Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
7321 conjugacy classes of subgroups.
The subgroup lattice has 942 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #62800 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #62595 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #62583 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #62541 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #62538 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #62529 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #62526 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #61317 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #61161 | C2 | 1 | 12 | yes | maximal, complemented |
| 11 | #60860 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #60803 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #60700 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | C2×#3141 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | M16×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×2−1+4 | — | 2 | 1 | no | — |
| 17 | #3522 | — | 2 | 1 | no | — |
| 18 | #3519 | — | 2 | 3 | no | — |
| 19 | #3517 | C22 | 1 | 2 | yes | complemented |
| 20 | #3514 | C22 | 1 | 6 | yes | complemented |
| 21 | #3511 | C22 | 1 | 3 | yes | complemented |
| 22 | #3508 | C22 | 1 | 3 | yes | complemented |
| 23 | #3503 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #3499 | — | 2 | 1 | no | — |
| 25 | #3499 | — | 2 | 3 | no | — |
| 26 | #3499 | — | 2 | 3 | no | — |
| 27 | #3499 | — | 2 | 1 | no | — |
| 28 | #3499 | C22 | 1 | 2 | yes | — |
| 29 | #3499 | C22 | 1 | 6 | yes | complemented |
| 30 | #3499 | C22 | 1 | 6 | yes | complemented |
| 31 | #3499 | C22 | 1 | 2 | yes | complemented |
| 32 | #3498 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #3494 | — | 2 | 3 | no | — |
| 34 | #3488 | — | 2 | 1 | no | — |
| 35 | #3483 | — | 2 | 1 | no | — |
| 36 | #3481 | — | 2 | 3 | no | — |
| 37 | #3480 | C22 | 1 | 2 | yes | — |
| 38 | D4×#41 | C22 | 1 | 6 | yes | — |
| 39 | C2×D4×Q8 | — | 2 | 1 | no | — |
| 40 | C2×D4×Q8 | C22 | 1 | 2 | yes | complemented |
| 41 | C2×#547 | — | 2 | 3 | no | — |
| 42 | C2×#547 | C22 | 1 | 6 | yes | complemented |
| 43 | #3460 | — | 2 | 3 | no | — |
| 44 | C2×#536 | — | 2 | 3 | no | — |
| 45 | #3444 | C22 | 1 | 3 | yes | — |
| 46 | C2×#532 | C22 | 1 | 3 | yes | — |
| 47 | C2×#532 | C22 | 1 | 3 | yes | complemented |
| 48 | C22×C4⋊Q8 | C22 | 1 | 3 | yes | complemented |
| 49 | C4×H(5,𝔽2) | — | 2 | 1 | no | — |
| 50 | C2×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 51 | #3373 | C22 | 1 | 24 | yes | complemented |
| 52 | #3367 | C22 | 1 | 24 | yes | complemented |
| 53 | #3359 | C22 | 1 | 8 | yes | complemented |
| 54 | #3358 | C22 | 1 | 8 | yes | complemented |
| 55 | #3332 | C22 | 1 | 24 | yes | complemented |
| 56 | #3330 | C22 | 1 | 24 | yes | complemented |
| 57 | #3308 | C22 | 1 | 48 | yes | complemented |
| 58 | #3306 | C22 | 1 | 48 | yes | complemented |
| 59 | #3298 | C22 | 1 | 24 | yes | complemented |
| 60 | #3294 | C22 | 1 | 24 | yes | complemented |
| 61 | #3239 | C22 | 1 | 12 | yes | complemented |
| 62 | #3238 | C22 | 1 | 12 | yes | complemented |
| 63 | #3230 | C22 | 1 | 6 | yes | complemented |
| 64 | #3229 | C22 | 1 | 6 | yes | complemented |
| 65 | #3227 | C22 | 1 | 6 | yes | complemented |
| 66 | #3226 | C22 | 1 | 6 | yes | complemented |
| 67 | #3214 | C22 | 1 | 12 | yes | complemented |
| 68 | #3213 | C22 | 1 | 12 | yes | complemented |
| 69 | #3207 | C22 | 1 | 12 | yes | complemented |
| 70 | #3206 | C22 | 1 | 6 | yes | complemented |
| 71 | #3205 | C22 | 1 | 6 | yes | complemented |
| 72 | #3184 | C22 | 1 | 6 | yes | complemented |
| 73 | #3182 | C22 | 1 | 6 | yes | complemented |
| 74 | #3180 | C22 | 1 | 12 | yes | complemented |
| 75 | #3171 | C22 | 1 | 12 | yes | complemented |
| 76 | #3169 | C22 | 1 | 6 | yes | complemented |
| 77 | #3167 | C22 | 1 | 6 | yes | complemented |
| 78 | #3165 | C22 | 1 | 3 | yes | complemented |
| 79 | #3151 | C22 | 1 | 3 | yes | complemented |
| 80 | #3141 | C22 | 1 | 3 | yes | complemented |
| 81 | #3141 | C22 | 1 | 12 | yes | complemented |
| 82 | #3141 | C22 | 1 | 12 | yes | complemented |
| 83 | #3141 | C22 | 1 | 6 | yes | complemented |
| 84 | #3141 | C22 | 1 | 12 | yes | complemented |
| 85 | #3138 | C22 | 1 | 1 | yes | characteristic, complemented |
| 86 | C2×#489 | C22 | 1 | 12 | yes | complemented |
| 87 | C2×#487 | C22 | 1 | 6 | yes | complemented |
| 88 | C2×#486 | C22 | 1 | 6 | yes | complemented |
| 89 | #3092 | C22 | 1 | 12 | yes | complemented |
| 90 | #3079 | C22 | 1 | 12 | yes | complemented |
| 91 | #3055 | C22 | 1 | 12 | yes | complemented |
| 92 | #3036 | C22 | 1 | 12 | yes | complemented |
| 93 | #3006 | C22 | 1 | 12 | yes | complemented |
| 94 | #2971 | C22 | 1 | 2 | yes | complemented |
| 95 | #2970 | C22 | 1 | 6 | yes | complemented |
| 96 | #2965 | C22 | 1 | 6 | yes | complemented |
| 97 | C8×#41 | C22 | 1 | 2 | yes | complemented |
| 98 | Q8×M16 | C22 | 1 | 2 | yes | complemented |
| 99 | C4×AGL(1,ℤ/8) | C22 | 1 | 12 | yes | complemented |
| 100 | D4×M16 | C22 | 1 | 6 | yes | complemented |
| 101 | #2920 | C22 | 1 | 3 | yes | complemented |
| 102 | C2×#417 | C22 | 1 | 12 | yes | complemented |
| 103 | C2×C4×M16 | C22 | 1 | 3 | yes | complemented |
| 104 | C2×2−1+4 | — | 2 | 2 | no | — |
| 105 | C2×2−1+4 | — | 2 | 6 | no | — |
| 106 | C2×2−1+4 | — | 2 | 6 | no | — |
| 107 | C2×2−1+4 | — | 2 | 2 | no | — |
| 108 | C2×2−1+4 | — | 4 | 16 | no | — |
| 109 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 110 | C22×#41 | — | 2 | 6 | no | — |
| 111 | C22×#41 | — | 2 | 3 | no | — |
| 112 | C22×#41 | D4 | 1 | 1 | yes | characteristic |
| 113 | C22×#41 | C23 | 1 | 6 | yes | — |
| 114 | C23×Q8 | — | 2 | 2 | no | — |
| 115 | C23×Q8 | — | 2 | 3 | no | — |
| 116 | C2×AGL(1,ℤ/8) | C23 | 1 | 12 | yes | — |
| 117 | C22×M16 | C23 | 1 | 6 | yes | — |
| 118 | #559 | — | 2 | 3 | no | — |
| 119 | #559 | C23 | 1 | 6 | yes | — |
| 120 | Q82 | — | 2 | 1 | no | — |
| 121 | #557 | C23 | 1 | 2 | yes | — |
| 122 | #556 | C23 | 1 | 6 | yes | — |
| 123 | #555 | — | 2 | 3 | no | — |
| 124 | #555 | — | 2 | 6 | no | — |
| 125 | #554 | — | 2 | 3 | no | — |
| 126 | #554 | — | 2 | 3 | no | — |
| 127 | #553 | — | 2 | 6 | no | — |
| 128 | #553 | — | 2 | 6 | no | — |
| 129 | #553 | — | 2 | 6 | no | — |
| 130 | #551 | — | 2 | 12 | no | — |
| 131 | #550 | — | 2 | 2 | no | — |
| 132 | #550 | — | 2 | 1 | no | — |
| 133 | #550 | — | 2 | 3 | no | — |
| 134 | #550 | C23 | 1 | 6 | yes | — |
| 135 | #550 | C23 | 1 | 2 | yes | — |
| 136 | D4×Q8 | — | 2 | 2 | no | — |
| 137 | D4×Q8 | — | 2 | 2 | no | — |
| 138 | D4×Q8 | — | 2 | 6 | no | — |
| 139 | D4×Q8 | — | 2 | 6 | no | — |
| 140 | D4×Q8 | — | 2 | 2 | no | — |
| 141 | D4×Q8 | — | 2 | 6 | no | — |
| 142 | D4×Q8 | C23 | 1 | 6 | yes | — |
| 143 | D4×Q8 | C23 | 1 | 4 | yes | — |
| 144 | D4×Q8 | C23 | 1 | 12 | yes | — |
| 145 | #548 | — | 2 | 2 | no | — |
| 146 | #548 | C23 | 1 | 12 | yes | — |
| 147 | #547 | — | 2 | 6 | no | — |
| 148 | #547 | — | 2 | 6 | no | — |
| 149 | #547 | — | 2 | 12 | no | — |
| 150 | #547 | — | 2 | 6 | no | — |
| 151 | #547 | — | 2 | 12 | no | — |
| 152 | #547 | — | 2 | 6 | no | — |
| 153 | #547 | — | 2 | 6 | no | — |
| 154 | #547 | — | 2 | 12 | no | — |
| 155 | #547 | — | 2 | 6 | no | — |
| 156 | #547 | — | 2 | 6 | no | — |
| 157 | #547 | C23 | 1 | 6 | yes | — |
| 158 | #547 | C23 | 1 | 12 | yes | — |
| 159 | #547 | C23 | 1 | 12 | yes | — |
| 160 | #547 | C23 | 1 | 24 | yes | — |
| 161 | #546 | — | 2 | 6 | no | — |
| 162 | #546 | — | 2 | 6 | no | — |
| 163 | #546 | — | 2 | 12 | no | — |
| 164 | #546 | C23 | 1 | 12 | yes | — |
| 165 | D42 | — | 2 | 6 | no | — |
| 166 | D42 | — | 2 | 3 | no | — |
| 167 | D42 | C23 | 1 | 6 | yes | — |
| 168 | #544 | — | 2 | 3 | no | — |
| 169 | #542 | — | 2 | 6 | no | — |
| 170 | #542 | — | 2 | 6 | no | — |
| 171 | #540 | — | 2 | 6 | no | — |
| 172 | #540 | — | 2 | 6 | no | — |
| 173 | #538 | — | 2 | 12 | no | — |
| 174 | #537 | — | 2 | 3 | no | — |
| 175 | #536 | — | 2 | 6 | no | — |
| 176 | #536 | — | 2 | 6 | no | — |
| 177 | #536 | — | 2 | 12 | no | — |
| 178 | #536 | — | 2 | 12 | no | — |
| 179 | #536 | — | 2 | 6 | no | — |
| 180 | #536 | — | 2 | 6 | no | — |
| 181 | #535 | — | 2 | 3 | no | — |
| 182 | #535 | — | 2 | 3 | no | — |
| 183 | #533 | C23 | 1 | 3 | yes | — |
| 184 | #533 | C23 | 1 | 3 | yes | — |
| 185 | #533 | C23 | 1 | 1 | yes | characteristic |
| 186 | #532 | — | 2 | 6 | no | — |
| 187 | #532 | — | 2 | 3 | no | — |
| 188 | #532 | — | 2 | 3 | no | — |
| 189 | #532 | — | 2 | 3 | no | — |
| 190 | #532 | — | 2 | 3 | no | — |
| 191 | #532 | — | 2 | 3 | no | — |
| 192 | #532 | — | 2 | 3 | no | — |
| 193 | #532 | — | 2 | 3 | no | — |
| 194 | #532 | — | 2 | 3 | no | — |
| 195 | #532 | C23 | 1 | 3 | yes | — |
| 196 | #532 | C23 | 1 | 6 | yes | — |
| 197 | #532 | C23 | 1 | 6 | yes | — |
| 198 | #532 | C23 | 1 | 6 | yes | — |
| 199 | #532 | C23 | 1 | 6 | yes | — |
| 200 | #532 | C23 | 1 | 3 | yes | — |
| 201 | #532 | C23 | 1 | 6 | yes | — |
| 202 | #532 | C23 | 1 | 6 | yes | — |
| 203 | #532 | C23 | 1 | 6 | yes | — |
| 204 | #532 | C23 | 1 | 3 | yes | — |
| 205 | C2×C4⋊Q8 | — | 2 | 3 | no | — |
| 206 | C2×C4⋊Q8 | — | 2 | 3 | no | — |
| 207 | C2×C4⋊Q8 | — | 2 | 3 | no | — |
| 208 | C2×C4⋊Q8 | — | 2 | 3 | no | — |
| 209 | C2×C4⋊Q8 | — | 2 | 3 | no | — |
| 210 | C2×C4⋊Q8 | — | 2 | 3 | no | — |
| 211 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 212 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 213 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 214 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 215 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 216 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 217 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 218 | C2×#127 | C23 | 1 | 3 | yes | — |
| 219 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 220 | #529 | — | 2 | 6 | no | — |
| 221 | #529 | — | 2 | 3 | no | — |
| 222 | #529 | — | 2 | 3 | no | — |
| 223 | #529 | — | 2 | 3 | no | — |
| 224 | #529 | — | 2 | 3 | no | — |
| 225 | #529 | C23 | 1 | 6 | yes | — |
| 226 | #529 | C23 | 1 | 6 | yes | — |
| 227 | C2×#124 | — | 2 | 3 | no | — |
| 228 | C2×#124 | C23 | 1 | 6 | yes | — |
| 229 | #525 | — | 2 | 3 | no | — |
| 230 | #525 | — | 2 | 3 | no | — |
| 231 | #525 | — | 2 | 12 | no | — |
| 232 | #525 | C23 | 1 | 6 | yes | — |
| 233 | C2×#123 | — | 2 | 12 | no | — |
| 234 | C2×C22⋊Q8 | — | 2 | 6 | no | — |
| 235 | C2×C22⋊Q8 | — | 2 | 6 | no | — |
| 236 | C2×#121 | — | 2 | 3 | no | — |
| 237 | C2×#121 | — | 2 | 3 | no | — |
| 238 | C2×#121 | — | 2 | 3 | no | — |
| 239 | C2×#121 | C23 | 1 | 6 | yes | — |
| 240 | #520 | — | 2 | 1 | no | — |
| 241 | #520 | — | 2 | 2 | no | — |
| 242 | #520 | — | 2 | 3 | no | — |
| 243 | #518 | — | 2 | 6 | no | — |
| 244 | #518 | — | 2 | 3 | no | — |
| 245 | C4×#41 | — | 2 | 2 | no | — |
| 246 | C4×#41 | — | 2 | 3 | no | — |
| 247 | C4×#41 | — | 2 | 3 | no | — |
| 248 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 249 | C4×#41 | D4 | 1 | 3 | yes | — |
| 250 | C4×#41 | D4 | 1 | 3 | yes | — |
| 251 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 252 | C4×#41 | C23 | 1 | 6 | yes | — |
| 253 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 254 | C4×#41 | C23 | 1 | 3 | yes | — |
| 255 | C4×#41 | C23 | 1 | 3 | yes | — |
| 256 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×D4 | — | 2 | 6 | no | — |
| 260 | C2×C4×D4 | — | 2 | 3 | no | — |
| 261 | C2×C4×D4 | — | 2 | 3 | no | — |
| 262 | C2×C4×D4 | — | 2 | 3 | no | — |
| 263 | C2×C4×D4 | D4 | 1 | 3 | yes | — |
| 264 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 265 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 266 | C2×#117 | D4 | 1 | 3 | yes | — |
| 267 | C22×C4⋊C4 | — | 2 | 3 | no | — |
| 268 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 269 | C22×C42 | C23 | 1 | 3 | yes | — |
| 270 | #501 | C23 | 1 | 12 | yes | — |
| 271 | #500 | C23 | 1 | 6 | yes | — |
| 272 | #498 | C23 | 1 | 6 | yes | — |
| 273 | #496 | C23 | 1 | 12 | yes | — |
| 274 | #493 | C23 | 1 | 6 | yes | — |
| 275 | #492 | C23 | 1 | 6 | yes | — |
| 276 | #490 | C23 | 1 | 4 | yes | — |
| 277 | #489 | C23 | 1 | 48 | yes | — |
| 278 | #489 | C23 | 1 | 12 | yes | — |
| 279 | #489 | C23 | 1 | 24 | yes | — |
| 280 | #487 | C23 | 1 | 24 | yes | — |
| 281 | #487 | C23 | 1 | 6 | yes | — |
| 282 | #487 | C23 | 1 | 12 | yes | — |
| 283 | #486 | C23 | 1 | 24 | yes | — |
| 284 | #486 | C23 | 1 | 6 | yes | — |
| 285 | #486 | C23 | 1 | 12 | yes | — |
| 286 | #486 | C23 | 1 | 2 | yes | — |
| 287 | #486 | C23 | 1 | 2 | yes | — |
| 288 | #484 | C23 | 1 | 24 | yes | — |
| 289 | #483 | C23 | 1 | 24 | yes | — |
| 290 | #481 | C23 | 1 | 24 | yes | — |
| 291 | #480 | C23 | 1 | 24 | yes | — |
| 292 | #477 | C23 | 1 | 24 | yes | — |
| 293 | #476 | C23 | 1 | 24 | yes | — |
| 294 | #475 | C23 | 1 | 24 | yes | — |
| 295 | #474 | C23 | 1 | 24 | yes | — |
| 296 | #469 | C23 | 1 | 24 | yes | — |
| 297 | #468 | C23 | 1 | 24 | yes | — |
| 298 | #466 | C23 | 1 | 24 | yes | — |
| 299 | #465 | C23 | 1 | 24 | yes | — |
| 300 | #463 | C23 | 1 | 48 | yes | — |
| 301 | #461 | C23 | 1 | 24 | yes | — |
| 302 | #459 | C23 | 1 | 24 | yes | — |
| 303 | #449 | C23 | 1 | 48 | yes | — |
| 304 | #448 | C23 | 1 | 24 | yes | — |
| 305 | #447 | C23 | 1 | 24 | yes | — |
| 306 | #446 | C23 | 1 | 12 | yes | — |
| 307 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 308 | #442 | C23 | 1 | 24 | yes | — |
| 309 | #440 | C23 | 1 | 24 | yes | — |
| 310 | C4×SD16 | C23 | 1 | 24 | yes | — |
| 311 | C4×D8 | C23 | 1 | 24 | yes | — |
| 312 | #436 | C23 | 1 | 12 | yes | — |
| 313 | #435 | C23 | 1 | 24 | yes | — |
| 314 | C8×D4 | C23 | 1 | 12 | yes | — |
| 315 | #432 | C23 | 1 | 6 | yes | — |
| 316 | #432 | C23 | 1 | 6 | yes | — |
| 317 | #431 | C23 | 1 | 6 | yes | — |
| 318 | #431 | C23 | 1 | 6 | yes | — |
| 319 | #428 | C23 | 1 | 12 | yes | — |
| 320 | #423 | C23 | 1 | 6 | yes | — |
| 321 | #418 | C23 | 1 | 4 | yes | — |
| 322 | #417 | C23 | 1 | 48 | yes | — |
| 323 | #417 | C23 | 1 | 24 | yes | — |
| 324 | #417 | C23 | 1 | 12 | yes | — |
| 325 | C2×#103 | C23 | 1 | 24 | yes | — |
| 326 | C2×#102 | C23 | 1 | 24 | yes | — |
| 327 | #407 | C23 | 1 | 6 | yes | — |
| 328 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 329 | C4×M16 | C23 | 1 | 3 | yes | — |
| 330 | C4×M16 | C23 | 1 | 6 | yes | — |
| 331 | C4×M16 | C23 | 1 | 6 | yes | — |
| 332 | C4×M16 | C23 | 1 | 6 | yes | — |
| 333 | C2×#97 | C23 | 1 | 6 | yes | — |
| 334 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 335 | 2−1+4 | — | 4 | 48 | no | — |
| 336 | 2−1+4 | — | 4 | 16 | no | — |
| 337 | 2−1+4 | — | 4 | 48 | no | — |
| 338 | 2−1+4 | — | 4 | 16 | no | — |
| 339 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 340 | C2×#41 | — | 2 | 8 | no | — |
| 341 | C2×#41 | — | 2 | 2 | no | — |
| 342 | C2×#41 | — | 2 | 24 | no | — |
| 343 | C2×#41 | — | 2 | 12 | no | — |
| 344 | C2×#41 | — | 2 | 12 | no | — |
| 345 | C2×#41 | — | 2 | 3 | no | — |
| 346 | C2×#41 | — | 2 | 6 | no | — |
| 347 | C2×#41 | — | 2 | 6 | no | — |
| 348 | C2×#41 | — | 2 | 6 | no | — |
| 349 | C2×#41 | — | 2 | 6 | no | — |
| 350 | C2×#41 | — | 2 | 3 | no | — |
| 351 | C2×#41 | — | 2 | 6 | no | — |
| 352 | C2×#41 | — | 2 | 6 | no | — |
| 353 | C2×#41 | — | 4 | 24 | no | — |
| 354 | C2×#41 | — | 4 | 24 | no | — |
| 355 | C2×#41 | — | 4 | 48 | no | — |
| 356 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 357 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 358 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 359 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 360 | C2×#41 | C24 | 1 | 6 | yes | — |
| 361 | C2×#41 | C24 | 1 | 12 | yes | — |
| 362 | C22×Q8 | — | 2 | 12 | no | — |
| 363 | C22×Q8 | — | 2 | 4 | no | — |
| 364 | C22×Q8 | — | 2 | 6 | no | — |
| 365 | C22×Q8 | — | 2 | 3 | no | — |
| 366 | C22×Q8 | — | 2 | 6 | no | — |
| 367 | C22×Q8 | — | 2 | 6 | no | — |
| 368 | C22×Q8 | — | 2 | 6 | no | — |
| 369 | C22×Q8 | — | 2 | 6 | no | — |
| 370 | C22×Q8 | — | 4 | 24 | no | — |
| 371 | C22×Q8 | — | 4 | 16 | no | — |
| 372 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 373 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 374 | C22×D4 | — | 2 | 6 | no | — |
| 375 | C22×D4 | — | 2 | 6 | no | — |
| 376 | C22×D4 | — | 2 | 6 | no | — |
| 377 | C22×D4 | — | 2 | 1 | no | — |
| 378 | C22×D4 | — | 2 | 3 | no | — |
| 379 | C22×D4 | — | 2 | 1 | no | — |
| 380 | C22×D4 | — | 2 | 3 | no | — |
| 381 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 382 | C22×D4 | C24 | 1 | 2 | yes | — |
| 383 | C22×D4 | C24 | 1 | 6 | yes | — |
| 384 | C23×C4 | — | 2 | 6 | no | — |
| 385 | C23×C4 | — | 2 | 6 | no | — |
| 386 | C23×C4 | — | 2 | 6 | no | — |
| 387 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 388 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 389 | C23×C4 | C24 | 1 | 3 | yes | — |
| 390 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 391 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 392 | C2×D8 | C24 | 1 | 24 | yes | — |
| 393 | C2×M16 | — | 4 | 12 | no | — |
| 394 | C2×M16 | C24 | 1 | 2 | yes | — |
| 395 | C2×M16 | C24 | 1 | 6 | yes | — |
| 396 | C2×M16 | C24 | 1 | 12 | yes | — |
| 397 | C22×C8 | C24 | 1 | 12 | yes | — |
| 398 | C4⋊Q8 | — | 2 | 6 | no | — |
| 399 | C4⋊Q8 | — | 2 | 3 | no | — |
| 400 | C4⋊Q8 | — | 2 | 3 | no | — |
| 401 | C4⋊Q8 | — | 2 | 6 | no | — |
| 402 | C4⋊Q8 | — | 2 | 6 | no | — |
| 403 | C4⋊Q8 | — | 2 | 6 | no | — |
| 404 | C4⋊Q8 | — | 2 | 6 | no | — |
| 405 | C4⋊Q8 | — | 2 | 6 | no | — |
| 406 | C4⋊Q8 | — | 2 | 6 | no | — |
| 407 | C4⋊Q8 | — | 2 | 6 | no | — |
| 408 | C4⋊Q8 | — | 2 | 6 | no | — |
| 409 | C4⋊Q8 | — | 2 | 6 | no | — |
| 410 | C4⋊Q8 | — | 2 | 6 | no | — |
| 411 | C4⋊Q8 | — | 2 | 3 | no | — |
| 412 | C4⋊Q8 | — | 2 | 3 | no | — |
| 413 | C4⋊Q8 | C24 | 1 | 3 | yes | — |
| 414 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 415 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 416 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 417 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 418 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 419 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 420 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 421 | #127 | — | 2 | 6 | no | — |
| 422 | #127 | — | 2 | 1 | no | — |
| 423 | #127 | — | 2 | 1 | no | — |
| 424 | #127 | — | 2 | 3 | no | — |
| 425 | #127 | — | 2 | 3 | no | — |
| 426 | #127 | C24 | 1 | 3 | yes | — |
| 427 | #127 | C24 | 1 | 2 | yes | — |
| 428 | #127 | C24 | 1 | 2 | yes | — |
| 429 | #127 | C24 | 1 | 6 | yes | — |
| 430 | #126 | — | 2 | 12 | no | — |
| 431 | #126 | — | 2 | 6 | no | — |
| 432 | #126 | — | 2 | 6 | no | — |
| 433 | #125 | — | 2 | 6 | no | — |
| 434 | #125 | — | 2 | 3 | no | — |
| 435 | #125 | — | 2 | 3 | no | — |
| 436 | #125 | C24 | 1 | 2 | yes | — |
| 437 | #124 | — | 2 | 6 | no | — |
| 438 | #124 | — | 2 | 12 | no | — |
| 439 | #124 | — | 2 | 6 | no | — |
| 440 | #124 | — | 2 | 6 | no | — |
| 441 | #124 | — | 2 | 6 | no | — |
| 442 | #124 | — | 2 | 6 | no | — |
| 443 | #124 | — | 2 | 6 | no | — |
| 444 | #124 | — | 2 | 6 | no | — |
| 445 | #124 | — | 2 | 3 | no | — |
| 446 | #124 | — | 2 | 3 | no | — |
| 447 | #124 | C24 | 1 | 6 | yes | — |
| 448 | #124 | C24 | 1 | 12 | yes | — |
| 449 | #123 | — | 2 | 6 | no | — |
| 450 | #123 | — | 2 | 6 | no | — |
| 451 | #123 | — | 2 | 6 | no | — |
| 452 | #123 | — | 2 | 12 | no | — |
| 453 | #123 | — | 2 | 12 | no | — |
| 454 | #123 | — | 2 | 24 | no | — |
| 455 | #123 | — | 2 | 24 | no | — |
| 456 | #123 | — | 2 | 24 | no | — |
| 457 | #123 | — | 2 | 24 | no | — |
| 458 | #123 | — | 2 | 12 | no | — |
| 459 | C22⋊Q8 | — | 2 | 6 | no | — |
| 460 | C22⋊Q8 | — | 2 | 1 | no | — |
| 461 | C22⋊Q8 | — | 2 | 1 | no | — |
| 462 | C22⋊Q8 | — | 2 | 3 | no | — |
| 463 | C22⋊Q8 | — | 2 | 3 | no | — |
| 464 | C22⋊Q8 | — | 2 | 12 | no | — |
| 465 | C22⋊Q8 | — | 2 | 12 | no | — |
| 466 | C22⋊Q8 | — | 2 | 24 | no | — |
| 467 | C22⋊Q8 | — | 2 | 12 | no | — |
| 468 | C22⋊Q8 | — | 2 | 12 | no | — |
| 469 | C22⋊Q8 | — | 2 | 24 | no | — |
| 470 | C22⋊Q8 | — | 2 | 12 | no | — |
| 471 | C22⋊Q8 | — | 2 | 12 | no | — |
| 472 | C22⋊Q8 | C24 | 1 | 6 | yes | — |
| 473 | C22⋊Q8 | C24 | 1 | 6 | yes | — |
| 474 | #121 | — | 2 | 12 | no | — |
| 475 | #121 | — | 2 | 6 | no | — |
| 476 | #121 | — | 2 | 3 | no | — |
| 477 | #121 | — | 2 | 3 | no | — |
| 478 | #121 | — | 2 | 6 | no | — |
| 479 | #121 | — | 2 | 6 | no | — |
| 480 | #121 | — | 2 | 6 | no | — |
| 481 | #121 | — | 2 | 6 | no | — |
| 482 | #121 | — | 2 | 6 | no | — |
| 483 | #121 | — | 2 | 6 | no | — |
| 484 | #121 | — | 2 | 6 | no | — |
| 485 | #121 | — | 2 | 6 | no | — |
| 486 | #121 | — | 2 | 6 | no | — |
| 487 | #121 | — | 2 | 6 | no | — |
| 488 | #121 | — | 2 | 6 | no | — |
| 489 | #121 | — | 2 | 6 | no | — |
| 490 | #121 | — | 2 | 3 | no | — |
| 491 | #121 | — | 2 | 3 | no | — |
| 492 | #121 | — | 2 | 6 | no | — |
| 493 | #121 | — | 2 | 6 | no | — |
| 494 | #121 | — | 2 | 12 | no | — |
| 495 | #121 | — | 2 | 12 | no | — |
| 496 | #121 | C24 | 1 | 12 | yes | — |
| 497 | #121 | C24 | 1 | 12 | yes | — |
| 498 | #121 | C24 | 1 | 6 | yes | — |
| 499 | #121 | C24 | 1 | 6 | yes | — |
| 500 | #120 | — | 2 | 6 | no | — |
| 501 | #120 | — | 2 | 12 | no | — |
| 502 | #120 | — | 2 | 12 | no | — |
| 503 | C4×Q8 | — | 2 | 2 | no | — |
| 504 | C4×Q8 | — | 2 | 1 | no | — |
| 505 | C4×Q8 | — | 2 | 1 | no | — |
| 506 | C4×Q8 | — | 2 | 3 | no | — |
| 507 | C4×Q8 | — | 2 | 3 | no | — |
| 508 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 509 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 510 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 511 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 512 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 513 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 514 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 515 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 516 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 517 | C4×Q8 | C24 | 1 | 3 | yes | — |
| 518 | C4×D4 | — | 2 | 6 | no | — |
| 519 | C4×D4 | — | 2 | 6 | no | — |
| 520 | C4×D4 | — | 2 | 6 | no | — |
| 521 | C4×D4 | — | 2 | 6 | no | — |
| 522 | C4×D4 | — | 2 | 6 | no | — |
| 523 | C4×D4 | — | 2 | 6 | no | — |
| 524 | C4×D4 | — | 2 | 6 | no | — |
| 525 | C4×D4 | — | 2 | 6 | no | — |
| 526 | C4×D4 | — | 2 | 6 | no | — |
| 527 | C4×D4 | — | 2 | 12 | no | — |
| 528 | C4×D4 | — | 2 | 6 | no | — |
| 529 | C4×D4 | — | 2 | 3 | no | — |
| 530 | C4×D4 | — | 2 | 3 | no | — |
| 531 | C4×D4 | — | 2 | 6 | no | — |
| 532 | C4×D4 | — | 2 | 6 | no | — |
| 533 | C4×D4 | — | 2 | 6 | no | — |
| 534 | C4×D4 | — | 2 | 6 | no | — |
| 535 | C4×D4 | — | 2 | 6 | no | — |
| 536 | C4×D4 | — | 2 | 6 | no | — |
| 537 | C4×D4 | — | 2 | 6 | no | — |
| 538 | C4×D4 | — | 2 | 6 | no | — |
| 539 | C4×D4 | — | 2 | 6 | no | — |
| 540 | C4×D4 | — | 2 | 6 | no | — |
| 541 | C4×D4 | — | 2 | 6 | no | — |
| 542 | C4×D4 | — | 2 | 3 | no | — |
| 543 | C4×D4 | — | 2 | 3 | no | — |
| 544 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 545 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 546 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 547 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 548 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 549 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 550 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 551 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 552 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 553 | C4×D4 | C24 | 1 | 12 | yes | — |
| 554 | C4×D4 | C24 | 1 | 12 | yes | — |
| 555 | C4×D4 | C24 | 1 | 6 | yes | — |
| 556 | C4×D4 | C24 | 1 | 6 | yes | — |
| 557 | C4×D4 | C24 | 1 | 3 | yes | — |
| 558 | C4×D4 | C24 | 1 | 6 | yes | — |
| 559 | C4×D4 | C24 | 1 | 3 | yes | — |
| 560 | #117 | — | 2 | 3 | no | — |
| 561 | #117 | — | 2 | 3 | no | — |
| 562 | #117 | — | 2 | 6 | no | — |
| 563 | #117 | — | 2 | 6 | no | — |
| 564 | #117 | — | 2 | 6 | no | — |
| 565 | #117 | — | 2 | 6 | no | — |
| 566 | #117 | C2×D4 | 1 | 3 | yes | — |
| 567 | #117 | C2×D4 | 1 | 3 | yes | — |
| 568 | #117 | C2×D4 | 1 | 6 | yes | — |
| 569 | #117 | C2×D4 | 1 | 6 | yes | — |
| 570 | #117 | C2×D4 | 1 | 3 | yes | — |
| 571 | #117 | C2×D4 | 1 | 3 | yes | — |
| 572 | #117 | C24 | 1 | 2 | yes | — |
| 573 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 574 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 575 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 576 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 577 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 578 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 579 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 580 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 581 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 582 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 583 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 584 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 585 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 586 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 587 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 588 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 589 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 590 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 591 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 592 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 593 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 594 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 595 | C2×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 596 | C2×C42 | — | 2 | 6 | no | — |
| 597 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 598 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 599 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 600 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 601 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 602 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 603 | C2×C42 | C24 | 1 | 3 | yes | — |
| 604 | C2×C42 | C24 | 1 | 3 | yes | — |
| 605 | C2×C42 | C24 | 1 | 3 | yes | — |
| 606 | C2×C42 | C24 | 1 | 3 | yes | — |
| 607 | C2×C42 | C24 | 1 | 3 | yes | — |
| 608 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 609 | #107 | C24 | 1 | 24 | yes | — |
| 610 | #106 | C24 | 1 | 24 | yes | — |
| 611 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 612 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 613 | #103 | C24 | 1 | 24 | yes | — |
| 614 | #103 | C24 | 1 | 48 | yes | — |
| 615 | #102 | C24 | 1 | 24 | yes | — |
| 616 | #102 | C24 | 1 | 48 | yes | — |
| 617 | #102 | C24 | 1 | 8 | yes | — |
| 618 | #102 | C24 | 1 | 8 | yes | — |
| 619 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 620 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 621 | #97 | C24 | 1 | 2 | yes | — |
| 622 | #97 | C24 | 1 | 6 | yes | — |
| 623 | #97 | C24 | 1 | 12 | yes | — |
| 624 | C4×C8 | C24 | 1 | 2 | yes | — |
| 625 | C4×C8 | C24 | 1 | 6 | yes | — |
| 626 | C4×C8 | C24 | 1 | 12 | yes | — |
| 627 | C24 | — | 2 | 2 | no | — |
| 628 | C24 | — | 2 | 6 | no | — |
| 629 | C24 | C22×D4 | 1 | 3 | yes | — |
| 630 | #41 | — | 2 | 4 | no | — |
| 631 | #41 | — | 2 | 12 | no | — |
| 632 | #41 | — | 2 | 12 | no | — |
| 633 | #41 | — | 2 | 24 | no | — |
| 634 | #41 | — | 4 | 24 | no | — |
| 635 | #41 | — | 4 | 24 | no | — |
| 636 | #41 | — | 4 | 24 | no | — |
| 637 | #41 | — | 4 | 24 | no | — |
| 638 | #41 | — | 4 | 96 | no | — |
| 639 | #41 | — | 4 | 48 | no | — |
| 640 | #41 | — | 4 | 8 | no | — |
| 641 | #41 | — | 4 | 48 | no | — |
| 642 | #41 | — | 4 | 24 | no | — |
| 643 | #41 | — | 4 | 12 | no | — |
| 644 | #41 | — | 8 | 12 | no | — |
| 645 | #41 | — | 8 | 12 | no | — |
| 646 | #41 | — | 8 | 6 | no | — |
| 647 | #41 | AGL(1,ℤ/8) | 1 | 8 | yes | complemented |
| 648 | C2×Q8 | — | 2 | 4 | no | — |
| 649 | C2×Q8 | — | 2 | 1 | no | — |
| 650 | C2×Q8 | — | 2 | 1 | no | — |
| 651 | C2×Q8 | — | 2 | 12 | no | — |
| 652 | C2×Q8 | — | 2 | 12 | no | — |
| 653 | C2×Q8 | — | 2 | 6 | no | — |
| 654 | C2×Q8 | — | 2 | 6 | no | — |
| 655 | C2×Q8 | — | 2 | 6 | no | — |
| 656 | C2×Q8 | — | 4 | 12 | no | — |
| 657 | C2×Q8 | — | 4 | 24 | no | — |
| 658 | C2×Q8 | — | 4 | 24 | no | — |
| 659 | C2×Q8 | — | 4 | 24 | no | — |
| 660 | C2×Q8 | — | 4 | 24 | no | — |
| 661 | C2×Q8 | — | 4 | 12 | no | — |
| 662 | C2×Q8 | — | 4 | 48 | no | — |
| 663 | C2×Q8 | — | 4 | 16 | no | — |
| 664 | C2×Q8 | — | 4 | 24 | no | — |
| 665 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 666 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 667 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 668 | C2×D4 | — | 2 | 12 | no | — |
| 669 | C2×D4 | — | 2 | 6 | no | — |
| 670 | C2×D4 | — | 2 | 6 | no | — |
| 671 | C2×D4 | — | 2 | 12 | no | — |
| 672 | C2×D4 | — | 2 | 12 | no | — |
| 673 | C2×D4 | — | 2 | 6 | no | — |
| 674 | C2×D4 | — | 2 | 12 | no | — |
| 675 | C2×D4 | — | 2 | 2 | no | — |
| 676 | C2×D4 | — | 2 | 2 | no | — |
| 677 | C2×D4 | — | 2 | 2 | no | — |
| 678 | C2×D4 | — | 2 | 3 | no | — |
| 679 | C2×D4 | — | 2 | 6 | no | — |
| 680 | C2×D4 | — | 2 | 3 | no | — |
| 681 | C2×D4 | — | 2 | 2 | no | — |
| 682 | C2×D4 | — | 2 | 2 | no | — |
| 683 | C2×D4 | — | 2 | 6 | no | — |
| 684 | C2×D4 | — | 2 | 6 | no | — |
| 685 | C2×D4 | — | 2 | 8 | no | — |
| 686 | C2×D4 | — | 4 | 12 | no | — |
| 687 | C2×D4 | — | 4 | 4 | no | — |
| 688 | C2×D4 | — | 4 | 4 | no | — |
| 689 | C2×D4 | — | 4 | 24 | no | — |
| 690 | C2×D4 | — | 4 | 24 | no | — |
| 691 | C2×D4 | — | 4 | 12 | no | — |
| 692 | C2×D4 | — | 8 | 6 | no | — |
| 693 | C2×D4 | — | 8 | 12 | no | — |
| 694 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 695 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 696 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 697 | C2×D4 | C25 | 1 | 6 | yes | — |
| 698 | C2×D4 | C25 | 1 | 4 | yes | — |
| 699 | C22×C4 | — | 2 | 12 | no | — |
| 700 | C22×C4 | — | 2 | 12 | no | — |
| 701 | C22×C4 | — | 2 | 6 | no | — |
| 702 | C22×C4 | — | 2 | 12 | no | — |
| 703 | C22×C4 | — | 2 | 12 | no | — |
| 704 | C22×C4 | — | 2 | 6 | no | — |
| 705 | C22×C4 | — | 2 | 6 | no | — |
| 706 | C22×C4 | — | 2 | 6 | no | — |
| 707 | C22×C4 | — | 2 | 12 | no | — |
| 708 | C22×C4 | — | 2 | 12 | no | — |
| 709 | C22×C4 | — | 2 | 6 | no | — |
| 710 | C22×C4 | — | 2 | 12 | no | — |
| 711 | C22×C4 | — | 4 | 6 | no | — |
| 712 | C22×C4 | — | 4 | 24 | no | — |
| 713 | C22×C4 | — | 4 | 24 | no | — |
| 714 | C22×C4 | — | 8 | 12 | no | — |
| 715 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 716 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 717 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 718 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 719 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 720 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 721 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 722 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 723 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 724 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 725 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 726 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 727 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 728 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 729 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 730 | C22×C4 | C25 | 1 | 3 | yes | — |
| 731 | C22×C4 | C25 | 1 | 3 | yes | — |
| 732 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 733 | SD16 | — | 4 | 24 | no | — |
| 734 | D8 | — | 4 | 24 | no | — |
| 735 | M16 | — | 2 | 4 | no | — |
| 736 | M16 | — | 2 | 12 | no | — |
| 737 | M16 | — | 4 | 12 | no | — |
| 738 | C2×C8 | — | 4 | 12 | no | — |
| 739 | C2×C8 | C25 | 1 | 4 | yes | — |
| 740 | C2×C8 | C25 | 1 | 12 | yes | — |
| 741 | C4⋊C4 | — | 2 | 6 | no | — |
| 742 | C4⋊C4 | — | 2 | 6 | no | — |
| 743 | C4⋊C4 | — | 2 | 6 | no | — |
| 744 | C4⋊C4 | — | 2 | 12 | no | — |
| 745 | C4⋊C4 | — | 2 | 12 | no | — |
| 746 | C4⋊C4 | — | 2 | 12 | no | — |
| 747 | C4⋊C4 | — | 2 | 12 | no | — |
| 748 | C4⋊C4 | — | 2 | 3 | no | — |
| 749 | C4⋊C4 | — | 2 | 6 | no | — |
| 750 | C4⋊C4 | — | 2 | 3 | no | — |
| 751 | C4⋊C4 | — | 2 | 6 | no | — |
| 752 | C4⋊C4 | — | 2 | 6 | no | — |
| 753 | C4⋊C4 | — | 2 | 1 | no | — |
| 754 | C4⋊C4 | — | 2 | 1 | no | — |
| 755 | C4⋊C4 | — | 2 | 2 | no | — |
| 756 | C4⋊C4 | — | 2 | 2 | no | — |
| 757 | C4⋊C4 | — | 2 | 6 | no | — |
| 758 | C4⋊C4 | — | 2 | 6 | no | — |
| 759 | C4⋊C4 | — | 2 | 6 | no | — |
| 760 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 761 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 762 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 763 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 764 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 765 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 766 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 767 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 768 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 769 | C22⋊C4 | — | 2 | 6 | no | — |
| 770 | C22⋊C4 | — | 2 | 6 | no | — |
| 771 | C22⋊C4 | — | 2 | 2 | no | — |
| 772 | C22⋊C4 | — | 2 | 12 | no | — |
| 773 | C22⋊C4 | — | 2 | 6 | no | — |
| 774 | C22⋊C4 | — | 2 | 6 | no | — |
| 775 | C22⋊C4 | — | 2 | 6 | no | — |
| 776 | C22⋊C4 | — | 2 | 12 | no | — |
| 777 | C22⋊C4 | — | 2 | 12 | no | — |
| 778 | C22⋊C4 | — | 2 | 12 | no | — |
| 779 | C22⋊C4 | — | 2 | 12 | no | — |
| 780 | C22⋊C4 | — | 2 | 12 | no | — |
| 781 | C22⋊C4 | — | 2 | 6 | no | — |
| 782 | C22⋊C4 | — | 2 | 6 | no | — |
| 783 | C22⋊C4 | — | 2 | 6 | no | — |
| 784 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 785 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 786 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 787 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 788 | C42 | — | 2 | 2 | no | — |
| 789 | C42 | — | 2 | 6 | no | — |
| 790 | C42 | — | 2 | 6 | no | — |
| 791 | C42 | C22×D4 | 1 | 3 | yes | — |
| 792 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 793 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 794 | C42 | C22×D4 | 1 | 3 | yes | — |
| 795 | C42 | C22×D4 | 1 | 3 | yes | — |
| 796 | C42 | C22×D4 | 1 | 3 | yes | — |
| 797 | C42 | C22×D4 | 1 | 3 | yes | — |
| 798 | C42 | C22×D4 | 1 | 3 | yes | — |
| 799 | C42 | C22×D4 | 1 | 3 | yes | — |
| 800 | C42 | C22×D4 | 1 | 3 | yes | — |
| 801 | C42 | C22×D4 | 1 | 3 | yes | — |
| 802 | C42 | C22×D4 | 1 | 3 | yes | — |
| 803 | C42 | C25 | 1 | 1 | yes | characteristic |
| 804 | C42 | C25 | 1 | 3 | yes | — |
| 805 | C42 | C25 | 1 | 1 | yes | characteristic |
| 806 | C42 | C25 | 1 | 3 | yes | — |
| 807 | C23 | — | 2 | 6 | no | — |
| 808 | C23 | — | 2 | 6 | no | — |
| 809 | C23 | — | 2 | 4 | no | — |
| 810 | C23 | — | 2 | 6 | no | — |
| 811 | C23 | — | 4 | 3 | no | — |
| 812 | C23 | — | 4 | 4 | no | — |
| 813 | C23 | — | 4 | 4 | no | — |
| 814 | C23 | — | 4 | 4 | no | — |
| 815 | C23 | — | 4 | 12 | no | — |
| 816 | C23 | — | 8 | 6 | no | — |
| 817 | C23 | — | 8 | 6 | no | — |
| 818 | C23 | C23×D4 | 1 | 3 | yes | — |
| 819 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 820 | C23 | C23×D4 | 1 | 3 | yes | — |
| 821 | Q8 | — | 2 | 6 | no | — |
| 822 | Q8 | — | 2 | 12 | no | — |
| 823 | Q8 | — | 4 | 12 | no | — |
| 824 | Q8 | — | 4 | 24 | no | — |
| 825 | Q8 | — | 4 | 2 | no | — |
| 826 | Q8 | — | 4 | 12 | no | — |
| 827 | Q8 | — | 4 | 24 | no | — |
| 828 | Q8 | — | 4 | 2 | no | — |
| 829 | Q8 | — | 8 | 6 | no | — |
| 830 | Q8 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 831 | D4 | — | 2 | 12 | no | — |
| 832 | D4 | — | 2 | 8 | no | — |
| 833 | D4 | — | 2 | 12 | no | — |
| 834 | D4 | — | 2 | 6 | no | — |
| 835 | D4 | — | 4 | 4 | no | — |
| 836 | D4 | — | 4 | 4 | no | — |
| 837 | D4 | — | 4 | 24 | no | — |
| 838 | D4 | — | 4 | 12 | no | — |
| 839 | D4 | — | 4 | 12 | no | — |
| 840 | D4 | — | 4 | 24 | no | — |
| 841 | D4 | — | 4 | 4 | no | — |
| 842 | D4 | — | 4 | 6 | no | — |
| 843 | D4 | — | 4 | 4 | no | — |
| 844 | D4 | — | 4 | 6 | no | — |
| 845 | D4 | — | 4 | 12 | no | — |
| 846 | D4 | — | 4 | 4 | no | — |
| 847 | D4 | — | 8 | 6 | no | — |
| 848 | D4 | — | 8 | 6 | no | — |
| 849 | D4 | — | 8 | 12 | no | — |
| 850 | D4 | — | 8 | 6 | no | — |
| 851 | D4 | C2×AGL(1,ℤ/8) | 1 | 12 | yes | — |
| 852 | C2×C4 | — | 2 | 6 | no | — |
| 853 | C2×C4 | — | 2 | 6 | no | — |
| 854 | C2×C4 | — | 2 | 2 | no | — |
| 855 | C2×C4 | — | 2 | 6 | no | — |
| 856 | C2×C4 | — | 2 | 6 | no | — |
| 857 | C2×C4 | — | 2 | 6 | no | — |
| 858 | C2×C4 | — | 2 | 6 | no | — |
| 859 | C2×C4 | — | 2 | 6 | no | — |
| 860 | C2×C4 | — | 2 | 6 | no | — |
| 861 | C2×C4 | — | 2 | 2 | no | — |
| 862 | C2×C4 | — | 2 | 6 | no | — |
| 863 | C2×C4 | — | 2 | 6 | no | — |
| 864 | C2×C4 | — | 2 | 6 | no | — |
| 865 | C2×C4 | — | 2 | 2 | no | — |
| 866 | C2×C4 | — | 2 | 2 | no | — |
| 867 | C2×C4 | — | 2 | 6 | no | — |
| 868 | C2×C4 | — | 2 | 12 | no | — |
| 869 | C2×C4 | — | 4 | 3 | no | — |
| 870 | C2×C4 | — | 4 | 3 | no | — |
| 871 | C2×C4 | — | 4 | 3 | no | — |
| 872 | C2×C4 | — | 4 | 24 | no | — |
| 873 | C2×C4 | — | 4 | 12 | no | — |
| 874 | C2×C4 | — | 4 | 24 | no | — |
| 875 | C2×C4 | — | 4 | 24 | no | — |
| 876 | C2×C4 | — | 4 | 12 | no | — |
| 877 | C2×C4 | — | 4 | 24 | no | — |
| 878 | C2×C4 | — | 4 | 12 | no | — |
| 879 | C2×C4 | — | 8 | 12 | no | — |
| 880 | C2×C4 | — | 8 | 6 | no | — |
| 881 | C2×C4 | — | 8 | 6 | no | — |
| 882 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 12 | yes | — |
| 883 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 884 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 885 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 886 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 887 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 888 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 889 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 890 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 891 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 892 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 893 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 894 | C2×C4 | #585 | 1 | 4 | yes | — |
| 895 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 896 | C8 | — | 2 | 4 | no | — |
| 897 | C8 | — | 2 | 12 | no | — |
| 898 | C22 | — | 2 | 3 | no | — |
| 899 | C22 | — | 2 | 1 | no | — |
| 900 | C22 | — | 2 | 1 | no | — |
| 901 | C22 | — | 2 | 3 | no | — |
| 902 | C22 | — | 2 | 3 | no | — |
| 903 | C22 | — | 2 | 3 | no | — |
| 904 | C22 | — | 2 | 3 | no | — |
| 905 | C22 | — | 4 | 12 | no | — |
| 906 | C22 | — | 4 | 6 | no | — |
| 907 | C22 | — | 4 | 4 | no | — |
| 908 | C22 | — | 4 | 4 | no | — |
| 909 | C22 | — | 4 | 6 | no | — |
| 910 | C22 | — | 4 | 6 | no | — |
| 911 | C22 | — | 4 | 4 | no | — |
| 912 | C22 | — | 8 | 8 | no | — |
| 913 | C22 | — | 16 | 12 | no | — |
| 914 | C22 | #3500 | 1 | 2 | yes | — |
| 915 | C22 | C22×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 916 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 917 | C4 | — | 2 | 3 | no | — |
| 918 | C4 | — | 2 | 3 | no | — |
| 919 | C4 | — | 2 | 1 | no | — |
| 920 | C4 | — | 2 | 3 | no | — |
| 921 | C4 | — | 2 | 1 | no | — |
| 922 | C4 | — | 2 | 3 | no | — |
| 923 | C4 | — | 2 | 3 | no | — |
| 924 | C4 | — | 4 | 6 | no | — |
| 925 | C4 | — | 4 | 12 | no | — |
| 926 | C4 | — | 4 | 2 | no | — |
| 927 | C4 | — | 4 | 2 | no | — |
| 928 | C4 | #3500 | 1 | 2 | yes | — |
| 929 | C4 | C22×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 930 | C4 | C22×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 931 | C4 | #3586 | 1 | 2 | yes | — |
| 932 | C4 | C2×#585 | 1 | 2 | yes | — |
| 933 | C2 | — | 2 | 2 | no | — |
| 934 | C2 | — | 2 | 6 | no | — |
| 935 | C2 | — | 4 | 3 | no | — |
| 936 | C2 | — | 8 | 4 | no | — |
| 937 | C2 | — | 8 | 6 | no | — |
| 938 | C2 | C2×#3500 | 1 | 1 | yes | characteristic |
| 939 | C2 | C23×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 940 | C2 | C2×#3586 | 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 ◁ C2×C4×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3499 | C2 | semidirect |
| 2. #62800 | C2 | semidirect |
| 3. #62595 | C2 | semidirect |
| 4. #62583 | C2 | semidirect |
| 5. #62541 | C2 | semidirect |
| 6. #62538 | C2 | semidirect |
| 7. #62529 | C2 | semidirect |
| 8. #62526 | C2 | semidirect |
| 9. #61317 | C2 | semidirect |
| 10. #61161 | C2 | semidirect |
| 11. #60860 | C2 | semidirect |
| 12. #60803 | C2 | semidirect |
| 13. #60700 | C2 | semidirect |
| 14. C2×#3141 | C2 | semidirect |
| 15. M16×#41 | C2 | semidirect |
| 19. #3517 | C22 | semidirect |
| 20. #3514 | C22 | semidirect |
| 21. #3511 | C22 | semidirect |
| 22. #3508 | C22 | semidirect |
| 23. #3503 | C22 | semidirect |
| 29. #3499 | C22 | semidirect |
| 30. #3499 | C22 | semidirect |
| 31. #3499 | C22 | semidirect |
| 32. #3498 | C22 | semidirect |
| 40. C2×D4×Q8 | C22 | semidirect |
| 42. C2×#547 | C22 | semidirect |
| 47. C2×#532 | C22 | semidirect |
| 48. C22×C4⋊Q8 | C22 | semidirect |
| 51. #3373 | C22 | semidirect |
| 52. #3367 | C22 | semidirect |
| 53. #3359 | C22 | semidirect |
| 54. #3358 | C22 | semidirect |
| 55. #3332 | C22 | semidirect |
| 56. #3330 | C22 | semidirect |
| 57. #3308 | C22 | semidirect |
| 58. #3306 | C22 | semidirect |
| 59. #3298 | C22 | semidirect |
| 60. #3294 | C22 | semidirect |
| 61. #3239 | C22 | semidirect |
| 62. #3238 | C22 | semidirect |
| 63. #3230 | C22 | semidirect |
| 64. #3229 | C22 | semidirect |
| 65. #3227 | C22 | semidirect |
| 66. #3226 | C22 | semidirect |
| 67. #3214 | C22 | semidirect |
| 68. #3213 | C22 | semidirect |
| 69. #3207 | C22 | semidirect |
| 70. #3206 | C22 | semidirect |
| 71. #3205 | C22 | semidirect |
| 72. #3184 | C22 | semidirect |
| 73. #3182 | C22 | semidirect |
| 74. #3180 | C22 | semidirect |
| 75. #3171 | C22 | semidirect |
| 76. #3169 | C22 | semidirect |
| 77. #3167 | C22 | semidirect |
| 78. #3165 | C22 | semidirect |
| 79. #3151 | C22 | semidirect |
| 80. #3141 | C22 | semidirect |
| 81. #3141 | C22 | semidirect |
| 82. #3141 | C22 | semidirect |
| 83. #3141 | C22 | semidirect |
| 84. #3141 | C22 | semidirect |
| 85. #3138 | C22 | semidirect |
| 86. C2×#489 | C22 | semidirect |
| 87. C2×#487 | C22 | semidirect |
| 88. C2×#486 | C22 | semidirect |
| 89. #3092 | C22 | semidirect |
| 90. #3079 | C22 | semidirect |
| 91. #3055 | C22 | semidirect |
| 92. #3036 | C22 | semidirect |
| 93. #3006 | C22 | semidirect |
| 94. #2971 | C22 | semidirect |
| 95. #2970 | C22 | semidirect |
| 96. #2965 | C22 | semidirect |
| 97. C8×#41 | C22 | semidirect |
| 98. Q8×M16 | C22 | semidirect |
| 99. C4×AGL(1,ℤ/8) | C22 | semidirect |
| 100. D4×M16 | C22 | semidirect |
| 101. #2920 | C22 | semidirect |
| 102. C2×#417 | C22 | semidirect |
| 103. C2×C4×M16 | C22 | semidirect |
| 647. #41 | AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3499 | 2 |
| #62800 | 2 |
| #62595 | 2 |
| #62583 | 2 |
| #62541 | 2 |
| #62538 | 2 |
| #62529 | 2 |
| #62526 | 2 |
| #61317 | 2 |
| #61161 | 2 |
| #60860 | 2 |
| #60803 | 2 |
| #60700 | 2 |
| C2×#3141 | 2 |
| M16×#41 | 2 |