 2 | no | — |
| 853 | C4⋊C4 | — | 4 | 2 | no | — |
| 854 | C4⋊C4 | — | 4 | 2 | no | — |
| 855 | C4⋊C4 | — | 4 | 2 | no | — |
| 856 | C4⋊C4 | — | 4 | 2 | no | — |
| 857 | C4⋊C4 | — | 4 | 2 | no | — |
| 858 | C4⋊C4 | — | 4 | 2 | no | — |
| 859 | C4⋊C4 | — | 4 | 2 | no | — |
| 860 | C4⋊C4 | — | 4 | 2 | no | — |
| 861 | C4⋊C4 | — | 4 | 2 | no | — |
| 862 | C4⋊C4 | — | 4 | 2 | no | — |
| 863 | C4⋊C4 | — | 4 | 2 | no | — |
| 864 | C4⋊C4 | — | 4 | 2 | no | — |
| 865 | C4⋊C4 | — | 4 | 2 | no | — |
| 866 | C4⋊C4 | — | 4 | 1 | no | — |
| 867 | C4⋊C4 | — | 4 | 1 | no | — |
| 868 | C4⋊C4 | — | 4 | 1 | no | — |
| 869 | C4⋊C4 | — | 4 | 1 | no | — |
| 870 | C4⋊C4 | — | 4 | 1 | no | — |
| 871 | C4⋊C4 | — | 4 | 1 | no | — |
| 872 | C4⋊C4 | — | 16 | 2 | no | — |
| 873 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 874 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 875 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 876 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 877 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 878 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 879 | C22⋊C4 | — | 2 | 1 | no | — |
| 880 | C22⋊C4 | — | 2 | 2 | no | — |
| 881 | C22⋊C4 | — | 2 | 2 | no | — |
| 882 | C22⋊C4 | — | 2 | 1 | no | — |
| 883 | C22⋊C4 | — | 2 | 1 | no | — |
| 884 | C22⋊C4 | — | 2 | 2 | no | — |
| 885 | C22⋊C4 | — | 2 | 2 | no | — |
| 886 | C22⋊C4 | — | 4 | 2 | no | — |
| 887 | C22⋊C4 | — | 4 | 2 | no | — |
| 888 | C22⋊C4 | — | 4 | 2 | no | — |
| 889 | C22⋊C4 | — | 4 | 2 | no | — |
| 890 | C22⋊C4 | — | 4 | 2 | no | — |
| 891 | C22⋊C4 | — | 4 | 2 | no | — |
| 892 | C22⋊C4 | — | 4 | 2 | no | — |
| 893 | C22⋊C4 | — | 4 | 2 | no | — |
| 894 | C22⋊C4 | — | 4 | 1 | no | — |
| 895 | C22⋊C4 | — | 4 | 1 | no | — |
| 896 | C22⋊C4 | — | 16 | 2 | no | — |
| 897 | C42 | — | 2 | 1 | no | — |
| 898 | C42 | — | 2 | 1 | no | — |
| 899 | C42 | — | 2 | 1 | no | — |
| 900 | C42 | — | 2 | 2 | no | — |
| 901 | C42 | — | 2 | 2 | no | — |
| 902 | C42 | — | 2 | 2 | no | — |
| 903 | C42 | — | 2 | 2 | no | — |
| 904 | C42 | — | 4 | 2 | no | — |
| 905 | C42 | — | 4 | 2 | no | — |
| 906 | C42 | — | 4 | 2 | no | — |
| 907 | C42 | — | 4 | 2 | no | — |
| 908 | C42 | — | 4 | 1 | no | — |
| 909 | C42 | — | 4 | 1 | no | — |
| 910 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 911 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 912 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 913 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 914 | C23 | — | 2 | 1 | no | — |
| 915 | C23 | — | 2 | 2 | no | — |
| 916 | C23 | — | 4 | 1 | no | — |
| 917 | C23 | — | 4 | 1 | no | — |
| 918 | C23 | — | 4 | 1 | no | — |
| 919 | C23 | — | 8 | 1 | no | — |
| 920 | C23 | — | 8 | 1 | no | — |
| 921 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 922 | Q8 | — | 2 | 1 | no | — |
| 923 | Q8 | — | 2 | 2 | no | — |
| 924 | Q8 | — | 2 | 2 | no | — |
| 925 | Q8 | — | 4 | 2 | no | — |
| 926 | Q8 | — | 4 | 2 | no | — |
| 927 | Q8 | — | 4 | 1 | no | — |
| 928 | Q8 | — | 4 | 1 | no | — |
| 929 | Q8 | — | 4 | 1 | no | — |
| 930 | Q8 | — | 4 | 1 | no | — |
| 931 | Q8 | — | 8 | 1 | no | — |
| 932 | Q8 | — | 8 | 1 | no | — |
| 933 | Q8 | — | 8 | 2 | no | — |
| 934 | Q8 | — | 8 | 2 | no | — |
| 935 | Q8 | — | 16 | 1 | no | — |
| 936 | Q8 | — | 16 | 1 | no | — |
| 937 | Q8 | — | 16 | 2 | no | — |
| 938 | Q8 | — | 16 | 2 | no | — |
| 939 | Q8 | #547 | 1 | 2 | yes | — |
| 940 | D4 | — | 2 | 2 | no | — |
| 941 | D4 | — | 2 | 2 | no | — |
| 942 | D4 | — | 2 | 2 | no | — |
| 943 | D4 | — | 2 | 1 | no | — |
| 944 | D4 | — | 2 | 2 | no | — |
| 945 | D4 | — | 4 | 2 | no | — |
| 946 | D4 | — | 4 | 2 | no | — |
| 947 | D4 | — | 4 | 1 | no | — |
| 948 | D4 | — | 4 | 1 | no | — |
| 949 | D4 | — | 4 | 1 | no | — |
| 950 | D4 | — | 4 | 1 | no | — |
| 951 | D4 | — | 4 | 2 | no | — |
| 952 | D4 | — | 8 | 1 | no | — |
| 953 | D4 | — | 16 | 2 | no | — |
| 954 | D4 | — | 16 | 2 | no | — |
| 955 | D4 | #547 | 1 | 2 | yes | — |
| 956 | C2×C4 | — | 2 | 1 | no | — |
| 957 | C2×C4 | — | 2 | 2 | no | — |
| 958 | C2×C4 | — | 2 | 2 | no | — |
| 959 | C2×C4 | — | 2 | 2 | no | — |
| 960 | C2×C4 | — | 2 | 1 | no | — |
| 961 | C2×C4 | — | 2 | 1 | no | — |
| 962 | C2×C4 | — | 2 | 2 | no | — |
| 963 | C2×C4 | — | 2 | 2 | no | — |
| 964 | C2×C4 | — | 2 | 2 | no | — |
| 965 | C2×C4 | — | 2 | 2 | no | — |
| 966 | C2×C4 | — | 2 | 2 | no | — |
| 967 | C2×C4 | — | 4 | 1 | no | — |
| 968 | C2×C4 | — | 4 | 2 | no | — |
| 969 | C2×C4 | — | 4 | 2 | no | — |
| 970 | C2×C4 | — | 4 | 2 | no | — |
| 971 | C2×C4 | — | 4 | 2 | no | — |
| 972 | C2×C4 | — | 4 | 2 | no | — |
| 973 | C2×C4 | — | 4 | 2 | no | — |
| 974 | C2×C4 | — | 4 | 1 | no | — |
| 975 | C2×C4 | — | 4 | 1 | no | — |
| 976 | C2×C4 | — | 4 | 1 | no | — |
| 977 | C2×C4 | — | 4 | 2 | no | — |
| 978 | C2×C4 | — | 4 | 2 | no | — |
| 979 | C2×C4 | — | 4 | 2 | no | — |
| 980 | C2×C4 | — | 4 | 1 | no | — |
| 981 | C2×C4 | — | 4 | 1 | no | — |
| 982 | C2×C4 | — | 8 | 2 | no | — |
| 983 | C2×C4 | — | 8 | 2 | no | — |
| 984 | C2×C4 | — | 8 | 1 | no | — |
| 985 | C2×C4 | — | 8 | 2 | no | — |
| 986 | C2×C4 | — | 8 | 1 | no | — |
| 987 | C2×C4 | — | 16 | 1 | no | — |
| 988 | C2×C4 | — | 16 | 2 | no | — |
| 989 | C2×C4 | — | 16 | 2 | no | — |
| 990 | C2×C4 | — | 16 | 2 | no | — |
| 991 | C2×C4 | — | 16 | 2 | no | — |
| 992 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 993 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 994 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 995 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 996 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 997 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 998 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 999 | C2×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 1000 | C2×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 1001 | C2×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 1002 | C8 | — | 2 | 2 | no | — |
| 1003 | C8 | — | 2 | 2 | no | — |
| 1004 | C8 | — | 2 | 2 | no | — |
| 1005 | C8 | — | 2 | 1 | no | — |
| 1006 | C8 | — | 2 | 2 | no | — |
| 1007 | C8 | — | 2 | 1 | no | — |
| 1008 | C8 | — | 4 | 1 | no | — |
| 1009 | C8 | — | 4 | 1 | no | — |
| 1010 | C8 | — | 4 | 2 | no | — |
| 1011 | C8 | — | 4 | 1 | no | — |
| 1012 | C8 | — | 4 | 1 | no | — |
| 1013 | C8 | #548 | 1 | 2 | yes | — |
| 1014 | C8 | #548 | 1 | 2 | yes | — |
| 1015 | C22 | — | 2 | 1 | no | — |
| 1016 | C22 | — | 2 | 1 | no | — |
| 1017 | C22 | — | 2 | 2 | no | — |
| 1018 | C22 | — | 4 | 1 | no | — |
| 1019 | C22 | — | 4 | 1 | no | — |
| 1020 | C22 | — | 4 | 2 | no | — |
| 1021 | C22 | — | 4 | 2 | no | — |
| 1022 | C22 | — | 4 | 2 | no | — |
| 1023 | C22 | — | 8 | 2 | no | — |
| 1024 | C22 | — | 8 | 1 | no | — |
| 1025 | C22 | — | 8 | 1 | no | — |
| 1026 | C22 | — | 8 | 1 | no | — |
| 1027 | C22 | — | 16 | 1 | no | — |
| 1028 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 1029 | C22 | #3511 | 1 | 1 | yes | characteristic |
| 1030 | C22 | #3552 | 1 | 1 | yes | characteristic |
| 1031 | C4 | — | 2 | 1 | no | — |
| 1032 | C4 | — | 2 | 1 | no | — |
| 1033 | C4 | — | 2 | 1 | no | — |
| 1034 | C4 | — | 2 | 2 | no | — |
| 1035 | C4 | — | 4 | 1 | no | — |
| 1036 | C4 | — | 4 | 2 | no | — |
| 1037 | C4 | — | 4 | 2 | no | — |
| 1038 | C4 | — | 4 | 1 | no | — |
| 1039 | C4 | — | 4 | 2 | no | — |
| 1040 | C4 | — | 4 | 2 | no | — |
| 1041 | C4 | — | 4 | 2 | no | — |
| 1042 | C4 | — | 8 | 2 | no | — |
| 1043 | C4 | — | 8 | 1 | no | — |
| 1044 | C4 | — | 8 | 1 | no | — |
| 1045 | C4 | — | 8 | 2 | no | — |
| 1046 | C4 | — | 8 | 2 | no | — |
| 1047 | C4 | — | 8 | 1 | no | — |
| 1048 | C4 | #3289 | 1 | 2 | yes | — |
| 1049 | C4 | C2×#547 | 1 | 1 | yes | characteristic |
| 1050 | C4 | C2×#548 | 1 | 1 | yes | characteristic |
| 1051 | C4 | #3486 | 1 | 1 | yes | characteristic |
| 1052 | C4 | #3499 | 1 | 1 | yes | characteristic |
| 1053 | C2 | — | 2 | 1 | no | — |
| 1054 | C2 | — | 2 | 1 | no | — |
| 1055 | C2 | — | 4 | 2 | no | — |
| 1056 | C2 | — | 8 | 2 | no | — |
| 1057 | C2 | — | 16 | 1 | no | — |
| 1058 | C2 | #59125 | 1 | 1 | yes | characteristic |
| 1059 | C2 | C2×#3289 | 1 | 1 | yes | characteristic |
| 1060 | C2 | #61106 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | #61347 | 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. #61348 | C2 | semidirect |
| 3. #61285 | C2 | semidirect |
| 4. #60667 | C2 | semidirect |
| 5. #30840 | C2 | semidirect |
| 6. #30837 | C2 | semidirect |
| 7. #28731 | C2 | semidirect |
| 8. #28539 | C2 | semidirect |
| 9. #27812 | C2 | semidirect |
| 10. #26193 | C2 | semidirect |
| 11. #26190 | C2 | semidirect |
| 12. #26084 | C2 | semidirect |
| 13. #25695 | C2 | semidirect |
| 14. #25693 | C2 | semidirect |
| 15. #25491 | C2 | semidirect |
| 16. #25490 | C2 | semidirect |
| 17. #24801 | C2 | semidirect |
| 18. #24323 | C2 | semidirect |
| 19. #24321 | C2 | semidirect |
| 20. #23171 | C2 | semidirect |
| 21. #22693 | C2 | semidirect |
| 22. C4×#471 | C2 | semidirect |
| 23. #21518 | C2 | semidirect |
| 449. #131 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61348 | 2 |
| #61347 | 2 |
| #61285 | 2 |
| #60667 | 2 |
| #30840 | 2 |
| #30837 | 2 |
| #28731 | 2 |
| #28539 | 2 |
| #27812 | 2 |
| #26193 | 2 |
| #26190 | 2 |
| #26084 | 2 |
| #25695 | 2 |
| #25693 | 2 |
| #25491 | 2 |
| #25490 | 2 |
| #24801 | 2 |
| #24323 | 2 |
| #24321 | 2 |
| #23171 | 2 |
| #22693 | 2 |
| C4×#471 | 2 |
| #21518 | 2 |