Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
4269 conjugacy classes of subgroups.
The subgroup lattice has 951 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#550 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #60798 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #60560 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #60558 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #18771 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #18770 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #18767 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #18766 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #18550 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #18545 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #17741 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #17449 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #17448 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C23×#41 | — | 2 | 1 | no | — |
| 15 | C2×#550 | — | 2 | 2 | no | — |
| 16 | C2×#550 | — | 2 | 2 | no | — |
| 17 | C2×#550 | — | 2 | 2 | no | — |
| 18 | C2×#550 | — | 2 | 2 | no | — |
| 19 | C2×#550 | — | 2 | 2 | no | — |
| 20 | C2×#550 | — | 2 | 2 | no | — |
| 21 | C2×#550 | — | 2 | 2 | no | — |
| 22 | C2×#550 | — | 2 | 2 | no | — |
| 23 | C2×#550 | — | 2 | 2 | no | — |
| 24 | C2×#550 | C22 | 1 | 4 | yes | — |
| 25 | C2×#550 | C22 | 1 | 4 | yes | — |
| 26 | C2×#550 | C22 | 1 | 4 | yes | — |
| 27 | #3444 | C22 | 1 | 1 | yes | characteristic |
| 28 | C22×#127 | — | 2 | 1 | no | — |
| 29 | C22×#127 | C22 | 1 | 1 | yes | characteristic |
| 30 | C22×#121 | — | 2 | 2 | no | — |
| 31 | C22×#121 | — | 2 | 1 | no | — |
| 32 | C22×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 33 | C22×C4×D4 | — | 2 | 1 | no | — |
| 34 | C22×C4×D4 | C22 | 1 | 1 | yes | characteristic |
| 35 | #3217 | — | 2 | 2 | no | — |
| 36 | #3217 | — | 2 | 2 | no | — |
| 37 | #3208 | C22 | 1 | 2 | yes | complemented |
| 38 | #3208 | C22 | 1 | 2 | yes | complemented |
| 39 | #3205 | C22 | 1 | 2 | yes | complemented |
| 40 | #3205 | C22 | 1 | 2 | yes | complemented |
| 41 | #3151 | C22 | 1 | 2 | yes | complemented |
| 42 | #3138 | C22 | 1 | 2 | yes | complemented |
| 43 | #3117 | — | 2 | 2 | no | — |
| 44 | #3114 | — | 2 | 2 | no | — |
| 45 | #3113 | C22 | 1 | 2 | yes | complemented |
| 46 | #3112 | C22 | 1 | 2 | yes | complemented |
| 47 | #3110 | C22 | 1 | 2 | yes | complemented |
| 48 | #3109 | C22 | 1 | 2 | yes | complemented |
| 49 | #3108 | — | 2 | 2 | no | — |
| 50 | #3105 | — | 2 | 2 | no | — |
| 51 | #3104 | C22 | 1 | 2 | yes | complemented |
| 52 | #3103 | C22 | 1 | 2 | yes | complemented |
| 53 | #3101 | C22 | 1 | 2 | yes | complemented |
| 54 | #3100 | C22 | 1 | 2 | yes | complemented |
| 55 | #3092 | — | 2 | 1 | no | — |
| 56 | #3092 | — | 2 | 1 | no | — |
| 57 | #3078 | C22 | 1 | 2 | yes | complemented |
| 58 | #3077 | C22 | 1 | 2 | yes | complemented |
| 59 | #3038 | — | 2 | 2 | no | — |
| 60 | #3037 | C22 | 1 | 2 | yes | complemented |
| 61 | #3036 | C22 | 1 | 2 | yes | complemented |
| 62 | #3004 | — | 2 | 1 | no | — |
| 63 | #3003 | — | 2 | 2 | no | — |
| 64 | #3003 | — | 2 | 1 | no | — |
| 65 | C4×#137 | — | 2 | 2 | no | — |
| 66 | C4×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 67 | #2920 | C22 | 1 | 1 | yes | characteristic |
| 68 | #2920 | C22 | 1 | 1 | yes | characteristic |
| 69 | #2920 | C22 | 1 | 1 | yes | characteristic |
| 70 | #1642 | C22 | 1 | 16 | yes | complemented |
| 71 | #1641 | C22 | 1 | 16 | yes | complemented |
| 72 | #1631 | C22 | 1 | 16 | yes | complemented |
| 73 | #1621 | C22 | 1 | 16 | yes | complemented |
| 74 | #1555 | C22 | 1 | 4 | yes | complemented |
| 75 | #1545 | C22 | 1 | 4 | yes | complemented |
| 76 | #1545 | C22 | 1 | 4 | yes | complemented |
| 77 | #1491 | C22 | 1 | 4 | yes | complemented |
| 78 | #1490 | C22 | 1 | 4 | yes | complemented |
| 79 | #1487 | C22 | 1 | 4 | yes | complemented |
| 80 | #1486 | C22 | 1 | 4 | yes | complemented |
| 81 | #1479 | C22 | 1 | 4 | yes | complemented |
| 82 | #1478 | C22 | 1 | 4 | yes | complemented |
| 83 | C22×#41 | — | 2 | 4 | no | — |
| 84 | C22×#41 | — | 2 | 4 | no | — |
| 85 | C22×#41 | — | 2 | 4 | no | — |
| 86 | C22×#41 | — | 2 | 4 | no | — |
| 87 | C22×#41 | — | 2 | 4 | no | — |
| 88 | C22×#41 | — | 2 | 4 | no | — |
| 89 | C22×#41 | — | 4 | 16 | no | — |
| 90 | C23×Q8 | D4 | 1 | 1 | yes | characteristic |
| 91 | C23×D4 | — | 2 | 2 | no | — |
| 92 | C23×D4 | — | 2 | 2 | no | — |
| 93 | C23×D4 | — | 2 | 1 | no | — |
| 94 | C23×D4 | — | 2 | 1 | no | — |
| 95 | C23×D4 | D4 | 1 | 1 | yes | characteristic |
| 96 | C23×D4 | D4 | 1 | 2 | yes | — |
| 97 | C24×C4 | — | 2 | 2 | no | — |
| 98 | C24×C4 | — | 2 | 1 | no | — |
| 99 | C2×#137 | — | 2 | 2 | no | — |
| 100 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 101 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 102 | #550 | — | 2 | 8 | no | — |
| 103 | #550 | — | 2 | 8 | no | — |
| 104 | #550 | — | 2 | 8 | no | — |
| 105 | #550 | — | 2 | 8 | no | — |
| 106 | #550 | — | 2 | 8 | no | — |
| 107 | #550 | — | 2 | 8 | no | — |
| 108 | #550 | — | 2 | 8 | no | — |
| 109 | #550 | — | 2 | 8 | no | — |
| 110 | #550 | — | 2 | 8 | no | — |
| 111 | #550 | — | 2 | 8 | no | — |
| 112 | #550 | — | 2 | 8 | no | — |
| 113 | #550 | — | 2 | 8 | no | — |
| 114 | #550 | — | 2 | 8 | no | — |
| 115 | #550 | — | 2 | 8 | no | — |
| 116 | #550 | — | 2 | 8 | no | — |
| 117 | #550 | C23 | 1 | 16 | yes | — |
| 118 | #533 | C23 | 1 | 1 | yes | characteristic |
| 119 | #533 | C23 | 1 | 1 | yes | characteristic |
| 120 | #533 | C23 | 1 | 1 | yes | characteristic |
| 121 | #532 | C23 | 1 | 1 | yes | characteristic |
| 122 | #532 | C23 | 1 | 1 | yes | characteristic |
| 123 | #532 | C23 | 1 | 1 | yes | characteristic |
| 124 | C2×#127 | — | 2 | 4 | no | — |
| 125 | C2×#127 | — | 2 | 4 | no | — |
| 126 | C2×#127 | — | 2 | 4 | no | — |
| 127 | C2×#127 | — | 2 | 4 | no | — |
| 128 | C2×#127 | — | 2 | 4 | no | — |
| 129 | C2×#127 | — | 2 | 4 | no | — |
| 130 | C2×#127 | — | 2 | 1 | no | — |
| 131 | C2×#127 | — | 2 | 1 | no | — |
| 132 | C2×#127 | — | 2 | 1 | no | — |
| 133 | C2×#127 | — | 2 | 1 | no | — |
| 134 | C2×#127 | — | 2 | 1 | no | — |
| 135 | C2×#127 | — | 2 | 1 | no | — |
| 136 | C2×#127 | D4 | 1 | 2 | yes | — |
| 137 | C2×#127 | D4 | 1 | 2 | yes | — |
| 138 | C2×#127 | D4 | 1 | 2 | yes | — |
| 139 | C2×#127 | C23 | 1 | 2 | yes | — |
| 140 | C2×#127 | C23 | 1 | 2 | yes | — |
| 141 | C2×#127 | C23 | 1 | 2 | yes | — |
| 142 | #529 | — | 2 | 1 | no | — |
| 143 | #529 | — | 2 | 1 | no | — |
| 144 | #529 | — | 2 | 1 | no | — |
| 145 | #529 | — | 2 | 1 | no | — |
| 146 | #529 | — | 2 | 1 | no | — |
| 147 | #529 | — | 2 | 1 | no | — |
| 148 | #525 | — | 2 | 1 | no | — |
| 149 | #525 | — | 2 | 1 | no | — |
| 150 | #525 | — | 2 | 1 | no | — |
| 151 | C2×#121 | — | 2 | 4 | no | — |
| 152 | C2×#121 | — | 2 | 4 | no | — |
| 153 | C2×#121 | — | 2 | 4 | no | — |
| 154 | C2×#121 | — | 2 | 8 | no | — |
| 155 | C2×#121 | — | 2 | 8 | no | — |
| 156 | C2×#121 | — | 2 | 8 | no | — |
| 157 | C2×#121 | — | 2 | 8 | no | — |
| 158 | C2×#121 | — | 2 | 8 | no | — |
| 159 | C2×#121 | — | 2 | 8 | no | — |
| 160 | C2×#121 | — | 2 | 4 | no | — |
| 161 | C2×#121 | — | 2 | 4 | no | — |
| 162 | C2×#121 | — | 2 | 4 | no | — |
| 163 | C4×#41 | — | 2 | 1 | no | — |
| 164 | C4×#41 | — | 2 | 1 | no | — |
| 165 | C4×#41 | — | 2 | 1 | no | — |
| 166 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 167 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 168 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 169 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 170 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 171 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 172 | C2×C4×Q8 | D4 | 1 | 2 | yes | — |
| 173 | C2×C4×Q8 | D4 | 1 | 2 | yes | — |
| 174 | C2×C4×Q8 | D4 | 1 | 2 | yes | — |
| 175 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 176 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 177 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 178 | C2×C4×D4 | — | 2 | 4 | no | — |
| 179 | C2×C4×D4 | — | 2 | 4 | no | — |
| 180 | C2×C4×D4 | — | 2 | 4 | no | — |
| 181 | C2×C4×D4 | — | 2 | 4 | no | — |
| 182 | C2×C4×D4 | — | 2 | 4 | no | — |
| 183 | C2×C4×D4 | — | 2 | 4 | no | — |
| 184 | C2×C4×D4 | — | 2 | 1 | no | — |
| 185 | C2×C4×D4 | — | 2 | 1 | no | — |
| 186 | C2×C4×D4 | — | 2 | 1 | no | — |
| 187 | C2×C4×D4 | — | 2 | 1 | no | — |
| 188 | C2×C4×D4 | — | 2 | 1 | no | — |
| 189 | C2×C4×D4 | — | 2 | 1 | no | — |
| 190 | C2×C4×D4 | D4 | 1 | 2 | yes | — |
| 191 | C2×C4×D4 | D4 | 1 | 2 | yes | — |
| 192 | C2×C4×D4 | D4 | 1 | 2 | yes | — |
| 193 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 194 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 195 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 196 | C22×C4⋊C4 | — | 2 | 1 | no | — |
| 197 | C22×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 198 | C22×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 199 | C22×C22⋊C4 | — | 2 | 2 | no | — |
| 200 | C22×C22⋊C4 | — | 2 | 1 | no | — |
| 201 | C22×C42 | — | 2 | 1 | no | — |
| 202 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 203 | #496 | — | 2 | 4 | no | — |
| 204 | #493 | C23 | 1 | 4 | yes | complemented |
| 205 | #492 | C23 | 1 | 4 | yes | complemented |
| 206 | #490 | — | 2 | 4 | no | — |
| 207 | #486 | C23 | 1 | 4 | yes | complemented |
| 208 | #486 | C23 | 1 | 4 | yes | complemented |
| 209 | #484 | — | 2 | 2 | no | — |
| 210 | #484 | — | 2 | 2 | no | — |
| 211 | #483 | — | 2 | 2 | no | — |
| 212 | #483 | — | 2 | 2 | no | — |
| 213 | #481 | — | 2 | 2 | no | — |
| 214 | #481 | — | 2 | 2 | no | — |
| 215 | #480 | — | 2 | 2 | no | — |
| 216 | #480 | — | 2 | 2 | no | — |
| 217 | #479 | — | 2 | 4 | no | — |
| 218 | #478 | — | 2 | 4 | no | — |
| 219 | #477 | C23 | 1 | 4 | yes | complemented |
| 220 | #476 | C23 | 1 | 4 | yes | complemented |
| 221 | #475 | C23 | 1 | 4 | yes | complemented |
| 222 | #474 | C23 | 1 | 4 | yes | complemented |
| 223 | #464 | — | 2 | 4 | no | — |
| 224 | #463 | — | 2 | 4 | no | — |
| 225 | #462 | C23 | 1 | 4 | yes | complemented |
| 226 | #461 | C23 | 1 | 4 | yes | complemented |
| 227 | #460 | — | 2 | 4 | no | — |
| 228 | #460 | — | 2 | 4 | no | — |
| 229 | #460 | C23 | 1 | 4 | yes | complemented |
| 230 | #459 | — | 2 | 4 | no | — |
| 231 | #459 | — | 2 | 4 | no | — |
| 232 | #459 | C23 | 1 | 4 | yes | complemented |
| 233 | #451 | — | 2 | 2 | no | — |
| 234 | #451 | — | 2 | 2 | no | — |
| 235 | #450 | — | 2 | 2 | no | — |
| 236 | #450 | — | 2 | 2 | no | — |
| 237 | #450 | — | 2 | 4 | no | — |
| 238 | #450 | — | 2 | 4 | no | — |
| 239 | #448 | — | 2 | 2 | no | — |
| 240 | #448 | — | 2 | 2 | no | — |
| 241 | #447 | — | 2 | 2 | no | — |
| 242 | #447 | — | 2 | 2 | no | — |
| 243 | #447 | — | 2 | 4 | no | — |
| 244 | #447 | — | 2 | 4 | no | — |
| 245 | #442 | — | 2 | 4 | no | — |
| 246 | #441 | — | 2 | 4 | no | — |
| 247 | #440 | — | 2 | 4 | no | — |
| 248 | #440 | — | 2 | 4 | no | — |
| 249 | C4×Q16 | — | 2 | 4 | no | — |
| 250 | C4×SD16 | — | 2 | 4 | no | — |
| 251 | C4×SD16 | — | 2 | 4 | no | — |
| 252 | C4×D8 | — | 2 | 4 | no | — |
| 253 | #432 | — | 2 | 1 | no | — |
| 254 | #432 | — | 2 | 1 | no | — |
| 255 | #432 | — | 2 | 1 | no | — |
| 256 | #432 | — | 2 | 1 | no | — |
| 257 | #432 | C23 | 1 | 2 | yes | — |
| 258 | #432 | C23 | 1 | 2 | yes | — |
| 259 | #431 | — | 2 | 1 | no | — |
| 260 | #431 | — | 2 | 1 | no | — |
| 261 | #431 | C23 | 1 | 2 | yes | — |
| 262 | #431 | C23 | 1 | 2 | yes | — |
| 263 | #431 | C23 | 1 | 2 | yes | — |
| 264 | #431 | C23 | 1 | 2 | yes | — |
| 265 | #428 | — | 2 | 2 | no | — |
| 266 | #428 | — | 2 | 2 | no | — |
| 267 | #423 | — | 2 | 1 | no | — |
| 268 | #423 | C23 | 1 | 2 | yes | — |
| 269 | #423 | C23 | 1 | 2 | yes | — |
| 270 | #419 | — | 2 | 2 | no | — |
| 271 | #418 | — | 2 | 2 | no | — |
| 272 | #418 | — | 2 | 4 | no | — |
| 273 | #417 | — | 2 | 2 | no | — |
| 274 | #417 | — | 2 | 2 | no | — |
| 275 | #407 | — | 2 | 1 | no | — |
| 276 | #407 | — | 2 | 1 | no | — |
| 277 | #407 | — | 2 | 1 | no | — |
| 278 | C4×M16 | — | 2 | 1 | no | — |
| 279 | C4×M16 | — | 2 | 1 | no | — |
| 280 | C4×M16 | C23 | 1 | 2 | yes | — |
| 281 | #331 | C23 | 1 | 16 | yes | complemented |
| 282 | Q8⋊C8 | C23 | 1 | 16 | yes | complemented |
| 283 | D4⋊C8 | C23 | 1 | 16 | yes | complemented |
| 284 | C25 | — | 2 | 2 | no | — |
| 285 | C25 | — | 2 | 1 | no | — |
| 286 | C2×#41 | — | 2 | 16 | no | — |
| 287 | C2×#41 | — | 2 | 16 | no | — |
| 288 | C2×#41 | — | 2 | 16 | no | — |
| 289 | C2×#41 | — | 2 | 16 | no | — |
| 290 | C2×#41 | — | 2 | 1 | no | — |
| 291 | C2×#41 | — | 2 | 1 | no | — |
| 292 | C2×#41 | — | 2 | 1 | no | — |
| 293 | C2×#41 | — | 4 | 32 | no | — |
| 294 | C2×#41 | — | 4 | 32 | no | — |
| 295 | C2×#41 | — | 4 | 32 | no | — |
| 296 | C2×#41 | — | 4 | 32 | no | — |
| 297 | C2×#41 | — | 4 | 32 | no | — |
| 298 | C2×#41 | — | 4 | 16 | no | — |
| 299 | C2×#41 | — | 4 | 16 | no | — |
| 300 | C22×Q8 | — | 2 | 8 | no | — |
| 301 | C22×Q8 | — | 2 | 1 | no | — |
| 302 | C22×Q8 | — | 2 | 1 | no | — |
| 303 | C22×Q8 | — | 2 | 1 | no | — |
| 304 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 305 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 306 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 307 | C22×D4 | — | 2 | 8 | no | — |
| 308 | C22×D4 | — | 2 | 8 | no | — |
| 309 | C22×D4 | — | 2 | 8 | no | — |
| 310 | C22×D4 | — | 2 | 8 | no | — |
| 311 | C22×D4 | — | 2 | 8 | no | — |
| 312 | C22×D4 | — | 2 | 8 | no | — |
| 313 | C22×D4 | — | 2 | 1 | no | — |
| 314 | C22×D4 | — | 2 | 1 | no | — |
| 315 | C22×D4 | — | 2 | 1 | no | — |
| 316 | C22×D4 | — | 2 | 2 | no | — |
| 317 | C22×D4 | — | 2 | 2 | no | — |
| 318 | C22×D4 | — | 2 | 2 | no | — |
| 319 | C22×D4 | — | 2 | 2 | no | — |
| 320 | C22×D4 | — | 2 | 2 | no | — |
| 321 | C22×D4 | — | 2 | 2 | no | — |
| 322 | C22×D4 | — | 2 | 2 | no | — |
| 323 | C22×D4 | — | 2 | 2 | no | — |
| 324 | C22×D4 | — | 2 | 2 | no | — |
| 325 | C22×D4 | — | 2 | 2 | no | — |
| 326 | C22×D4 | — | 2 | 2 | no | — |
| 327 | C22×D4 | — | 2 | 2 | no | — |
| 328 | C22×D4 | — | 2 | 2 | no | — |
| 329 | C22×D4 | — | 2 | 2 | no | — |
| 330 | C22×D4 | — | 2 | 2 | no | — |
| 331 | C22×D4 | — | 4 | 4 | no | — |
| 332 | C22×D4 | — | 4 | 8 | no | — |
| 333 | C22×D4 | — | 4 | 16 | no | — |
| 334 | C22×D4 | — | 4 | 8 | no | — |
| 335 | C22×D4 | — | 8 | 4 | no | — |
| 336 | C22×D4 | — | 8 | 8 | no | — |
| 337 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 338 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 339 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 340 | C22×D4 | C2×D4 | 1 | 4 | yes | — |
| 341 | C22×D4 | C2×D4 | 1 | 4 | yes | — |
| 342 | C22×D4 | C2×D4 | 1 | 4 | yes | — |
| 343 | C23×C4 | — | 2 | 1 | no | — |
| 344 | C23×C4 | — | 2 | 8 | no | — |
| 345 | C23×C4 | — | 2 | 8 | no | — |
| 346 | C23×C4 | — | 2 | 8 | no | — |
| 347 | C23×C4 | — | 2 | 1 | no | — |
| 348 | C23×C4 | — | 2 | 1 | no | — |
| 349 | C23×C4 | — | 2 | 2 | no | — |
| 350 | C23×C4 | — | 2 | 2 | no | — |
| 351 | C23×C4 | — | 2 | 2 | no | — |
| 352 | C23×C4 | — | 2 | 2 | no | — |
| 353 | C23×C4 | — | 2 | 2 | no | — |
| 354 | C23×C4 | — | 2 | 2 | no | — |
| 355 | C23×C4 | — | 4 | 16 | no | — |
| 356 | C23×C4 | — | 4 | 8 | no | — |
| 357 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 358 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 359 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 360 | #137 | — | 4 | 8 | no | — |
| 361 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 362 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 363 | C2×Q16 | — | 2 | 4 | no | — |
| 364 | C2×SD16 | — | 2 | 4 | no | — |
| 365 | C2×SD16 | — | 2 | 4 | no | — |
| 366 | C2×SD16 | — | 2 | 8 | no | — |
| 367 | C2×D8 | — | 2 | 4 | no | — |
| 368 | C2×D8 | — | 2 | 8 | no | — |
| 369 | C2×M16 | — | 2 | 2 | no | — |
| 370 | C2×M16 | — | 2 | 2 | no | — |
| 371 | C2×M16 | — | 2 | 2 | no | — |
| 372 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 373 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 374 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 375 | #127 | — | 2 | 16 | no | — |
| 376 | #127 | — | 2 | 16 | no | — |
| 377 | #127 | — | 2 | 16 | no | — |
| 378 | #127 | — | 2 | 16 | no | — |
| 379 | #127 | — | 2 | 2 | no | — |
| 380 | #127 | — | 2 | 2 | no | — |
| 381 | #127 | — | 2 | 2 | no | — |
| 382 | #127 | — | 2 | 2 | no | — |
| 383 | #127 | — | 2 | 2 | no | — |
| 384 | #127 | — | 2 | 2 | no | — |
| 385 | #127 | — | 2 | 2 | no | — |
| 386 | #127 | — | 2 | 2 | no | — |
| 387 | #127 | — | 2 | 2 | no | — |
| 388 | #127 | — | 2 | 2 | no | — |
| 389 | #127 | — | 2 | 2 | no | — |
| 390 | #127 | — | 2 | 2 | no | — |
| 391 | #127 | C2×D4 | 1 | 4 | yes | — |
| 392 | #127 | C2×D4 | 1 | 4 | yes | — |
| 393 | #127 | C2×D4 | 1 | 4 | yes | — |
| 394 | #127 | C24 | 1 | 1 | yes | characteristic |
| 395 | #127 | C24 | 1 | 4 | yes | — |
| 396 | #126 | — | 4 | 1 | no | — |
| 397 | #126 | — | 4 | 1 | no | — |
| 398 | #125 | — | 2 | 1 | no | — |
| 399 | #125 | — | 2 | 1 | no | — |
| 400 | #125 | — | 2 | 1 | no | — |
| 401 | #124 | — | 2 | 1 | no | — |
| 402 | #124 | — | 2 | 1 | no | — |
| 403 | #124 | — | 2 | 1 | no | — |
| 404 | #123 | — | 4 | 1 | no | — |
| 405 | #123 | — | 4 | 1 | no | — |
| 406 | #123 | — | 4 | 1 | no | — |
| 407 | C22⋊Q8 | — | 2 | 1 | no | — |
| 408 | C22⋊Q8 | — | 2 | 1 | no | — |
| 409 | C22⋊Q8 | — | 2 | 1 | no | — |
| 410 | C22⋊Q8 | — | 2 | 1 | no | — |
| 411 | C22⋊Q8 | — | 2 | 1 | no | — |
| 412 | C22⋊Q8 | — | 2 | 1 | no | — |
| 413 | #121 | — | 2 | 16 | no | — |
| 414 | #121 | — | 2 | 16 | no | — |
| 415 | #121 | — | 2 | 16 | no | — |
| 416 | #121 | — | 2 | 32 | no | — |
| 417 | #121 | — | 2 | 32 | no | — |
| 418 | #121 | — | 2 | 32 | no | — |
| 419 | #121 | — | 2 | 32 | no | — |
| 420 | #121 | — | 2 | 16 | no | — |
| 421 | #121 | — | 2 | 1 | no | — |
| 422 | #121 | — | 2 | 1 | no | — |
| 423 | #121 | — | 2 | 1 | no | — |
| 424 | #121 | — | 2 | 1 | no | — |
| 425 | #121 | — | 2 | 1 | no | — |
| 426 | #121 | — | 2 | 1 | no | — |
| 427 | #120 | — | 4 | 1 | no | — |
| 428 | C4×Q8 | — | 2 | 2 | no | — |
| 429 | C4×Q8 | — | 2 | 2 | no | — |
| 430 | C4×Q8 | — | 2 | 2 | no | — |
| 431 | C4×Q8 | — | 2 | 2 | no | — |
| 432 | C4×Q8 | — | 2 | 2 | no | — |
| 433 | C4×Q8 | — | 2 | 2 | no | — |
| 434 | C4×Q8 | — | 2 | 2 | no | — |
| 435 | C4×Q8 | — | 2 | 2 | no | — |
| 436 | C4×Q8 | — | 2 | 2 | no | — |
| 437 | C4×Q8 | — | 2 | 2 | no | — |
| 438 | C4×Q8 | — | 2 | 2 | no | — |
| 439 | C4×Q8 | — | 2 | 2 | no | — |
| 440 | C4×Q8 | — | 2 | 1 | no | — |
| 441 | C4×Q8 | — | 2 | 1 | no | — |
| 442 | C4×Q8 | — | 2 | 1 | no | — |
| 443 | C4×Q8 | — | 2 | 1 | no | — |
| 444 | C4×Q8 | — | 2 | 1 | no | — |
| 445 | C4×Q8 | — | 2 | 1 | no | — |
| 446 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 447 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 448 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 449 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 450 | C4×D4 | — | 2 | 16 | no | — |
| 451 | C4×D4 | — | 2 | 16 | no | — |
| 452 | C4×D4 | — | 2 | 16 | no | — |
| 453 | C4×D4 | — | 2 | 16 | no | — |
| 454 | C4×D4 | — | 2 | 2 | no | — |
| 455 | C4×D4 | — | 2 | 2 | no | — |
| 456 | C4×D4 | — | 2 | 2 | no | — |
| 457 | C4×D4 | — | 2 | 2 | no | — |
| 458 | C4×D4 | — | 2 | 2 | no | — |
| 459 | C4×D4 | — | 2 | 2 | no | — |
| 460 | C4×D4 | — | 2 | 2 | no | — |
| 461 | C4×D4 | — | 2 | 2 | no | — |
| 462 | C4×D4 | — | 2 | 2 | no | — |
| 463 | C4×D4 | — | 2 | 2 | no | — |
| 464 | C4×D4 | — | 2 | 2 | no | — |
| 465 | C4×D4 | — | 2 | 2 | no | — |
| 466 | C4×D4 | — | 2 | 1 | no | — |
| 467 | C4×D4 | — | 2 | 1 | no | — |
| 468 | C4×D4 | — | 2 | 1 | no | — |
| 469 | C4×D4 | — | 2 | 1 | no | — |
| 470 | C4×D4 | — | 2 | 1 | no | — |
| 471 | C4×D4 | — | 2 | 1 | no | — |
| 472 | C4×D4 | — | 4 | 1 | no | — |
| 473 | C4×D4 | — | 4 | 1 | no | — |
| 474 | C4×D4 | — | 4 | 1 | no | — |
| 475 | C4×D4 | — | 4 | 1 | no | — |
| 476 | C4×D4 | — | 4 | 1 | no | — |
| 477 | C4×D4 | — | 4 | 1 | no | — |
| 478 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 479 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 480 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 481 | C4×D4 | C24 | 1 | 4 | yes | — |
| 482 | #117 | — | 2 | 1 | no | — |
| 483 | #117 | — | 2 | 1 | no | — |
| 484 | #117 | — | 2 | 1 | no | — |
| 485 | #117 | — | 4 | 1 | no | — |
| 486 | #117 | — | 4 | 1 | no | — |
| 487 | #117 | — | 4 | 1 | no | — |
| 488 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 489 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 490 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 491 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 492 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 493 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 494 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 495 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 496 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 497 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 498 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 499 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 500 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 501 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 502 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 503 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 504 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 505 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 506 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 507 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 508 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 509 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 510 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 511 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 512 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 513 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 514 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 515 | C2×C42 | — | 2 | 2 | no | — |
| 516 | C2×C42 | — | 2 | 2 | no | — |
| 517 | C2×C42 | — | 2 | 2 | no | — |
| 518 | C2×C42 | — | 2 | 2 | no | — |
| 519 | C2×C42 | — | 2 | 2 | no | — |
| 520 | C2×C42 | — | 2 | 2 | no | — |
| 521 | C2×C42 | — | 4 | 1 | no | — |
| 522 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 523 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 524 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 525 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 526 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 527 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 528 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 529 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 530 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 531 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 532 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 533 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 534 | #107 | — | 2 | 4 | no | — |
| 535 | #107 | — | 2 | 4 | no | — |
| 536 | #106 | — | 2 | 4 | no | — |
| 537 | #106 | — | 2 | 4 | no | — |
| 538 | C4⋊C8 | — | 2 | 2 | no | — |
| 539 | C4⋊C8 | — | 2 | 2 | no | — |
| 540 | C4⋊C8 | — | 2 | 2 | no | — |
| 541 | C4⋊C8 | — | 2 | 2 | no | — |
| 542 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 543 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 544 | #103 | — | 2 | 4 | no | — |
| 545 | #103 | — | 2 | 4 | no | — |
| 546 | #103 | — | 2 | 4 | no | — |
| 547 | #103 | — | 2 | 4 | no | — |
| 548 | #102 | — | 2 | 4 | no | — |
| 549 | #102 | — | 2 | 4 | no | — |
| 550 | #102 | — | 2 | 8 | no | — |
| 551 | #102 | — | 2 | 8 | no | — |
| 552 | #102 | — | 2 | 4 | no | — |
| 553 | #102 | — | 2 | 4 | no | — |
| 554 | C22⋊C8 | — | 2 | 2 | no | — |
| 555 | C22⋊C8 | — | 2 | 2 | no | — |
| 556 | C22⋊C8 | — | 2 | 2 | no | — |
| 557 | C22⋊C8 | — | 2 | 2 | no | — |
| 558 | C22⋊C8 | — | 2 | 2 | no | — |
| 559 | C22⋊C8 | — | 2 | 2 | no | — |
| 560 | #97 | — | 2 | 2 | no | — |
| 561 | #97 | — | 2 | 2 | no | — |
| 562 | #97 | — | 2 | 2 | no | — |
| 563 | C4×C8 | — | 2 | 2 | no | — |
| 564 | C4×C8 | — | 2 | 2 | no | — |
| 565 | C4×C8 | C24 | 1 | 4 | yes | — |
| 566 | C24 | — | 2 | 4 | no | — |
| 567 | C24 | — | 2 | 2 | no | — |
| 568 | C24 | — | 2 | 2 | no | — |
| 569 | C24 | — | 2 | 4 | no | — |
| 570 | C24 | — | 2 | 4 | no | — |
| 571 | C24 | — | 2 | 2 | no | — |
| 572 | C24 | — | 4 | 8 | no | — |
| 573 | C24 | — | 4 | 4 | no | — |
| 574 | C24 | — | 4 | 4 | no | — |
| 575 | C24 | — | 4 | 8 | no | — |
| 576 | C24 | — | 4 | 8 | no | — |
| 577 | C24 | — | 4 | 4 | no | — |
| 578 | C24 | #120 | 1 | 1 | yes | characteristic |
| 579 | #41 | — | 4 | 4 | no | — |
| 580 | #41 | — | 4 | 64 | no | — |
| 581 | #41 | — | 4 | 64 | no | — |
| 582 | #41 | — | 4 | 64 | no | — |
| 583 | #41 | — | 4 | 32 | no | — |
| 584 | #41 | — | 4 | 32 | no | — |
| 585 | #41 | — | 4 | 4 | no | — |
| 586 | #41 | — | 4 | 4 | no | — |
| 587 | C2×Q8 | — | 2 | 8 | no | — |
| 588 | C2×Q8 | — | 2 | 8 | no | — |
| 589 | C2×Q8 | — | 2 | 8 | no | — |
| 590 | C2×Q8 | — | 2 | 8 | no | — |
| 591 | C2×Q8 | — | 2 | 8 | no | — |
| 592 | C2×Q8 | — | 2 | 2 | no | — |
| 593 | C2×Q8 | — | 2 | 2 | no | — |
| 594 | C2×Q8 | — | 2 | 2 | no | — |
| 595 | C2×Q8 | — | 2 | 4 | no | — |
| 596 | C2×Q8 | — | 2 | 1 | no | — |
| 597 | C2×Q8 | — | 2 | 1 | no | — |
| 598 | C2×Q8 | — | 2 | 1 | no | — |
| 599 | C2×Q8 | AGL(1,ℤ/8) | 1 | 8 | yes | complemented |
| 600 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 601 | C2×D4 | — | 2 | 32 | no | — |
| 602 | C2×D4 | — | 2 | 32 | no | — |
| 603 | C2×D4 | — | 2 | 2 | no | — |
| 604 | C2×D4 | — | 2 | 2 | no | — |
| 605 | C2×D4 | — | 2 | 2 | no | — |
| 606 | C2×D4 | — | 2 | 4 | no | — |
| 607 | C2×D4 | — | 2 | 4 | no | — |
| 608 | C2×D4 | — | 2 | 4 | no | — |
| 609 | C2×D4 | — | 2 | 4 | no | — |
| 610 | C2×D4 | — | 2 | 4 | no | — |
| 611 | C2×D4 | — | 2 | 4 | no | — |
| 612 | C2×D4 | — | 2 | 4 | no | — |
| 613 | C2×D4 | — | 2 | 4 | no | — |
| 614 | C2×D4 | — | 2 | 4 | no | — |
| 615 | C2×D4 | — | 2 | 4 | no | — |
| 616 | C2×D4 | — | 2 | 4 | no | — |
| 617 | C2×D4 | — | 2 | 4 | no | — |
| 618 | C2×D4 | — | 2 | 4 | no | — |
| 619 | C2×D4 | — | 2 | 1 | no | — |
| 620 | C2×D4 | — | 2 | 1 | no | — |
| 621 | C2×D4 | — | 2 | 1 | no | — |
| 622 | C2×D4 | — | 4 | 4 | no | — |
| 623 | C2×D4 | — | 4 | 4 | no | — |
| 624 | C2×D4 | — | 4 | 4 | no | — |
| 625 | C2×D4 | — | 4 | 8 | no | — |
| 626 | C2×D4 | — | 4 | 4 | no | — |
| 627 | C2×D4 | — | 4 | 4 | no | — |
| 628 | C2×D4 | — | 4 | 8 | no | — |
| 629 | C2×D4 | — | 4 | 8 | no | — |
| 630 | C2×D4 | — | 4 | 8 | no | — |
| 631 | C2×D4 | — | 4 | 8 | no | — |
| 632 | C2×D4 | — | 4 | 32 | no | — |
| 633 | C2×D4 | — | 4 | 32 | no | — |
| 634 | C2×D4 | — | 4 | 32 | no | — |
| 635 | C2×D4 | — | 4 | 8 | no | — |
| 636 | C2×D4 | — | 4 | 8 | no | — |
| 637 | C2×D4 | — | 4 | 8 | no | — |
| 638 | C2×D4 | — | 4 | 8 | no | — |
| 639 | C2×D4 | — | 4 | 8 | no | — |
| 640 | C2×D4 | — | 4 | 8 | no | — |
| 641 | C2×D4 | — | 4 | 1 | no | — |
| 642 | C2×D4 | — | 4 | 1 | no | — |
| 643 | C2×D4 | — | 4 | 1 | no | — |
| 644 | C2×D4 | — | 4 | 8 | no | — |
| 645 | C2×D4 | — | 4 | 8 | no | — |
| 646 | C2×D4 | — | 8 | 4 | no | — |
| 647 | C2×D4 | — | 8 | 4 | no | — |
| 648 | C2×D4 | — | 8 | 4 | no | — |
| 649 | C2×D4 | — | 8 | 4 | no | — |
| 650 | C2×D4 | — | 8 | 4 | no | — |
| 651 | C2×D4 | — | 8 | 16 | no | — |
| 652 | C2×D4 | — | 8 | 16 | no | — |
| 653 | C2×D4 | — | 8 | 16 | no | — |
| 654 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 655 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 656 | C22×C4 | — | 2 | 8 | no | — |
| 657 | C22×C4 | — | 2 | 2 | no | — |
| 658 | C22×C4 | — | 2 | 2 | no | — |
| 659 | C22×C4 | — | 2 | 2 | no | — |
| 660 | C22×C4 | — | 2 | 4 | no | — |
| 661 | C22×C4 | — | 2 | 4 | no | — |
| 662 | C22×C4 | — | 2 | 32 | no | — |
| 663 | C22×C4 | — | 2 | 2 | no | — |
| 664 | C22×C4 | — | 2 | 2 | no | — |
| 665 | C22×C4 | — | 2 | 2 | no | — |
| 666 | C22×C4 | — | 2 | 2 | no | — |
| 667 | C22×C4 | — | 2 | 2 | no | — |
| 668 | C22×C4 | — | 2 | 2 | no | — |
| 669 | C22×C4 | — | 2 | 4 | no | — |
| 670 | C22×C4 | — | 2 | 4 | no | — |
| 671 | C22×C4 | — | 2 | 4 | no | — |
| 672 | C22×C4 | — | 2 | 4 | no | — |
| 673 | C22×C4 | — | 4 | 2 | no | — |
| 674 | C22×C4 | — | 4 | 32 | no | — |
| 675 | C22×C4 | — | 4 | 32 | no | — |
| 676 | C22×C4 | — | 4 | 32 | no | — |
| 677 | C22×C4 | — | 4 | 8 | no | — |
| 678 | C22×C4 | — | 4 | 8 | no | — |
| 679 | C22×C4 | — | 4 | 8 | no | — |
| 680 | C22×C4 | — | 4 | 8 | no | — |
| 681 | C22×C4 | — | 4 | 8 | no | — |
| 682 | C22×C4 | — | 4 | 4 | no | — |
| 683 | C22×C4 | — | 4 | 4 | no | — |
| 684 | C22×C4 | — | 4 | 8 | no | — |
| 685 | C22×C4 | — | 4 | 1 | no | — |
| 686 | C22×C4 | — | 4 | 1 | no | — |
| 687 | C22×C4 | — | 4 | 1 | no | — |
| 688 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 689 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 690 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 691 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 692 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 693 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 694 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 695 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 696 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 697 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 698 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 699 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 700 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 701 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 702 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 703 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 704 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 705 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 706 | Q16 | — | 4 | 8 | no | — |
| 707 | SD16 | — | 4 | 8 | no | — |
| 708 | SD16 | — | 4 | 8 | no | — |
| 709 | SD16 | — | 8 | 8 | no | — |
| 710 | D8 | — | 4 | 8 | no | — |
| 711 | D8 | — | 8 | 8 | no | — |
| 712 | M16 | — | 4 | 4 | no | — |
| 713 | M16 | — | 4 | 4 | no | — |
| 714 | M16 | — | 4 | 4 | no | — |
| 715 | C2×C8 | — | 2 | 4 | no | — |
| 716 | C2×C8 | — | 2 | 4 | no | — |
| 717 | C2×C8 | — | 2 | 4 | no | — |
| 718 | C4⋊C4 | — | 2 | 4 | no | — |
| 719 | C4⋊C4 | — | 2 | 4 | no | — |
| 720 | C4⋊C4 | — | 2 | 4 | no | — |
| 721 | C4⋊C4 | — | 2 | 2 | no | — |
| 722 | C4⋊C4 | — | 2 | 2 | no | — |
| 723 | C4⋊C4 | — | 2 | 2 | no | — |
| 724 | C4⋊C4 | — | 2 | 2 | no | — |
| 725 | C4⋊C4 | — | 2 | 2 | no | — |
| 726 | C4⋊C4 | — | 2 | 2 | no | — |
| 727 | C4⋊C4 | — | 2 | 4 | no | — |
| 728 | C4⋊C4 | — | 2 | 1 | no | — |
| 729 | C4⋊C4 | — | 2 | 1 | no | — |
| 730 | C4⋊C4 | — | 2 | 1 | no | — |
| 731 | C4⋊C4 | — | 2 | 1 | no | — |
| 732 | C4⋊C4 | — | 2 | 1 | no | — |
| 733 | C4⋊C4 | — | 2 | 1 | no | — |
| 734 | C4⋊C4 | — | 4 | 1 | no | — |
| 735 | C4⋊C4 | — | 4 | 1 | no | — |
| 736 | C4⋊C4 | — | 4 | 1 | no | — |
| 737 | C4⋊C4 | — | 4 | 1 | no | — |
| 738 | C4⋊C4 | — | 4 | 1 | no | — |
| 739 | C4⋊C4 | — | 4 | 1 | no | — |
| 740 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 741 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 742 | C22⋊C4 | — | 2 | 32 | no | — |
| 743 | C22⋊C4 | — | 2 | 4 | no | — |
| 744 | C22⋊C4 | — | 2 | 4 | no | — |
| 745 | C22⋊C4 | — | 2 | 4 | no | — |
| 746 | C22⋊C4 | — | 2 | 4 | no | — |
| 747 | C22⋊C4 | — | 4 | 1 | no | — |
| 748 | C22⋊C4 | — | 4 | 1 | no | — |
| 749 | C22⋊C4 | — | 4 | 1 | no | — |
| 750 | C22⋊C4 | — | 4 | 1 | no | — |
| 751 | C22⋊C4 | — | 4 | 1 | no | — |
| 752 | C22⋊C4 | — | 4 | 1 | no | — |
| 753 | C22⋊C4 | — | 4 | 1 | no | — |
| 754 | C22⋊C4 | — | 4 | 1 | no | — |
| 755 | C22⋊C4 | — | 4 | 1 | no | — |
| 756 | C42 | — | 2 | 4 | no | — |
| 757 | C42 | — | 2 | 4 | no | — |
| 758 | C42 | — | 2 | 4 | no | — |
| 759 | C42 | — | 2 | 4 | no | — |
| 760 | C42 | — | 4 | 1 | no | — |
| 761 | C42 | — | 4 | 1 | no | — |
| 762 | C42 | — | 4 | 1 | no | — |
| 763 | C42 | #120 | 1 | 1 | yes | characteristic |
| 764 | C42 | #120 | 1 | 1 | yes | characteristic |
| 765 | C42 | #120 | 1 | 1 | yes | characteristic |
| 766 | C42 | #120 | 1 | 1 | yes | characteristic |
| 767 | C42 | #120 | 1 | 1 | yes | characteristic |
| 768 | C42 | #120 | 1 | 1 | yes | characteristic |
| 769 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 770 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 771 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 772 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 773 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 774 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 775 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 776 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 777 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 778 | C42 | C25 | 1 | 1 | yes | characteristic |
| 779 | C23 | — | 2 | 2 | no | — |
| 780 | C23 | — | 2 | 2 | no | — |
| 781 | C23 | — | 2 | 2 | no | — |
| 782 | C23 | — | 2 | 4 | no | — |
| 783 | C23 | — | 2 | 8 | no | — |
| 784 | C23 | — | 4 | 8 | no | — |
| 785 | C23 | — | 4 | 4 | no | — |
| 786 | C23 | — | 4 | 8 | no | — |
| 787 | C23 | — | 4 | 4 | no | — |
| 788 | C23 | — | 4 | 4 | no | — |
| 789 | C23 | — | 4 | 4 | no | — |
| 790 | C23 | — | 4 | 8 | no | — |
| 791 | C23 | — | 4 | 8 | no | — |
| 792 | C23 | — | 4 | 8 | no | — |
| 793 | C23 | — | 4 | 8 | no | — |
| 794 | C23 | — | 4 | 4 | no | — |
| 795 | C23 | — | 4 | 4 | no | — |
| 796 | C23 | — | 4 | 8 | no | — |
| 797 | C23 | — | 4 | 4 | no | — |
| 798 | C23 | — | 4 | 4 | no | — |
| 799 | C23 | — | 4 | 8 | no | — |
| 800 | C23 | — | 4 | 8 | no | — |
| 801 | C23 | — | 4 | 4 | no | — |
| 802 | C23 | — | 4 | 1 | no | — |
| 803 | C23 | — | 8 | 16 | no | — |
| 804 | C23 | — | 8 | 32 | no | — |
| 805 | C23 | C2×#120 | 1 | 1 | yes | characteristic |
| 806 | C23 | C2×#120 | 1 | 1 | yes | characteristic |
| 807 | C23 | C2×#120 | 1 | 1 | yes | characteristic |
| 808 | Q8 | — | 2 | 8 | no | — |
| 809 | Q8 | — | 2 | 8 | no | — |
| 810 | Q8 | — | 2 | 8 | no | — |
| 811 | Q8 | — | 2 | 4 | no | — |
| 812 | Q8 | — | 4 | 2 | no | — |
| 813 | Q8 | — | 4 | 2 | no | — |
| 814 | Q8 | — | 4 | 2 | no | — |
| 815 | Q8 | C2×AGL(1,ℤ/8) | 1 | 8 | yes | — |
| 816 | D4 | — | 2 | 4 | no | — |
| 817 | D4 | — | 2 | 4 | no | — |
| 818 | D4 | — | 4 | 8 | no | — |
| 819 | D4 | — | 4 | 4 | no | — |
| 820 | D4 | — | 4 | 4 | no | — |
| 821 | D4 | — | 4 | 8 | no | — |
| 822 | D4 | — | 4 | 8 | no | — |
| 823 | D4 | — | 4 | 64 | no | — |
| 824 | D4 | — | 4 | 8 | no | — |
| 825 | D4 | — | 4 | 8 | no | — |
| 826 | D4 | — | 4 | 2 | no | — |
| 827 | D4 | — | 4 | 8 | no | — |
| 828 | D4 | — | 4 | 4 | no | — |
| 829 | D4 | — | 4 | 8 | no | — |
| 830 | D4 | — | 4 | 8 | no | — |
| 831 | D4 | — | 4 | 2 | no | — |
| 832 | D4 | — | 4 | 8 | no | — |
| 833 | D4 | — | 4 | 2 | no | — |
| 834 | D4 | — | 8 | 4 | no | — |
| 835 | D4 | — | 8 | 4 | no | — |
| 836 | D4 | — | 8 | 4 | no | — |
| 837 | D4 | — | 8 | 32 | no | — |
| 838 | D4 | — | 8 | 2 | no | — |
| 839 | D4 | — | 8 | 2 | no | — |
| 840 | D4 | — | 8 | 2 | no | — |
| 841 | C2×C4 | — | 2 | 8 | no | — |
| 842 | C2×C4 | — | 2 | 8 | no | — |
| 843 | C2×C4 | — | 2 | 4 | no | — |
| 844 | C2×C4 | — | 2 | 8 | no | — |
| 845 | C2×C4 | — | 2 | 2 | no | — |
| 846 | C2×C4 | — | 2 | 2 | no | — |
| 847 | C2×C4 | — | 2 | 2 | no | — |
| 848 | C2×C4 | — | 2 | 2 | no | — |
| 849 | C2×C4 | — | 2 | 2 | no | — |
| 850 | C2×C4 | — | 2 | 2 | no | — |
| 851 | C2×C4 | — | 2 | 2 | no | — |
| 852 | C2×C4 | — | 2 | 2 | no | — |
| 853 | C2×C4 | — | 2 | 2 | no | — |
| 854 | C2×C4 | — | 2 | 2 | no | — |
| 855 | C2×C4 | — | 2 | 2 | no | — |
| 856 | C2×C4 | — | 2 | 2 | no | — |
| 857 | C2×C4 | — | 2 | 4 | no | — |
| 858 | C2×C4 | — | 2 | 4 | no | — |
| 859 | C2×C4 | — | 4 | 1 | no | — |
| 860 | C2×C4 | — | 4 | 1 | no | — |
| 861 | C2×C4 | — | 4 | 1 | no | — |
| 862 | C2×C4 | — | 4 | 1 | no | — |
| 863 | C2×C4 | — | 4 | 64 | no | — |
| 864 | C2×C4 | — | 4 | 8 | no | — |
| 865 | C2×C4 | — | 4 | 8 | no | — |
| 866 | C2×C4 | — | 4 | 4 | no | — |
| 867 | C2×C4 | — | 4 | 4 | no | — |
| 868 | C2×C4 | — | 4 | 4 | no | — |
| 869 | C2×C4 | — | 4 | 4 | no | — |
| 870 | C2×C4 | — | 4 | 4 | no | — |
| 871 | C2×C4 | — | 4 | 4 | no | — |
| 872 | C2×C4 | — | 4 | 8 | no | — |
| 873 | C2×C4 | — | 4 | 8 | no | — |
| 874 | C2×C4 | — | 4 | 1 | no | — |
| 875 | C2×C4 | — | 4 | 1 | no | — |
| 876 | C2×C4 | — | 4 | 1 | no | — |
| 877 | C2×C4 | — | 8 | 2 | no | — |
| 878 | C2×C4 | — | 8 | 2 | no | — |
| 879 | C2×C4 | — | 8 | 2 | no | — |
| 880 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 881 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 882 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 883 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 884 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 885 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 886 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 887 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 888 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 889 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 890 | C2×C4 | #575 | 1 | 4 | yes | — |
| 891 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 892 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 893 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 894 | C8 | — | 4 | 4 | no | — |
| 895 | C8 | — | 4 | 4 | no | — |
| 896 | C8 | — | 4 | 4 | no | — |
| 897 | C22 | — | 2 | 8 | no | — |
| 898 | C22 | — | 2 | 1 | no | — |
| 899 | C22 | — | 2 | 1 | no | — |
| 900 | C22 | — | 2 | 1 | no | — |
| 901 | C22 | — | 2 | 1 | no | — |
| 902 | C22 | — | 2 | 1 | no | — |
| 903 | C22 | — | 2 | 1 | no | — |
| 904 | C22 | — | 4 | 8 | no | — |
| 905 | C22 | — | 4 | 4 | no | — |
| 906 | C22 | — | 4 | 4 | no | — |
| 907 | C22 | — | 4 | 8 | no | — |
| 908 | C22 | — | 4 | 8 | no | — |
| 909 | C22 | — | 4 | 4 | no | — |
| 910 | C22 | — | 8 | 8 | no | — |
| 911 | C22 | — | 8 | 16 | no | — |
| 912 | C22 | — | 8 | 8 | no | — |
| 913 | C22 | — | 8 | 16 | no | — |
| 914 | C22 | — | 8 | 16 | no | — |
| 915 | C22 | — | 8 | 8 | no | — |
| 916 | C22 | — | 8 | 1 | no | — |
| 917 | C22 | — | 8 | 1 | no | — |
| 918 | C22 | — | 8 | 1 | no | — |
| 919 | C22 | #3003 | 1 | 2 | yes | — |
| 920 | C22 | #3005 | 1 | 2 | yes | — |
| 921 | C22 | #3019 | 1 | 2 | yes | — |
| 922 | C22 | C22×#120 | 1 | 1 | yes | characteristic |
| 923 | C4 | — | 2 | 8 | no | — |
| 924 | C4 | — | 2 | 1 | no | — |
| 925 | C4 | — | 2 | 1 | no | — |
| 926 | C4 | — | 2 | 1 | no | — |
| 927 | C4 | — | 2 | 1 | no | — |
| 928 | C4 | — | 2 | 1 | no | — |
| 929 | C4 | — | 2 | 1 | no | — |
| 930 | C4 | — | 2 | 1 | no | — |
| 931 | C4 | — | 2 | 1 | no | — |
| 932 | C4 | — | 4 | 4 | no | — |
| 933 | C4 | — | 4 | 4 | no | — |
| 934 | C4 | — | 8 | 1 | no | — |
| 935 | C4 | — | 8 | 1 | no | — |
| 936 | C4 | — | 8 | 1 | no | — |
| 937 | C4 | #3003 | 1 | 2 | yes | — |
| 938 | C4 | #3005 | 1 | 2 | yes | — |
| 939 | C4 | C22×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 940 | C4 | C2×#575 | 1 | 2 | yes | — |
| 941 | C2 | — | 2 | 2 | no | — |
| 942 | C2 | — | 2 | 2 | no | — |
| 943 | C2 | — | 2 | 2 | no | — |
| 944 | C2 | — | 8 | 4 | no | — |
| 945 | C2 | — | 8 | 8 | no | — |
| 946 | C2 | — | 16 | 1 | no | — |
| 947 | C2 | C2×#3003 | 1 | 1 | yes | characteristic |
| 948 | C2 | C2×#3005 | 1 | 1 | yes | characteristic |
| 949 | C2 | C2×#3019 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#120 |
| commutator, Frattini, cosocle | C42 | C25 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#550 | C2 | semidirect |
| 2. #60798 | C2 | semidirect |
| 3. #60560 | C2 | semidirect |
| 4. #60558 | C2 | semidirect |
| 5. #18771 | C2 | semidirect |
| 6. #18770 | C2 | semidirect |
| 7. #18767 | C2 | semidirect |
| 8. #18766 | C2 | semidirect |
| 9. #18550 | C2 | semidirect |
| 10. #18545 | C2 | semidirect |
| 11. #17741 | C2 | semidirect |
| 12. #17449 | C2 | semidirect |
| 13. #17448 | C2 | semidirect |
| 37. #3208 | C22 | semidirect |
| 38. #3208 | C22 | semidirect |
| 39. #3205 | C22 | semidirect |
| 40. #3205 | C22 | semidirect |
| 41. #3151 | C22 | semidirect |
| 42. #3138 | C22 | semidirect |
| 45. #3113 | C22 | semidirect |
| 46. #3112 | C22 | semidirect |
| 47. #3110 | C22 | semidirect |
| 48. #3109 | C22 | semidirect |
| 51. #3104 | C22 | semidirect |
| 52. #3103 | C22 | semidirect |
| 53. #3101 | C22 | semidirect |
| 54. #3100 | C22 | semidirect |
| 57. #3078 | C22 | semidirect |
| 58. #3077 | C22 | semidirect |
| 60. #3037 | C22 | semidirect |
| 61. #3036 | C22 | semidirect |
| 70. #1642 | C22 | semidirect |
| 71. #1641 | C22 | semidirect |
| 72. #1631 | C22 | semidirect |
| 73. #1621 | C22 | semidirect |
| 74. #1555 | C22 | semidirect |
| 75. #1545 | C22 | semidirect |
| 76. #1545 | C22 | semidirect |
| 77. #1491 | C22 | semidirect |
| 78. #1490 | C22 | semidirect |
| 79. #1487 | C22 | semidirect |
| 80. #1486 | C22 | semidirect |
| 81. #1479 | C22 | semidirect |
| 82. #1478 | C22 | semidirect |
| 204. #493 | C23 | semidirect |
| 205. #492 | C23 | semidirect |
| 207. #486 | C23 | semidirect |
| 208. #486 | C23 | semidirect |
| 219. #477 | C23 | semidirect |
| 220. #476 | C23 | semidirect |
| 221. #475 | C23 | semidirect |
| 222. #474 | C23 | semidirect |
| 225. #462 | C23 | semidirect |
| 226. #461 | C23 | semidirect |
| 229. #460 | C23 | semidirect |
| 232. #459 | C23 | semidirect |
| 281. #331 | C23 | semidirect |
| 282. Q8⋊C8 | C23 | semidirect |
| 283. D4⋊C8 | C23 | semidirect |
| 599. C2×Q8 | AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#550 | 2 |
| #60798 | 2 |
| #60560 | 2 |
| #60558 | 2 |
| #18771 | 2 |
| #18770 | 2 |
| #18767 | 2 |
| #18766 | 2 |
| #18550 | 2 |
| #18545 | 2 |
| #17741 | 2 |
| #17449 | 2 |
| #17448 | 2 |