Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1901 conjugacy classes of subgroups.
The subgroup lattice has 792 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61157 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×D4×Q16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #60271 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #29820 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #29789 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #28762 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #28591 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #28219 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #25314 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #25142 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #24772 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #24522 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #24282 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #23717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×#2047 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #22717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | D4×#101 | C2 | 1 | 2 | yes | maximal, complemented |
| 18 | C23×Q16 | C22 | 1 | 2 | yes | — |
| 19 | #3475 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×D4×Q8 | C22 | 1 | 2 | yes | — |
| 21 | #3329 | — | 2 | 2 | no | — |
| 22 | #3328 | — | 2 | 2 | no | — |
| 23 | #3320 | — | 2 | 4 | no | — |
| 24 | #3312 | — | 2 | 4 | no | — |
| 25 | #3299 | — | 2 | 2 | no | — |
| 26 | #3298 | — | 2 | 2 | no | — |
| 27 | D4×Q16 | — | 2 | 1 | no | — |
| 28 | D4×Q16 | — | 2 | 1 | no | — |
| 29 | D4×Q16 | — | 2 | 2 | no | — |
| 30 | D4×Q16 | — | 2 | 1 | no | — |
| 31 | D4×Q16 | — | 2 | 2 | no | — |
| 32 | D4×Q16 | — | 2 | 1 | no | — |
| 33 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 34 | #3139 | C22 | 1 | 2 | yes | — |
| 35 | #3095 | C22 | 1 | 4 | yes | — |
| 36 | #3078 | C22 | 1 | 2 | yes | — |
| 37 | C2×#473 | C22 | 1 | 4 | yes | — |
| 38 | #3056 | C22 | 1 | 4 | yes | — |
| 39 | C2×#467 | C22 | 1 | 2 | yes | — |
| 40 | #3039 | C22 | 1 | 2 | yes | — |
| 41 | C2×#462 | C22 | 1 | 2 | yes | — |
| 42 | #3004 | C22 | 1 | 4 | yes | — |
| 43 | C2×#451 | C22 | 1 | 4 | yes | — |
| 44 | #2994 | — | 2 | 2 | no | — |
| 45 | #2994 | — | 2 | 1 | no | — |
| 46 | #2993 | — | 2 | 1 | no | — |
| 47 | #2992 | — | 2 | 2 | no | — |
| 48 | #2990 | — | 2 | 1 | no | — |
| 49 | #2988 | — | 2 | 1 | no | — |
| 50 | #2962 | C22 | 1 | 1 | yes | characteristic |
| 51 | #2960 | C22 | 1 | 1 | yes | characteristic |
| 52 | C4×#137 | C22 | 1 | 2 | yes | — |
| 53 | C2×C4×Q16 | C22 | 1 | 1 | yes | characteristic |
| 54 | D4×M16 | C22 | 1 | 1 | yes | characteristic |
| 55 | D4×M16 | C22 | 1 | 2 | yes | — |
| 56 | #2933 | C22 | 1 | 2 | yes | — |
| 57 | #2929 | C22 | 1 | 2 | yes | — |
| 58 | C2×C8×D4 | C22 | 1 | 1 | yes | characteristic |
| 59 | #2924 | C22 | 1 | 2 | yes | — |
| 60 | #2922 | C22 | 1 | 1 | yes | characteristic |
| 61 | #2906 | C22 | 1 | 1 | yes | characteristic |
| 62 | C2×#424 | C22 | 1 | 2 | yes | — |
| 63 | C2×#419 | C22 | 1 | 4 | yes | — |
| 64 | C22×#101 | C22 | 1 | 4 | yes | — |
| 65 | #2089 | C22 | 1 | 2 | yes | — |
| 66 | #2089 | C22 | 1 | 1 | yes | characteristic |
| 67 | #2078 | C22 | 1 | 1 | yes | characteristic |
| 68 | #2064 | C22 | 1 | 4 | yes | — |
| 69 | #2064 | C22 | 1 | 4 | yes | — |
| 70 | #2064 | C22 | 1 | 2 | yes | — |
| 71 | #2052 | C22 | 1 | 2 | yes | — |
| 72 | #2047 | C22 | 1 | 4 | yes | — |
| 73 | #2047 | C22 | 1 | 2 | yes | — |
| 74 | #2047 | C22 | 1 | 2 | yes | — |
| 75 | #2047 | C22 | 1 | 2 | yes | — |
| 76 | #2047 | C22 | 1 | 2 | yes | — |
| 77 | #2047 | C22 | 1 | 2 | yes | — |
| 78 | #2047 | C22 | 1 | 1 | yes | characteristic |
| 79 | #2047 | C22 | 1 | 4 | yes | — |
| 80 | #2020 | C22 | 1 | 2 | yes | — |
| 81 | #2020 | C22 | 1 | 2 | yes | — |
| 82 | #2020 | C22 | 1 | 1 | yes | characteristic |
| 83 | #1979 | C22 | 1 | 4 | yes | — |
| 84 | #1979 | C22 | 1 | 4 | yes | — |
| 85 | #1966 | C22 | 1 | 2 | yes | — |
| 86 | #1966 | C22 | 1 | 2 | yes | — |
| 87 | #1950 | C22 | 1 | 2 | yes | — |
| 88 | #1930 | C22 | 1 | 4 | yes | — |
| 89 | #1930 | C22 | 1 | 4 | yes | — |
| 90 | #1908 | C22 | 1 | 4 | yes | — |
| 91 | #1901 | C22 | 1 | 4 | yes | — |
| 92 | #1901 | C22 | 1 | 4 | yes | — |
| 93 | #1855 | C22 | 1 | 4 | yes | — |
| 94 | #1837 | C22 | 1 | 1 | yes | characteristic |
| 95 | #1810 | C22 | 1 | 2 | yes | — |
| 96 | #1801 | C22 | 1 | 2 | yes | — |
| 97 | #1784 | C22 | 1 | 4 | yes | — |
| 98 | C4×#108 | C22 | 1 | 1 | yes | characteristic |
| 99 | C4×#101 | C22 | 1 | 2 | yes | — |
| 100 | C2×#341 | C22 | 1 | 2 | yes | — |
| 101 | C23×Q8 | C23 | 1 | 4 | yes | — |
| 102 | C2×#137 | C23 | 1 | 2 | yes | — |
| 103 | C2×#137 | C23 | 1 | 4 | yes | — |
| 104 | C22×Q16 | — | 2 | 2 | no | — |
| 105 | C22×Q16 | — | 2 | 2 | no | — |
| 106 | C22×Q16 | — | 2 | 2 | no | — |
| 107 | C22×Q16 | — | 2 | 2 | no | — |
| 108 | C22×Q16 | — | 4 | 8 | no | — |
| 109 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 110 | C22×Q16 | C23 | 1 | 4 | yes | — |
| 111 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 112 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 113 | C2×#131 | C23 | 1 | 2 | yes | — |
| 114 | C22×M16 | C23 | 1 | 4 | yes | — |
| 115 | C22×M16 | C23 | 1 | 2 | yes | — |
| 116 | C23×C8 | C23 | 1 | 2 | yes | — |
| 117 | #556 | D4 | 1 | 1 | yes | characteristic |
| 118 | #555 | D4 | 1 | 1 | yes | characteristic |
| 119 | #554 | D4 | 1 | 1 | yes | characteristic |
| 120 | #553 | D4 | 1 | 2 | yes | — |
| 121 | #552 | — | 2 | 1 | no | — |
| 122 | #552 | D4 | 1 | 2 | yes | — |
| 123 | #551 | — | 2 | 2 | no | — |
| 124 | D4×Q8 | — | 2 | 2 | no | — |
| 125 | D4×Q8 | — | 2 | 2 | no | — |
| 126 | D4×Q8 | — | 2 | 4 | no | — |
| 127 | D4×Q8 | — | 2 | 2 | no | — |
| 128 | D4×Q8 | — | 2 | 2 | no | — |
| 129 | D4×Q8 | — | 2 | 4 | no | — |
| 130 | #547 | D4 | 1 | 1 | yes | characteristic |
| 131 | #546 | — | 2 | 1 | no | — |
| 132 | #533 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×C4⋊Q8 | — | 2 | 2 | no | — |
| 134 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 135 | #529 | — | 2 | 2 | no | — |
| 136 | #529 | — | 2 | 1 | no | — |
| 137 | #525 | C23 | 1 | 2 | yes | — |
| 138 | C2×C22⋊Q8 | — | 2 | 4 | no | — |
| 139 | C2×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 140 | C4×#41 | — | 2 | 1 | no | — |
| 141 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 142 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 143 | C2×C4×D4 | — | 2 | 2 | no | — |
| 144 | C2×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 145 | C2×#117 | C23 | 1 | 2 | yes | — |
| 146 | #494 | — | 2 | 1 | no | — |
| 147 | #494 | — | 2 | 1 | no | — |
| 148 | #494 | — | 2 | 1 | no | — |
| 149 | #494 | — | 2 | 1 | no | — |
| 150 | #491 | — | 2 | 4 | no | — |
| 151 | #487 | — | 2 | 2 | no | — |
| 152 | #487 | — | 2 | 2 | no | — |
| 153 | #485 | — | 2 | 4 | no | — |
| 154 | #485 | — | 2 | 4 | no | — |
| 155 | #484 | — | 2 | 4 | no | — |
| 156 | #483 | — | 2 | 4 | no | — |
| 157 | #479 | — | 2 | 4 | no | — |
| 158 | #477 | — | 2 | 2 | no | — |
| 159 | #475 | — | 2 | 2 | no | — |
| 160 | #473 | — | 4 | 8 | no | — |
| 161 | #470 | — | 2 | 4 | no | — |
| 162 | #468 | — | 2 | 4 | no | — |
| 163 | #467 | — | 2 | 2 | no | — |
| 164 | #467 | — | 2 | 2 | no | — |
| 165 | #467 | — | 2 | 2 | no | — |
| 166 | #467 | — | 2 | 2 | no | — |
| 167 | #467 | — | 2 | 4 | no | — |
| 168 | #465 | — | 2 | 4 | no | — |
| 169 | #462 | — | 2 | 2 | no | — |
| 170 | #462 | — | 2 | 2 | no | — |
| 171 | #462 | — | 2 | 2 | no | — |
| 172 | #462 | — | 2 | 2 | no | — |
| 173 | #462 | — | 2 | 4 | no | — |
| 174 | #461 | — | 2 | 2 | no | — |
| 175 | #461 | — | 2 | 2 | no | — |
| 176 | #451 | — | 2 | 4 | no | — |
| 177 | #451 | — | 2 | 4 | no | — |
| 178 | #451 | — | 2 | 4 | no | — |
| 179 | #451 | — | 2 | 4 | no | — |
| 180 | #451 | — | 2 | 4 | no | — |
| 181 | #451 | — | 2 | 4 | no | — |
| 182 | #448 | — | 2 | 4 | no | — |
| 183 | #448 | — | 2 | 4 | no | — |
| 184 | #446 | — | 2 | 1 | no | — |
| 185 | #446 | — | 2 | 2 | no | — |
| 186 | #446 | — | 2 | 1 | no | — |
| 187 | #446 | — | 2 | 1 | no | — |
| 188 | C8×Q8 | — | 2 | 1 | no | — |
| 189 | C8×Q8 | — | 2 | 1 | no | — |
| 190 | C8×Q8 | — | 2 | 1 | no | — |
| 191 | #441 | — | 2 | 2 | no | — |
| 192 | #440 | — | 2 | 2 | no | — |
| 193 | C4×Q16 | — | 2 | 2 | no | — |
| 194 | C4×Q16 | — | 2 | 1 | no | — |
| 195 | C4×Q16 | — | 2 | 1 | no | — |
| 196 | C4×Q16 | — | 2 | 1 | no | — |
| 197 | C4×Q16 | — | 2 | 1 | no | — |
| 198 | C4×SD16 | — | 2 | 2 | no | — |
| 199 | #436 | — | 2 | 2 | no | — |
| 200 | #436 | — | 2 | 1 | no | — |
| 201 | #436 | — | 2 | 2 | no | — |
| 202 | #435 | — | 2 | 2 | no | — |
| 203 | #435 | — | 2 | 2 | no | — |
| 204 | #435 | — | 2 | 2 | no | — |
| 205 | #435 | — | 2 | 4 | no | — |
| 206 | #435 | — | 2 | 2 | no | — |
| 207 | #435 | — | 2 | 2 | no | — |
| 208 | C8×D4 | — | 2 | 2 | no | — |
| 209 | C8×D4 | — | 2 | 2 | no | — |
| 210 | C8×D4 | — | 2 | 1 | no | — |
| 211 | C8×D4 | — | 2 | 2 | no | — |
| 212 | C8×D4 | — | 2 | 2 | no | — |
| 213 | C8×D4 | D4 | 1 | 1 | yes | characteristic |
| 214 | C8×D4 | D4 | 1 | 1 | yes | characteristic |
| 215 | C8×D4 | D4 | 1 | 2 | yes | — |
| 216 | C8×D4 | D4 | 1 | 1 | yes | characteristic |
| 217 | C8×D4 | D4 | 1 | 1 | yes | characteristic |
| 218 | C8×D4 | D4 | 1 | 2 | yes | — |
| 219 | #433 | — | 2 | 2 | no | — |
| 220 | #433 | — | 2 | 2 | no | — |
| 221 | #433 | — | 2 | 1 | no | — |
| 222 | #433 | — | 2 | 1 | no | — |
| 223 | #432 | — | 2 | 2 | no | — |
| 224 | #431 | — | 2 | 2 | no | — |
| 225 | #431 | — | 2 | 1 | no | — |
| 226 | #431 | — | 2 | 1 | no | — |
| 227 | C2×#108 | C23 | 1 | 2 | yes | — |
| 228 | C2×#108 | C23 | 1 | 4 | yes | — |
| 229 | #428 | C23 | 1 | 4 | yes | — |
| 230 | #428 | C23 | 1 | 2 | yes | — |
| 231 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 232 | #424 | — | 2 | 2 | no | — |
| 233 | #424 | — | 2 | 2 | no | — |
| 234 | #424 | — | 2 | 2 | no | — |
| 235 | #424 | C23 | 1 | 2 | yes | — |
| 236 | #424 | C23 | 1 | 2 | yes | — |
| 237 | #424 | C23 | 1 | 1 | yes | characteristic |
| 238 | #424 | C23 | 1 | 1 | yes | characteristic |
| 239 | #424 | C23 | 1 | 2 | yes | — |
| 240 | #423 | — | 2 | 1 | no | — |
| 241 | #423 | C23 | 1 | 2 | yes | — |
| 242 | #423 | C23 | 1 | 1 | yes | characteristic |
| 243 | C2×C4⋊C8 | — | 2 | 2 | no | — |
| 244 | C2×C4⋊C8 | — | 2 | 2 | no | — |
| 245 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 246 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 247 | #419 | — | 2 | 4 | no | — |
| 248 | #419 | — | 2 | 4 | no | — |
| 249 | #419 | C23 | 1 | 4 | yes | — |
| 250 | #419 | C23 | 1 | 4 | yes | — |
| 251 | #419 | C23 | 1 | 4 | yes | — |
| 252 | #419 | C23 | 1 | 2 | yes | — |
| 253 | #419 | C23 | 1 | 4 | yes | — |
| 254 | #417 | C23 | 1 | 2 | yes | — |
| 255 | C2×#103 | — | 2 | 4 | no | — |
| 256 | C2×#103 | — | 2 | 4 | no | — |
| 257 | C2×#103 | C23 | 1 | 2 | yes | — |
| 258 | C2×#103 | C23 | 1 | 4 | yes | — |
| 259 | C2×#101 | — | 4 | 8 | no | — |
| 260 | C2×#101 | C23 | 1 | 2 | yes | — |
| 261 | C2×#101 | C23 | 1 | 4 | yes | — |
| 262 | C2×#101 | C23 | 1 | 4 | yes | — |
| 263 | C2×#101 | C23 | 1 | 4 | yes | — |
| 264 | C2×#101 | C23 | 1 | 2 | yes | — |
| 265 | C2×#101 | C23 | 1 | 4 | yes | — |
| 266 | C2×#101 | C23 | 1 | 4 | yes | — |
| 267 | #408 | C23 | 1 | 1 | yes | characteristic |
| 268 | #408 | C23 | 1 | 1 | yes | characteristic |
| 269 | #407 | C23 | 1 | 4 | yes | — |
| 270 | #407 | C23 | 1 | 2 | yes | — |
| 271 | C2×C22⋊C8 | C23 | 1 | 2 | yes | — |
| 272 | #405 | C23 | 1 | 2 | yes | — |
| 273 | #405 | C23 | 1 | 2 | yes | — |
| 274 | C4×M16 | C23 | 1 | 2 | yes | — |
| 275 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 276 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 277 | #343 | C23 | 1 | 2 | yes | — |
| 278 | #343 | C23 | 1 | 4 | yes | — |
| 279 | #343 | C23 | 1 | 2 | yes | — |
| 280 | #341 | C23 | 1 | 1 | yes | characteristic |
| 281 | #341 | C23 | 1 | 2 | yes | — |
| 282 | #341 | C23 | 1 | 1 | yes | characteristic |
| 283 | #341 | C23 | 1 | 2 | yes | — |
| 284 | #341 | C23 | 1 | 4 | yes | — |
| 285 | C2×#41 | — | 2 | 1 | no | — |
| 286 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 287 | C22×Q8 | — | 2 | 4 | no | — |
| 288 | C22×Q8 | — | 2 | 8 | no | — |
| 289 | C22×Q8 | — | 2 | 4 | no | — |
| 290 | C22×Q8 | — | 2 | 4 | no | — |
| 291 | C22×Q8 | — | 2 | 4 | no | — |
| 292 | C22×Q8 | — | 2 | 4 | no | — |
| 293 | C22×Q8 | — | 4 | 4 | no | — |
| 294 | C22×Q8 | — | 4 | 4 | no | — |
| 295 | C22×Q8 | — | 4 | 4 | no | — |
| 296 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 297 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 298 | C22×D4 | #41 | 1 | 1 | yes | characteristic |
| 299 | C23×C4 | — | 2 | 4 | no | — |
| 300 | C23×C4 | C24 | 1 | 2 | yes | — |
| 301 | #137 | — | 2 | 4 | no | — |
| 302 | #137 | — | 4 | 2 | no | — |
| 303 | #137 | — | 4 | 4 | no | — |
| 304 | #137 | — | 4 | 4 | no | — |
| 305 | C2×Q16 | — | 2 | 4 | no | — |
| 306 | C2×Q16 | — | 2 | 2 | no | — |
| 307 | C2×Q16 | — | 2 | 8 | no | — |
| 308 | C2×Q16 | — | 2 | 4 | no | — |
| 309 | C2×Q16 | — | 2 | 1 | no | — |
| 310 | C2×Q16 | — | 2 | 1 | no | — |
| 311 | C2×Q16 | — | 2 | 4 | no | — |
| 312 | C2×Q16 | — | 2 | 4 | no | — |
| 313 | C2×Q16 | — | 2 | 2 | no | — |
| 314 | C2×Q16 | — | 2 | 2 | no | — |
| 315 | C2×Q16 | — | 2 | 2 | no | — |
| 316 | C2×Q16 | — | 2 | 2 | no | — |
| 317 | C2×Q16 | — | 4 | 4 | no | — |
| 318 | C2×Q16 | — | 4 | 4 | no | — |
| 319 | C2×Q16 | — | 4 | 4 | no | — |
| 320 | C2×Q16 | — | 4 | 8 | no | — |
| 321 | C2×Q16 | — | 4 | 8 | no | — |
| 322 | C2×Q16 | — | 4 | 8 | no | — |
| 323 | C2×Q16 | — | 4 | 8 | no | — |
| 324 | C2×SD16 | — | 2 | 2 | no | — |
| 325 | C2×SD16 | — | 2 | 4 | no | — |
| 326 | #131 | — | 4 | 4 | no | — |
| 327 | C2×M16 | — | 2 | 4 | no | — |
| 328 | C2×M16 | — | 2 | 2 | no | — |
| 329 | C2×M16 | — | 2 | 2 | no | — |
| 330 | C2×M16 | — | 4 | 4 | no | — |
| 331 | C2×M16 | — | 4 | 4 | no | — |
| 332 | C2×M16 | — | 4 | 4 | no | — |
| 333 | C2×M16 | C24 | 1 | 2 | yes | — |
| 334 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 335 | C2×M16 | C24 | 1 | 2 | yes | — |
| 336 | C2×M16 | C24 | 1 | 4 | yes | — |
| 337 | C2×M16 | C24 | 1 | 2 | yes | — |
| 338 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 339 | C22×C8 | — | 2 | 4 | no | — |
| 340 | C22×C8 | — | 2 | 2 | no | — |
| 341 | C22×C8 | — | 2 | 2 | no | — |
| 342 | C22×C8 | — | 4 | 4 | no | — |
| 343 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 344 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 345 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 346 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 347 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 348 | C22×C8 | C24 | 1 | 2 | yes | — |
| 349 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 350 | C4⋊Q8 | — | 2 | 2 | no | — |
| 351 | C4⋊Q8 | — | 2 | 2 | no | — |
| 352 | C4⋊Q8 | — | 2 | 2 | no | — |
| 353 | C4⋊Q8 | — | 2 | 2 | no | — |
| 354 | C4⋊Q8 | — | 4 | 2 | no | — |
| 355 | C4⋊Q8 | — | 4 | 2 | no | — |
| 356 | C4⋊Q8 | — | 4 | 4 | no | — |
| 357 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 358 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 359 | #126 | — | 2 | 2 | no | — |
| 360 | #126 | — | 2 | 2 | no | — |
| 361 | #126 | — | 2 | 2 | no | — |
| 362 | #125 | — | 2 | 2 | no | — |
| 363 | #125 | — | 2 | 1 | no | — |
| 364 | #125 | C2×D4 | 1 | 2 | yes | — |
| 365 | #124 | — | 2 | 1 | no | — |
| 366 | #124 | — | 2 | 2 | no | — |
| 367 | #123 | — | 2 | 2 | no | — |
| 368 | #123 | — | 2 | 2 | no | — |
| 369 | #123 | — | 2 | 2 | no | — |
| 370 | #123 | — | 2 | 2 | no | — |
| 371 | C22⋊Q8 | — | 2 | 1 | no | — |
| 372 | C22⋊Q8 | — | 2 | 1 | no | — |
| 373 | C22⋊Q8 | — | 2 | 1 | no | — |
| 374 | C22⋊Q8 | — | 2 | 2 | no | — |
| 375 | C22⋊Q8 | — | 2 | 4 | no | — |
| 376 | C22⋊Q8 | — | 2 | 4 | no | — |
| 377 | C22⋊Q8 | — | 2 | 4 | no | — |
| 378 | C22⋊Q8 | — | 2 | 4 | no | — |
| 379 | C22⋊Q8 | — | 4 | 4 | no | — |
| 380 | C22⋊Q8 | — | 4 | 4 | no | — |
| 381 | C22⋊Q8 | — | 4 | 4 | no | — |
| 382 | C22⋊Q8 | — | 4 | 4 | no | — |
| 383 | C22⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 384 | C22⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 385 | #121 | — | 2 | 2 | no | — |
| 386 | #121 | — | 2 | 1 | no | — |
| 387 | #121 | C2×D4 | 1 | 2 | yes | — |
| 388 | #121 | C2×D4 | 1 | 2 | yes | — |
| 389 | #120 | — | 2 | 2 | no | — |
| 390 | C4×Q8 | — | 2 | 1 | no | — |
| 391 | C4×Q8 | — | 2 | 1 | no | — |
| 392 | C4×Q8 | — | 2 | 1 | no | — |
| 393 | C4×Q8 | — | 2 | 2 | no | — |
| 394 | C4×Q8 | — | 2 | 2 | no | — |
| 395 | C4×Q8 | — | 2 | 2 | no | — |
| 396 | C4×Q8 | — | 2 | 2 | no | — |
| 397 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 398 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 399 | C4×D4 | — | 2 | 1 | no | — |
| 400 | C4×D4 | — | 2 | 2 | no | — |
| 401 | C4×D4 | — | 2 | 2 | no | — |
| 402 | C4×D4 | — | 2 | 1 | no | — |
| 403 | C4×D4 | — | 2 | 1 | no | — |
| 404 | C4×D4 | — | 2 | 2 | no | — |
| 405 | C4×D4 | — | 4 | 4 | no | — |
| 406 | C4×D4 | — | 4 | 2 | no | — |
| 407 | C4×D4 | — | 4 | 2 | no | — |
| 408 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 409 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 410 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 411 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 412 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 413 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 414 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 415 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 416 | #117 | — | 2 | 2 | no | — |
| 417 | #117 | — | 2 | 2 | no | — |
| 418 | #117 | — | 2 | 1 | no | — |
| 419 | #117 | — | 2 | 2 | no | — |
| 420 | #117 | — | 2 | 1 | no | — |
| 421 | #117 | C2×D4 | 1 | 2 | yes | — |
| 422 | #117 | C2×D4 | 1 | 2 | yes | — |
| 423 | #117 | C24 | 1 | 1 | yes | characteristic |
| 424 | #117 | C24 | 1 | 2 | yes | — |
| 425 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 426 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 427 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 428 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 429 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 430 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 431 | C2×C4⋊C4 | #41 | 1 | 1 | yes | characteristic |
| 432 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 433 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 434 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 435 | C2×C22⋊C4 | #41 | 1 | 2 | yes | — |
| 436 | C2×C42 | — | 2 | 2 | no | — |
| 437 | C2×C42 | — | 2 | 1 | no | — |
| 438 | C2×C42 | — | 2 | 2 | no | — |
| 439 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 440 | #108 | — | 4 | 2 | no | — |
| 441 | #108 | — | 4 | 4 | no | — |
| 442 | #107 | — | 2 | 1 | no | — |
| 443 | #107 | — | 2 | 1 | no | — |
| 444 | #107 | — | 2 | 2 | no | — |
| 445 | #107 | — | 2 | 4 | no | — |
| 446 | #106 | — | 2 | 2 | no | — |
| 447 | #106 | — | 2 | 4 | no | — |
| 448 | C4⋊C8 | — | 2 | 2 | no | — |
| 449 | C4⋊C8 | — | 2 | 1 | no | — |
| 450 | C4⋊C8 | — | 2 | 1 | no | — |
| 451 | C4⋊C8 | — | 2 | 2 | no | — |
| 452 | C4⋊C8 | — | 2 | 2 | no | — |
| 453 | C4⋊C8 | — | 2 | 2 | no | — |
| 454 | C4⋊C8 | — | 2 | 2 | no | — |
| 455 | C4⋊C8 | — | 2 | 2 | no | — |
| 456 | C4⋊C8 | — | 2 | 1 | no | — |
| 457 | C4⋊C8 | — | 2 | 1 | no | — |
| 458 | C4⋊C8 | — | 2 | 1 | no | — |
| 459 | C4⋊C8 | — | 2 | 1 | no | — |
| 460 | C4⋊C8 | — | 2 | 2 | no | — |
| 461 | C4⋊C8 | — | 2 | 2 | no | — |
| 462 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 463 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 464 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 465 | #103 | — | 2 | 2 | no | — |
| 466 | #103 | — | 2 | 2 | no | — |
| 467 | #103 | — | 2 | 2 | no | — |
| 468 | #103 | — | 2 | 4 | no | — |
| 469 | #103 | — | 2 | 4 | no | — |
| 470 | #103 | — | 2 | 2 | no | — |
| 471 | #103 | — | 2 | 2 | no | — |
| 472 | #103 | — | 2 | 4 | no | — |
| 473 | #103 | — | 2 | 4 | no | — |
| 474 | #103 | — | 2 | 4 | no | — |
| 475 | #103 | — | 2 | 4 | no | — |
| 476 | #103 | — | 2 | 4 | no | — |
| 477 | #103 | — | 2 | 4 | no | — |
| 478 | #103 | — | 2 | 4 | no | — |
| 479 | #103 | — | 2 | 4 | no | — |
| 480 | #102 | — | 2 | 2 | no | — |
| 481 | #101 | — | 2 | 4 | no | — |
| 482 | #101 | — | 2 | 8 | no | — |
| 483 | #101 | — | 4 | 4 | no | — |
| 484 | #101 | — | 4 | 4 | no | — |
| 485 | #101 | — | 4 | 2 | no | — |
| 486 | #101 | — | 4 | 4 | no | — |
| 487 | #101 | — | 4 | 4 | no | — |
| 488 | C22⋊C8 | — | 2 | 2 | no | — |
| 489 | C22⋊C8 | — | 2 | 2 | no | — |
| 490 | C22⋊C8 | — | 2 | 4 | no | — |
| 491 | C22⋊C8 | — | 2 | 4 | no | — |
| 492 | C22⋊C8 | — | 2 | 1 | no | — |
| 493 | C22⋊C8 | — | 2 | 1 | no | — |
| 494 | C22⋊C8 | — | 2 | 1 | no | — |
| 495 | C22⋊C8 | — | 2 | 1 | no | — |
| 496 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 497 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 498 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 499 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 500 | #97 | — | 2 | 2 | no | — |
| 501 | #97 | — | 2 | 2 | no | — |
| 502 | #97 | — | 2 | 1 | no | — |
| 503 | #97 | — | 2 | 2 | no | — |
| 504 | C4×C8 | — | 2 | 2 | no | — |
| 505 | C4×C8 | — | 2 | 2 | no | — |
| 506 | C4×C8 | — | 2 | 1 | no | — |
| 507 | C4×C8 | — | 2 | 2 | no | — |
| 508 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 509 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 510 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 511 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 512 | C24 | C2×#41 | 1 | 2 | yes | — |
| 513 | #41 | — | 2 | 2 | no | — |
| 514 | #41 | — | 2 | 2 | no | — |
| 515 | #41 | — | 4 | 4 | no | — |
| 516 | C2×Q8 | — | 2 | 1 | no | — |
| 517 | C2×Q8 | — | 2 | 1 | no | — |
| 518 | C2×Q8 | — | 2 | 2 | no | — |
| 519 | C2×Q8 | — | 2 | 2 | no | — |
| 520 | C2×Q8 | — | 2 | 2 | no | — |
| 521 | C2×Q8 | — | 2 | 4 | no | — |
| 522 | C2×Q8 | — | 2 | 4 | no | — |
| 523 | C2×Q8 | — | 2 | 2 | no | — |
| 524 | C2×Q8 | — | 2 | 4 | no | — |
| 525 | C2×Q8 | — | 2 | 4 | no | — |
| 526 | C2×Q8 | — | 2 | 2 | no | — |
| 527 | C2×Q8 | — | 2 | 4 | no | — |
| 528 | C2×Q8 | — | 2 | 4 | no | — |
| 529 | C2×Q8 | — | 4 | 8 | no | — |
| 530 | C2×Q8 | — | 4 | 8 | no | — |
| 531 | C2×Q8 | — | 4 | 8 | no | — |
| 532 | C2×Q8 | — | 4 | 8 | no | — |
| 533 | C2×Q8 | — | 4 | 8 | no | — |
| 534 | C2×Q8 | — | 4 | 4 | no | — |
| 535 | C2×Q8 | — | 4 | 4 | no | — |
| 536 | C2×Q8 | — | 8 | 4 | no | — |
| 537 | C2×Q8 | — | 8 | 4 | no | — |
| 538 | C2×Q8 | — | 8 | 4 | no | — |
| 539 | C2×Q8 | — | 8 | 4 | no | — |
| 540 | C2×Q8 | — | 8 | 4 | no | — |
| 541 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 542 | C2×Q8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 543 | C2×D4 | — | 2 | 4 | no | — |
| 544 | C2×D4 | — | 2 | 2 | no | — |
| 545 | C2×D4 | — | 2 | 1 | no | — |
| 546 | C2×D4 | — | 2 | 2 | no | — |
| 547 | C2×D4 | #121 | 1 | 2 | yes | — |
| 548 | C2×D4 | #121 | 1 | 1 | yes | characteristic |
| 549 | C2×D4 | #121 | 1 | 1 | yes | characteristic |
| 550 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 551 | C22×C4 | — | 2 | 4 | no | — |
| 552 | C22×C4 | — | 2 | 4 | no | — |
| 553 | C22×C4 | — | 2 | 2 | no | — |
| 554 | C22×C4 | — | 2 | 2 | no | — |
| 555 | C22×C4 | — | 2 | 2 | no | — |
| 556 | C22×C4 | — | 2 | 1 | no | — |
| 557 | C22×C4 | — | 2 | 1 | no | — |
| 558 | C22×C4 | — | 2 | 1 | no | — |
| 559 | C22×C4 | — | 2 | 4 | no | — |
| 560 | C22×C4 | — | 2 | 2 | no | — |
| 561 | C22×C4 | — | 4 | 8 | no | — |
| 562 | C22×C4 | — | 4 | 4 | no | — |
| 563 | C22×C4 | — | 4 | 4 | no | — |
| 564 | C22×C4 | — | 8 | 4 | no | — |
| 565 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 566 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 567 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 568 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 569 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 570 | C22×C4 | C2×#41 | 1 | 2 | yes | — |
| 571 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 572 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 573 | Q16 | — | 2 | 4 | no | — |
| 574 | Q16 | — | 2 | 4 | no | — |
| 575 | Q16 | — | 4 | 8 | no | — |
| 576 | Q16 | — | 4 | 8 | no | — |
| 577 | Q16 | — | 4 | 4 | no | — |
| 578 | Q16 | — | 4 | 4 | no | — |
| 579 | Q16 | — | 4 | 4 | no | — |
| 580 | Q16 | — | 8 | 2 | no | — |
| 581 | Q16 | — | 8 | 2 | no | — |
| 582 | Q16 | — | 8 | 4 | no | — |
| 583 | SD16 | — | 4 | 4 | no | — |
| 584 | SD16 | — | 8 | 4 | no | — |
| 585 | M16 | — | 2 | 2 | no | — |
| 586 | M16 | — | 2 | 2 | no | — |
| 587 | M16 | — | 2 | 4 | no | — |
| 588 | M16 | — | 2 | 4 | no | — |
| 589 | M16 | — | 2 | 2 | no | — |
| 590 | M16 | — | 2 | 2 | no | — |
| 591 | M16 | — | 2 | 2 | no | — |
| 592 | M16 | — | 2 | 4 | no | — |
| 593 | M16 | — | 2 | 2 | no | — |
| 594 | M16 | — | 8 | 2 | no | — |
| 595 | M16 | — | 8 | 2 | no | — |
| 596 | M16 | — | 8 | 4 | no | — |
| 597 | C2×C8 | — | 2 | 4 | no | — |
| 598 | C2×C8 | — | 2 | 2 | no | — |
| 599 | C2×C8 | — | 2 | 2 | no | — |
| 600 | C2×C8 | — | 2 | 1 | no | — |
| 601 | C2×C8 | — | 2 | 2 | no | — |
| 602 | C2×C8 | — | 2 | 2 | no | — |
| 603 | C2×C8 | — | 2 | 1 | no | — |
| 604 | C2×C8 | — | 2 | 2 | no | — |
| 605 | C2×C8 | — | 2 | 4 | no | — |
| 606 | C2×C8 | — | 4 | 2 | no | — |
| 607 | C2×C8 | — | 4 | 2 | no | — |
| 608 | C2×C8 | — | 4 | 2 | no | — |
| 609 | C2×C8 | — | 4 | 2 | no | — |
| 610 | C2×C8 | — | 8 | 2 | no | — |
| 611 | C2×C8 | — | 8 | 2 | no | — |
| 612 | C2×C8 | — | 8 | 4 | no | — |
| 613 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 614 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 615 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 616 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 617 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 618 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 619 | C4⋊C4 | — | 2 | 2 | no | — |
| 620 | C4⋊C4 | — | 2 | 2 | no | — |
| 621 | C4⋊C4 | — | 2 | 1 | no | — |
| 622 | C4⋊C4 | — | 2 | 2 | no | — |
| 623 | C4⋊C4 | — | 2 | 2 | no | — |
| 624 | C4⋊C4 | — | 2 | 1 | no | — |
| 625 | C4⋊C4 | — | 2 | 1 | no | — |
| 626 | C4⋊C4 | — | 2 | 2 | no | — |
| 627 | C4⋊C4 | — | 2 | 2 | no | — |
| 628 | C4⋊C4 | — | 2 | 1 | no | — |
| 629 | C4⋊C4 | — | 2 | 2 | no | — |
| 630 | C4⋊C4 | — | 2 | 2 | no | — |
| 631 | C4⋊C4 | — | 4 | 2 | no | — |
| 632 | C4⋊C4 | — | 4 | 2 | no | — |
| 633 | C4⋊C4 | — | 4 | 2 | no | — |
| 634 | C4⋊C4 | — | 4 | 2 | no | — |
| 635 | C4⋊C4 | — | 4 | 4 | no | — |
| 636 | C4⋊C4 | — | 4 | 4 | no | — |
| 637 | C4⋊C4 | — | 4 | 2 | no | — |
| 638 | C4⋊C4 | — | 4 | 2 | no | — |
| 639 | C4⋊C4 | #121 | 1 | 1 | yes | characteristic |
| 640 | C4⋊C4 | #121 | 1 | 1 | yes | characteristic |
| 641 | C4⋊C4 | #121 | 1 | 2 | yes | — |
| 642 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 643 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 644 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 645 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 646 | C22⋊C4 | — | 2 | 2 | no | — |
| 647 | C22⋊C4 | — | 2 | 2 | no | — |
| 648 | C22⋊C4 | — | 2 | 2 | no | — |
| 649 | C22⋊C4 | — | 2 | 2 | no | — |
| 650 | C22⋊C4 | — | 2 | 1 | no | — |
| 651 | C22⋊C4 | — | 2 | 2 | no | — |
| 652 | C22⋊C4 | — | 2 | 2 | no | — |
| 653 | C22⋊C4 | — | 2 | 1 | no | — |
| 654 | C22⋊C4 | — | 2 | 1 | no | — |
| 655 | C22⋊C4 | — | 2 | 2 | no | — |
| 656 | C22⋊C4 | — | 4 | 4 | no | — |
| 657 | C22⋊C4 | — | 4 | 4 | no | — |
| 658 | C22⋊C4 | #121 | 1 | 2 | yes | — |
| 659 | C22⋊C4 | #121 | 1 | 2 | yes | — |
| 660 | C22⋊C4 | #121 | 1 | 2 | yes | — |
| 661 | C22⋊C4 | #121 | 1 | 2 | yes | — |
| 662 | C42 | — | 2 | 2 | no | — |
| 663 | C42 | — | 2 | 1 | no | — |
| 664 | C42 | — | 2 | 2 | no | — |
| 665 | C42 | — | 2 | 1 | no | — |
| 666 | C42 | — | 2 | 2 | no | — |
| 667 | C42 | — | 2 | 1 | no | — |
| 668 | C42 | — | 4 | 2 | no | — |
| 669 | C42 | — | 4 | 2 | no | — |
| 670 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 671 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 672 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 673 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 674 | C23 | — | 2 | 4 | no | — |
| 675 | C23 | — | 2 | 4 | no | — |
| 676 | C23 | — | 2 | 1 | no | — |
| 677 | C23 | — | 4 | 2 | no | — |
| 678 | C23 | C2×#121 | 1 | 2 | yes | — |
| 679 | C23 | C2×#121 | 1 | 2 | yes | — |
| 680 | C23 | C22×#41 | 1 | 1 | yes | characteristic |
| 681 | Q8 | — | 2 | 4 | no | — |
| 682 | Q8 | — | 2 | 4 | no | — |
| 683 | Q8 | — | 2 | 2 | no | — |
| 684 | Q8 | — | 4 | 2 | no | — |
| 685 | Q8 | — | 4 | 2 | no | — |
| 686 | Q8 | — | 4 | 2 | no | — |
| 687 | Q8 | — | 4 | 4 | no | — |
| 688 | Q8 | — | 4 | 4 | no | — |
| 689 | Q8 | — | 4 | 4 | no | — |
| 690 | Q8 | — | 4 | 4 | no | — |
| 691 | Q8 | — | 8 | 1 | no | — |
| 692 | Q8 | — | 8 | 8 | no | — |
| 693 | Q8 | — | 8 | 8 | no | — |
| 694 | D4 | — | 2 | 4 | no | — |
| 695 | D4 | — | 2 | 2 | no | — |
| 696 | D4 | — | 2 | 2 | no | — |
| 697 | D4 | — | 4 | 2 | no | — |
| 698 | D4 | — | 4 | 4 | no | — |
| 699 | D4 | — | 8 | 2 | no | — |
| 700 | D4 | #473 | 1 | 4 | yes | complemented |
| 701 | C2×C4 | — | 2 | 4 | no | — |
| 702 | C2×C4 | — | 2 | 2 | no | — |
| 703 | C2×C4 | — | 2 | 2 | no | — |
| 704 | C2×C4 | — | 2 | 4 | no | — |
| 705 | C2×C4 | — | 2 | 4 | no | — |
| 706 | C2×C4 | — | 2 | 2 | no | — |
| 707 | C2×C4 | — | 2 | 2 | no | — |
| 708 | C2×C4 | — | 2 | 2 | no | — |
| 709 | C2×C4 | — | 2 | 1 | no | — |
| 710 | C2×C4 | — | 2 | 1 | no | — |
| 711 | C2×C4 | — | 2 | 1 | no | — |
| 712 | C2×C4 | — | 2 | 2 | no | — |
| 713 | C2×C4 | — | 2 | 2 | no | — |
| 714 | C2×C4 | — | 2 | 4 | no | — |
| 715 | C2×C4 | — | 4 | 1 | no | — |
| 716 | C2×C4 | — | 4 | 2 | no | — |
| 717 | C2×C4 | — | 4 | 2 | no | — |
| 718 | C2×C4 | — | 4 | 4 | no | — |
| 719 | C2×C4 | — | 4 | 1 | no | — |
| 720 | C2×C4 | — | 4 | 1 | no | — |
| 721 | C2×C4 | — | 4 | 2 | no | — |
| 722 | C2×C4 | — | 4 | 2 | no | — |
| 723 | C2×C4 | — | 4 | 4 | no | — |
| 724 | C2×C4 | — | 4 | 4 | no | — |
| 725 | C2×C4 | — | 4 | 4 | no | — |
| 726 | C2×C4 | — | 8 | 1 | no | — |
| 727 | C2×C4 | — | 8 | 2 | no | — |
| 728 | C2×C4 | — | 8 | 8 | no | — |
| 729 | C2×C4 | — | 8 | 8 | no | — |
| 730 | C2×C4 | — | 8 | 2 | no | — |
| 731 | C2×C4 | C2×#121 | 1 | 2 | yes | — |
| 732 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 733 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 734 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 735 | C2×C4 | C2×#121 | 1 | 2 | yes | — |
| 736 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 737 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 738 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 739 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 740 | C2×C4 | #585 | 1 | 2 | yes | — |
| 741 | C8 | — | 2 | 1 | no | — |
| 742 | C8 | — | 2 | 1 | no | — |
| 743 | C8 | — | 2 | 2 | no | — |
| 744 | C8 | — | 2 | 2 | no | — |
| 745 | C8 | — | 2 | 1 | no | — |
| 746 | C8 | — | 2 | 1 | no | — |
| 747 | C8 | — | 4 | 2 | no | — |
| 748 | C8 | — | 4 | 1 | no | — |
| 749 | C8 | — | 4 | 2 | no | — |
| 750 | C8 | — | 4 | 4 | no | — |
| 751 | C8 | — | 4 | 2 | no | — |
| 752 | C8 | — | 4 | 1 | no | — |
| 753 | C22 | — | 2 | 1 | no | — |
| 754 | C22 | — | 2 | 1 | no | — |
| 755 | C22 | — | 2 | 2 | no | — |
| 756 | C22 | — | 2 | 2 | no | — |
| 757 | C22 | — | 2 | 2 | no | — |
| 758 | C22 | — | 2 | 2 | no | — |
| 759 | C22 | — | 2 | 2 | no | — |
| 760 | C22 | — | 4 | 8 | no | — |
| 761 | C22 | — | 4 | 1 | no | — |
| 762 | C22 | — | 4 | 1 | no | — |
| 763 | C22 | — | 4 | 1 | no | — |
| 764 | C22 | C2×#473 | 1 | 4 | yes | — |
| 765 | C22 | C22×#121 | 1 | 1 | yes | characteristic |
| 766 | C22 | #3513 | 1 | 2 | yes | — |
| 767 | C4 | — | 2 | 1 | no | — |
| 768 | C4 | — | 2 | 1 | no | — |
| 769 | C4 | — | 2 | 1 | no | — |
| 770 | C4 | — | 2 | 2 | no | — |
| 771 | C4 | — | 2 | 2 | no | — |
| 772 | C4 | — | 4 | 1 | no | — |
| 773 | C4 | — | 4 | 2 | no | — |
| 774 | C4 | — | 4 | 1 | no | — |
| 775 | C4 | — | 4 | 2 | no | — |
| 776 | C4 | — | 4 | 4 | no | — |
| 777 | C4 | — | 4 | 1 | no | — |
| 778 | C4 | — | 8 | 2 | no | — |
| 779 | C4 | — | 8 | 4 | no | — |
| 780 | C4 | C2×#473 | 1 | 2 | yes | — |
| 781 | C4 | #3484 | 1 | 1 | yes | characteristic |
| 782 | C4 | #3488 | 1 | 2 | yes | — |
| 783 | C4 | #3500 | 1 | 1 | yes | characteristic |
| 784 | C2 | — | 2 | 2 | no | — |
| 785 | C2 | — | 2 | 4 | no | — |
| 786 | C2 | — | 4 | 2 | no | — |
| 787 | C2 | — | 8 | 1 | no | — |
| 788 | C2 | #35728 | 1 | 1 | yes | characteristic |
| 789 | C2 | C22×#473 | 1 | 1 | yes | characteristic |
| 790 | C2 | #60472 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#121 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | #3475 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D4×Q16 | C2 | semidirect |
| 4. #29820 | C2 | semidirect |
| 5. #29789 | C2 | semidirect |
| 6. #28762 | C2 | semidirect |
| 7. #28591 | C2 | semidirect |
| 8. #28219 | C2 | semidirect |
| 9. #25314 | C2 | semidirect |
| 10. #25142 | C2 | semidirect |
| 11. #24772 | C2 | semidirect |
| 12. #24522 | C2 | semidirect |
| 13. #24282 | C2 | semidirect |
| 14. #23717 | C2 | semidirect |
| 15. C2×#2047 | C2 | semidirect |
| 16. #22717 | C2 | semidirect |
| 17. D4×#101 | C2 | semidirect |
| 700. D4 | #473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61157 | 2 |
| C2×D4×Q16 | 2 |
| #60271 | 2 |
| #29820 | 2 |
| #29789 | 2 |
| #28762 | 2 |
| #28591 | 2 |
| #28219 | 2 |
| #25314 | 2 |
| #25142 | 2 |
| #24772 | 2 |
| #24522 | 2 |
| #24282 | 2 |
| #23717 | 2 |
| C2×#2047 | 2 |
| #22717 | 2 |
| D4×#101 | 2 |