Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1039 conjugacy classes of subgroups.
The subgroup lattice has 932 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #3482⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #85423 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #85421 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85401 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #85398 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85387 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #85384 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #85382 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #85377 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #85343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C4×#986 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #85329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C4×#983 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #85325 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×C4×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #61445 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×#986 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#983 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 20 | #5547 | — | 4 | 1 | no | maximal |
| 21 | #557⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | D4×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #548⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 24 | #548⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C4×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C4×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×C4×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #5427 | C22 | 1 | 1 | yes | characteristic |
| 29 | #5426 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #5425 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5421 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5421 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #5421 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #5420 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #5419 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×#859 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #5395 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #5395 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #5394 | C22 | 1 | 1 | yes | characteristic |
| 40 | #5394 | C22 | 1 | 1 | yes | characteristic |
| 41 | #5394 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C4⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 43 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 44 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 45 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #5389 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #5389 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #5388 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C4×#226 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | #5386 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #3482 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #3481 | — | 3 | 1 | no | — |
| 55 | #3401 | — | 3 | 1 | no | — |
| 56 | #3388 | — | 3 | 1 | no | — |
| 57 | #3376 | — | 3 | 1 | no | — |
| 58 | #3371 | — | 3 | 1 | no | — |
| 59 | #3351 | — | 3 | 1 | no | — |
| 60 | #3345 | — | 3 | 1 | no | — |
| 61 | #3344 | — | 3 | 1 | no | — |
| 62 | #3326 | — | 3 | 1 | no | — |
| 63 | #3323 | — | 3 | 1 | no | — |
| 64 | #3320 | — | 3 | 1 | no | — |
| 65 | #3316 | — | 3 | 1 | no | — |
| 66 | #3310 | — | 3 | 1 | no | — |
| 67 | #3306 | — | 3 | 1 | no | — |
| 68 | #3275 | — | 3 | 1 | no | — |
| 69 | #3266 | — | 3 | 1 | no | — |
| 70 | #3265 | — | 3 | 1 | no | — |
| 71 | #3172 | — | 3 | 1 | no | — |
| 72 | #3171 | — | 3 | 1 | no | — |
| 73 | #3168 | — | 3 | 1 | no | — |
| 74 | #3108 | — | 3 | 1 | no | — |
| 75 | #3105 | — | 3 | 1 | no | — |
| 76 | #3103 | — | 3 | 1 | no | — |
| 77 | #3102 | — | 3 | 1 | no | — |
| 78 | #3102 | — | 3 | 1 | no | — |
| 79 | #3101 | — | 3 | 1 | no | — |
| 80 | #2965 | — | 3 | 1 | no | — |
| 81 | C4×#137 | — | 3 | 1 | no | — |
| 82 | C4×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 83 | C2×C4×SD16 | — | 3 | 1 | no | — |
| 84 | C2×#235 | — | 4 | 1 | no | — |
| 85 | C22×C4×D3 | — | 4 | 1 | no | — |
| 86 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 87 | C22×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 88 | C22×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 89 | #986 | — | 2 | 2 | no | — |
| 90 | #983 | — | 2 | 2 | no | — |
| 91 | C2×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 92 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×#226 | C23 | 1 | 1 | yes | characteristic |
| 96 | C3×C4×D4 | — | 4 | 1 | no | — |
| 97 | #939 | — | 4 | 1 | no | — |
| 98 | #937 | — | 4 | 1 | no | — |
| 99 | C4×#67 | — | 4 | 1 | no | — |
| 100 | C4×#67 | — | 4 | 1 | no | — |
| 101 | #896 | — | 4 | 1 | no | — |
| 102 | #894 | — | 4 | 1 | no | — |
| 103 | #884 | — | 4 | 1 | no | — |
| 104 | #883 | — | 4 | 1 | no | — |
| 105 | #882 | — | 4 | 1 | no | — |
| 106 | #878 | — | 4 | 1 | no | — |
| 107 | C4×D12 | — | 4 | 1 | no | — |
| 108 | #872 | — | 4 | 1 | no | — |
| 109 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 110 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 111 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 112 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 113 | #859 | C23 | 1 | 1 | yes | characteristic |
| 114 | #859 | C23 | 1 | 1 | yes | characteristic |
| 115 | #859 | C23 | 1 | 1 | yes | characteristic |
| 116 | #859 | C23 | 1 | 1 | yes | characteristic |
| 117 | C2×#137 | — | 3 | 1 | no | — |
| 118 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 119 | C22×SD16 | — | 3 | 1 | no | — |
| 120 | #559 | — | 3 | 1 | no | — |
| 121 | #557 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 122 | #556 | — | 3 | 1 | no | — |
| 123 | #554 | — | 3 | 1 | no | — |
| 124 | #554 | — | 3 | 1 | no | — |
| 125 | #553 | — | 3 | 1 | no | — |
| 126 | #553 | — | 3 | 1 | no | — |
| 127 | #553 | — | 6 | 1 | no | — |
| 128 | #552 | — | 3 | 1 | no | — |
| 129 | #552 | — | 3 | 1 | no | — |
| 130 | #551 | — | 6 | 1 | no | — |
| 131 | #551 | — | 6 | 1 | no | — |
| 132 | D4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 133 | #548 | C2×D3 | 1 | 1 | yes | characteristic |
| 134 | #548 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 135 | #547 | — | 3 | 1 | no | — |
| 136 | #546 | — | 3 | 1 | no | — |
| 137 | #546 | — | 3 | 1 | no | — |
| 138 | #546 | — | 6 | 1 | no | — |
| 139 | D42 | — | 3 | 1 | no | — |
| 140 | #533 | — | 3 | 1 | no | — |
| 141 | #532 | — | 3 | 1 | no | — |
| 142 | #529 | — | 3 | 1 | no | — |
| 143 | #529 | — | 3 | 1 | no | — |
| 144 | #529 | — | 3 | 1 | no | — |
| 145 | #529 | — | 3 | 1 | no | — |
| 146 | #529 | — | 6 | 1 | no | — |
| 147 | #525 | — | 6 | 1 | no | — |
| 148 | #525 | — | 6 | 1 | no | — |
| 149 | C4×#41 | — | 3 | 1 | no | — |
| 150 | C4×#41 | — | 3 | 1 | no | — |
| 151 | C4×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 152 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 154 | C2×C4×D4 | — | 3 | 1 | no | — |
| 155 | C2×C4×D4 | — | 3 | 1 | no | — |
| 156 | C2×C4×D4 | — | 6 | 1 | no | — |
| 157 | #501 | — | 3 | 1 | no | — |
| 158 | #501 | — | 3 | 1 | no | — |
| 159 | #499 | — | 3 | 1 | no | — |
| 160 | #497 | — | 3 | 1 | no | — |
| 161 | #496 | — | 3 | 1 | no | — |
| 162 | #495 | — | 3 | 1 | no | — |
| 163 | #491 | — | 3 | 1 | no | — |
| 164 | #490 | — | 3 | 1 | no | — |
| 165 | #489 | — | 3 | 1 | no | — |
| 166 | #489 | — | 3 | 1 | no | — |
| 167 | #488 | — | 3 | 1 | no | — |
| 168 | #488 | — | 3 | 1 | no | — |
| 169 | #485 | — | 3 | 1 | no | — |
| 170 | #485 | — | 3 | 1 | no | — |
| 171 | #484 | — | 3 | 1 | no | — |
| 172 | #483 | — | 3 | 1 | no | — |
| 173 | #483 | — | 3 | 1 | no | — |
| 174 | #483 | — | 3 | 1 | no | — |
| 175 | #482 | — | 3 | 1 | no | — |
| 176 | #482 | — | 3 | 1 | no | — |
| 177 | #481 | — | 3 | 1 | no | — |
| 178 | #481 | — | 3 | 1 | no | — |
| 179 | #481 | — | 3 | 1 | no | — |
| 180 | #480 | — | 3 | 1 | no | — |
| 181 | #479 | — | 3 | 1 | no | — |
| 182 | #479 | — | 3 | 1 | no | — |
| 183 | #479 | — | 3 | 1 | no | — |
| 184 | #479 | — | 3 | 1 | no | — |
| 185 | #478 | — | 3 | 1 | no | — |
| 186 | #478 | — | 3 | 1 | no | — |
| 187 | #478 | — | 3 | 1 | no | — |
| 188 | #478 | — | 3 | 1 | no | — |
| 189 | #476 | — | 3 | 1 | no | — |
| 190 | #476 | — | 3 | 1 | no | — |
| 191 | #475 | — | 3 | 1 | no | — |
| 192 | #475 | — | 3 | 1 | no | — |
| 193 | #470 | — | 3 | 1 | no | — |
| 194 | #470 | — | 3 | 1 | no | — |
| 195 | #469 | — | 3 | 1 | no | — |
| 196 | #469 | — | 3 | 1 | no | — |
| 197 | #468 | — | 3 | 1 | no | — |
| 198 | #468 | — | 3 | 1 | no | — |
| 199 | #468 | — | 3 | 1 | no | — |
| 200 | #468 | — | 3 | 1 | no | — |
| 201 | #467 | — | 3 | 1 | no | — |
| 202 | #466 | — | 3 | 1 | no | — |
| 203 | #465 | — | 3 | 1 | no | — |
| 204 | #465 | — | 3 | 1 | no | — |
| 205 | #464 | — | 3 | 1 | no | — |
| 206 | #464 | — | 3 | 1 | no | — |
| 207 | #464 | — | 3 | 1 | no | — |
| 208 | #464 | — | 3 | 1 | no | — |
| 209 | #463 | — | 3 | 1 | no | — |
| 210 | #463 | — | 3 | 1 | no | — |
| 211 | #463 | — | 3 | 1 | no | — |
| 212 | #463 | — | 3 | 1 | no | — |
| 213 | #461 | — | 3 | 1 | no | — |
| 214 | #461 | — | 3 | 1 | no | — |
| 215 | #460 | — | 3 | 1 | no | — |
| 216 | #460 | — | 3 | 1 | no | — |
| 217 | #452 | — | 3 | 1 | no | — |
| 218 | #452 | — | 3 | 1 | no | — |
| 219 | #451 | — | 3 | 1 | no | — |
| 220 | #450 | — | 3 | 1 | no | — |
| 221 | #450 | — | 3 | 1 | no | — |
| 222 | #450 | — | 3 | 1 | no | — |
| 223 | #449 | — | 3 | 1 | no | — |
| 224 | #449 | — | 3 | 1 | no | — |
| 225 | #448 | — | 3 | 1 | no | — |
| 226 | #448 | — | 3 | 1 | no | — |
| 227 | #448 | — | 3 | 1 | no | — |
| 228 | #447 | — | 3 | 1 | no | — |
| 229 | #446 | — | 3 | 1 | no | — |
| 230 | #446 | — | 3 | 1 | no | — |
| 231 | #442 | — | 3 | 1 | no | — |
| 232 | #442 | — | 3 | 1 | no | — |
| 233 | #441 | — | 3 | 1 | no | — |
| 234 | #441 | — | 3 | 1 | no | — |
| 235 | #440 | — | 3 | 1 | no | — |
| 236 | #440 | — | 3 | 1 | no | — |
| 237 | #440 | — | 3 | 1 | no | — |
| 238 | #440 | — | 3 | 1 | no | — |
| 239 | C4×Q16 | — | 3 | 1 | no | — |
| 240 | C4×Q16 | — | 3 | 1 | no | — |
| 241 | C4×Q16 | — | 3 | 1 | no | — |
| 242 | C4×SD16 | — | 3 | 1 | no | — |
| 243 | C4×SD16 | — | 3 | 1 | no | — |
| 244 | C4×SD16 | — | 3 | 1 | no | — |
| 245 | C4×SD16 | — | 3 | 1 | no | — |
| 246 | C4×SD16 | — | 3 | 1 | no | — |
| 247 | C4×SD16 | — | 3 | 1 | no | — |
| 248 | C4×SD16 | — | 3 | 1 | no | — |
| 249 | C4×SD16 | — | 3 | 1 | no | — |
| 250 | C4×SD16 | — | 3 | 1 | no | — |
| 251 | C4×SD16 | — | 3 | 1 | no | — |
| 252 | C4×SD16 | — | 3 | 1 | no | — |
| 253 | C4×SD16 | — | 3 | 1 | no | — |
| 254 | C4×SD16 | — | 3 | 1 | no | — |
| 255 | C4×SD16 | — | 3 | 1 | no | — |
| 256 | C4×D8 | — | 3 | 1 | no | — |
| 257 | C4×D8 | — | 3 | 1 | no | — |
| 258 | C4×D8 | — | 3 | 1 | no | — |
| 259 | #436 | — | 3 | 1 | no | — |
| 260 | #436 | — | 3 | 1 | no | — |
| 261 | #435 | — | 3 | 1 | no | — |
| 262 | #435 | — | 3 | 1 | no | — |
| 263 | #435 | — | 3 | 1 | no | — |
| 264 | #435 | — | 3 | 1 | no | — |
| 265 | #431 | — | 3 | 1 | no | — |
| 266 | #431 | — | 3 | 1 | no | — |
| 267 | #431 | — | 3 | 1 | no | — |
| 268 | #428 | — | 3 | 1 | no | — |
| 269 | #428 | — | 3 | 1 | no | — |
| 270 | C2×#106 | — | 3 | 1 | no | — |
| 271 | #419 | — | 3 | 1 | no | — |
| 272 | #418 | — | 3 | 1 | no | — |
| 273 | #417 | — | 3 | 1 | no | — |
| 274 | #417 | — | 3 | 1 | no | — |
| 275 | C2×#103 | — | 3 | 1 | no | — |
| 276 | C2×#102 | — | 3 | 1 | no | — |
| 277 | C4×M16 | — | 3 | 1 | no | — |
| 278 | C4×M16 | — | 3 | 1 | no | — |
| 279 | C2×C4×C8 | — | 3 | 1 | no | — |
| 280 | C23×D3 | — | 4 | 1 | no | — |
| 281 | C2×C3×D4 | — | 4 | 1 | no | — |
| 282 | C22×C3×C4 | — | 4 | 1 | no | — |
| 283 | C22×C3×C4 | — | 4 | 1 | no | — |
| 284 | C2×#67 | — | 4 | 1 | no | — |
| 285 | C2×#67 | — | 4 | 1 | no | — |
| 286 | C2×#67 | — | 4 | 1 | no | — |
| 287 | C2×#67 | — | 4 | 1 | no | — |
| 288 | C22×Dic3 | — | 4 | 1 | no | — |
| 289 | #235 | — | 8 | 4 | no | — |
| 290 | C2×D12 | — | 4 | 1 | no | — |
| 291 | C2×D12 | — | 4 | 1 | no | — |
| 292 | C2×C4×D3 | — | 4 | 1 | no | — |
| 293 | C2×C4×D3 | — | 4 | 1 | no | — |
| 294 | C2×C4×D3 | — | 4 | 1 | no | — |
| 295 | C2×C4×D3 | — | 4 | 1 | no | — |
| 296 | C2×C4×D3 | — | 4 | 1 | no | — |
| 297 | C2×C4×D3 | — | 8 | 4 | no | — |
| 298 | C2×Dic6 | — | 4 | 1 | no | — |
| 299 | #41⋊C3 | — | 2 | 1 | no | — |
| 300 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 301 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 302 | C2×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 303 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 304 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 305 | GL(2,𝔽3) | #41 | 1 | 2 | yes | complemented |
| 306 | #226 | — | 2 | 1 | no | — |
| 307 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 308 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 309 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 310 | C3×C42 | — | 4 | 1 | no | — |
| 311 | #217 | — | 4 | 1 | no | — |
| 312 | #217 | — | 4 | 1 | no | — |
| 313 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 314 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 315 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 316 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 317 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 318 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 319 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 320 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 321 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 322 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 323 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 324 | C4×Dic3 | — | 4 | 1 | no | — |
| 325 | C2×#41 | — | 3 | 1 | no | — |
| 326 | C2×#41 | — | 3 | 1 | no | — |
| 327 | C2×#41 | — | 6 | 1 | no | — |
| 328 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 329 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 330 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 331 | C22×D4 | — | 3 | 1 | no | — |
| 332 | C22×D4 | — | 3 | 1 | no | — |
| 333 | C22×D4 | — | 6 | 1 | no | — |
| 334 | C23×C4 | — | 6 | 1 | no | — |
| 335 | C23×C4 | — | 6 | 1 | no | — |
| 336 | #137 | — | 6 | 2 | no | — |
| 337 | #137 | — | 6 | 2 | no | — |
| 338 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 339 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 340 | C2×Q16 | — | 3 | 1 | no | — |
| 341 | C2×Q16 | — | 3 | 1 | no | — |
| 342 | C2×Q16 | — | 3 | 1 | no | — |
| 343 | C2×SD16 | — | 3 | 1 | no | — |
| 344 | C2×SD16 | — | 3 | 1 | no | — |
| 345 | C2×SD16 | — | 3 | 1 | no | — |
| 346 | C2×SD16 | — | 3 | 1 | no | — |
| 347 | C2×SD16 | — | 3 | 1 | no | — |
| 348 | C2×SD16 | — | 3 | 1 | no | — |
| 349 | C2×SD16 | — | 3 | 1 | no | — |
| 350 | C2×SD16 | — | 3 | 1 | no | — |
| 351 | C2×SD16 | — | 3 | 1 | no | — |
| 352 | C2×SD16 | — | 3 | 1 | no | — |
| 353 | C2×SD16 | — | 6 | 2 | no | — |
| 354 | C2×SD16 | — | 6 | 2 | no | — |
| 355 | C2×D8 | — | 3 | 1 | no | — |
| 356 | C2×D8 | — | 3 | 1 | no | — |
| 357 | C2×D8 | — | 3 | 1 | no | — |
| 358 | C2×M16 | — | 3 | 1 | no | — |
| 359 | C2×M16 | — | 3 | 1 | no | — |
| 360 | C2×M16 | — | 3 | 1 | no | — |
| 361 | C2×M16 | — | 3 | 1 | no | — |
| 362 | C22×C8 | — | 3 | 1 | no | — |
| 363 | C22×C8 | — | 3 | 1 | no | — |
| 364 | C4⋊Q8 | — | 3 | 1 | no | — |
| 365 | C4⋊Q8 | — | 3 | 1 | no | — |
| 366 | C4⋊Q8 | — | 3 | 1 | no | — |
| 367 | #127 | — | 3 | 1 | no | — |
| 368 | #126 | — | 6 | 1 | no | — |
| 369 | #126 | — | 6 | 1 | no | — |
| 370 | #126 | — | 6 | 1 | no | — |
| 371 | #126 | — | 6 | 1 | no | — |
| 372 | #126 | — | 6 | 1 | no | — |
| 373 | #126 | — | 6 | 1 | no | — |
| 374 | #125 | — | 3 | 1 | no | — |
| 375 | #125 | — | 3 | 1 | no | — |
| 376 | #125 | — | 3 | 1 | no | — |
| 377 | #125 | — | 3 | 1 | no | — |
| 378 | #125 | — | 6 | 1 | no | — |
| 379 | #125 | — | 6 | 1 | no | — |
| 380 | #124 | — | 3 | 1 | no | — |
| 381 | #124 | — | 3 | 1 | no | — |
| 382 | #124 | — | 3 | 1 | no | — |
| 383 | #124 | — | 3 | 1 | no | — |
| 384 | #124 | — | 6 | 1 | no | — |
| 385 | #124 | — | 6 | 1 | no | — |
| 386 | #123 | — | 6 | 1 | no | — |
| 387 | #123 | — | 6 | 1 | no | — |
| 388 | #123 | — | 6 | 1 | no | — |
| 389 | #123 | — | 6 | 1 | no | — |
| 390 | #123 | — | 6 | 1 | no | — |
| 391 | #123 | — | 6 | 1 | no | — |
| 392 | #123 | — | 6 | 1 | no | — |
| 393 | #123 | — | 6 | 1 | no | — |
| 394 | #123 | — | 6 | 1 | no | — |
| 395 | #123 | — | 6 | 1 | no | — |
| 396 | C22⋊Q8 | — | 3 | 1 | no | — |
| 397 | C22⋊Q8 | — | 3 | 1 | no | — |
| 398 | C22⋊Q8 | — | 3 | 1 | no | — |
| 399 | C22⋊Q8 | — | 3 | 1 | no | — |
| 400 | C22⋊Q8 | — | 3 | 1 | no | — |
| 401 | C22⋊Q8 | — | 3 | 1 | no | — |
| 402 | C22⋊Q8 | — | 6 | 1 | no | — |
| 403 | C22⋊Q8 | — | 6 | 1 | no | — |
| 404 | C22⋊Q8 | — | 6 | 1 | no | — |
| 405 | C22⋊Q8 | — | 6 | 1 | no | — |
| 406 | C22⋊Q8 | — | 6 | 1 | no | — |
| 407 | C22⋊Q8 | — | 6 | 1 | no | — |
| 408 | #121 | — | 3 | 1 | no | — |
| 409 | #121 | — | 3 | 1 | no | — |
| 410 | #121 | — | 3 | 1 | no | — |
| 411 | #121 | — | 3 | 1 | no | — |
| 412 | #121 | — | 3 | 1 | no | — |
| 413 | #121 | — | 3 | 1 | no | — |
| 414 | #121 | — | 6 | 1 | no | — |
| 415 | #121 | — | 6 | 1 | no | — |
| 416 | #121 | — | 6 | 1 | no | — |
| 417 | #121 | — | 6 | 1 | no | — |
| 418 | #121 | — | 6 | 1 | no | — |
| 419 | #121 | — | 6 | 1 | no | — |
| 420 | #120 | — | 6 | 1 | no | — |
| 421 | #120 | — | 6 | 1 | no | — |
| 422 | #120 | — | 6 | 1 | no | — |
| 423 | #120 | — | 6 | 1 | no | — |
| 424 | C4×Q8 | — | 3 | 1 | no | — |
| 425 | C4×Q8 | — | 3 | 1 | no | — |
| 426 | C4×Q8 | — | 3 | 1 | no | — |
| 427 | C4×Q8 | — | 3 | 1 | no | — |
| 428 | C4×Q8 | — | 3 | 1 | no | — |
| 429 | C4×Q8 | — | 3 | 1 | no | — |
| 430 | C4×Q8 | — | 3 | 1 | no | — |
| 431 | C4×Q8 | — | 3 | 1 | no | — |
| 432 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 433 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 434 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 435 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 436 | C4×D4 | — | 3 | 1 | no | — |
| 437 | C4×D4 | — | 3 | 1 | no | — |
| 438 | C4×D4 | — | 3 | 1 | no | — |
| 439 | C4×D4 | — | 3 | 1 | no | — |
| 440 | C4×D4 | — | 3 | 1 | no | — |
| 441 | C4×D4 | — | 3 | 1 | no | — |
| 442 | C4×D4 | — | 3 | 1 | no | — |
| 443 | C4×D4 | — | 3 | 1 | no | — |
| 444 | C4×D4 | — | 3 | 1 | no | — |
| 445 | C4×D4 | — | 3 | 1 | no | — |
| 446 | C4×D4 | — | 3 | 1 | no | — |
| 447 | C4×D4 | — | 3 | 1 | no | — |
| 448 | C4×D4 | — | 3 | 1 | no | — |
| 449 | C4×D4 | — | 3 | 1 | no | — |
| 450 | C4×D4 | — | 3 | 1 | no | — |
| 451 | C4×D4 | — | 6 | 1 | no | — |
| 452 | C4×D4 | — | 6 | 1 | no | — |
| 453 | C4×D4 | — | 6 | 1 | no | — |
| 454 | C4×D4 | — | 6 | 1 | no | — |
| 455 | C4×D4 | — | 6 | 1 | no | — |
| 456 | C4×D4 | — | 6 | 1 | no | — |
| 457 | C4×D4 | — | 6 | 1 | no | — |
| 458 | C4×D4 | — | 6 | 1 | no | — |
| 459 | C4×D4 | — | 6 | 1 | no | — |
| 460 | C4×D4 | — | 6 | 1 | no | — |
| 461 | C4×D4 | — | 6 | 1 | no | — |
| 462 | C4×D4 | — | 6 | 1 | no | — |
| 463 | C4×D4 | — | 6 | 1 | no | — |
| 464 | C4×D4 | S4 | 1 | 1 | yes | characteristic |
| 465 | #117 | — | 3 | 1 | no | — |
| 466 | #117 | — | 3 | 1 | no | — |
| 467 | #117 | — | 3 | 1 | no | — |
| 468 | #117 | — | 3 | 1 | no | — |
| 469 | #117 | — | 3 | 1 | no | — |
| 470 | #117 | — | 6 | 1 | no | — |
| 471 | #117 | — | 6 | 1 | no | — |
| 472 | #117 | — | 6 | 1 | no | — |
| 473 | #117 | — | 6 | 1 | no | — |
| 474 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 475 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 476 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 477 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 478 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 479 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 480 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 481 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 482 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 483 | C2×C42 | — | 3 | 1 | no | — |
| 484 | C2×C42 | — | 3 | 1 | no | — |
| 485 | C2×C42 | — | 3 | 1 | no | — |
| 486 | C2×C42 | — | 6 | 1 | no | — |
| 487 | #107 | — | 3 | 1 | no | — |
| 488 | #107 | — | 3 | 1 | no | — |
| 489 | #107 | — | 3 | 1 | no | — |
| 490 | #107 | — | 3 | 1 | no | — |
| 491 | #107 | — | 3 | 1 | no | — |
| 492 | #107 | — | 3 | 1 | no | — |
| 493 | #106 | — | 3 | 1 | no | — |
| 494 | #106 | — | 3 | 1 | no | — |
| 495 | #106 | — | 3 | 1 | no | — |
| 496 | #106 | — | 3 | 1 | no | — |
| 497 | #106 | — | 3 | 1 | no | — |
| 498 | #106 | — | 3 | 1 | no | — |
| 499 | #106 | — | 3 | 1 | no | — |
| 500 | #106 | — | 3 | 1 | no | — |
| 501 | #106 | — | 3 | 1 | no | — |
| 502 | #106 | — | 3 | 1 | no | — |
| 503 | C4⋊C8 | — | 3 | 1 | no | — |
| 504 | C4⋊C8 | — | 3 | 1 | no | — |
| 505 | C4⋊C8 | — | 3 | 1 | no | — |
| 506 | C4⋊C8 | — | 3 | 1 | no | — |
| 507 | C4⋊C8 | — | 3 | 1 | no | — |
| 508 | C4⋊C8 | — | 3 | 1 | no | — |
| 509 | #103 | — | 3 | 1 | no | — |
| 510 | #103 | — | 3 | 1 | no | — |
| 511 | #103 | — | 3 | 1 | no | — |
| 512 | #103 | — | 3 | 1 | no | — |
| 513 | #103 | — | 3 | 1 | no | — |
| 514 | #103 | — | 3 | 1 | no | — |
| 515 | #103 | — | 3 | 1 | no | — |
| 516 | #103 | — | 3 | 1 | no | — |
| 517 | #103 | — | 3 | 1 | no | — |
| 518 | #103 | — | 3 | 1 | no | — |
| 519 | #103 | — | 3 | 1 | no | — |
| 520 | #103 | — | 3 | 1 | no | — |
| 521 | #103 | — | 3 | 1 | no | — |
| 522 | #103 | — | 3 | 1 | no | — |
| 523 | #103 | — | 3 | 1 | no | — |
| 524 | #103 | — | 3 | 1 | no | — |
| 525 | #102 | — | 3 | 1 | no | — |
| 526 | #102 | — | 3 | 1 | no | — |
| 527 | #102 | — | 3 | 1 | no | — |
| 528 | #102 | — | 3 | 1 | no | — |
| 529 | #102 | — | 3 | 1 | no | — |
| 530 | #102 | — | 3 | 1 | no | — |
| 531 | #102 | — | 3 | 1 | no | — |
| 532 | #102 | — | 3 | 1 | no | — |
| 533 | #102 | — | 3 | 1 | no | — |
| 534 | #102 | — | 3 | 1 | no | — |
| 535 | #102 | — | 3 | 1 | no | — |
| 536 | #102 | — | 3 | 1 | no | — |
| 537 | #102 | — | 3 | 1 | no | — |
| 538 | #102 | — | 3 | 1 | no | — |
| 539 | #102 | — | 3 | 1 | no | — |
| 540 | #102 | — | 3 | 1 | no | — |
| 541 | C22⋊C8 | — | 3 | 1 | no | — |
| 542 | C22⋊C8 | — | 3 | 1 | no | — |
| 543 | C22⋊C8 | — | 3 | 1 | no | — |
| 544 | C22⋊C8 | — | 3 | 1 | no | — |
| 545 | C22⋊C8 | — | 3 | 1 | no | — |
| 546 | C22⋊C8 | — | 3 | 1 | no | — |
| 547 | #97 | — | 3 | 1 | no | — |
| 548 | #97 | — | 3 | 1 | no | — |
| 549 | #97 | — | 3 | 1 | no | — |
| 550 | #97 | — | 3 | 1 | no | — |
| 551 | C4×C8 | — | 3 | 1 | no | — |
| 552 | C4×C8 | — | 3 | 1 | no | — |
| 553 | C4×C8 | — | 3 | 1 | no | — |
| 554 | C4×C8 | — | 3 | 1 | no | — |
| 555 | C4×C8 | — | 3 | 1 | no | — |
| 556 | C4×C8 | — | 3 | 1 | no | — |
| 557 | C23×C3 | — | 4 | 1 | no | — |
| 558 | C23×C3 | — | 4 | 1 | no | — |
| 559 | C22×D3 | — | 4 | 1 | no | — |
| 560 | C22×D3 | — | 4 | 1 | no | — |
| 561 | C22×D3 | — | 4 | 1 | no | — |
| 562 | C22×D3 | — | 8 | 2 | no | — |
| 563 | C22×D3 | — | 8 | 2 | no | — |
| 564 | C22×D3 | — | 8 | 2 | no | — |
| 565 | C3×D4 | — | 8 | 2 | no | — |
| 566 | C2×C3×C4 | — | 4 | 1 | no | — |
| 567 | C2×C3×C4 | — | 4 | 1 | no | — |
| 568 | C2×C3×C4 | — | 4 | 1 | no | — |
| 569 | C2×C3×C4 | — | 4 | 1 | no | — |
| 570 | C2×C3×C4 | — | 4 | 1 | no | — |
| 571 | C2×C3×C4 | — | 8 | 2 | no | — |
| 572 | C2×C3×C4 | — | 8 | 2 | no | — |
| 573 | #67 | — | 8 | 2 | no | — |
| 574 | #67 | — | 8 | 2 | no | — |
| 575 | #67 | — | 8 | 2 | no | — |
| 576 | #67 | — | 8 | 2 | no | — |
| 577 | C2×Dic3 | — | 4 | 1 | no | — |
| 578 | C2×Dic3 | — | 4 | 1 | no | — |
| 579 | C2×Dic3 | — | 4 | 1 | no | — |
| 580 | C2×Dic3 | — | 4 | 1 | no | — |
| 581 | C2×Dic3 | — | 4 | 1 | no | — |
| 582 | C2×Dic3 | — | 8 | 2 | no | — |
| 583 | D12 | — | 8 | 2 | no | — |
| 584 | D12 | — | 8 | 2 | no | — |
| 585 | C4×D3 | — | 4 | 4 | no | — |
| 586 | C4×D3 | — | 8 | 2 | no | — |
| 587 | C4×D3 | — | 8 | 2 | no | — |
| 588 | C4×D3 | — | 8 | 2 | no | — |
| 589 | C4×D3 | — | 8 | 2 | no | — |
| 590 | Dic6 | — | 8 | 2 | no | — |
| 591 | SL(2,𝔽3) | C2×#41 | 1 | 1 | yes | characteristic |
| 592 | C24 | — | 6 | 1 | no | — |
| 593 | C24 | — | 6 | 1 | no | — |
| 594 | #41 | — | 2 | 1 | no | — |
| 595 | #41 | — | 6 | 1 | no | — |
| 596 | #41 | — | 6 | 2 | no | — |
| 597 | #41 | — | 12 | 2 | no | — |
| 598 | #41 | — | 12 | 1 | no | — |
| 599 | #41 | — | 24 | 2 | no | — |
| 600 | C2×Q8 | — | 2 | 1 | no | — |
| 601 | C2×Q8 | — | 2 | 1 | no | — |
| 602 | C2×Q8 | — | 3 | 1 | no | — |
| 603 | C2×Q8 | — | 3 | 1 | no | — |
| 604 | C2×Q8 | — | 3 | 1 | no | — |
| 605 | C2×Q8 | — | 3 | 1 | no | — |
| 606 | C2×Q8 | — | 6 | 1 | no | — |
| 607 | C2×Q8 | — | 6 | 1 | no | — |
| 608 | C2×Q8 | — | 6 | 1 | no | — |
| 609 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 610 | C2×D4 | — | 3 | 1 | no | — |
| 611 | C2×D4 | — | 3 | 1 | no | — |
| 612 | C2×D4 | — | 3 | 1 | no | — |
| 613 | C2×D4 | — | 3 | 1 | no | — |
| 614 | C2×D4 | — | 3 | 1 | no | — |
| 615 | C2×D4 | — | 3 | 1 | no | — |
| 616 | C2×D4 | — | 6 | 1 | no | — |
| 617 | C2×D4 | — | 6 | 1 | no | — |
| 618 | C2×D4 | — | 6 | 2 | no | — |
| 619 | C2×D4 | — | 6 | 2 | no | — |
| 620 | C2×D4 | — | 6 | 1 | no | — |
| 621 | C2×D4 | — | 6 | 1 | no | — |
| 622 | C2×D4 | — | 6 | 1 | no | — |
| 623 | C2×D4 | — | 6 | 1 | no | — |
| 624 | C2×D4 | — | 6 | 1 | no | — |
| 625 | C2×D4 | — | 6 | 1 | no | — |
| 626 | C2×D4 | — | 6 | 1 | no | — |
| 627 | C2×D4 | — | 12 | 1 | no | — |
| 628 | C2×D4 | — | 12 | 1 | no | — |
| 629 | C2×D4 | — | 12 | 4 | no | — |
| 630 | C2×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 631 | C22×C4 | — | 3 | 1 | no | — |
| 632 | C22×C4 | — | 3 | 1 | no | — |
| 633 | C22×C4 | — | 3 | 1 | no | — |
| 634 | C22×C4 | — | 3 | 1 | no | — |
| 635 | C22×C4 | — | 3 | 1 | no | — |
| 636 | C22×C4 | — | 3 | 1 | no | — |
| 637 | C22×C4 | — | 3 | 1 | no | — |
| 638 | C22×C4 | — | 6 | 1 | no | — |
| 639 | C22×C4 | — | 6 | 1 | no | — |
| 640 | C22×C4 | — | 6 | 1 | no | — |
| 641 | C22×C4 | — | 6 | 1 | no | — |
| 642 | C22×C4 | — | 6 | 1 | no | — |
| 643 | C22×C4 | — | 6 | 1 | no | — |
| 644 | C22×C4 | — | 6 | 1 | no | — |
| 645 | C22×C4 | — | 6 | 1 | no | — |
| 646 | C22×C4 | — | 6 | 1 | no | — |
| 647 | C22×C4 | — | 6 | 1 | no | — |
| 648 | C22×C4 | — | 6 | 1 | no | — |
| 649 | C22×C4 | — | 24 | 2 | no | — |
| 650 | C22×C4 | — | 24 | 2 | no | — |
| 651 | C22×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 652 | C22×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 653 | Q16 | — | 6 | 2 | no | — |
| 654 | Q16 | — | 6 | 1 | no | — |
| 655 | Q16 | — | 6 | 1 | no | — |
| 656 | Q16 | — | 12 | 1 | no | — |
| 657 | SD16 | — | 3 | 2 | no | — |
| 658 | SD16 | — | 3 | 2 | no | — |
| 659 | SD16 | — | 6 | 2 | no | — |
| 660 | SD16 | — | 6 | 2 | no | — |
| 661 | SD16 | — | 6 | 2 | no | — |
| 662 | SD16 | — | 6 | 1 | no | — |
| 663 | SD16 | — | 6 | 1 | no | — |
| 664 | SD16 | — | 6 | 1 | no | — |
| 665 | SD16 | — | 6 | 1 | no | — |
| 666 | SD16 | — | 12 | 1 | no | — |
| 667 | SD16 | — | 12 | 1 | no | — |
| 668 | SD16 | — | 12 | 1 | no | — |
| 669 | SD16 | — | 12 | 1 | no | — |
| 670 | D8 | — | 6 | 2 | no | — |
| 671 | D8 | — | 6 | 2 | no | — |
| 672 | D8 | — | 12 | 1 | no | — |
| 673 | M16 | — | 6 | 2 | no | — |
| 674 | M16 | — | 6 | 2 | no | — |
| 675 | M16 | — | 12 | 1 | no | — |
| 676 | M16 | — | 12 | 1 | no | — |
| 677 | C2×C8 | — | 3 | 1 | no | — |
| 678 | C2×C8 | — | 3 | 1 | no | — |
| 679 | C2×C8 | — | 3 | 1 | no | — |
| 680 | C2×C8 | — | 3 | 1 | no | — |
| 681 | C2×C8 | — | 3 | 1 | no | — |
| 682 | C2×C8 | — | 3 | 1 | no | — |
| 683 | C2×C8 | — | 3 | 1 | no | — |
| 684 | C2×C8 | — | 3 | 1 | no | — |
| 685 | C2×C8 | — | 6 | 2 | no | — |
| 686 | C2×C8 | — | 12 | 1 | no | — |
| 687 | C4⋊C4 | — | 3 | 1 | no | — |
| 688 | C4⋊C4 | — | 3 | 1 | no | — |
| 689 | C4⋊C4 | — | 3 | 1 | no | — |
| 690 | C4⋊C4 | — | 3 | 1 | no | — |
| 691 | C4⋊C4 | — | 3 | 1 | no | — |
| 692 | C4⋊C4 | — | 3 | 1 | no | — |
| 693 | C4⋊C4 | — | 3 | 1 | no | — |
| 694 | C4⋊C4 | — | 3 | 1 | no | — |
| 695 | C4⋊C4 | — | 3 | 1 | no | — |
| 696 | C4⋊C4 | — | 3 | 1 | no | — |
| 697 | C4⋊C4 | — | 3 | 1 | no | — |
| 698 | C4⋊C4 | — | 3 | 1 | no | — |
| 699 | C4⋊C4 | — | 3 | 1 | no | — |
| 700 | C4⋊C4 | — | 6 | 1 | no | — |
| 701 | C4⋊C4 | — | 6 | 1 | no | — |
| 702 | C4⋊C4 | — | 6 | 1 | no | — |
| 703 | C4⋊C4 | — | 6 | 1 | no | — |
| 704 | C4⋊C4 | — | 6 | 1 | no | — |
| 705 | C4⋊C4 | — | 6 | 1 | no | — |
| 706 | C4⋊C4 | — | 6 | 1 | no | — |
| 707 | C4⋊C4 | — | 6 | 1 | no | — |
| 708 | C4⋊C4 | — | 6 | 1 | no | — |
| 709 | C4⋊C4 | — | 6 | 1 | no | — |
| 710 | C4⋊C4 | — | 6 | 1 | no | — |
| 711 | C4⋊C4 | — | 6 | 1 | no | — |
| 712 | C4⋊C4 | — | 6 | 1 | no | — |
| 713 | C4⋊C4 | — | 6 | 1 | no | — |
| 714 | C4⋊C4 | — | 6 | 1 | no | — |
| 715 | C4⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 716 | C22⋊C4 | — | 3 | 1 | no | — |
| 717 | C22⋊C4 | — | 3 | 1 | no | — |
| 718 | C22⋊C4 | — | 3 | 1 | no | — |
| 719 | C22⋊C4 | — | 3 | 1 | no | — |
| 720 | C22⋊C4 | — | 6 | 1 | no | — |
| 721 | C22⋊C4 | — | 6 | 1 | no | — |
| 722 | C22⋊C4 | — | 6 | 1 | no | — |
| 723 | C22⋊C4 | — | 6 | 1 | no | — |
| 724 | C22⋊C4 | — | 6 | 1 | no | — |
| 725 | C22⋊C4 | — | 6 | 1 | no | — |
| 726 | C22⋊C4 | — | 6 | 1 | no | — |
| 727 | C22⋊C4 | — | 6 | 1 | no | — |
| 728 | C22⋊C4 | — | 6 | 1 | no | — |
| 729 | C22⋊C4 | — | 6 | 1 | no | — |
| 730 | C22⋊C4 | — | 6 | 1 | no | — |
| 731 | C22⋊C4 | — | 6 | 1 | no | — |
| 732 | C22⋊C4 | — | 6 | 1 | no | — |
| 733 | C22⋊C4 | — | 6 | 1 | no | — |
| 734 | C22⋊C4 | — | 6 | 1 | no | — |
| 735 | C22⋊C4 | — | 6 | 1 | no | — |
| 736 | C22⋊C4 | — | 6 | 1 | no | — |
| 737 | C22⋊C4 | — | 6 | 1 | no | — |
| 738 | C22⋊C4 | — | 6 | 1 | no | — |
| 739 | C22⋊C4 | — | 6 | 1 | no | — |
| 740 | C22⋊C4 | — | 6 | 1 | no | — |
| 741 | C22⋊C4 | — | 6 | 1 | no | — |
| 742 | C22⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 743 | C22⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 744 | C42 | — | 3 | 1 | no | — |
| 745 | C42 | — | 3 | 1 | no | — |
| 746 | C42 | — | 3 | 1 | no | — |
| 747 | C42 | — | 3 | 1 | no | — |
| 748 | C42 | — | 3 | 1 | no | — |
| 749 | C42 | — | 3 | 1 | no | — |
| 750 | C42 | — | 3 | 1 | no | — |
| 751 | C42 | — | 3 | 1 | no | — |
| 752 | C42 | — | 3 | 1 | no | — |
| 753 | C42 | — | 6 | 1 | no | — |
| 754 | C42 | — | 6 | 1 | no | — |
| 755 | C42 | — | 6 | 1 | no | — |
| 756 | C42 | C2×S4 | 1 | 1 | yes | characteristic |
| 757 | C22×C3 | — | 4 | 2 | no | — |
| 758 | C22×C3 | — | 4 | 1 | no | — |
| 759 | C22×C3 | — | 8 | 1 | no | — |
| 760 | C22×C3 | — | 8 | 1 | no | — |
| 761 | C22×C3 | — | 8 | 1 | no | — |
| 762 | C22×C3 | — | 8 | 1 | no | — |
| 763 | C22×C3 | — | 8 | 1 | no | — |
| 764 | C2×D3 | — | 4 | 2 | no | — |
| 765 | C2×D3 | — | 4 | 2 | no | — |
| 766 | C2×D3 | — | 8 | 1 | no | — |
| 767 | C2×D3 | — | 8 | 1 | no | — |
| 768 | C2×D3 | — | 8 | 1 | no | — |
| 769 | C2×D3 | — | 8 | 1 | no | — |
| 770 | C2×D3 | — | 8 | 1 | no | — |
| 771 | C2×D3 | — | 8 | 1 | no | — |
| 772 | C2×D3 | — | 8 | 1 | no | — |
| 773 | C2×D3 | — | 8 | 8 | no | — |
| 774 | C3×C4 | — | 4 | 2 | no | — |
| 775 | C3×C4 | — | 8 | 1 | no | — |
| 776 | C3×C4 | — | 8 | 1 | no | — |
| 777 | C3×C4 | — | 8 | 1 | no | — |
| 778 | C3×C4 | — | 8 | 1 | no | — |
| 779 | Dic3 | — | 4 | 2 | no | — |
| 780 | Dic3 | — | 8 | 1 | no | — |
| 781 | Dic3 | — | 8 | 1 | no | — |
| 782 | Dic3 | — | 8 | 1 | no | — |
| 783 | Dic3 | — | 8 | 1 | no | — |
| 784 | C23 | — | 3 | 1 | no | — |
| 785 | C23 | — | 6 | 1 | no | — |
| 786 | C23 | — | 6 | 1 | no | — |
| 787 | C23 | — | 6 | 1 | no | — |
| 788 | C23 | — | 12 | 2 | no | — |
| 789 | C23 | — | 12 | 2 | no | — |
| 790 | C23 | — | 12 | 2 | no | — |
| 791 | C23 | — | 12 | 2 | no | — |
| 792 | C23 | — | 24 | 1 | no | — |
| 793 | C23 | — | 24 | 1 | no | — |
| 794 | C23 | C22×S4 | 1 | 1 | yes | characteristic |
| 795 | C23 | C22×S4 | 1 | 1 | yes | characteristic |
| 796 | Q8 | — | 3 | 1 | no | — |
| 797 | Q8 | — | 6 | 1 | no | — |
| 798 | Q8 | — | 6 | 1 | no | — |
| 799 | Q8 | — | 6 | 1 | no | — |
| 800 | Q8 | — | 6 | 1 | no | — |
| 801 | Q8 | — | 6 | 1 | no | — |
| 802 | Q8 | — | 6 | 1 | no | — |
| 803 | Q8 | — | 12 | 1 | no | — |
| 804 | Q8 | — | 24 | 1 | no | — |
| 805 | Q8 | D3×#41 | 1 | 1 | yes | characteristic |
| 806 | D4 | — | 2 | 2 | no | — |
| 807 | D4 | — | 3 | 2 | no | — |
| 808 | D4 | — | 6 | 1 | no | — |
| 809 | D4 | — | 6 | 1 | no | — |
| 810 | D4 | — | 6 | 1 | no | — |
| 811 | D4 | — | 6 | 1 | no | — |
| 812 | D4 | — | 6 | 1 | no | — |
| 813 | D4 | — | 6 | 1 | no | — |
| 814 | D4 | — | 6 | 1 | no | — |
| 815 | D4 | — | 6 | 2 | no | — |
| 816 | D4 | — | 12 | 2 | no | — |
| 817 | D4 | — | 12 | 1 | no | — |
| 818 | D4 | — | 12 | 2 | no | — |
| 819 | D4 | — | 12 | 2 | no | — |
| 820 | D4 | — | 12 | 2 | no | — |
| 821 | D4 | — | 12 | 2 | no | — |
| 822 | D4 | — | 12 | 2 | no | — |
| 823 | D4 | — | 24 | 1 | no | — |
| 824 | D4 | — | 24 | 1 | no | — |
| 825 | D4 | — | 24 | 1 | no | — |
| 826 | C2×C4 | — | 2 | 2 | no | — |
| 827 | C2×C4 | — | 2 | 2 | no | — |
| 828 | C2×C4 | — | 3 | 1 | no | — |
| 829 | C2×C4 | — | 3 | 1 | no | — |
| 830 | C2×C4 | — | 3 | 1 | no | — |
| 831 | C2×C4 | — | 3 | 1 | no | — |
| 832 | C2×C4 | — | 3 | 1 | no | — |
| 833 | C2×C4 | — | 3 | 1 | no | — |
| 834 | C2×C4 | — | 3 | 1 | no | — |
| 835 | C2×C4 | — | 6 | 1 | no | — |
| 836 | C2×C4 | — | 6 | 1 | no | — |
| 837 | C2×C4 | — | 6 | 1 | no | — |
| 838 | C2×C4 | — | 6 | 1 | no | — |
| 839 | C2×C4 | — | 6 | 1 | no | — |
| 840 | C2×C4 | — | 6 | 1 | no | — |
| 841 | C2×C4 | — | 6 | 2 | no | — |
| 842 | C2×C4 | — | 6 | 2 | no | — |
| 843 | C2×C4 | — | 6 | 1 | no | — |
| 844 | C2×C4 | — | 6 | 1 | no | — |
| 845 | C2×C4 | — | 6 | 1 | no | — |
| 846 | C2×C4 | — | 6 | 1 | no | — |
| 847 | C2×C4 | — | 6 | 1 | no | — |
| 848 | C2×C4 | — | 12 | 1 | no | — |
| 849 | C2×C4 | — | 12 | 1 | no | — |
| 850 | C2×C4 | — | 12 | 2 | no | — |
| 851 | C2×C4 | — | 12 | 2 | no | — |
| 852 | C2×C4 | — | 12 | 2 | no | — |
| 853 | C2×C4 | — | 12 | 2 | no | — |
| 854 | C2×C4 | — | 12 | 2 | no | — |
| 855 | C2×C4 | — | 24 | 1 | no | — |
| 856 | C2×C4 | — | 24 | 1 | no | — |
| 857 | C2×C4 | — | 24 | 1 | no | — |
| 858 | C2×C4 | — | 24 | 1 | no | — |
| 859 | C2×C4 | — | 24 | 1 | no | — |
| 860 | C2×C4 | — | 24 | 1 | no | — |
| 861 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 862 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 863 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 864 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 865 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 866 | C8 | — | 3 | 2 | no | — |
| 867 | C8 | — | 6 | 1 | no | — |
| 868 | C8 | — | 6 | 1 | no | — |
| 869 | C8 | — | 6 | 1 | no | — |
| 870 | C8 | — | 6 | 1 | no | — |
| 871 | C8 | — | 6 | 1 | no | — |
| 872 | C8 | — | 6 | 1 | no | — |
| 873 | C8 | — | 6 | 1 | no | — |
| 874 | C2×C3 | — | 4 | 1 | no | — |
| 875 | C2×C3 | — | 4 | 1 | no | — |
| 876 | C2×C3 | — | 4 | 1 | no | — |
| 877 | C2×C3 | — | 8 | 2 | no | — |
| 878 | C2×C3 | — | 16 | 1 | no | — |
| 879 | D3 | — | 8 | 2 | no | — |
| 880 | D3 | — | 8 | 2 | no | — |
| 881 | D3 | — | 16 | 1 | no | — |
| 882 | C22 | — | 2 | 1 | no | — |
| 883 | C22 | — | 2 | 1 | no | — |
| 884 | C22 | — | 2 | 1 | no | — |
| 885 | C22 | — | 2 | 1 | no | — |
| 886 | C22 | — | 2 | 1 | no | — |
| 887 | C22 | — | 6 | 1 | no | — |
| 888 | C22 | — | 6 | 2 | no | — |
| 889 | C22 | — | 6 | 1 | no | — |
| 890 | C22 | — | 6 | 1 | no | — |
| 891 | C22 | — | 12 | 1 | no | — |
| 892 | C22 | — | 12 | 1 | no | — |
| 893 | C22 | — | 12 | 1 | no | — |
| 894 | C22 | — | 12 | 1 | no | — |
| 895 | C22 | — | 12 | 1 | no | — |
| 896 | C22 | — | 12 | 1 | no | — |
| 897 | C22 | — | 12 | 1 | no | — |
| 898 | C22 | — | 12 | 1 | no | — |
| 899 | C22 | — | 24 | 4 | no | — |
| 900 | C22 | — | 24 | 4 | no | — |
| 901 | C22 | #5923 | 1 | 2 | yes | — |
| 902 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 903 | C4 | — | 2 | 1 | no | — |
| 904 | C4 | — | 2 | 1 | no | — |
| 905 | C4 | — | 2 | 1 | no | — |
| 906 | C4 | — | 2 | 1 | no | — |
| 907 | C4 | — | 3 | 1 | no | — |
| 908 | C4 | — | 3 | 1 | no | — |
| 909 | C4 | — | 6 | 1 | no | — |
| 910 | C4 | — | 6 | 1 | no | — |
| 911 | C4 | — | 6 | 1 | no | — |
| 912 | C4 | — | 6 | 1 | no | — |
| 913 | C4 | — | 6 | 1 | no | — |
| 914 | C4 | — | 6 | 1 | no | — |
| 915 | C4 | — | 12 | 1 | no | — |
| 916 | C4 | — | 12 | 1 | no | — |
| 917 | C4 | — | 12 | 1 | no | — |
| 918 | C4 | — | 12 | 1 | no | — |
| 919 | C4 | — | 12 | 1 | no | — |
| 920 | C4 | #5926 | 1 | 2 | yes | — |
| 921 | C3 | — | 4 | 1 | no | Sylow |
| 922 | C2 | — | 2 | 2 | no | — |
| 923 | C2 | — | 4 | 1 | no | — |
| 924 | C2 | — | 12 | 1 | no | — |
| 925 | C2 | — | 12 | 2 | no | — |
| 926 | C2 | — | 24 | 1 | no | — |
| 927 | C2 | — | 24 | 1 | no | — |
| 928 | C2 | #41×S4 | 1 | 1 | yes | characteristic |
| 929 | C2 | C2×#5923 | 1 | 1 | yes | characteristic |
| 930 | C2 | C2×#5926 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×S4 |
| commutator, cosocle | C2×SL(2,𝔽3) | C24 |
| Frattini, socle | C22 | C23×S4 |
| Fitting | #3482 | D3 |
| hypercenter | C4×D4 | S4 |
| hypocenter | SL(2,𝔽3) | C2×#41 |
| LCS | G ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3482⋊C3 | C2 | semidirect |
| 2. #85423 | C2 | semidirect |
| 3. #85421 | C2 | semidirect |
| 4. #85401 | C2 | semidirect |
| 5. #85398 | C2 | semidirect |
| 6. #85387 | C2 | semidirect |
| 7. #85384 | C2 | semidirect |
| 8. #85382 | C2 | semidirect |
| 9. #85377 | C2 | semidirect |
| 10. #85343 | C2 | semidirect |
| 11. C4×#986 | C2 | semidirect |
| 12. #85329 | C2 | semidirect |
| 13. C4×#983 | C2 | semidirect |
| 14. #85325 | C2 | semidirect |
| 15. C2×C4×GL(2,𝔽3) | C2 | semidirect |
| 21. #557⋊C3 | C22 | semidirect |
| 22. D4×SL(2,𝔽3) | C22 | semidirect |
| 24. #548⋊C3 | C22 | semidirect |
| 25. C4×#41⋊C3 | C22 | semidirect |
| 26. C2×C4×SL(2,𝔽3) | C22 | semidirect |
| 27. C2×C4×SL(2,𝔽3) | C22 | semidirect |
| 29. #5426 | C22 | semidirect |
| 30. #5425 | C22 | semidirect |
| 32. #5421 | C22 | semidirect |
| 33. #5421 | C22 | semidirect |
| 34. #5420 | C22 | semidirect |
| 35. #5419 | C22 | semidirect |
| 36. C2×#859 | C22 | semidirect |
| 37. #5395 | C22 | semidirect |
| 38. #5395 | C22 | semidirect |
| 41. #5394 | C22 | semidirect |
| 45. C4×GL(2,𝔽3) | C22 | semidirect |
| 46. C4×GL(2,𝔽3) | C22 | semidirect |
| 47. C4×GL(2,𝔽3) | C22 | semidirect |
| 48. #5389 | C22 | semidirect |
| 49. #5389 | C22 | semidirect |
| 50. #5388 | C22 | semidirect |
| 51. C4×#226 | C22 | semidirect |
| 52. #5386 | C22 | semidirect |
| 53. #3482 | D3 | semidirect |
| 121. #557 | C2×D3 | semidirect |
| 134. #548 | C2×D3 | semidirect |
| 151. C4×#41 | C2×D3 | semidirect |
| 153. C2×C4×Q8 | C2×D3 | semidirect |
| 305. GL(2,𝔽3) | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3482⋊C3 | 2 |
| #85423 | 2 |
| #85421 | 2 |
| #85401 | 2 |
| #85398 | 2 |
| #85387 | 2 |
| #85384 | 2 |
| #85382 | 2 |
| #85377 | 2 |
| #85343 | 2 |
| C4×#986 | 2 |
| #85329 | 2 |
| C4×#983 | 2 |
| #85325 | 2 |
| C2×C4×GL(2,𝔽3) | 2 |
| #61445 | 3 |
| #5547 | 4 |