Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
6518 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 | C7×#3556 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11744211 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #11744207 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #11744104 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11744103 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11744102 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11744085 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11744084 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11744083 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11743584 | C2 | 1 | 8 | yes | maximal, complemented |
| 11 | #11743571 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #11743564 | C2 | 1 | 8 | yes | maximal, complemented |
| 13 | #11743563 | C2 | 1 | 4 | yes | maximal, complemented |
| 14 | #11743356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | D7×#533 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #11743335 | C2 | 1 | 2 | yes | maximal, complemented |
| 17 | #11743325 | C2 | 1 | 2 | yes | maximal, complemented |
| 18 | C7×#564 | C22 | 1 | 4 | yes | complemented |
| 19 | C7×#557 | C22 | 1 | 4 | yes | complemented |
| 20 | C7×#557 | C22 | 1 | 4 | yes | complemented |
| 21 | C7×#557 | C22 | 1 | 4 | yes | complemented |
| 22 | C7×#541 | C22 | 1 | 4 | yes | — |
| 23 | C7×#541 | C22 | 1 | 8 | yes | — |
| 24 | C7×#533 | C22 | 1 | 2 | yes | — |
| 25 | C7×#533 | C22 | 1 | 1 | yes | characteristic |
| 26 | #90423 | C22 | 1 | 8 | yes | complemented |
| 27 | #90423 | C22 | 1 | 4 | yes | complemented |
| 28 | #90422 | C22 | 1 | 4 | yes | — |
| 29 | #90419 | C22 | 1 | 2 | yes | — |
| 30 | #90419 | C22 | 1 | 2 | yes | — |
| 31 | #90419 | C22 | 1 | 2 | yes | — |
| 32 | #90419 | C22 | 1 | 8 | yes | complemented |
| 33 | #90418 | C22 | 1 | 8 | yes | — |
| 34 | #90418 | C22 | 1 | 4 | yes | complemented |
| 35 | #90417 | C22 | 1 | 8 | yes | — |
| 36 | #90417 | C22 | 1 | 4 | yes | complemented |
| 37 | #90416 | C22 | 1 | 4 | yes | — |
| 38 | #90416 | C22 | 1 | 2 | yes | — |
| 39 | #90416 | C22 | 1 | 2 | yes | — |
| 40 | #90415 | C22 | 1 | 8 | yes | complemented |
| 41 | D7×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 42 | #90401 | C22 | 1 | 16 | yes | — |
| 43 | #90398 | C22 | 1 | 16 | yes | — |
| 44 | #90397 | C22 | 1 | 16 | yes | — |
| 45 | #90395 | C22 | 1 | 16 | yes | — |
| 46 | #90391 | C22 | 1 | 16 | yes | — |
| 47 | #90391 | C22 | 1 | 4 | yes | complemented |
| 48 | #90390 | C22 | 1 | 16 | yes | — |
| 49 | #90390 | C22 | 1 | 16 | yes | complemented |
| 50 | #90390 | C22 | 1 | 8 | yes | complemented |
| 51 | #90389 | C22 | 1 | 4 | yes | — |
| 52 | #90387 | C22 | 1 | 16 | yes | complemented |
| 53 | #90386 | C22 | 1 | 8 | yes | — |
| 54 | #90386 | C22 | 1 | 16 | yes | — |
| 55 | #90385 | C22 | 1 | 8 | yes | — |
| 56 | #90385 | C22 | 1 | 16 | yes | complemented |
| 57 | #90383 | C22 | 1 | 16 | yes | — |
| 58 | #90383 | C22 | 1 | 16 | yes | complemented |
| 59 | #90382 | C22 | 1 | 16 | yes | — |
| 60 | #90382 | C22 | 1 | 4 | yes | — |
| 61 | #90382 | C22 | 1 | 4 | yes | — |
| 62 | #90382 | C22 | 1 | 8 | yes | complemented |
| 63 | #90382 | C22 | 1 | 16 | yes | complemented |
| 64 | #90381 | C22 | 1 | 16 | yes | — |
| 65 | #90381 | C22 | 1 | 8 | yes | complemented |
| 66 | #90380 | C22 | 1 | 8 | yes | complemented |
| 67 | #90379 | C22 | 1 | 4 | yes | — |
| 68 | #90379 | C22 | 1 | 2 | yes | — |
| 69 | #90379 | C22 | 1 | 16 | yes | complemented |
| 70 | D7×#125 | C22 | 1 | 2 | yes | — |
| 71 | #90334 | C22 | 1 | 8 | yes | — |
| 72 | #90320 | C22 | 1 | 8 | yes | — |
| 73 | #90319 | C22 | 1 | 8 | yes | — |
| 74 | #90318 | C22 | 1 | 4 | yes | — |
| 75 | #90318 | C22 | 1 | 4 | yes | — |
| 76 | D7×C22⋊Q8 | C22 | 1 | 4 | yes | — |
| 77 | #90315 | C22 | 1 | 4 | yes | — |
| 78 | #90315 | C22 | 1 | 4 | yes | — |
| 79 | #90313 | C22 | 1 | 4 | yes | — |
| 80 | #90276 | C22 | 1 | 8 | yes | complemented |
| 81 | #90276 | C22 | 1 | 4 | yes | complemented |
| 82 | #90275 | C22 | 1 | 8 | yes | — |
| 83 | #90275 | C22 | 1 | 4 | yes | complemented |
| 84 | #90274 | C22 | 1 | 8 | yes | complemented |
| 85 | #90273 | C22 | 1 | 8 | yes | — |
| 86 | #90273 | C22 | 1 | 8 | yes | complemented |
| 87 | #90271 | C22 | 1 | 4 | yes | — |
| 88 | #90271 | C22 | 1 | 4 | yes | — |
| 89 | #90270 | C22 | 1 | 8 | yes | — |
| 90 | #90270 | C22 | 1 | 4 | yes | complemented |
| 91 | #90269 | C22 | 1 | 4 | yes | — |
| 92 | #90268 | C22 | 1 | 4 | yes | complemented |
| 93 | #90267 | C22 | 1 | 8 | yes | — |
| 94 | #90267 | C22 | 1 | 8 | yes | — |
| 95 | Q8×D28 | C22 | 1 | 4 | yes | complemented |
| 96 | C4×#1161 | C22 | 1 | 8 | yes | — |
| 97 | C4×#1161 | C22 | 1 | 4 | yes | — |
| 98 | C4×#1161 | C22 | 1 | 4 | yes | — |
| 99 | C4×#1161 | C22 | 1 | 8 | yes | complemented |
| 100 | C4×Q8×D7 | C22 | 1 | 4 | yes | — |
| 101 | C4×Q8×D7 | C22 | 1 | 8 | yes | complemented |
| 102 | #90260 | C22 | 1 | 8 | yes | complemented |
| 103 | Q8×Dic14 | C22 | 1 | 4 | yes | complemented |
| 104 | #90226 | C22 | 1 | 4 | yes | — |
| 105 | #90225 | C22 | 1 | 8 | yes | — |
| 106 | #90215 | C22 | 1 | 4 | yes | — |
| 107 | #90213 | C22 | 1 | 4 | yes | — |
| 108 | D7×#117 | C22 | 1 | 2 | yes | — |
| 109 | #90208 | C22 | 1 | 2 | yes | — |
| 110 | #90168 | C22 | 1 | 2 | yes | — |
| 111 | C2×C42×D7 | C22 | 1 | 1 | yes | characteristic |
| 112 | #90161 | C22 | 1 | 1 | yes | characteristic |
| 113 | #62761 | — | 7 | 1 | no | maximal, Sylow |
| 114 | C2×#1161 | C23 | 1 | 4 | yes | — |
| 115 | C2×#1161 | C23 | 1 | 8 | yes | — |
| 116 | C2×#1161 | C23 | 1 | 4 | yes | — |
| 117 | C2×Q8×D7 | C23 | 1 | 4 | yes | — |
| 118 | C2×Q8×D7 | C23 | 1 | 8 | yes | — |
| 119 | C2×#1157 | C23 | 1 | 4 | yes | — |
| 120 | C22×C4×D7 | C23 | 1 | 1 | yes | characteristic |
| 121 | C22×C4×D7 | C23 | 1 | 2 | yes | — |
| 122 | C7×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 123 | C7×C4⋊Q8 | C23 | 1 | 8 | yes | — |
| 124 | C7×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 125 | C7×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 126 | C7×C4⋊Q8 | C23 | 1 | 4 | yes | — |
| 127 | C7×#126 | C23 | 1 | 16 | yes | — |
| 128 | C7×#125 | C23 | 1 | 2 | yes | — |
| 129 | C7×#125 | C23 | 1 | 4 | yes | — |
| 130 | C7×#125 | C23 | 1 | 16 | yes | — |
| 131 | C7×#125 | C23 | 1 | 8 | yes | — |
| 132 | C7×#125 | C23 | 1 | 4 | yes | — |
| 133 | C7×#125 | C23 | 1 | 16 | yes | — |
| 134 | C7×#125 | C23 | 1 | 16 | yes | — |
| 135 | C7×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 136 | C7×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 137 | C7×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 138 | C4×C7×Q8 | C23 | 1 | 4 | yes | — |
| 139 | C4×C7×Q8 | C23 | 1 | 8 | yes | — |
| 140 | C4×C7×Q8 | C23 | 1 | 4 | yes | — |
| 141 | C4×C7×Q8 | C23 | 1 | 8 | yes | — |
| 142 | C4×C7×Q8 | C23 | 1 | 4 | yes | — |
| 143 | C4×C7×Q8 | C23 | 1 | 8 | yes | — |
| 144 | C7×#117 | C23 | 1 | 2 | yes | — |
| 145 | C7×#117 | C23 | 1 | 4 | yes | — |
| 146 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 147 | #6510 | C23 | 1 | 4 | yes | — |
| 148 | #6510 | C23 | 1 | 4 | yes | — |
| 149 | #6510 | C23 | 1 | 8 | yes | — |
| 150 | #6509 | C23 | 1 | 4 | yes | — |
| 151 | #6509 | C23 | 1 | 8 | yes | — |
| 152 | #6509 | C23 | 1 | 8 | yes | — |
| 153 | #6509 | C23 | 1 | 4 | yes | — |
| 154 | #6509 | C23 | 1 | 4 | yes | — |
| 155 | Q8×Dic7 | C23 | 1 | 4 | yes | — |
| 156 | Q8×Dic7 | C23 | 1 | 4 | yes | — |
| 157 | Q8×Dic7 | C23 | 1 | 4 | yes | — |
| 158 | Q8×Dic7 | C23 | 1 | 8 | yes | — |
| 159 | #6507 | C23 | 1 | 4 | yes | — |
| 160 | #6493 | C23 | 1 | 4 | yes | — |
| 161 | #6493 | C23 | 1 | 4 | yes | — |
| 162 | #6489 | C23 | 1 | 2 | yes | — |
| 163 | #6487 | C23 | 1 | 4 | yes | — |
| 164 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×Dic7 | C23 | 1 | 2 | yes | — |
| 166 | #6461 | C23 | 1 | 16 | yes | — |
| 167 | #6461 | C23 | 1 | 8 | yes | — |
| 168 | #6461 | C23 | 1 | 16 | yes | — |
| 169 | #6461 | C23 | 1 | 8 | yes | — |
| 170 | #6461 | C23 | 1 | 16 | yes | — |
| 171 | #6461 | C23 | 1 | 16 | yes | — |
| 172 | #6461 | C23 | 1 | 16 | yes | — |
| 173 | #6460 | C23 | 1 | 16 | yes | — |
| 174 | #6460 | C23 | 1 | 4 | yes | — |
| 175 | #6460 | C23 | 1 | 16 | yes | — |
| 176 | #6460 | C23 | 1 | 16 | yes | — |
| 177 | #6460 | C23 | 1 | 4 | yes | — |
| 178 | #6460 | C23 | 1 | 8 | yes | — |
| 179 | #6460 | C23 | 1 | 4 | yes | — |
| 180 | #6459 | C23 | 1 | 16 | yes | — |
| 181 | #6459 | C23 | 1 | 8 | yes | — |
| 182 | #6459 | C23 | 1 | 16 | yes | — |
| 183 | #6459 | C23 | 1 | 16 | yes | — |
| 184 | #6459 | C23 | 1 | 16 | yes | — |
| 185 | #6459 | C23 | 1 | 16 | yes | — |
| 186 | #6459 | C23 | 1 | 16 | yes | — |
| 187 | #6458 | C23 | 1 | 4 | yes | — |
| 188 | #6458 | C23 | 1 | 16 | yes | — |
| 189 | #6458 | C23 | 1 | 4 | yes | — |
| 190 | #6458 | C23 | 1 | 16 | yes | — |
| 191 | #6458 | C23 | 1 | 8 | yes | — |
| 192 | #6458 | C23 | 1 | 16 | yes | — |
| 193 | #6458 | C23 | 1 | 4 | yes | — |
| 194 | #6458 | C23 | 1 | 4 | yes | — |
| 195 | #6457 | C23 | 1 | 8 | yes | — |
| 196 | #6457 | C23 | 1 | 16 | yes | — |
| 197 | #6457 | C23 | 1 | 16 | yes | — |
| 198 | #6457 | C23 | 1 | 8 | yes | — |
| 199 | #6457 | C23 | 1 | 16 | yes | — |
| 200 | #6457 | C23 | 1 | 16 | yes | — |
| 201 | #6457 | C23 | 1 | 16 | yes | — |
| 202 | #6457 | C23 | 1 | 16 | yes | — |
| 203 | #6456 | C23 | 1 | 8 | yes | — |
| 204 | #6456 | C23 | 1 | 16 | yes | — |
| 205 | #6456 | C23 | 1 | 4 | yes | — |
| 206 | #6456 | C23 | 1 | 8 | yes | — |
| 207 | #6456 | C23 | 1 | 8 | yes | — |
| 208 | #6456 | C23 | 1 | 4 | yes | — |
| 209 | #6456 | C23 | 1 | 16 | yes | — |
| 210 | #6456 | C23 | 1 | 4 | yes | — |
| 211 | #6456 | C23 | 1 | 4 | yes | — |
| 212 | #6455 | C23 | 1 | 4 | yes | — |
| 213 | #6455 | C23 | 1 | 4 | yes | — |
| 214 | #6455 | C23 | 1 | 8 | yes | — |
| 215 | #6455 | C23 | 1 | 16 | yes | — |
| 216 | #6455 | C23 | 1 | 8 | yes | — |
| 217 | #6455 | C23 | 1 | 8 | yes | — |
| 218 | #6455 | C23 | 1 | 4 | yes | — |
| 219 | #6455 | C23 | 1 | 16 | yes | — |
| 220 | D7×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 221 | D7×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 222 | D7×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 223 | D7×C4⋊C4 | C23 | 1 | 16 | yes | — |
| 224 | D7×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 225 | #6453 | C23 | 1 | 4 | yes | — |
| 226 | #6453 | C23 | 1 | 4 | yes | — |
| 227 | #6453 | C23 | 1 | 16 | yes | — |
| 228 | #6453 | C23 | 1 | 4 | yes | — |
| 229 | #6452 | C23 | 1 | 8 | yes | — |
| 230 | #6452 | C23 | 1 | 16 | yes | — |
| 231 | #6451 | C23 | 1 | 8 | yes | — |
| 232 | #6451 | C23 | 1 | 4 | yes | — |
| 233 | #6451 | C23 | 1 | 16 | yes | — |
| 234 | #6451 | C23 | 1 | 16 | yes | — |
| 235 | #6451 | C23 | 1 | 4 | yes | — |
| 236 | #6450 | C23 | 1 | 16 | yes | — |
| 237 | #6450 | C23 | 1 | 8 | yes | — |
| 238 | #6450 | C23 | 1 | 4 | yes | — |
| 239 | #6450 | C23 | 1 | 4 | yes | — |
| 240 | #6450 | C23 | 1 | 4 | yes | — |
| 241 | #6449 | C23 | 1 | 8 | yes | — |
| 242 | #6448 | C23 | 1 | 16 | yes | — |
| 243 | #6447 | C23 | 1 | 16 | yes | — |
| 244 | #6446 | C23 | 1 | 16 | yes | — |
| 245 | #6445 | C23 | 1 | 8 | yes | — |
| 246 | (C22⋊D7)⋊C4 | C23 | 1 | 8 | yes | — |
| 247 | (C22⋊D7)⋊C4 | C23 | 1 | 8 | yes | — |
| 248 | D7×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 249 | #6441 | C23 | 1 | 8 | yes | — |
| 250 | #6440 | C23 | 1 | 4 | yes | — |
| 251 | #6439 | C23 | 1 | 16 | yes | — |
| 252 | #6438 | C23 | 1 | 4 | yes | — |
| 253 | #6438 | C23 | 1 | 16 | yes | — |
| 254 | #6438 | C23 | 1 | 16 | yes | — |
| 255 | #6438 | C23 | 1 | 8 | yes | — |
| 256 | #6437 | C23 | 1 | 4 | yes | — |
| 257 | #6437 | C23 | 1 | 2 | yes | — |
| 258 | C4×D28 | C23 | 1 | 16 | yes | — |
| 259 | C4×D28 | C23 | 1 | 8 | yes | — |
| 260 | C4×D28 | C23 | 1 | 16 | yes | — |
| 261 | C4×D28 | C23 | 1 | 8 | yes | — |
| 262 | C4×D28 | C23 | 1 | 8 | yes | — |
| 263 | C4×D28 | C23 | 1 | 8 | yes | — |
| 264 | C4×D28 | C23 | 1 | 4 | yes | — |
| 265 | C4×D28 | C23 | 1 | 4 | yes | — |
| 266 | #6435 | C23 | 1 | 8 | yes | — |
| 267 | #6435 | C23 | 1 | 4 | yes | — |
| 268 | C42×D7 | C23 | 1 | 1 | yes | characteristic |
| 269 | C42×D7 | C23 | 1 | 1 | yes | characteristic |
| 270 | C42×D7 | C23 | 1 | 4 | yes | — |
| 271 | C42×D7 | C23 | 1 | 16 | yes | — |
| 272 | C42×D7 | C23 | 1 | 8 | yes | — |
| 273 | C42×D7 | C23 | 1 | 1 | yes | characteristic |
| 274 | C42×D7 | C23 | 1 | 2 | yes | — |
| 275 | C42×D7 | C23 | 1 | 2 | yes | — |
| 276 | C42×D7 | C23 | 1 | 1 | yes | characteristic |
| 277 | #6433 | C23 | 1 | 2 | yes | — |
| 278 | #6433 | C23 | 1 | 4 | yes | — |
| 279 | #6433 | C23 | 1 | 16 | yes | — |
| 280 | #6432 | C23 | 1 | 8 | yes | — |
| 281 | #6432 | C23 | 1 | 2 | yes | — |
| 282 | #6432 | C23 | 1 | 2 | yes | — |
| 283 | C4×Dic14 | C23 | 1 | 16 | yes | — |
| 284 | C4×Dic14 | C23 | 1 | 8 | yes | — |
| 285 | C4×Dic14 | C23 | 1 | 8 | yes | — |
| 286 | C4×Dic14 | C23 | 1 | 4 | yes | — |
| 287 | #3557 | — | 7 | 4 | no | — |
| 288 | #3556 | D7 | 1 | 1 | yes | characteristic, complemented |
| 289 | #3555 | — | 7 | 4 | no | — |
| 290 | #3554 | — | 7 | 4 | no | — |
| 291 | #3553 | — | 7 | 4 | no | — |
| 292 | #3552 | — | 7 | 4 | no | — |
| 293 | #3550 | — | 7 | 2 | no | — |
| 294 | #3548 | — | 7 | 1 | no | — |
| 295 | #3541 | — | 7 | 8 | no | — |
| 296 | #3531 | — | 7 | 4 | no | — |
| 297 | #3482 | — | 7 | 4 | no | — |
| 298 | #3480 | — | 7 | 4 | no | — |
| 299 | Q8×#41 | — | 7 | 4 | no | — |
| 300 | #3461 | — | 7 | 8 | no | — |
| 301 | #3455 | — | 7 | 4 | no | — |
| 302 | #3444 | — | 7 | 2 | no | — |
| 303 | C2×#533 | — | 7 | 1 | no | — |
| 304 | C23×D7 | C24 | 1 | 1 | yes | characteristic |
| 305 | C2×C7×Q8 | C24 | 1 | 4 | yes | — |
| 306 | C2×C7×Q8 | C24 | 1 | 4 | yes | — |
| 307 | C2×C7×Q8 | C24 | 1 | 4 | yes | — |
| 308 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 309 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 310 | C2×C22⋊D7 | C24 | 1 | 8 | yes | — |
| 311 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 312 | C22×Dic7 | C24 | 1 | 2 | yes | — |
| 313 | #1161 | — | 2 | 16 | no | — |
| 314 | #1161 | — | 4 | 8 | no | — |
| 315 | #1161 | — | 4 | 16 | no | — |
| 316 | Q8×D7 | — | 4 | 8 | no | — |
| 317 | Q8×D7 | — | 4 | 16 | no | — |
| 318 | #1157 | — | 4 | 8 | no | — |
| 319 | C2×D28 | C24 | 1 | 4 | yes | — |
| 320 | C2×D28 | C24 | 1 | 4 | yes | — |
| 321 | C2×D28 | C24 | 1 | 8 | yes | — |
| 322 | C2×D28 | C24 | 1 | 16 | yes | — |
| 323 | C2×D28 | C24 | 1 | 8 | yes | — |
| 324 | C2×D28 | C24 | 1 | 4 | yes | — |
| 325 | C2×C4×D7 | — | 2 | 4 | no | — |
| 326 | C2×C4×D7 | — | 4 | 4 | no | — |
| 327 | C2×C4×D7 | C24 | 1 | 8 | yes | — |
| 328 | C2×C4×D7 | C24 | 1 | 1 | yes | characteristic |
| 329 | C2×C4×D7 | C24 | 1 | 2 | yes | — |
| 330 | C2×C4×D7 | C24 | 1 | 2 | yes | — |
| 331 | C2×C4×D7 | C24 | 1 | 1 | yes | characteristic |
| 332 | C2×C4×D7 | C24 | 1 | 1 | yes | characteristic |
| 333 | C2×C4×D7 | C24 | 1 | 8 | yes | — |
| 334 | C2×C4×D7 | C24 | 1 | 2 | yes | — |
| 335 | C2×C4×D7 | C24 | 1 | 2 | yes | — |
| 336 | C2×C4×D7 | C24 | 1 | 8 | yes | — |
| 337 | C2×C4×D7 | C24 | 1 | 8 | yes | — |
| 338 | C2×C4×D7 | C24 | 1 | 16 | yes | — |
| 339 | C2×C4×D7 | C24 | 1 | 16 | yes | — |
| 340 | C2×C4×D7 | C24 | 1 | 1 | yes | characteristic |
| 341 | C2×Dic14 | C24 | 1 | 4 | yes | — |
| 342 | C2×Dic14 | C24 | 1 | 16 | yes | — |
| 343 | C2×Dic14 | C24 | 1 | 8 | yes | — |
| 344 | C2×Dic14 | C24 | 1 | 4 | yes | — |
| 345 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 346 | C7×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 347 | C7×C4⋊C4 | C24 | 1 | 16 | yes | — |
| 348 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 349 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 350 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 351 | C7×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 352 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 353 | C7×C4⋊C4 | C24 | 1 | 16 | yes | — |
| 354 | C7×C4⋊C4 | C24 | 1 | 16 | yes | — |
| 355 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 356 | C7×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 357 | C7×C22⋊C4 | C24 | 1 | 4 | yes | — |
| 358 | C7×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 359 | C42×C7 | C24 | 1 | 2 | yes | — |
| 360 | C42×C7 | C24 | 1 | 4 | yes | — |
| 361 | C42×C7 | C24 | 1 | 8 | yes | — |
| 362 | C42×C7 | C24 | 1 | 16 | yes | — |
| 363 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 364 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 365 | C22⋊Dic7 | C24 | 1 | 4 | yes | — |
| 366 | (C2×D7)⋊C4 | C24 | 1 | 8 | yes | — |
| 367 | (C2×D7)⋊C4 | C24 | 1 | 8 | yes | — |
| 368 | (C2×D7)⋊C4 | C24 | 1 | 8 | yes | — |
| 369 | (C2×D7)⋊C4 | C24 | 1 | 8 | yes | — |
| 370 | (C2×D7)⋊C4 | C24 | 1 | 8 | yes | — |
| 371 | (C2×D7)⋊C4 | C24 | 1 | 8 | yes | — |
| 372 | (C2×D7)⋊C4 | C24 | 1 | 16 | yes | — |
| 373 | (C2×D7)⋊C4 | C24 | 1 | 16 | yes | — |
| 374 | (C2×D7)⋊C4 | C24 | 1 | 8 | yes | — |
| 375 | (C2×D7)⋊C4 | C24 | 1 | 16 | yes | — |
| 376 | (C2×D7)⋊C4 | C24 | 1 | 16 | yes | — |
| 377 | (C2×D7)⋊C4 | C24 | 1 | 8 | yes | — |
| 378 | (C2×D7)⋊C4 | C24 | 1 | 8 | yes | — |
| 379 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 380 | C4⋊Dic7 | C24 | 1 | 8 | yes | — |
| 381 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 382 | C4⋊Dic7 | C24 | 1 | 8 | yes | — |
| 383 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 384 | C4⋊Dic7 | C24 | 1 | 16 | yes | — |
| 385 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 386 | C4⋊Dic7 | C24 | 1 | 8 | yes | — |
| 387 | Dic7⋊C4 | C24 | 1 | 8 | yes | — |
| 388 | Dic7⋊C4 | C24 | 1 | 8 | yes | — |
| 389 | Dic7⋊C4 | C24 | 1 | 16 | yes | — |
| 390 | Dic7⋊C4 | C24 | 1 | 16 | yes | — |
| 391 | Dic7⋊C4 | C24 | 1 | 8 | yes | — |
| 392 | Dic7⋊C4 | C24 | 1 | 8 | yes | — |
| 393 | Dic7⋊C4 | C24 | 1 | 8 | yes | — |
| 394 | Dic7⋊C4 | C24 | 1 | 8 | yes | — |
| 395 | C4×Dic7 | C24 | 1 | 2 | yes | — |
| 396 | C4×Dic7 | C24 | 1 | 4 | yes | — |
| 397 | C4×Dic7 | C24 | 1 | 8 | yes | — |
| 398 | C4×Dic7 | C24 | 1 | 16 | yes | — |
| 399 | C4×Dic7 | C24 | 1 | 2 | yes | — |
| 400 | C4×Dic7 | C24 | 1 | 8 | yes | — |
| 401 | C4×Dic7 | C24 | 1 | 8 | yes | — |
| 402 | C4×Dic7 | C24 | 1 | 2 | yes | — |
| 403 | C4×Dic7 | C24 | 1 | 2 | yes | — |
| 404 | C4×Dic7 | C24 | 1 | 2 | yes | — |
| 405 | C4×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 406 | C4×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 407 | #564 | C2×D7 | 1 | 4 | yes | complemented |
| 408 | #563 | — | 7 | 16 | no | — |
| 409 | #563 | — | 7 | 8 | no | — |
| 410 | #563 | — | 7 | 16 | no | — |
| 411 | #562 | — | 7 | 16 | no | — |
| 412 | #562 | — | 7 | 4 | no | — |
| 413 | #559 | — | 7 | 4 | no | — |
| 414 | #559 | — | 7 | 8 | no | — |
| 415 | Q82 | — | 7 | 4 | no | — |
| 416 | #557 | — | 7 | 8 | no | — |
| 417 | #557 | C2×D7 | 1 | 4 | yes | complemented |
| 418 | #557 | C2×D7 | 1 | 4 | yes | complemented |
| 419 | #557 | C2×D7 | 1 | 4 | yes | complemented |
| 420 | #556 | — | 7 | 4 | no | — |
| 421 | #556 | — | 7 | 8 | no | — |
| 422 | #556 | — | 7 | 8 | no | — |
| 423 | #556 | — | 7 | 4 | no | — |
| 424 | #554 | — | 7 | 16 | no | — |
| 425 | #554 | — | 7 | 8 | no | — |
| 426 | #554 | — | 7 | 8 | no | — |
| 427 | #554 | — | 7 | 4 | no | — |
| 428 | #553 | — | 7 | 8 | no | — |
| 429 | #553 | — | 7 | 16 | no | — |
| 430 | #552 | — | 7 | 8 | no | — |
| 431 | #552 | — | 7 | 16 | no | — |
| 432 | #550 | — | 7 | 4 | no | — |
| 433 | D4×Q8 | — | 7 | 8 | no | — |
| 434 | D4×Q8 | — | 7 | 4 | no | — |
| 435 | D4×Q8 | — | 7 | 4 | no | — |
| 436 | #548 | — | 7 | 8 | no | — |
| 437 | #548 | — | 7 | 8 | no | — |
| 438 | #547 | — | 7 | 8 | no | — |
| 439 | #547 | — | 7 | 4 | no | — |
| 440 | #544 | — | 7 | 8 | no | — |
| 441 | #542 | — | 7 | 16 | no | — |
| 442 | #542 | — | 7 | 8 | no | — |
| 443 | #542 | — | 7 | 8 | no | — |
| 444 | #542 | — | 7 | 8 | no | — |
| 445 | #542 | — | 7 | 8 | no | — |
| 446 | #541 | — | 7 | 4 | no | — |
| 447 | #541 | — | 7 | 16 | no | — |
| 448 | #541 | — | 7 | 8 | no | — |
| 449 | #541 | C2×D7 | 1 | 4 | yes | — |
| 450 | #541 | C2×D7 | 1 | 8 | yes | — |
| 451 | #540 | — | 7 | 4 | no | — |
| 452 | #540 | — | 7 | 4 | no | — |
| 453 | #539 | — | 7 | 16 | no | — |
| 454 | #539 | — | 7 | 16 | no | — |
| 455 | #539 | — | 7 | 16 | no | — |
| 456 | #538 | — | 7 | 16 | no | — |
| 457 | #537 | — | 7 | 8 | no | — |
| 458 | #536 | — | 7 | 8 | no | — |
| 459 | #536 | — | 7 | 8 | no | — |
| 460 | #533 | — | 7 | 2 | no | — |
| 461 | #533 | — | 7 | 2 | no | — |
| 462 | #533 | — | 7 | 2 | no | — |
| 463 | #533 | — | 7 | 8 | no | — |
| 464 | #533 | — | 7 | 2 | no | — |
| 465 | #533 | — | 7 | 4 | no | — |
| 466 | #533 | — | 7 | 16 | no | — |
| 467 | #533 | — | 7 | 4 | no | — |
| 468 | #533 | — | 7 | 4 | no | — |
| 469 | #533 | — | 7 | 2 | no | — |
| 470 | #533 | — | 7 | 1 | no | — |
| 471 | #533 | C2×D7 | 1 | 1 | yes | characteristic |
| 472 | #533 | C2×D7 | 1 | 2 | yes | — |
| 473 | #532 | — | 7 | 2 | no | — |
| 474 | #532 | — | 7 | 2 | no | — |
| 475 | #532 | — | 7 | 4 | no | — |
| 476 | #532 | — | 7 | 2 | no | — |
| 477 | C2×C4⋊Q8 | — | 7 | 2 | no | — |
| 478 | #529 | — | 7 | 16 | no | — |
| 479 | #529 | — | 7 | 4 | no | — |
| 480 | #529 | — | 7 | 4 | no | — |
| 481 | #529 | — | 7 | 16 | no | — |
| 482 | #529 | — | 7 | 8 | no | — |
| 483 | #529 | — | 7 | 16 | no | — |
| 484 | #529 | — | 7 | 4 | no | — |
| 485 | #529 | — | 7 | 4 | no | — |
| 486 | #529 | — | 7 | 4 | no | — |
| 487 | #529 | — | 7 | 4 | no | — |
| 488 | C2×#125 | — | 7 | 2 | no | — |
| 489 | #525 | — | 7 | 4 | no | — |
| 490 | #525 | — | 7 | 4 | no | — |
| 491 | #525 | — | 7 | 4 | no | — |
| 492 | C2×C22⋊Q8 | — | 7 | 4 | no | — |
| 493 | C4×#41 | — | 7 | 4 | no | — |
| 494 | C4×#41 | — | 7 | 4 | no | — |
| 495 | C4×#41 | — | 7 | 8 | no | — |
| 496 | C4×#41 | — | 7 | 8 | no | — |
| 497 | C4×#41 | — | 7 | 4 | no | — |
| 498 | C2×C4×Q8 | — | 7 | 4 | no | — |
| 499 | C2×C4×Q8 | — | 7 | 8 | no | — |
| 500 | C2×#117 | — | 7 | 2 | no | — |
| 501 | C22×C42 | — | 7 | 1 | no | — |
| 502 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 503 | C22×D7 | — | 2 | 2 | no | — |
| 504 | C22×D7 | — | 4 | 2 | no | — |
| 505 | C22×D7 | C25 | 1 | 1 | yes | characteristic |
| 506 | C22×D7 | C25 | 1 | 8 | yes | — |
| 507 | C22×D7 | C25 | 1 | 1 | yes | characteristic |
| 508 | C7×Q8 | — | 2 | 8 | no | — |
| 509 | C7×Q8 | — | 2 | 8 | no | — |
| 510 | C7×Q8 | — | 2 | 8 | no | — |
| 511 | C2×C4×C7 | — | 2 | 2 | no | — |
| 512 | C2×C4×C7 | — | 2 | 4 | no | — |
| 513 | C2×C4×C7 | C25 | 1 | 8 | yes | — |
| 514 | C2×C4×C7 | C25 | 1 | 2 | yes | — |
| 515 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 516 | C2×C4×C7 | C25 | 1 | 8 | yes | — |
| 517 | C2×C4×C7 | C25 | 1 | 8 | yes | — |
| 518 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 519 | C2×C4×C7 | C25 | 1 | 2 | yes | — |
| 520 | C22⋊D7 | — | 4 | 8 | no | — |
| 521 | C2×Dic7 | — | 2 | 2 | no | — |
| 522 | C2×Dic7 | — | 4 | 2 | no | — |
| 523 | C2×Dic7 | C25 | 1 | 2 | yes | — |
| 524 | C2×Dic7 | C25 | 1 | 1 | yes | characteristic |
| 525 | C2×Dic7 | C25 | 1 | 8 | yes | — |
| 526 | C2×Dic7 | C25 | 1 | 2 | yes | — |
| 527 | C2×Dic7 | C25 | 1 | 8 | yes | — |
| 528 | C2×Dic7 | C25 | 1 | 1 | yes | characteristic |
| 529 | D28 | — | 2 | 16 | no | — |
| 530 | D28 | — | 2 | 8 | no | — |
| 531 | D28 | — | 2 | 8 | no | — |
| 532 | D28 | — | 4 | 4 | no | — |
| 533 | D28 | — | 4 | 8 | no | — |
| 534 | D28 | — | 4 | 16 | no | — |
| 535 | C4×D7 | — | 2 | 2 | no | — |
| 536 | C4×D7 | — | 2 | 2 | no | — |
| 537 | C4×D7 | — | 2 | 4 | no | — |
| 538 | C4×D7 | — | 2 | 4 | no | — |
| 539 | C4×D7 | — | 2 | 16 | no | — |
| 540 | C4×D7 | — | 2 | 2 | no | — |
| 541 | C4×D7 | — | 2 | 16 | no | — |
| 542 | C4×D7 | — | 4 | 2 | no | — |
| 543 | C4×D7 | — | 4 | 2 | no | — |
| 544 | C4×D7 | — | 4 | 16 | no | — |
| 545 | C4×D7 | — | 4 | 8 | no | — |
| 546 | C4×D7 | — | 4 | 16 | no | — |
| 547 | C4×D7 | — | 4 | 8 | no | — |
| 548 | C4×D7 | 2−1+4 | 1 | 4 | yes | — |
| 549 | Dic14 | — | 2 | 8 | no | — |
| 550 | Dic14 | — | 4 | 4 | no | — |
| 551 | Dic14 | — | 4 | 8 | no | — |
| 552 | Dic14 | — | 4 | 16 | no | — |
| 553 | C2×#41 | — | 7 | 4 | no | — |
| 554 | C2×#41 | — | 7 | 4 | no | — |
| 555 | C2×#41 | — | 7 | 8 | no | — |
| 556 | C2×#41 | — | 7 | 4 | no | — |
| 557 | C22×Q8 | — | 7 | 4 | no | — |
| 558 | C22×Q8 | — | 7 | 8 | no | — |
| 559 | C23×C4 | — | 7 | 1 | no | — |
| 560 | C23×C4 | — | 7 | 2 | no | — |
| 561 | C4⋊Q8 | — | 7 | 4 | no | — |
| 562 | C4⋊Q8 | — | 7 | 4 | no | — |
| 563 | C4⋊Q8 | — | 7 | 4 | no | — |
| 564 | C4⋊Q8 | — | 7 | 16 | no | — |
| 565 | C4⋊Q8 | — | 7 | 8 | no | — |
| 566 | C4⋊Q8 | — | 7 | 16 | no | — |
| 567 | C4⋊Q8 | — | 7 | 2 | no | — |
| 568 | C4⋊Q8 | — | 7 | 2 | no | — |
| 569 | C4⋊Q8 | — | 7 | 8 | no | — |
| 570 | C4⋊Q8 | C22×D7 | 1 | 2 | yes | — |
| 571 | C4⋊Q8 | C22×D7 | 1 | 2 | yes | — |
| 572 | C4⋊Q8 | C22×D7 | 1 | 2 | yes | — |
| 573 | C4⋊Q8 | C22×D7 | 1 | 4 | yes | — |
| 574 | C4⋊Q8 | C22×D7 | 1 | 8 | yes | — |
| 575 | #127 | — | 7 | 2 | no | — |
| 576 | #127 | — | 7 | 4 | no | — |
| 577 | #126 | — | 7 | 8 | no | — |
| 578 | #126 | — | 7 | 8 | no | — |
| 579 | #126 | — | 7 | 16 | no | — |
| 580 | #126 | — | 7 | 16 | no | — |
| 581 | #126 | — | 7 | 16 | no | — |
| 582 | #126 | — | 7 | 16 | no | — |
| 583 | #126 | — | 7 | 16 | no | — |
| 584 | #126 | — | 7 | 16 | no | — |
| 585 | #126 | C22×D7 | 1 | 16 | yes | — |
| 586 | #125 | — | 7 | 8 | no | — |
| 587 | #125 | — | 7 | 4 | no | — |
| 588 | #125 | — | 7 | 4 | no | — |
| 589 | #125 | — | 7 | 4 | no | — |
| 590 | #125 | — | 7 | 16 | no | — |
| 591 | #125 | — | 7 | 16 | no | — |
| 592 | #125 | — | 7 | 2 | no | — |
| 593 | #125 | — | 7 | 16 | no | — |
| 594 | #125 | — | 7 | 4 | no | — |
| 595 | #125 | C22×D7 | 1 | 2 | yes | — |
| 596 | #125 | C22×D7 | 1 | 4 | yes | — |
| 597 | #125 | C22×D7 | 1 | 16 | yes | — |
| 598 | #125 | C22×D7 | 1 | 16 | yes | — |
| 599 | #125 | C22×D7 | 1 | 8 | yes | — |
| 600 | #125 | C22×D7 | 1 | 16 | yes | — |
| 601 | #125 | C22×D7 | 1 | 4 | yes | — |
| 602 | #124 | — | 7 | 4 | no | — |
| 603 | #124 | — | 7 | 4 | no | — |
| 604 | #124 | — | 7 | 8 | no | — |
| 605 | #124 | — | 7 | 16 | no | — |
| 606 | #124 | — | 7 | 4 | no | — |
| 607 | #124 | — | 7 | 8 | no | — |
| 608 | #124 | — | 7 | 16 | no | — |
| 609 | #124 | — | 7 | 16 | no | — |
| 610 | #123 | — | 7 | 8 | no | — |
| 611 | #123 | — | 7 | 8 | no | — |
| 612 | #123 | — | 7 | 16 | no | — |
| 613 | #123 | — | 7 | 16 | no | — |
| 614 | #123 | — | 7 | 16 | no | — |
| 615 | #123 | — | 7 | 16 | no | — |
| 616 | #123 | — | 7 | 16 | no | — |
| 617 | #123 | — | 7 | 16 | no | — |
| 618 | #123 | — | 7 | 8 | no | — |
| 619 | #123 | — | 7 | 16 | no | — |
| 620 | C22⋊Q8 | — | 7 | 4 | no | — |
| 621 | C22⋊Q8 | — | 7 | 4 | no | — |
| 622 | C22⋊Q8 | — | 7 | 4 | no | — |
| 623 | C22⋊Q8 | — | 7 | 8 | no | — |
| 624 | C22⋊Q8 | — | 7 | 8 | no | — |
| 625 | C22⋊Q8 | — | 7 | 4 | no | — |
| 626 | C22⋊Q8 | — | 7 | 4 | no | — |
| 627 | C22⋊Q8 | — | 7 | 8 | no | — |
| 628 | C22⋊Q8 | — | 7 | 4 | no | — |
| 629 | C22⋊Q8 | — | 7 | 4 | no | — |
| 630 | C22⋊Q8 | — | 7 | 16 | no | — |
| 631 | C22⋊Q8 | — | 7 | 8 | no | — |
| 632 | C22⋊Q8 | — | 7 | 16 | no | — |
| 633 | C22⋊Q8 | — | 7 | 16 | no | — |
| 634 | C22⋊Q8 | — | 7 | 16 | no | — |
| 635 | C22⋊Q8 | — | 7 | 16 | no | — |
| 636 | C22⋊Q8 | — | 7 | 16 | no | — |
| 637 | C22⋊Q8 | — | 7 | 16 | no | — |
| 638 | C22⋊Q8 | — | 7 | 16 | no | — |
| 639 | C22⋊Q8 | — | 7 | 16 | no | — |
| 640 | C22⋊Q8 | — | 7 | 8 | no | — |
| 641 | C22⋊Q8 | C22×D7 | 1 | 4 | yes | — |
| 642 | C22⋊Q8 | C22×D7 | 1 | 4 | yes | — |
| 643 | C22⋊Q8 | C22×D7 | 1 | 4 | yes | — |
| 644 | #121 | — | 7 | 4 | no | — |
| 645 | #121 | — | 7 | 4 | no | — |
| 646 | #121 | — | 7 | 4 | no | — |
| 647 | #121 | — | 7 | 4 | no | — |
| 648 | #121 | — | 7 | 4 | no | — |
| 649 | #121 | — | 7 | 4 | no | — |
| 650 | #121 | — | 7 | 16 | no | — |
| 651 | #121 | — | 7 | 8 | no | — |
| 652 | #121 | — | 7 | 16 | no | — |
| 653 | #121 | — | 7 | 16 | no | — |
| 654 | #121 | — | 7 | 16 | no | — |
| 655 | #120 | — | 7 | 8 | no | — |
| 656 | C4×Q8 | — | 7 | 4 | no | — |
| 657 | C4×Q8 | — | 7 | 4 | no | — |
| 658 | C4×Q8 | — | 7 | 4 | no | — |
| 659 | C4×Q8 | — | 7 | 8 | no | — |
| 660 | C4×Q8 | — | 7 | 4 | no | — |
| 661 | C4×Q8 | — | 7 | 16 | no | — |
| 662 | C4×Q8 | — | 7 | 8 | no | — |
| 663 | C4×Q8 | — | 7 | 4 | no | — |
| 664 | C4×Q8 | — | 7 | 4 | no | — |
| 665 | C4×Q8 | — | 7 | 4 | no | — |
| 666 | C4×Q8 | — | 7 | 8 | no | — |
| 667 | C4×Q8 | — | 7 | 8 | no | — |
| 668 | C4×Q8 | — | 7 | 16 | no | — |
| 669 | C4×Q8 | C22×D7 | 1 | 4 | yes | — |
| 670 | C4×Q8 | C22×D7 | 1 | 8 | yes | — |
| 671 | C4×Q8 | C22×D7 | 1 | 4 | yes | — |
| 672 | C4×Q8 | C22×D7 | 1 | 4 | yes | — |
| 673 | C4×Q8 | C22×D7 | 1 | 8 | yes | — |
| 674 | C4×Q8 | C22×D7 | 1 | 8 | yes | — |
| 675 | C4×D4 | — | 7 | 4 | no | — |
| 676 | C4×D4 | — | 7 | 8 | no | — |
| 677 | C4×D4 | — | 7 | 8 | no | — |
| 678 | C4×D4 | — | 7 | 16 | no | — |
| 679 | C4×D4 | — | 7 | 4 | no | — |
| 680 | C4×D4 | — | 7 | 4 | no | — |
| 681 | C4×D4 | — | 7 | 4 | no | — |
| 682 | C4×D4 | — | 7 | 16 | no | — |
| 683 | C4×D4 | — | 7 | 8 | no | — |
| 684 | C4×D4 | — | 7 | 8 | no | — |
| 685 | C4×D4 | — | 7 | 8 | no | — |
| 686 | C4×D4 | — | 7 | 8 | no | — |
| 687 | C4×D4 | — | 7 | 8 | no | — |
| 688 | C4×D4 | — | 7 | 4 | no | — |
| 689 | C4×D4 | — | 7 | 4 | no | — |
| 690 | C4×D4 | — | 7 | 16 | no | — |
| 691 | C4×D4 | — | 7 | 16 | no | — |
| 692 | C4×D4 | — | 7 | 8 | no | — |
| 693 | C4×D4 | — | 7 | 8 | no | — |
| 694 | #117 | — | 7 | 2 | no | — |
| 695 | #117 | — | 7 | 4 | no | — |
| 696 | #117 | — | 7 | 4 | no | — |
| 697 | #117 | — | 7 | 4 | no | — |
| 698 | #117 | — | 7 | 16 | no | — |
| 699 | #117 | — | 7 | 8 | no | — |
| 700 | #117 | — | 7 | 8 | no | — |
| 701 | #117 | — | 7 | 8 | no | — |
| 702 | #117 | — | 7 | 16 | no | — |
| 703 | #117 | — | 7 | 4 | no | — |
| 704 | #117 | — | 7 | 4 | no | — |
| 705 | #117 | — | 7 | 8 | no | — |
| 706 | #117 | C22×D7 | 1 | 2 | yes | — |
| 707 | #117 | C22×D7 | 1 | 4 | yes | — |
| 708 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 709 | C2×C4⋊C4 | — | 7 | 8 | no | — |
| 710 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 711 | C2×C4⋊C4 | — | 7 | 8 | no | — |
| 712 | C2×C4⋊C4 | — | 7 | 16 | no | — |
| 713 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 714 | C2×C42 | — | 7 | 2 | no | — |
| 715 | C2×C42 | — | 7 | 1 | no | — |
| 716 | C2×C42 | — | 7 | 4 | no | — |
| 717 | C2×C42 | — | 7 | 2 | no | — |
| 718 | C2×C42 | — | 7 | 8 | no | — |
| 719 | C2×C42 | — | 7 | 16 | no | — |
| 720 | C2×C42 | — | 7 | 1 | no | — |
| 721 | C2×C42 | — | 7 | 1 | no | — |
| 722 | C2×C42 | — | 7 | 1 | no | — |
| 723 | C2×C42 | — | 7 | 1 | no | — |
| 724 | C2×C42 | — | 7 | 2 | no | — |
| 725 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 726 | C22×C7 | — | 2 | 1 | no | — |
| 727 | C22×C7 | — | 2 | 2 | no | — |
| 728 | C22×C7 | C26 | 1 | 1 | yes | characteristic |
| 729 | C2×D7 | — | 2 | 2 | no | — |
| 730 | C2×D7 | — | 2 | 1 | no | — |
| 731 | C2×D7 | — | 2 | 8 | no | — |
| 732 | C2×D7 | — | 2 | 8 | no | — |
| 733 | C2×D7 | — | 2 | 2 | no | — |
| 734 | C2×D7 | — | 2 | 8 | no | — |
| 735 | C2×D7 | — | 4 | 4 | no | — |
| 736 | C2×D7 | C2×2−1+4 | 1 | 2 | yes | — |
| 737 | C4×C7 | — | 2 | 1 | no | — |
| 738 | C4×C7 | — | 2 | 8 | no | — |
| 739 | C4×C7 | — | 2 | 8 | no | — |
| 740 | C4×C7 | — | 2 | 2 | no | — |
| 741 | C4×C7 | — | 2 | 8 | no | — |
| 742 | C4×C7 | C2×2−1+4 | 1 | 2 | yes | — |
| 743 | C4×C7 | #585 | 1 | 4 | yes | — |
| 744 | Dic7 | — | 2 | 1 | no | — |
| 745 | Dic7 | — | 2 | 8 | no | — |
| 746 | Dic7 | — | 2 | 2 | no | — |
| 747 | Dic7 | — | 2 | 8 | no | — |
| 748 | Dic7 | — | 2 | 2 | no | — |
| 749 | Dic7 | C2×2−1+4 | 1 | 2 | yes | — |
| 750 | C24 | — | 7 | 1 | no | — |
| 751 | #41 | — | 14 | 16 | no | — |
| 752 | #41 | — | 28 | 8 | no | — |
| 753 | #41 | — | 28 | 8 | no | — |
| 754 | #41 | — | 28 | 16 | no | — |
| 755 | C2×Q8 | — | 7 | 4 | no | — |
| 756 | C2×Q8 | — | 7 | 8 | no | — |
| 757 | C2×Q8 | — | 7 | 16 | no | — |
| 758 | C2×Q8 | — | 7 | 4 | no | — |
| 759 | C2×Q8 | — | 28 | 8 | no | — |
| 760 | C2×Q8 | — | 28 | 16 | no | — |
| 761 | C2×Q8 | C23×D7 | 1 | 4 | yes | — |
| 762 | C2×Q8 | C23×D7 | 1 | 4 | yes | — |
| 763 | C2×Q8 | C23×D7 | 1 | 4 | yes | — |
| 764 | C2×D4 | — | 7 | 8 | no | — |
| 765 | C2×D4 | — | 7 | 8 | no | — |
| 766 | C2×D4 | — | 7 | 4 | no | — |
| 767 | C2×D4 | — | 7 | 4 | no | — |
| 768 | C2×D4 | — | 7 | 8 | no | — |
| 769 | C2×D4 | — | 7 | 4 | no | — |
| 770 | C2×D4 | — | 7 | 16 | no | — |
| 771 | C22×C4 | — | 7 | 1 | no | — |
| 772 | C22×C4 | — | 7 | 1 | no | — |
| 773 | C22×C4 | — | 7 | 2 | no | — |
| 774 | C22×C4 | — | 7 | 8 | no | — |
| 775 | C22×C4 | — | 7 | 1 | no | — |
| 776 | C22×C4 | — | 7 | 2 | no | — |
| 777 | C22×C4 | — | 7 | 1 | no | — |
| 778 | C22×C4 | — | 7 | 1 | no | — |
| 779 | C22×C4 | — | 7 | 2 | no | — |
| 780 | C22×C4 | — | 7 | 8 | no | — |
| 781 | C22×C4 | — | 7 | 2 | no | — |
| 782 | C22×C4 | — | 7 | 2 | no | — |
| 783 | C22×C4 | — | 7 | 8 | no | — |
| 784 | C22×C4 | — | 7 | 8 | no | — |
| 785 | C22×C4 | — | 7 | 16 | no | — |
| 786 | C22×C4 | — | 7 | 16 | no | — |
| 787 | C22×C4 | — | 14 | 4 | no | — |
| 788 | C22×C4 | — | 28 | 4 | no | — |
| 789 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 790 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 791 | C4⋊C4 | — | 7 | 8 | no | — |
| 792 | C4⋊C4 | — | 7 | 8 | no | — |
| 793 | C4⋊C4 | — | 7 | 16 | no | — |
| 794 | C4⋊C4 | — | 7 | 8 | no | — |
| 795 | C4⋊C4 | — | 7 | 8 | no | — |
| 796 | C4⋊C4 | — | 7 | 16 | no | — |
| 797 | C4⋊C4 | — | 7 | 8 | no | — |
| 798 | C4⋊C4 | — | 7 | 8 | no | — |
| 799 | C4⋊C4 | — | 7 | 4 | no | — |
| 800 | C4⋊C4 | — | 7 | 8 | no | — |
| 801 | C4⋊C4 | — | 7 | 8 | no | — |
| 802 | C4⋊C4 | — | 7 | 4 | no | — |
| 803 | C4⋊C4 | — | 7 | 4 | no | — |
| 804 | C4⋊C4 | — | 7 | 4 | no | — |
| 805 | C4⋊C4 | — | 7 | 16 | no | — |
| 806 | C4⋊C4 | — | 7 | 8 | no | — |
| 807 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 808 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 809 | C4⋊C4 | C23×D7 | 1 | 8 | yes | — |
| 810 | C4⋊C4 | C23×D7 | 1 | 16 | yes | — |
| 811 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 812 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 813 | C4⋊C4 | C23×D7 | 1 | 16 | yes | — |
| 814 | C4⋊C4 | C23×D7 | 1 | 8 | yes | — |
| 815 | C4⋊C4 | C23×D7 | 1 | 16 | yes | — |
| 816 | C4⋊C4 | C23×D7 | 1 | 8 | yes | — |
| 817 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 818 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 819 | C22⋊C4 | — | 7 | 4 | no | — |
| 820 | C22⋊C4 | — | 7 | 8 | no | — |
| 821 | C22⋊C4 | — | 7 | 8 | no | — |
| 822 | C22⋊C4 | — | 7 | 8 | no | — |
| 823 | C22⋊C4 | — | 7 | 8 | no | — |
| 824 | C22⋊C4 | — | 7 | 8 | no | — |
| 825 | C22⋊C4 | — | 7 | 16 | no | — |
| 826 | C22⋊C4 | — | 7 | 16 | no | — |
| 827 | C22⋊C4 | — | 7 | 8 | no | — |
| 828 | C22⋊C4 | — | 7 | 8 | no | — |
| 829 | C22⋊C4 | — | 7 | 8 | no | — |
| 830 | C22⋊C4 | — | 7 | 8 | no | — |
| 831 | C22⋊C4 | — | 7 | 16 | no | — |
| 832 | C22⋊C4 | — | 7 | 16 | no | — |
| 833 | C22⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 834 | C22⋊C4 | C23×D7 | 1 | 8 | yes | — |
| 835 | C42 | — | 7 | 2 | no | — |
| 836 | C42 | — | 7 | 1 | no | — |
| 837 | C42 | — | 7 | 2 | no | — |
| 838 | C42 | — | 7 | 8 | no | — |
| 839 | C42 | — | 7 | 8 | no | — |
| 840 | C42 | — | 7 | 2 | no | — |
| 841 | C42 | — | 7 | 2 | no | — |
| 842 | C42 | — | 7 | 2 | no | — |
| 843 | C42 | — | 7 | 1 | no | — |
| 844 | C42 | — | 7 | 8 | no | — |
| 845 | C42 | — | 7 | 4 | no | — |
| 846 | C42 | — | 7 | 16 | no | — |
| 847 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 848 | C42 | C23×D7 | 1 | 2 | yes | — |
| 849 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 850 | C42 | C23×D7 | 1 | 8 | yes | — |
| 851 | C42 | C23×D7 | 1 | 4 | yes | — |
| 852 | C42 | C23×D7 | 1 | 16 | yes | — |
| 853 | C2×C7 | — | 4 | 1 | no | — |
| 854 | C2×C7 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 855 | C2×C7 | C2×#585 | 1 | 2 | yes | — |
| 856 | D7 | — | 2 | 2 | no | — |
| 857 | D7 | — | 4 | 8 | no | — |
| 858 | D7 | — | 4 | 1 | no | — |
| 859 | C23 | — | 7 | 1 | no | — |
| 860 | C23 | — | 7 | 1 | no | — |
| 861 | C23 | — | 7 | 8 | no | — |
| 862 | C23 | — | 14 | 2 | no | — |
| 863 | C23 | — | 28 | 2 | no | — |
| 864 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 865 | Q8 | — | 2 | 8 | no | — |
| 866 | Q8 | — | 2 | 8 | no | — |
| 867 | Q8 | — | 2 | 8 | no | — |
| 868 | Q8 | — | 14 | 8 | no | — |
| 869 | Q8 | — | 28 | 8 | no | — |
| 870 | Q8 | — | 28 | 16 | no | — |
| 871 | Q8 | — | 28 | 4 | no | — |
| 872 | D4 | — | 14 | 16 | no | — |
| 873 | D4 | — | 14 | 8 | no | — |
| 874 | D4 | — | 14 | 8 | no | — |
| 875 | D4 | — | 28 | 4 | no | — |
| 876 | D4 | — | 28 | 16 | no | — |
| 877 | D4 | — | 28 | 8 | no | — |
| 878 | D4 | — | 28 | 8 | no | — |
| 879 | C2×C4 | — | 2 | 2 | no | — |
| 880 | C2×C4 | — | 2 | 4 | no | — |
| 881 | C2×C4 | — | 7 | 1 | no | — |
| 882 | C2×C4 | — | 7 | 4 | no | — |
| 883 | C2×C4 | — | 7 | 2 | no | — |
| 884 | C2×C4 | — | 7 | 1 | no | — |
| 885 | C2×C4 | — | 7 | 2 | no | — |
| 886 | C2×C4 | — | 7 | 8 | no | — |
| 887 | C2×C4 | — | 7 | 8 | no | — |
| 888 | C2×C4 | — | 14 | 2 | no | — |
| 889 | C2×C4 | — | 14 | 16 | no | — |
| 890 | C2×C4 | — | 14 | 2 | no | — |
| 891 | C2×C4 | — | 14 | 2 | no | — |
| 892 | C2×C4 | — | 14 | 2 | no | — |
| 893 | C2×C4 | — | 14 | 4 | no | — |
| 894 | C2×C4 | — | 14 | 4 | no | — |
| 895 | C2×C4 | — | 14 | 16 | no | — |
| 896 | C2×C4 | — | 28 | 2 | no | — |
| 897 | C2×C4 | — | 28 | 2 | no | — |
| 898 | C2×C4 | — | 28 | 8 | no | — |
| 899 | C2×C4 | — | 28 | 16 | no | — |
| 900 | C2×C4 | — | 28 | 16 | no | — |
| 901 | C2×C4 | — | 28 | 8 | no | — |
| 902 | C2×C4 | — | 28 | 2 | no | — |
| 903 | C2×C4 | C24×D7 | 1 | 8 | yes | — |
| 904 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 905 | C2×C4 | C24×D7 | 1 | 2 | yes | — |
| 906 | C2×C4 | C24×D7 | 1 | 8 | yes | — |
| 907 | C2×C4 | C24×D7 | 1 | 8 | yes | — |
| 908 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 909 | C2×C4 | C24×D7 | 1 | 2 | yes | — |
| 910 | C7 | #62761 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 911 | C22 | — | 2 | 2 | no | — |
| 912 | C22 | — | 2 | 1 | no | — |
| 913 | C22 | — | 7 | 2 | no | — |
| 914 | C22 | — | 14 | 2 | no | — |
| 915 | C22 | — | 14 | 8 | no | — |
| 916 | C22 | — | 14 | 2 | no | — |
| 917 | C22 | — | 14 | 8 | no | — |
| 918 | C22 | — | 14 | 1 | no | — |
| 919 | C22 | — | 14 | 8 | no | — |
| 920 | C22 | — | 28 | 4 | no | — |
| 921 | C22 | C25×D7 | 1 | 1 | yes | characteristic |
| 922 | C4 | — | 2 | 2 | no | — |
| 923 | C4 | — | 2 | 8 | no | — |
| 924 | C4 | — | 2 | 8 | no | — |
| 925 | C4 | — | 2 | 1 | no | — |
| 926 | C4 | — | 2 | 8 | no | — |
| 927 | C4 | — | 7 | 2 | no | — |
| 928 | C4 | — | 14 | 2 | no | — |
| 929 | C4 | — | 14 | 8 | no | — |
| 930 | C4 | — | 14 | 2 | no | — |
| 931 | C4 | — | 14 | 8 | no | — |
| 932 | C4 | — | 14 | 1 | no | — |
| 933 | C4 | D7×2−1+4 | 1 | 2 | yes | — |
| 934 | C4 | #90620 | 1 | 4 | yes | — |
| 935 | C2 | — | 4 | 1 | no | — |
| 936 | C2 | — | 14 | 2 | no | — |
| 937 | C2 | — | 28 | 1 | no | — |
| 938 | C2 | — | 28 | 8 | no | — |
| 939 | C2 | C2×#90620 | 1 | 2 | yes | — |
| 940 | C2 | C2×D7×2−1+4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D7 |
| commutator, socle, cosocle | C22×C7 | C26 |
| Fitting | C7×#3556 | C2 |
| hypercenter | #3556 | D7 |
| hypocenter | C7 | #62761 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #3556 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#3556 | C2 | semidirect |
| 2. #11744211 | C2 | semidirect |
| 3. #11744207 | C2 | semidirect |
| 4. #11744104 | C2 | semidirect |
| 5. #11744103 | C2 | semidirect |
| 6. #11744102 | C2 | semidirect |
| 7. #11744085 | C2 | semidirect |
| 8. #11744084 | C2 | semidirect |
| 9. #11744083 | C2 | semidirect |
| 10. #11743584 | C2 | semidirect |
| 11. #11743571 | C2 | semidirect |
| 12. #11743564 | C2 | semidirect |
| 13. #11743563 | C2 | semidirect |
| 14. #11743356 | C2 | semidirect |
| 15. D7×#533 | C2 | semidirect |
| 16. #11743335 | C2 | semidirect |
| 17. #11743325 | C2 | semidirect |
| 18. C7×#564 | C22 | semidirect |
| 19. C7×#557 | C22 | semidirect |
| 20. C7×#557 | C22 | semidirect |
| 21. C7×#557 | C22 | semidirect |
| 26. #90423 | C22 | semidirect |
| 27. #90423 | C22 | semidirect |
| 32. #90419 | C22 | semidirect |
| 34. #90418 | C22 | semidirect |
| 36. #90417 | C22 | semidirect |
| 40. #90415 | C22 | semidirect |
| 47. #90391 | C22 | semidirect |
| 49. #90390 | C22 | semidirect |
| 50. #90390 | C22 | semidirect |
| 52. #90387 | C22 | semidirect |
| 56. #90385 | C22 | semidirect |
| 58. #90383 | C22 | semidirect |
| 62. #90382 | C22 | semidirect |
| 63. #90382 | C22 | semidirect |
| 65. #90381 | C22 | semidirect |
| 66. #90380 | C22 | semidirect |
| 69. #90379 | C22 | semidirect |
| 80. #90276 | C22 | semidirect |
| 81. #90276 | C22 | semidirect |
| 83. #90275 | C22 | semidirect |
| 84. #90274 | C22 | semidirect |
| 86. #90273 | C22 | semidirect |
| 90. #90270 | C22 | semidirect |
| 92. #90268 | C22 | semidirect |
| 95. Q8×D28 | C22 | semidirect |
| 99. C4×#1161 | C22 | semidirect |
| 101. C4×Q8×D7 | C22 | semidirect |
| 102. #90260 | C22 | semidirect |
| 103. Q8×Dic14 | C22 | semidirect |
| 288. #3556 | D7 | semidirect |
| 407. #564 | C2×D7 | semidirect |
| 417. #557 | C2×D7 | semidirect |
| 418. #557 | C2×D7 | semidirect |
| 419. #557 | C2×D7 | semidirect |
| 910. C7 | #62761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3556 | 2 |
| #11744211 | 2 |
| #11744207 | 2 |
| #11744104 | 2 |
| #11744103 | 2 |
| #11744102 | 2 |
| #11744085 | 2 |
| #11744084 | 2 |
| #11744083 | 2 |
| #11743584 | 2 |
| #11743571 | 2 |
| #11743564 | 2 |
| #11743563 | 2 |
| #11743356 | 2 |
| D7×#533 | 2 |
| #11743335 | 2 |
| #11743325 | 2 |
| #62761 | 7 |