Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
5989 conjugacy classes of subgroups.
The subgroup lattice has 1003 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62998 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62507 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #62482 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #62476 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #62398 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #62369 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #62141 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #62133 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #62116 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #62105 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #61846 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #61837 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #61834 | C2 | 1 | 6 | yes | maximal, complemented |
| 14 | #61461 | C2 | 1 | 6 | yes | maximal, complemented |
| 15 | #61442 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | #61435 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | Q8×AGL(1,ℤ/8) | C2 | 1 | 2 | yes | maximal, complemented |
| 18 | #61365 | C2 | 1 | 3 | yes | maximal, complemented |
| 19 | #60343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | #3523 | — | 2 | 6 | no | — |
| 21 | #3523 | — | 2 | 2 | no | — |
| 22 | #3523 | C22 | 1 | 2 | yes | — |
| 23 | #3523 | C22 | 1 | 6 | yes | complemented |
| 24 | #3518 | C22 | 1 | 6 | yes | — |
| 25 | #3518 | C22 | 1 | 2 | yes | complemented |
| 26 | #3516 | — | 2 | 2 | no | — |
| 27 | #3516 | — | 2 | 6 | no | — |
| 28 | #3509 | C22 | 1 | 6 | yes | — |
| 29 | #3509 | C22 | 1 | 6 | yes | complemented |
| 30 | #3502 | C22 | 1 | 2 | yes | complemented |
| 31 | #3495 | — | 2 | 6 | no | — |
| 32 | #3495 | — | 2 | 6 | no | — |
| 33 | #3486 | — | 2 | 2 | no | — |
| 34 | #3482 | C22 | 1 | 6 | yes | — |
| 35 | #3482 | C22 | 1 | 2 | yes | complemented |
| 36 | Q8×#41 | C22 | 1 | 2 | yes | — |
| 37 | Q8×#41 | C22 | 1 | 6 | yes | complemented |
| 38 | #3475 | C22 | 1 | 6 | yes | — |
| 39 | #3475 | C22 | 1 | 6 | yes | complemented |
| 40 | C2×D4×Q8 | C22 | 1 | 2 | yes | complemented |
| 41 | C4×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#519 | — | 2 | 2 | no | — |
| 43 | #3402 | C22 | 1 | 3 | yes | — |
| 44 | #3398 | C22 | 1 | 6 | yes | complemented |
| 45 | #3395 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #3390 | C22 | 1 | 6 | yes | complemented |
| 47 | #3390 | C22 | 1 | 6 | yes | complemented |
| 48 | #3389 | C22 | 1 | 3 | yes | — |
| 49 | #3388 | C22 | 1 | 12 | yes | complemented |
| 50 | #3387 | C22 | 1 | 6 | yes | complemented |
| 51 | #3387 | C22 | 1 | 6 | yes | complemented |
| 52 | #3386 | C22 | 1 | 6 | yes | complemented |
| 53 | #3386 | C22 | 1 | 6 | yes | complemented |
| 54 | #3386 | C22 | 1 | 6 | yes | complemented |
| 55 | #3386 | C22 | 1 | 6 | yes | complemented |
| 56 | #3385 | C22 | 1 | 6 | yes | complemented |
| 57 | #3384 | C22 | 1 | 6 | yes | — |
| 58 | #3384 | C22 | 1 | 6 | yes | — |
| 59 | Q8×Q16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | Q8×SD16 | C22 | 1 | 2 | yes | complemented |
| 61 | Q8×SD16 | C22 | 1 | 2 | yes | complemented |
| 62 | Q8×D8 | C22 | 1 | 1 | yes | characteristic |
| 63 | Q8×D8 | C22 | 1 | 2 | yes | — |
| 64 | Q8×D8 | C22 | 1 | 1 | yes | characteristic |
| 65 | #3377 | C22 | 1 | 12 | yes | complemented |
| 66 | #3376 | C22 | 1 | 6 | yes | — |
| 67 | #3374 | C22 | 1 | 6 | yes | complemented |
| 68 | #3374 | C22 | 1 | 6 | yes | complemented |
| 69 | #3372 | C22 | 1 | 6 | yes | complemented |
| 70 | #3369 | C22 | 1 | 6 | yes | complemented |
| 71 | #3367 | C22 | 1 | 6 | yes | — |
| 72 | #3367 | C22 | 1 | 6 | yes | — |
| 73 | #3363 | C22 | 1 | 2 | yes | complemented |
| 74 | #3359 | C22 | 1 | 2 | yes | complemented |
| 75 | #3359 | C22 | 1 | 2 | yes | complemented |
| 76 | #3352 | C22 | 1 | 3 | yes | — |
| 77 | #3352 | C22 | 1 | 6 | yes | — |
| 78 | #3349 | C22 | 1 | 12 | yes | complemented |
| 79 | #3349 | C22 | 1 | 12 | yes | complemented |
| 80 | #3349 | C22 | 1 | 12 | yes | complemented |
| 81 | #3348 | C22 | 1 | 6 | yes | — |
| 82 | #3348 | C22 | 1 | 12 | yes | — |
| 83 | #3342 | C22 | 1 | 3 | yes | complemented |
| 84 | #3342 | C22 | 1 | 3 | yes | complemented |
| 85 | #3342 | C22 | 1 | 6 | yes | complemented |
| 86 | #3341 | C22 | 1 | 3 | yes | — |
| 87 | #3340 | C22 | 1 | 6 | yes | complemented |
| 88 | #3340 | C22 | 1 | 6 | yes | complemented |
| 89 | #3323 | C22 | 1 | 6 | yes | — |
| 90 | #3319 | C22 | 1 | 6 | yes | — |
| 91 | #3315 | C22 | 1 | 6 | yes | — |
| 92 | #3315 | C22 | 1 | 12 | yes | — |
| 93 | #3311 | C22 | 1 | 12 | yes | complemented |
| 94 | #3303 | C22 | 1 | 6 | yes | — |
| 95 | #3302 | C22 | 1 | 6 | yes | complemented |
| 96 | #3302 | C22 | 1 | 6 | yes | complemented |
| 97 | #3283 | C22 | 1 | 3 | yes | — |
| 98 | #3273 | C22 | 1 | 1 | yes | characteristic |
| 99 | #3267 | C22 | 1 | 6 | yes | — |
| 100 | #3255 | C22 | 1 | 6 | yes | complemented |
| 101 | #3252 | C22 | 1 | 6 | yes | — |
| 102 | #3250 | C22 | 1 | 6 | yes | — |
| 103 | #3249 | C22 | 1 | 6 | yes | complemented |
| 104 | #3248 | C22 | 1 | 6 | yes | complemented |
| 105 | #3240 | C22 | 1 | 12 | yes | complemented |
| 106 | #3239 | C22 | 1 | 6 | yes | — |
| 107 | #3237 | C22 | 1 | 12 | yes | complemented |
| 108 | #3237 | C22 | 1 | 6 | yes | complemented |
| 109 | #3233 | C22 | 1 | 6 | yes | complemented |
| 110 | #3231 | C22 | 1 | 6 | yes | complemented |
| 111 | #3231 | C22 | 1 | 6 | yes | complemented |
| 112 | #3230 | C22 | 1 | 6 | yes | complemented |
| 113 | #3185 | C22 | 1 | 6 | yes | complemented |
| 114 | #3181 | C22 | 1 | 12 | yes | complemented |
| 115 | #3172 | C22 | 1 | 6 | yes | — |
| 116 | #3170 | C22 | 1 | 3 | yes | complemented |
| 117 | #3168 | C22 | 1 | 3 | yes | — |
| 118 | #3165 | C22 | 1 | 6 | yes | complemented |
| 119 | #3162 | C22 | 1 | 6 | yes | complemented |
| 120 | #3160 | C22 | 1 | 3 | yes | complemented |
| 121 | #3116 | C22 | 1 | 6 | yes | — |
| 122 | #3116 | C22 | 1 | 12 | yes | complemented |
| 123 | #3111 | C22 | 1 | 12 | yes | — |
| 124 | #3110 | C22 | 1 | 6 | yes | complemented |
| 125 | #3107 | C22 | 1 | 6 | yes | — |
| 126 | #3107 | C22 | 1 | 6 | yes | complemented |
| 127 | #3105 | C22 | 1 | 6 | yes | — |
| 128 | #3102 | C22 | 1 | 6 | yes | — |
| 129 | #3079 | C22 | 1 | 6 | yes | — |
| 130 | #3077 | C22 | 1 | 6 | yes | complemented |
| 131 | #3076 | C22 | 1 | 6 | yes | complemented |
| 132 | #3076 | C22 | 1 | 12 | yes | complemented |
| 133 | #2990 | C22 | 1 | 6 | yes | complemented |
| 134 | #2989 | C22 | 1 | 3 | yes | — |
| 135 | #2988 | C22 | 1 | 1 | yes | characteristic, complemented |
| 136 | #2984 | C22 | 1 | 2 | yes | complemented |
| 137 | #2983 | C22 | 1 | 3 | yes | complemented |
| 138 | #2970 | C22 | 1 | 6 | yes | complemented |
| 139 | #2965 | C22 | 1 | 3 | yes | — |
| 140 | C8×#41 | C22 | 1 | 1 | yes | characteristic, complemented |
| 141 | Q8×M16 | C22 | 1 | 2 | yes | complemented |
| 142 | C2×#446 | C22 | 1 | 3 | yes | complemented |
| 143 | C4×AGL(1,ℤ/8) | C22 | 1 | 6 | yes | — |
| 144 | #2943 | C22 | 1 | 6 | yes | — |
| 145 | C4×#135 | C22 | 1 | 3 | yes | — |
| 146 | C2×2−1+4 | D4 | 1 | 1 | yes | characteristic |
| 147 | C23×Q8 | — | 2 | 2 | no | — |
| 148 | C2×AGL(1,ℤ/8) | C23 | 1 | 2 | yes | — |
| 149 | C2×#135 | C23 | 1 | 3 | yes | — |
| 150 | Q82 | C23 | 1 | 2 | yes | — |
| 151 | Q82 | C23 | 1 | 6 | yes | — |
| 152 | #557 | — | 2 | 2 | no | — |
| 153 | #557 | — | 2 | 6 | no | — |
| 154 | #557 | — | 2 | 6 | no | — |
| 155 | #557 | — | 2 | 6 | no | — |
| 156 | #557 | C23 | 1 | 2 | yes | — |
| 157 | #557 | C23 | 1 | 6 | yes | — |
| 158 | #557 | C23 | 1 | 6 | yes | — |
| 159 | #557 | C23 | 1 | 6 | yes | — |
| 160 | #557 | C23 | 1 | 12 | yes | — |
| 161 | #556 | — | 2 | 6 | no | — |
| 162 | #556 | — | 2 | 6 | no | — |
| 163 | #556 | — | 2 | 6 | no | — |
| 164 | #556 | — | 2 | 12 | no | — |
| 165 | #556 | — | 2 | 6 | no | — |
| 166 | #556 | C23 | 1 | 6 | yes | — |
| 167 | #556 | C23 | 1 | 6 | yes | — |
| 168 | #556 | C23 | 1 | 6 | yes | — |
| 169 | #556 | C23 | 1 | 6 | yes | — |
| 170 | #556 | C23 | 1 | 12 | yes | — |
| 171 | #555 | C23 | 1 | 6 | yes | — |
| 172 | #555 | C23 | 1 | 6 | yes | — |
| 173 | #554 | — | 2 | 6 | no | — |
| 174 | #554 | — | 2 | 6 | no | — |
| 175 | #554 | — | 2 | 12 | no | — |
| 176 | #554 | C23 | 1 | 6 | yes | — |
| 177 | #554 | C23 | 1 | 6 | yes | — |
| 178 | #553 | — | 2 | 6 | no | — |
| 179 | #553 | — | 2 | 6 | no | — |
| 180 | #552 | — | 2 | 6 | no | — |
| 181 | #552 | — | 2 | 6 | no | — |
| 182 | #552 | — | 2 | 6 | no | — |
| 183 | #552 | — | 2 | 6 | no | — |
| 184 | #552 | — | 2 | 12 | no | — |
| 185 | #552 | — | 2 | 6 | no | — |
| 186 | #552 | — | 2 | 12 | no | — |
| 187 | #552 | — | 2 | 6 | no | — |
| 188 | #552 | — | 2 | 6 | no | — |
| 189 | #552 | — | 2 | 6 | no | — |
| 190 | #552 | — | 2 | 12 | no | — |
| 191 | #552 | C23 | 1 | 6 | yes | — |
| 192 | #552 | C23 | 1 | 12 | yes | — |
| 193 | #552 | C23 | 1 | 6 | yes | — |
| 194 | #551 | — | 2 | 6 | no | — |
| 195 | #551 | — | 2 | 6 | no | — |
| 196 | #551 | — | 2 | 12 | no | — |
| 197 | D4×Q8 | — | 2 | 2 | no | — |
| 198 | D4×Q8 | — | 2 | 6 | no | — |
| 199 | D4×Q8 | — | 2 | 2 | no | — |
| 200 | D4×Q8 | — | 2 | 6 | no | — |
| 201 | D4×Q8 | — | 2 | 2 | no | — |
| 202 | D4×Q8 | — | 2 | 6 | no | — |
| 203 | D4×Q8 | C23 | 1 | 2 | yes | — |
| 204 | D4×Q8 | C23 | 1 | 2 | yes | — |
| 205 | D4×Q8 | C23 | 1 | 6 | yes | — |
| 206 | D4×Q8 | C23 | 1 | 6 | yes | — |
| 207 | #548 | — | 2 | 6 | no | — |
| 208 | #548 | — | 2 | 2 | no | — |
| 209 | #548 | — | 2 | 6 | no | — |
| 210 | #548 | — | 2 | 2 | no | — |
| 211 | #547 | C23 | 1 | 6 | yes | — |
| 212 | #547 | C23 | 1 | 6 | yes | — |
| 213 | #546 | C23 | 1 | 2 | yes | — |
| 214 | #546 | C23 | 1 | 6 | yes | — |
| 215 | #544 | — | 2 | 6 | no | — |
| 216 | #542 | — | 2 | 12 | no | — |
| 217 | #542 | — | 2 | 6 | no | — |
| 218 | #542 | — | 2 | 6 | no | — |
| 219 | #541 | — | 2 | 6 | no | — |
| 220 | #541 | — | 2 | 6 | no | — |
| 221 | #541 | — | 2 | 12 | no | — |
| 222 | #541 | — | 2 | 6 | no | — |
| 223 | #541 | — | 2 | 6 | no | — |
| 224 | #541 | — | 2 | 12 | no | — |
| 225 | #536 | — | 2 | 6 | no | — |
| 226 | #536 | — | 2 | 6 | no | — |
| 227 | #533 | — | 2 | 6 | no | — |
| 228 | #533 | — | 2 | 6 | no | — |
| 229 | #533 | — | 2 | 12 | no | — |
| 230 | #533 | C23 | 1 | 6 | yes | — |
| 231 | #533 | C23 | 1 | 6 | yes | — |
| 232 | #533 | C23 | 1 | 6 | yes | — |
| 233 | #533 | C23 | 1 | 6 | yes | — |
| 234 | #533 | C23 | 1 | 12 | yes | — |
| 235 | #533 | C23 | 1 | 6 | yes | — |
| 236 | #533 | C23 | 1 | 12 | yes | — |
| 237 | #533 | C23 | 1 | 6 | yes | — |
| 238 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 239 | #529 | — | 2 | 12 | no | — |
| 240 | #529 | — | 2 | 6 | no | — |
| 241 | #529 | — | 2 | 6 | no | — |
| 242 | #529 | — | 2 | 6 | no | — |
| 243 | #529 | — | 2 | 6 | no | — |
| 244 | #529 | — | 2 | 12 | no | — |
| 245 | #529 | C23 | 1 | 6 | yes | — |
| 246 | #529 | C23 | 1 | 6 | yes | — |
| 247 | #529 | C23 | 1 | 12 | yes | — |
| 248 | #525 | — | 2 | 6 | no | — |
| 249 | #525 | — | 2 | 6 | no | — |
| 250 | C2×C22⋊Q8 | — | 2 | 6 | no | — |
| 251 | #520 | D4 | 1 | 3 | yes | — |
| 252 | #520 | D4 | 1 | 6 | yes | — |
| 253 | #520 | D4 | 1 | 1 | yes | characteristic |
| 254 | #519 | — | 2 | 2 | no | — |
| 255 | #519 | — | 2 | 2 | no | — |
| 256 | #519 | — | 2 | 6 | no | — |
| 257 | #519 | — | 2 | 6 | no | — |
| 258 | #519 | — | 2 | 2 | no | — |
| 259 | #519 | — | 2 | 6 | no | — |
| 260 | #519 | — | 2 | 6 | no | — |
| 261 | #519 | D4 | 1 | 2 | yes | — |
| 262 | #519 | D4 | 1 | 3 | yes | — |
| 263 | C4×#41 | C23 | 1 | 6 | yes | — |
| 264 | C4×#41 | C23 | 1 | 12 | yes | — |
| 265 | C4×#41 | C23 | 1 | 6 | yes | — |
| 266 | C4×#41 | C23 | 1 | 3 | yes | — |
| 267 | C4×#41 | C23 | 1 | 6 | yes | — |
| 268 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 269 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 270 | C2×C4×Q8 | — | 2 | 6 | no | — |
| 271 | C2×C4×Q8 | — | 2 | 6 | no | — |
| 272 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 273 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 274 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 275 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 276 | C2×#117 | — | 2 | 6 | no | — |
| 277 | C2×#117 | — | 2 | 6 | no | — |
| 278 | #501 | C23 | 1 | 12 | yes | — |
| 279 | #501 | C23 | 1 | 6 | yes | — |
| 280 | #501 | C23 | 1 | 12 | yes | — |
| 281 | #501 | C23 | 1 | 12 | yes | — |
| 282 | #501 | C23 | 1 | 12 | yes | — |
| 283 | #500 | C23 | 1 | 3 | yes | — |
| 284 | #500 | C23 | 1 | 3 | yes | — |
| 285 | #500 | C23 | 1 | 3 | yes | — |
| 286 | #500 | C23 | 1 | 6 | yes | — |
| 287 | #499 | C23 | 1 | 6 | yes | — |
| 288 | #499 | C23 | 1 | 3 | yes | — |
| 289 | #498 | C23 | 1 | 6 | yes | — |
| 290 | #498 | C23 | 1 | 6 | yes | — |
| 291 | #497 | C23 | 1 | 6 | yes | — |
| 292 | #495 | C23 | 1 | 1 | yes | characteristic |
| 293 | #494 | C23 | 1 | 3 | yes | — |
| 294 | #491 | C23 | 1 | 12 | yes | — |
| 295 | #491 | C23 | 1 | 6 | yes | — |
| 296 | #489 | C23 | 1 | 12 | yes | — |
| 297 | #489 | C23 | 1 | 6 | yes | — |
| 298 | #488 | C23 | 1 | 6 | yes | — |
| 299 | #487 | C23 | 1 | 6 | yes | — |
| 300 | #487 | C23 | 1 | 6 | yes | — |
| 301 | #487 | C23 | 1 | 6 | yes | — |
| 302 | #485 | C23 | 1 | 12 | yes | — |
| 303 | #485 | C23 | 1 | 12 | yes | — |
| 304 | #485 | C23 | 1 | 6 | yes | — |
| 305 | #485 | C23 | 1 | 12 | yes | — |
| 306 | #485 | C23 | 1 | 12 | yes | — |
| 307 | #485 | C23 | 1 | 6 | yes | — |
| 308 | #485 | C23 | 1 | 12 | yes | — |
| 309 | #485 | C23 | 1 | 6 | yes | — |
| 310 | #484 | C23 | 1 | 6 | yes | — |
| 311 | #484 | C23 | 1 | 12 | yes | — |
| 312 | #482 | C23 | 1 | 6 | yes | — |
| 313 | #482 | C23 | 1 | 12 | yes | — |
| 314 | #481 | C23 | 1 | 6 | yes | — |
| 315 | #479 | C23 | 1 | 12 | yes | — |
| 316 | #479 | C23 | 1 | 12 | yes | — |
| 317 | #479 | C23 | 1 | 12 | yes | — |
| 318 | #479 | C23 | 1 | 12 | yes | — |
| 319 | #479 | C23 | 1 | 6 | yes | — |
| 320 | #478 | C23 | 1 | 6 | yes | — |
| 321 | #478 | C23 | 1 | 6 | yes | — |
| 322 | #478 | C23 | 1 | 12 | yes | — |
| 323 | #478 | C23 | 1 | 12 | yes | — |
| 324 | #478 | C23 | 1 | 6 | yes | — |
| 325 | #477 | C23 | 1 | 6 | yes | — |
| 326 | #477 | C23 | 1 | 12 | yes | — |
| 327 | #477 | C23 | 1 | 12 | yes | — |
| 328 | #477 | C23 | 1 | 6 | yes | — |
| 329 | #477 | C23 | 1 | 12 | yes | — |
| 330 | #476 | C23 | 1 | 6 | yes | — |
| 331 | #476 | C23 | 1 | 12 | yes | — |
| 332 | #476 | C23 | 1 | 6 | yes | — |
| 333 | #475 | C23 | 1 | 6 | yes | — |
| 334 | #475 | C23 | 1 | 12 | yes | — |
| 335 | #475 | C23 | 1 | 6 | yes | — |
| 336 | #475 | C23 | 1 | 6 | yes | — |
| 337 | #475 | C23 | 1 | 6 | yes | — |
| 338 | #475 | C23 | 1 | 6 | yes | — |
| 339 | #474 | C23 | 1 | 6 | yes | — |
| 340 | #474 | C23 | 1 | 6 | yes | — |
| 341 | #474 | C23 | 1 | 6 | yes | — |
| 342 | #474 | C23 | 1 | 6 | yes | — |
| 343 | #474 | C23 | 1 | 6 | yes | — |
| 344 | #470 | C23 | 1 | 6 | yes | — |
| 345 | #470 | C23 | 1 | 6 | yes | — |
| 346 | #470 | C23 | 1 | 12 | yes | — |
| 347 | #468 | C23 | 1 | 2 | yes | — |
| 348 | #468 | C23 | 1 | 6 | yes | — |
| 349 | #467 | C23 | 1 | 3 | yes | — |
| 350 | #467 | C23 | 1 | 6 | yes | — |
| 351 | #467 | C23 | 1 | 12 | yes | — |
| 352 | #467 | C23 | 1 | 6 | yes | — |
| 353 | #466 | C23 | 1 | 3 | yes | — |
| 354 | #465 | C23 | 1 | 6 | yes | — |
| 355 | #465 | C23 | 1 | 12 | yes | — |
| 356 | #464 | C23 | 1 | 6 | yes | — |
| 357 | #464 | C23 | 1 | 12 | yes | — |
| 358 | #463 | C23 | 1 | 2 | yes | — |
| 359 | #463 | C23 | 1 | 6 | yes | — |
| 360 | #463 | C23 | 1 | 6 | yes | — |
| 361 | #462 | C23 | 1 | 6 | yes | — |
| 362 | #462 | C23 | 1 | 6 | yes | — |
| 363 | #462 | C23 | 1 | 6 | yes | — |
| 364 | #462 | C23 | 1 | 12 | yes | — |
| 365 | #461 | C23 | 1 | 6 | yes | — |
| 366 | #461 | C23 | 1 | 6 | yes | — |
| 367 | #461 | C23 | 1 | 6 | yes | — |
| 368 | #452 | C23 | 1 | 6 | yes | — |
| 369 | #452 | C23 | 1 | 2 | yes | — |
| 370 | #452 | C23 | 1 | 6 | yes | — |
| 371 | #452 | C23 | 1 | 12 | yes | — |
| 372 | #450 | C23 | 1 | 6 | yes | — |
| 373 | #449 | C23 | 1 | 6 | yes | — |
| 374 | #447 | C23 | 1 | 2 | yes | — |
| 375 | #446 | C23 | 1 | 6 | yes | — |
| 376 | #446 | C23 | 1 | 6 | yes | — |
| 377 | #446 | C23 | 1 | 6 | yes | — |
| 378 | #446 | C23 | 1 | 3 | yes | — |
| 379 | #446 | C23 | 1 | 6 | yes | — |
| 380 | #446 | C23 | 1 | 6 | yes | — |
| 381 | #446 | C23 | 1 | 3 | yes | — |
| 382 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 383 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 384 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 385 | #442 | C23 | 1 | 6 | yes | — |
| 386 | #442 | C23 | 1 | 6 | yes | — |
| 387 | #441 | C23 | 1 | 12 | yes | — |
| 388 | #441 | C23 | 1 | 12 | yes | — |
| 389 | #441 | C23 | 1 | 12 | yes | — |
| 390 | #440 | C23 | 1 | 12 | yes | — |
| 391 | #440 | C23 | 1 | 6 | yes | — |
| 392 | #440 | C23 | 1 | 12 | yes | — |
| 393 | #440 | C23 | 1 | 12 | yes | — |
| 394 | #440 | C23 | 1 | 6 | yes | — |
| 395 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 396 | C4×Q16 | C23 | 1 | 3 | yes | — |
| 397 | C4×Q16 | C23 | 1 | 3 | yes | — |
| 398 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 399 | C4×Q16 | C23 | 1 | 3 | yes | — |
| 400 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 401 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 402 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 403 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 404 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 405 | C4×D8 | C23 | 1 | 3 | yes | — |
| 406 | C4×D8 | C23 | 1 | 6 | yes | — |
| 407 | C4×D8 | C23 | 1 | 3 | yes | — |
| 408 | C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 409 | #436 | C23 | 1 | 1 | yes | characteristic |
| 410 | #436 | C23 | 1 | 3 | yes | — |
| 411 | #435 | C23 | 1 | 6 | yes | — |
| 412 | #435 | C23 | 1 | 12 | yes | — |
| 413 | #435 | C23 | 1 | 6 | yes | — |
| 414 | C8×D4 | C23 | 1 | 3 | yes | — |
| 415 | C8×D4 | C23 | 1 | 6 | yes | — |
| 416 | C8×D4 | C23 | 1 | 3 | yes | — |
| 417 | #432 | C23 | 1 | 6 | yes | — |
| 418 | #432 | C23 | 1 | 12 | yes | — |
| 419 | #431 | C23 | 1 | 3 | yes | — |
| 420 | #431 | C23 | 1 | 6 | yes | — |
| 421 | #431 | C23 | 1 | 3 | yes | — |
| 422 | #428 | C23 | 1 | 12 | yes | — |
| 423 | #428 | C23 | 1 | 6 | yes | — |
| 424 | #427 | C23 | 1 | 12 | yes | — |
| 425 | #427 | C23 | 1 | 6 | yes | — |
| 426 | #427 | C23 | 1 | 6 | yes | — |
| 427 | #427 | C23 | 1 | 3 | yes | — |
| 428 | #423 | C23 | 1 | 6 | yes | — |
| 429 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 430 | C2×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 431 | #418 | C23 | 1 | 6 | yes | — |
| 432 | #417 | C23 | 1 | 6 | yes | — |
| 433 | #416 | C23 | 1 | 6 | yes | — |
| 434 | #416 | C23 | 1 | 12 | yes | — |
| 435 | C4×M16 | C23 | 1 | 6 | yes | — |
| 436 | C2×#97 | C23 | 1 | 6 | yes | — |
| 437 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 438 | 2−1+4 | — | 4 | 4 | no | — |
| 439 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 440 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 441 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 442 | C2×#41 | C24 | 1 | 6 | yes | — |
| 443 | C2×#41 | C24 | 1 | 2 | yes | — |
| 444 | C22×Q8 | — | 2 | 6 | no | — |
| 445 | C22×Q8 | — | 2 | 2 | no | — |
| 446 | C22×Q8 | — | 2 | 6 | no | — |
| 447 | C22×Q8 | — | 2 | 2 | no | — |
| 448 | C22×Q8 | — | 2 | 6 | no | — |
| 449 | C22×Q8 | — | 4 | 16 | no | — |
| 450 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 451 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 452 | C22×D4 | C24 | 1 | 2 | yes | — |
| 453 | C23×C4 | — | 2 | 6 | no | — |
| 454 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 455 | #135 | — | 2 | 12 | no | — |
| 456 | C2×Q16 | C24 | 1 | 3 | yes | — |
| 457 | C2×Q16 | C24 | 1 | 1 | yes | characteristic |
| 458 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 459 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 460 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 461 | C2×SD16 | C24 | 1 | 2 | yes | — |
| 462 | C2×SD16 | C24 | 1 | 2 | yes | — |
| 463 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 464 | C2×D8 | C24 | 1 | 2 | yes | — |
| 465 | C2×D8 | C24 | 1 | 1 | yes | characteristic |
| 466 | C2×D8 | C24 | 1 | 1 | yes | characteristic |
| 467 | C2×M16 | C24 | 1 | 2 | yes | — |
| 468 | C2×M16 | C24 | 1 | 6 | yes | — |
| 469 | C22×C8 | C24 | 1 | 3 | yes | — |
| 470 | C22×C8 | C24 | 1 | 3 | yes | — |
| 471 | C22×C8 | C24 | 1 | 6 | yes | — |
| 472 | C4⋊Q8 | — | 2 | 6 | no | — |
| 473 | C4⋊Q8 | — | 2 | 6 | no | — |
| 474 | C4⋊Q8 | — | 2 | 12 | no | — |
| 475 | C4⋊Q8 | — | 2 | 6 | no | — |
| 476 | C4⋊Q8 | — | 2 | 6 | no | — |
| 477 | C4⋊Q8 | — | 2 | 12 | no | — |
| 478 | C4⋊Q8 | — | 2 | 6 | no | — |
| 479 | C4⋊Q8 | — | 2 | 6 | no | — |
| 480 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 481 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 482 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 483 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 484 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 485 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 486 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 487 | #126 | — | 2 | 6 | no | — |
| 488 | #126 | — | 2 | 12 | no | — |
| 489 | #126 | — | 2 | 6 | no | — |
| 490 | #126 | — | 2 | 6 | no | — |
| 491 | #126 | — | 2 | 6 | no | — |
| 492 | #126 | — | 2 | 12 | no | — |
| 493 | #126 | — | 2 | 12 | no | — |
| 494 | #126 | — | 2 | 12 | no | — |
| 495 | #126 | — | 2 | 12 | no | — |
| 496 | #126 | — | 2 | 12 | no | — |
| 497 | #126 | — | 2 | 12 | no | — |
| 498 | #126 | — | 2 | 6 | no | — |
| 499 | #126 | — | 2 | 6 | no | — |
| 500 | #125 | — | 2 | 6 | no | — |
| 501 | #125 | — | 2 | 12 | no | — |
| 502 | #125 | — | 2 | 6 | no | — |
| 503 | #125 | — | 2 | 6 | no | — |
| 504 | #125 | — | 2 | 6 | no | — |
| 505 | #125 | — | 2 | 12 | no | — |
| 506 | #125 | — | 2 | 12 | no | — |
| 507 | #125 | — | 2 | 12 | no | — |
| 508 | #125 | — | 2 | 12 | no | — |
| 509 | #125 | — | 2 | 12 | no | — |
| 510 | #125 | — | 2 | 12 | no | — |
| 511 | #125 | — | 2 | 6 | no | — |
| 512 | #125 | — | 2 | 6 | no | — |
| 513 | #125 | — | 2 | 6 | no | — |
| 514 | #125 | — | 2 | 6 | no | — |
| 515 | #125 | C24 | 1 | 6 | yes | — |
| 516 | #125 | C24 | 1 | 12 | yes | — |
| 517 | #125 | C24 | 1 | 6 | yes | — |
| 518 | #124 | — | 2 | 6 | no | — |
| 519 | #124 | — | 2 | 6 | no | — |
| 520 | #124 | — | 2 | 12 | no | — |
| 521 | #124 | — | 2 | 6 | no | — |
| 522 | #124 | — | 2 | 6 | no | — |
| 523 | #124 | — | 2 | 12 | no | — |
| 524 | #124 | C24 | 1 | 6 | yes | — |
| 525 | #124 | C24 | 1 | 2 | yes | — |
| 526 | #123 | — | 2 | 6 | no | — |
| 527 | #123 | — | 2 | 6 | no | — |
| 528 | #123 | — | 2 | 12 | no | — |
| 529 | #123 | — | 2 | 6 | no | — |
| 530 | #123 | — | 2 | 6 | no | — |
| 531 | #123 | — | 2 | 12 | no | — |
| 532 | #123 | — | 2 | 6 | no | — |
| 533 | #123 | — | 2 | 2 | no | — |
| 534 | #123 | — | 2 | 6 | no | — |
| 535 | #123 | — | 2 | 6 | no | — |
| 536 | #123 | — | 2 | 12 | no | — |
| 537 | C22⋊Q8 | — | 2 | 6 | no | — |
| 538 | C22⋊Q8 | — | 2 | 6 | no | — |
| 539 | C22⋊Q8 | — | 2 | 6 | no | — |
| 540 | C22⋊Q8 | — | 2 | 6 | no | — |
| 541 | C22⋊Q8 | — | 2 | 6 | no | — |
| 542 | C22⋊Q8 | — | 2 | 6 | no | — |
| 543 | C22⋊Q8 | — | 2 | 12 | no | — |
| 544 | C22⋊Q8 | — | 2 | 6 | no | — |
| 545 | C22⋊Q8 | — | 2 | 6 | no | — |
| 546 | C22⋊Q8 | — | 2 | 12 | no | — |
| 547 | C22⋊Q8 | — | 2 | 6 | no | — |
| 548 | C22⋊Q8 | — | 2 | 6 | no | — |
| 549 | C22⋊Q8 | — | 2 | 12 | no | — |
| 550 | C22⋊Q8 | — | 2 | 6 | no | — |
| 551 | C22⋊Q8 | — | 2 | 6 | no | — |
| 552 | C22⋊Q8 | — | 2 | 6 | no | — |
| 553 | C22⋊Q8 | — | 2 | 6 | no | — |
| 554 | C22⋊Q8 | — | 2 | 12 | no | — |
| 555 | C22⋊Q8 | — | 2 | 6 | no | — |
| 556 | C22⋊Q8 | — | 2 | 6 | no | — |
| 557 | C22⋊Q8 | — | 2 | 12 | no | — |
| 558 | C22⋊Q8 | — | 2 | 6 | no | — |
| 559 | C22⋊Q8 | — | 2 | 12 | no | — |
| 560 | C22⋊Q8 | — | 2 | 6 | no | — |
| 561 | C22⋊Q8 | C24 | 1 | 6 | yes | — |
| 562 | C22⋊Q8 | C24 | 1 | 6 | yes | — |
| 563 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 564 | C22⋊Q8 | C24 | 1 | 2 | yes | — |
| 565 | C22⋊Q8 | C24 | 1 | 6 | yes | — |
| 566 | #121 | — | 2 | 6 | no | — |
| 567 | #121 | — | 2 | 6 | no | — |
| 568 | #121 | — | 2 | 6 | no | — |
| 569 | #121 | — | 2 | 6 | no | — |
| 570 | #121 | — | 2 | 2 | no | — |
| 571 | #121 | — | 2 | 6 | no | — |
| 572 | #121 | C24 | 1 | 2 | yes | — |
| 573 | #121 | C24 | 1 | 6 | yes | — |
| 574 | #120 | — | 2 | 2 | no | — |
| 575 | #120 | — | 2 | 6 | no | — |
| 576 | C4×Q8 | — | 2 | 6 | no | — |
| 577 | C4×Q8 | — | 2 | 2 | no | — |
| 578 | C4×Q8 | — | 2 | 6 | no | — |
| 579 | C4×Q8 | — | 2 | 2 | no | — |
| 580 | C4×Q8 | — | 2 | 6 | no | — |
| 581 | C4×Q8 | — | 2 | 6 | no | — |
| 582 | C4×Q8 | — | 2 | 12 | no | — |
| 583 | C4×Q8 | — | 2 | 6 | no | — |
| 584 | C4×Q8 | — | 2 | 6 | no | — |
| 585 | C4×Q8 | — | 2 | 12 | no | — |
| 586 | C4×Q8 | — | 2 | 6 | no | — |
| 587 | C4×Q8 | — | 2 | 12 | no | — |
| 588 | C4×Q8 | — | 2 | 6 | no | — |
| 589 | C4×Q8 | — | 2 | 6 | no | — |
| 590 | C4×Q8 | — | 2 | 12 | no | — |
| 591 | C4×Q8 | — | 2 | 6 | no | — |
| 592 | C4×Q8 | — | 2 | 6 | no | — |
| 593 | C4×Q8 | — | 2 | 6 | no | — |
| 594 | C4×Q8 | — | 2 | 12 | no | — |
| 595 | C4×Q8 | — | 2 | 6 | no | — |
| 596 | C4×Q8 | — | 2 | 6 | no | — |
| 597 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 598 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 599 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 600 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 601 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 602 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 603 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 604 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 605 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 606 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 607 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 608 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 609 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 610 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 611 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 612 | C4×Q8 | C24 | 1 | 3 | yes | — |
| 613 | C4×D4 | — | 2 | 6 | no | — |
| 614 | C4×D4 | — | 2 | 6 | no | — |
| 615 | C4×D4 | — | 2 | 12 | no | — |
| 616 | C4×D4 | — | 2 | 6 | no | — |
| 617 | C4×D4 | — | 2 | 6 | no | — |
| 618 | C4×D4 | — | 2 | 12 | no | — |
| 619 | C4×D4 | — | 2 | 6 | no | — |
| 620 | C4×D4 | — | 2 | 6 | no | — |
| 621 | C4×D4 | — | 2 | 12 | no | — |
| 622 | C4×D4 | — | 2 | 6 | no | — |
| 623 | C4×D4 | — | 2 | 6 | no | — |
| 624 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 625 | C4×D4 | C2×D4 | 1 | 12 | yes | — |
| 626 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 627 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 628 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 629 | C4×D4 | C24 | 1 | 6 | yes | — |
| 630 | C4×D4 | C24 | 1 | 6 | yes | — |
| 631 | C4×D4 | C24 | 1 | 6 | yes | — |
| 632 | C4×D4 | C24 | 1 | 6 | yes | — |
| 633 | C4×D4 | C24 | 1 | 2 | yes | — |
| 634 | C4×D4 | C24 | 1 | 6 | yes | — |
| 635 | C4×D4 | C24 | 1 | 1 | yes | characteristic |
| 636 | C4×D4 | C24 | 1 | 6 | yes | — |
| 637 | C4×D4 | C24 | 1 | 3 | yes | — |
| 638 | #117 | — | 2 | 6 | no | — |
| 639 | #117 | — | 2 | 6 | no | — |
| 640 | #117 | — | 2 | 6 | no | — |
| 641 | #117 | — | 2 | 12 | no | — |
| 642 | #117 | — | 2 | 6 | no | — |
| 643 | #117 | — | 2 | 6 | no | — |
| 644 | #117 | — | 2 | 6 | no | — |
| 645 | #117 | — | 2 | 6 | no | — |
| 646 | #117 | — | 2 | 6 | no | — |
| 647 | #117 | — | 2 | 6 | no | — |
| 648 | #117 | — | 2 | 6 | no | — |
| 649 | #117 | — | 2 | 12 | no | — |
| 650 | #117 | — | 2 | 6 | no | — |
| 651 | #117 | — | 2 | 12 | no | — |
| 652 | #117 | — | 2 | 6 | no | — |
| 653 | #117 | — | 2 | 12 | no | — |
| 654 | #117 | — | 2 | 6 | no | — |
| 655 | #117 | — | 2 | 6 | no | — |
| 656 | #117 | C2×D4 | 1 | 6 | yes | — |
| 657 | #117 | C2×D4 | 1 | 6 | yes | — |
| 658 | #117 | C2×D4 | 1 | 3 | yes | — |
| 659 | #117 | C2×D4 | 1 | 12 | yes | — |
| 660 | #117 | C2×D4 | 1 | 3 | yes | — |
| 661 | #117 | C24 | 1 | 6 | yes | — |
| 662 | #117 | C24 | 1 | 12 | yes | — |
| 663 | #117 | C24 | 1 | 6 | yes | — |
| 664 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 665 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 666 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 667 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 668 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 669 | C2×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 670 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 671 | C2×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 672 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 673 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 674 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 675 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 676 | C2×C42 | — | 2 | 6 | no | — |
| 677 | C2×C42 | — | 2 | 12 | no | — |
| 678 | C2×C42 | — | 2 | 6 | no | — |
| 679 | C2×C42 | C24 | 1 | 6 | yes | — |
| 680 | C2×C42 | C24 | 1 | 3 | yes | — |
| 681 | C2×C42 | C24 | 1 | 6 | yes | — |
| 682 | #107 | C24 | 1 | 1 | yes | characteristic |
| 683 | #107 | C24 | 1 | 3 | yes | — |
| 684 | #107 | C24 | 1 | 3 | yes | — |
| 685 | #107 | C24 | 1 | 6 | yes | — |
| 686 | #107 | C24 | 1 | 3 | yes | — |
| 687 | #107 | C24 | 1 | 12 | yes | — |
| 688 | #107 | C24 | 1 | 6 | yes | — |
| 689 | #107 | C24 | 1 | 6 | yes | — |
| 690 | #107 | C24 | 1 | 6 | yes | — |
| 691 | #107 | C24 | 1 | 6 | yes | — |
| 692 | #106 | C24 | 1 | 6 | yes | — |
| 693 | #106 | C24 | 1 | 6 | yes | — |
| 694 | #106 | C24 | 1 | 12 | yes | — |
| 695 | #106 | C24 | 1 | 12 | yes | — |
| 696 | #106 | C24 | 1 | 6 | yes | — |
| 697 | #106 | C24 | 1 | 6 | yes | — |
| 698 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 699 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 700 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 701 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 702 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 703 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 704 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 705 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 706 | #103 | C24 | 1 | 6 | yes | — |
| 707 | #103 | C24 | 1 | 6 | yes | — |
| 708 | #103 | C24 | 1 | 12 | yes | — |
| 709 | #103 | C24 | 1 | 12 | yes | — |
| 710 | #103 | C24 | 1 | 6 | yes | — |
| 711 | #103 | C24 | 1 | 6 | yes | — |
| 712 | #103 | C24 | 1 | 6 | yes | — |
| 713 | #103 | C24 | 1 | 2 | yes | — |
| 714 | #103 | C24 | 1 | 12 | yes | — |
| 715 | #103 | C24 | 1 | 6 | yes | — |
| 716 | #103 | C24 | 1 | 6 | yes | — |
| 717 | #102 | C24 | 1 | 2 | yes | — |
| 718 | #102 | C24 | 1 | 6 | yes | — |
| 719 | #102 | C24 | 1 | 6 | yes | — |
| 720 | #102 | C24 | 1 | 6 | yes | — |
| 721 | #102 | C24 | 1 | 6 | yes | — |
| 722 | #102 | C24 | 1 | 6 | yes | — |
| 723 | #102 | C24 | 1 | 6 | yes | — |
| 724 | #102 | C24 | 1 | 2 | yes | — |
| 725 | C22⋊C8 | C24 | 1 | 2 | yes | — |
| 726 | C22⋊C8 | C24 | 1 | 6 | yes | — |
| 727 | C22⋊C8 | C24 | 1 | 6 | yes | — |
| 728 | C22⋊C8 | C24 | 1 | 6 | yes | — |
| 729 | #97 | C24 | 1 | 6 | yes | — |
| 730 | #97 | C24 | 1 | 12 | yes | — |
| 731 | #97 | C24 | 1 | 6 | yes | — |
| 732 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 733 | C4×C8 | C24 | 1 | 3 | yes | — |
| 734 | C4×C8 | C24 | 1 | 3 | yes | — |
| 735 | C4×C8 | C24 | 1 | 3 | yes | — |
| 736 | C4×C8 | C24 | 1 | 6 | yes | — |
| 737 | C24 | — | 2 | 2 | no | — |
| 738 | #41 | — | 2 | 4 | no | — |
| 739 | #41 | — | 2 | 12 | no | — |
| 740 | #41 | — | 2 | 4 | no | — |
| 741 | #41 | — | 4 | 6 | no | — |
| 742 | #41 | — | 4 | 12 | no | — |
| 743 | #41 | — | 4 | 6 | no | — |
| 744 | #41 | — | 4 | 2 | no | — |
| 745 | C2×Q8 | — | 2 | 8 | no | — |
| 746 | C2×Q8 | — | 2 | 12 | no | — |
| 747 | C2×Q8 | — | 2 | 6 | no | — |
| 748 | C2×Q8 | — | 2 | 6 | no | — |
| 749 | C2×Q8 | — | 2 | 6 | no | — |
| 750 | C2×Q8 | — | 2 | 6 | no | — |
| 751 | C2×Q8 | — | 4 | 6 | no | — |
| 752 | C2×Q8 | — | 4 | 24 | no | — |
| 753 | C2×Q8 | — | 4 | 24 | no | — |
| 754 | C2×Q8 | — | 4 | 24 | no | — |
| 755 | C2×Q8 | — | 4 | 8 | no | — |
| 756 | C2×Q8 | — | 4 | 8 | no | — |
| 757 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 758 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 759 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 760 | C2×Q8 | C25 | 1 | 2 | yes | — |
| 761 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 762 | C2×D4 | — | 2 | 4 | no | — |
| 763 | C2×D4 | — | 2 | 6 | no | — |
| 764 | C2×D4 | — | 2 | 2 | no | — |
| 765 | C2×D4 | — | 2 | 6 | no | — |
| 766 | C2×D4 | — | 2 | 2 | no | — |
| 767 | C2×D4 | — | 2 | 2 | no | — |
| 768 | C2×D4 | — | 4 | 2 | no | — |
| 769 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 770 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 771 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 772 | C2×D4 | C25 | 1 | 2 | yes | — |
| 773 | C2×D4 | C25 | 1 | 2 | yes | — |
| 774 | C22×C4 | — | 2 | 6 | no | — |
| 775 | C22×C4 | — | 2 | 6 | no | — |
| 776 | C22×C4 | — | 2 | 2 | no | — |
| 777 | C22×C4 | — | 2 | 6 | no | — |
| 778 | C22×C4 | — | 2 | 6 | no | — |
| 779 | C22×C4 | — | 2 | 6 | no | — |
| 780 | C22×C4 | — | 2 | 6 | no | — |
| 781 | C22×C4 | — | 2 | 2 | no | — |
| 782 | C22×C4 | — | 2 | 6 | no | — |
| 783 | C22×C4 | — | 4 | 24 | no | — |
| 784 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 785 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 786 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 787 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 788 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 789 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 790 | C22×C4 | C25 | 1 | 2 | yes | — |
| 791 | C22×C4 | C25 | 1 | 3 | yes | — |
| 792 | Q16 | — | 2 | 6 | no | — |
| 793 | Q16 | — | 4 | 1 | no | — |
| 794 | Q16 | — | 4 | 6 | no | — |
| 795 | Q16 | — | 4 | 6 | no | — |
| 796 | SD16 | — | 2 | 12 | no | — |
| 797 | SD16 | — | 2 | 4 | no | — |
| 798 | SD16 | — | 2 | 4 | no | — |
| 799 | SD16 | — | 4 | 6 | no | — |
| 800 | D8 | — | 2 | 4 | no | — |
| 801 | D8 | — | 4 | 1 | no | — |
| 802 | D8 | 2−1+4 | 1 | 4 | yes | complemented |
| 803 | M16 | — | 2 | 4 | no | — |
| 804 | M16 | — | 4 | 6 | no | — |
| 805 | C2×C8 | — | 2 | 6 | no | — |
| 806 | C2×C8 | — | 4 | 3 | no | — |
| 807 | C2×C8 | — | 4 | 6 | no | — |
| 808 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 809 | C2×C8 | C25 | 1 | 2 | yes | — |
| 810 | C2×C8 | C25 | 1 | 3 | yes | — |
| 811 | C2×C8 | C25 | 1 | 3 | yes | — |
| 812 | C2×C8 | C25 | 1 | 6 | yes | — |
| 813 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 814 | C4⋊C4 | — | 2 | 6 | no | — |
| 815 | C4⋊C4 | — | 2 | 6 | no | — |
| 816 | C4⋊C4 | — | 2 | 6 | no | — |
| 817 | C4⋊C4 | — | 2 | 6 | no | — |
| 818 | C4⋊C4 | — | 2 | 6 | no | — |
| 819 | C4⋊C4 | — | 2 | 12 | no | — |
| 820 | C4⋊C4 | — | 2 | 6 | no | — |
| 821 | C4⋊C4 | — | 2 | 12 | no | — |
| 822 | C4⋊C4 | — | 2 | 6 | no | — |
| 823 | C4⋊C4 | — | 2 | 6 | no | — |
| 824 | C4⋊C4 | — | 2 | 12 | no | — |
| 825 | C4⋊C4 | — | 2 | 6 | no | — |
| 826 | C4⋊C4 | — | 2 | 6 | no | — |
| 827 | C4⋊C4 | — | 2 | 6 | no | — |
| 828 | C4⋊C4 | — | 2 | 6 | no | — |
| 829 | C4⋊C4 | — | 2 | 6 | no | — |
| 830 | C4⋊C4 | — | 2 | 12 | no | — |
| 831 | C4⋊C4 | — | 2 | 6 | no | — |
| 832 | C4⋊C4 | — | 2 | 6 | no | — |
| 833 | C4⋊C4 | — | 2 | 12 | no | — |
| 834 | C4⋊C4 | — | 2 | 6 | no | — |
| 835 | C4⋊C4 | — | 2 | 6 | no | — |
| 836 | C4⋊C4 | — | 2 | 6 | no | — |
| 837 | C4⋊C4 | — | 2 | 12 | no | — |
| 838 | C4⋊C4 | — | 2 | 6 | no | — |
| 839 | C4⋊C4 | — | 2 | 2 | no | — |
| 840 | C4⋊C4 | — | 2 | 6 | no | — |
| 841 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 842 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 843 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 844 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 845 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 846 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 847 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 848 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 849 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 850 | C4⋊C4 | C25 | 1 | 6 | yes | — |
| 851 | C4⋊C4 | C25 | 1 | 6 | yes | — |
| 852 | C4⋊C4 | C25 | 1 | 6 | yes | — |
| 853 | C22⋊C4 | — | 2 | 2 | no | — |
| 854 | C22⋊C4 | — | 2 | 6 | no | — |
| 855 | C22⋊C4 | — | 2 | 6 | no | — |
| 856 | C22⋊C4 | — | 2 | 12 | no | — |
| 857 | C22⋊C4 | — | 2 | 6 | no | — |
| 858 | C22⋊C4 | — | 2 | 6 | no | — |
| 859 | C22⋊C4 | — | 2 | 12 | no | — |
| 860 | C22⋊C4 | — | 2 | 6 | no | — |
| 861 | C22⋊C4 | — | 2 | 2 | no | — |
| 862 | C22⋊C4 | — | 2 | 6 | no | — |
| 863 | C22⋊C4 | — | 2 | 6 | no | — |
| 864 | C22⋊C4 | — | 2 | 2 | no | — |
| 865 | C22⋊C4 | — | 2 | 6 | no | — |
| 866 | C22⋊C4 | — | 2 | 6 | no | — |
| 867 | C22⋊C4 | — | 2 | 6 | no | — |
| 868 | C22⋊C4 | — | 2 | 6 | no | — |
| 869 | C22⋊C4 | — | 2 | 6 | no | — |
| 870 | C22⋊C4 | — | 2 | 2 | no | — |
| 871 | C22⋊C4 | — | 2 | 6 | no | — |
| 872 | C22⋊C4 | — | 2 | 2 | no | — |
| 873 | C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 874 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 875 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 876 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 877 | C42 | — | 2 | 6 | no | — |
| 878 | C42 | — | 2 | 12 | no | — |
| 879 | C42 | — | 2 | 6 | no | — |
| 880 | C42 | — | 2 | 6 | no | — |
| 881 | C42 | — | 2 | 12 | no | — |
| 882 | C42 | — | 2 | 6 | no | — |
| 883 | C42 | — | 2 | 12 | no | — |
| 884 | C42 | — | 2 | 6 | no | — |
| 885 | C42 | — | 2 | 6 | no | — |
| 886 | C42 | C22×D4 | 1 | 3 | yes | — |
| 887 | C42 | C22×D4 | 1 | 12 | yes | — |
| 888 | C42 | C22×D4 | 1 | 6 | yes | — |
| 889 | C42 | C22×D4 | 1 | 3 | yes | — |
| 890 | C42 | C22×D4 | 1 | 6 | yes | — |
| 891 | C42 | C25 | 1 | 3 | yes | — |
| 892 | C42 | C25 | 1 | 1 | yes | characteristic |
| 893 | C42 | C25 | 1 | 6 | yes | — |
| 894 | C23 | — | 2 | 2 | no | — |
| 895 | C23 | — | 2 | 2 | no | — |
| 896 | C23 | — | 4 | 4 | no | — |
| 897 | C23 | — | 4 | 4 | no | — |
| 898 | C23 | — | 8 | 2 | no | — |
| 899 | C23 | C23×D4 | 1 | 3 | yes | — |
| 900 | C23 | C23×D4 | 1 | 2 | yes | — |
| 901 | Q8 | — | 2 | 12 | no | — |
| 902 | Q8 | — | 2 | 2 | no | — |
| 903 | Q8 | — | 2 | 6 | no | — |
| 904 | Q8 | — | 2 | 6 | no | — |
| 905 | Q8 | — | 2 | 2 | no | — |
| 906 | Q8 | — | 4 | 3 | no | — |
| 907 | Q8 | — | 4 | 24 | no | — |
| 908 | Q8 | — | 4 | 12 | no | — |
| 909 | Q8 | — | 4 | 12 | no | — |
| 910 | Q8 | — | 8 | 6 | no | — |
| 911 | Q8 | — | 8 | 6 | no | — |
| 912 | Q8 | #575 | 1 | 4 | yes | — |
| 913 | D4 | — | 2 | 2 | no | — |
| 914 | D4 | — | 2 | 2 | no | — |
| 915 | D4 | — | 2 | 2 | no | — |
| 916 | D4 | — | 2 | 6 | no | — |
| 917 | D4 | — | 4 | 1 | no | — |
| 918 | D4 | — | 4 | 6 | no | — |
| 919 | D4 | — | 4 | 4 | no | — |
| 920 | D4 | — | 4 | 12 | no | — |
| 921 | D4 | — | 4 | 4 | no | — |
| 922 | D4 | — | 8 | 6 | no | — |
| 923 | D4 | — | 8 | 2 | no | — |
| 924 | D4 | C2×2−1+4 | 1 | 4 | yes | — |
| 925 | C2×C4 | — | 2 | 3 | no | — |
| 926 | C2×C4 | — | 2 | 2 | no | — |
| 927 | C2×C4 | — | 2 | 3 | no | — |
| 928 | C2×C4 | — | 2 | 2 | no | — |
| 929 | C2×C4 | — | 2 | 12 | no | — |
| 930 | C2×C4 | — | 2 | 6 | no | — |
| 931 | C2×C4 | — | 2 | 2 | no | — |
| 932 | C2×C4 | — | 2 | 6 | no | — |
| 933 | C2×C4 | — | 2 | 2 | no | — |
| 934 | C2×C4 | — | 2 | 6 | no | — |
| 935 | C2×C4 | — | 2 | 6 | no | — |
| 936 | C2×C4 | — | 2 | 6 | no | — |
| 937 | C2×C4 | — | 4 | 3 | no | — |
| 938 | C2×C4 | — | 4 | 6 | no | — |
| 939 | C2×C4 | — | 4 | 6 | no | — |
| 940 | C2×C4 | — | 4 | 6 | no | — |
| 941 | C2×C4 | — | 4 | 12 | no | — |
| 942 | C2×C4 | — | 4 | 4 | no | — |
| 943 | C2×C4 | — | 4 | 12 | no | — |
| 944 | C2×C4 | — | 4 | 12 | no | — |
| 945 | C2×C4 | — | 4 | 12 | no | — |
| 946 | C2×C4 | — | 4 | 12 | no | — |
| 947 | C2×C4 | — | 4 | 12 | no | — |
| 948 | C2×C4 | — | 8 | 2 | no | — |
| 949 | C2×C4 | — | 8 | 6 | no | — |
| 950 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 951 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 952 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 953 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 954 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 955 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 956 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 957 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 958 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 959 | C8 | — | 2 | 3 | no | — |
| 960 | C8 | — | 2 | 2 | no | — |
| 961 | C8 | — | 2 | 1 | no | — |
| 962 | C8 | — | 2 | 6 | no | — |
| 963 | C8 | — | 2 | 3 | no | — |
| 964 | C8 | C2×2−1+4 | 1 | 2 | yes | — |
| 965 | C22 | — | 2 | 3 | no | — |
| 966 | C22 | — | 2 | 2 | no | — |
| 967 | C22 | — | 2 | 4 | no | — |
| 968 | C22 | — | 2 | 2 | no | — |
| 969 | C22 | — | 2 | 3 | no | — |
| 970 | C22 | — | 2 | 3 | no | — |
| 971 | C22 | — | 2 | 2 | no | — |
| 972 | C22 | — | 4 | 2 | no | — |
| 973 | C22 | — | 4 | 2 | no | — |
| 974 | C22 | — | 4 | 2 | no | — |
| 975 | C22 | — | 4 | 2 | no | — |
| 976 | C22 | — | 4 | 2 | no | — |
| 977 | C22 | — | 8 | 8 | no | — |
| 978 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 979 | C4 | — | 2 | 3 | no | — |
| 980 | C4 | — | 2 | 2 | no | — |
| 981 | C4 | — | 2 | 1 | no | — |
| 982 | C4 | — | 2 | 6 | no | — |
| 983 | C4 | — | 2 | 1 | no | — |
| 984 | C4 | — | 2 | 6 | no | — |
| 985 | C4 | — | 2 | 3 | no | — |
| 986 | C4 | — | 4 | 2 | no | — |
| 987 | C4 | — | 4 | 6 | no | — |
| 988 | C4 | — | 4 | 6 | no | — |
| 989 | C4 | — | 4 | 6 | no | — |
| 990 | C4 | — | 4 | 2 | no | — |
| 991 | C4 | — | 4 | 6 | no | — |
| 992 | C4 | C2×#575 | 1 | 6 | yes | — |
| 993 | C4 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 994 | C4 | 2−1+6 | 1 | 1 | yes | characteristic |
| 995 | C2 | — | 4 | 3 | no | — |
| 996 | C2 | — | 4 | 2 | no | — |
| 997 | C2 | — | 4 | 4 | no | — |
| 998 | C2 | — | 8 | 2 | no | — |
| 999 | C2 | D4×2−1+4 | 1 | 1 | yes | characteristic |
| 1000 | C2 | C22×#575 | 1 | 1 | yes | characteristic |
| 1001 | C2 | #63093 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×2−1+4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62998 | C2 | semidirect |
| 2. #62507 | C2 | semidirect |
| 3. #62482 | C2 | semidirect |
| 4. #62476 | C2 | semidirect |
| 5. #62398 | C2 | semidirect |
| 6. #62369 | C2 | semidirect |
| 7. #62141 | C2 | semidirect |
| 8. #62133 | C2 | semidirect |
| 9. #62116 | C2 | semidirect |
| 10. #62105 | C2 | semidirect |
| 11. #61846 | C2 | semidirect |
| 12. #61837 | C2 | semidirect |
| 13. #61834 | C2 | semidirect |
| 14. #61461 | C2 | semidirect |
| 15. #61442 | C2 | semidirect |
| 16. #61435 | C2 | semidirect |
| 17. Q8×AGL(1,ℤ/8) | C2 | semidirect |
| 18. #61365 | C2 | semidirect |
| 19. #60343 | C2 | semidirect |
| 23. #3523 | C22 | semidirect |
| 25. #3518 | C22 | semidirect |
| 29. #3509 | C22 | semidirect |
| 30. #3502 | C22 | semidirect |
| 35. #3482 | C22 | semidirect |
| 37. Q8×#41 | C22 | semidirect |
| 39. #3475 | C22 | semidirect |
| 40. C2×D4×Q8 | C22 | semidirect |
| 44. #3398 | C22 | semidirect |
| 45. #3395 | C22 | semidirect |
| 46. #3390 | C22 | semidirect |
| 47. #3390 | C22 | semidirect |
| 49. #3388 | C22 | semidirect |
| 50. #3387 | C22 | semidirect |
| 51. #3387 | C22 | semidirect |
| 52. #3386 | C22 | semidirect |
| 53. #3386 | C22 | semidirect |
| 54. #3386 | C22 | semidirect |
| 55. #3386 | C22 | semidirect |
| 56. #3385 | C22 | semidirect |
| 59. Q8×Q16 | C22 | semidirect |
| 60. Q8×SD16 | C22 | semidirect |
| 61. Q8×SD16 | C22 | semidirect |
| 65. #3377 | C22 | semidirect |
| 67. #3374 | C22 | semidirect |
| 68. #3374 | C22 | semidirect |
| 69. #3372 | C22 | semidirect |
| 70. #3369 | C22 | semidirect |
| 73. #3363 | C22 | semidirect |
| 74. #3359 | C22 | semidirect |
| 75. #3359 | C22 | semidirect |
| 78. #3349 | C22 | semidirect |
| 79. #3349 | C22 | semidirect |
| 80. #3349 | C22 | semidirect |
| 83. #3342 | C22 | semidirect |
| 84. #3342 | C22 | semidirect |
| 85. #3342 | C22 | semidirect |
| 87. #3340 | C22 | semidirect |
| 88. #3340 | C22 | semidirect |
| 93. #3311 | C22 | semidirect |
| 95. #3302 | C22 | semidirect |
| 96. #3302 | C22 | semidirect |
| 100. #3255 | C22 | semidirect |
| 103. #3249 | C22 | semidirect |
| 104. #3248 | C22 | semidirect |
| 105. #3240 | C22 | semidirect |
| 107. #3237 | C22 | semidirect |
| 108. #3237 | C22 | semidirect |
| 109. #3233 | C22 | semidirect |
| 110. #3231 | C22 | semidirect |
| 111. #3231 | C22 | semidirect |
| 112. #3230 | C22 | semidirect |
| 113. #3185 | C22 | semidirect |
| 114. #3181 | C22 | semidirect |
| 116. #3170 | C22 | semidirect |
| 118. #3165 | C22 | semidirect |
| 119. #3162 | C22 | semidirect |
| 120. #3160 | C22 | semidirect |
| 122. #3116 | C22 | semidirect |
| 124. #3110 | C22 | semidirect |
| 126. #3107 | C22 | semidirect |
| 130. #3077 | C22 | semidirect |
| 131. #3076 | C22 | semidirect |
| 132. #3076 | C22 | semidirect |
| 133. #2990 | C22 | semidirect |
| 135. #2988 | C22 | semidirect |
| 136. #2984 | C22 | semidirect |
| 137. #2983 | C22 | semidirect |
| 138. #2970 | C22 | semidirect |
| 140. C8×#41 | C22 | semidirect |
| 141. Q8×M16 | C22 | semidirect |
| 142. C2×#446 | C22 | semidirect |
| 802. D8 | 2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62998 | 2 |
| #62507 | 2 |
| #62482 | 2 |
| #62476 | 2 |
| #62398 | 2 |
| #62369 | 2 |
| #62141 | 2 |
| #62133 | 2 |
| #62116 | 2 |
| #62105 | 2 |
| #61846 | 2 |
| #61837 | 2 |
| #61834 | 2 |
| #61461 | 2 |
| #61442 | 2 |
| #61435 | 2 |
| Q8×AGL(1,ℤ/8) | 2 |
| #61365 | 2 |
| #60343 | 2 |