Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
7190 conjugacy classes of subgroups.
The subgroup lattice has 934 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4×C7×2−1+4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11744359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11744358 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11742966 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11742964 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11742959 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #11742956 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #11742947 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11742946 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11742943 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11742942 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11742913 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #11742910 | C2 | 1 | 4 | yes | maximal, complemented |
| 14 | #11742906 | C2 | 1 | 6 | yes | maximal, complemented |
| 15 | #11742904 | C2 | 1 | 6 | yes | maximal, complemented |
| 16 | #11742885 | C2 | 1 | 4 | yes | maximal, complemented |
| 17 | #11742870 | C2 | 1 | 4 | yes | maximal, complemented |
| 18 | C4×#6551 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | C2×C4×#1161 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | C2×C7×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#6551 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×#1161 | C22 | 1 | 1 | yes | characteristic |
| 23 | C7×#520 | C22 | 1 | 6 | yes | — |
| 24 | C7×#520 | C22 | 1 | 4 | yes | complemented |
| 25 | C7×#519 | C22 | 1 | 1 | yes | characteristic |
| 26 | C7×#519 | C22 | 1 | 4 | yes | complemented |
| 27 | C4×C7×#41 | C22 | 1 | 6 | yes | — |
| 28 | C4×C7×#41 | C22 | 1 | 4 | yes | complemented |
| 29 | C2×C4×C7×Q8 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×C4×C7×Q8 | C22 | 1 | 4 | yes | complemented |
| 31 | #90525 | C22 | 1 | 4 | yes | — |
| 32 | #90525 | C22 | 1 | 4 | yes | — |
| 33 | #90525 | C22 | 1 | 4 | yes | complemented |
| 34 | #90524 | C22 | 1 | 6 | yes | — |
| 35 | #90523 | C22 | 1 | 6 | yes | — |
| 36 | #90522 | C22 | 1 | 4 | yes | complemented |
| 37 | #90521 | C22 | 1 | 6 | yes | — |
| 38 | #90519 | C22 | 1 | 6 | yes | — |
| 39 | #90508 | C22 | 1 | 4 | yes | — |
| 40 | #90508 | C22 | 1 | 4 | yes | — |
| 41 | #90508 | C22 | 1 | 4 | yes | complemented |
| 42 | Q8×C22⋊D7 | C22 | 1 | 4 | yes | complemented |
| 43 | #90503 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×Q8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 45 | #90276 | C22 | 1 | 12 | yes | complemented |
| 46 | #90275 | C22 | 1 | 12 | yes | complemented |
| 47 | #90273 | C22 | 1 | 12 | yes | complemented |
| 48 | #90272 | C22 | 1 | 12 | yes | complemented |
| 49 | #90271 | C22 | 1 | 6 | yes | complemented |
| 50 | #90271 | C22 | 1 | 12 | yes | complemented |
| 51 | #90271 | C22 | 1 | 6 | yes | complemented |
| 52 | #90269 | C22 | 1 | 6 | yes | complemented |
| 53 | #90269 | C22 | 1 | 6 | yes | complemented |
| 54 | #90268 | C22 | 1 | 4 | yes | — |
| 55 | #90268 | C22 | 1 | 4 | yes | — |
| 56 | #90267 | C22 | 1 | 4 | yes | — |
| 57 | #90267 | C22 | 1 | 4 | yes | — |
| 58 | #90265 | C22 | 1 | 4 | yes | complemented |
| 59 | C4×#1161 | C22 | 1 | 4 | yes | — |
| 60 | C4×#1161 | C22 | 1 | 4 | yes | — |
| 61 | C4×#1161 | C22 | 1 | 4 | yes | — |
| 62 | C4×#1161 | C22 | 1 | 4 | yes | — |
| 63 | C4×#1161 | C22 | 1 | 4 | yes | complemented |
| 64 | #90263 | C22 | 1 | 4 | yes | complemented |
| 65 | C4×Q8×D7 | C22 | 1 | 4 | yes | complemented |
| 66 | #90261 | C22 | 1 | 4 | yes | complemented |
| 67 | #90260 | C22 | 1 | 4 | yes | complemented |
| 68 | #90260 | C22 | 1 | 4 | yes | complemented |
| 69 | #90259 | C22 | 1 | 12 | yes | complemented |
| 70 | Q8×Dic14 | C22 | 1 | 4 | yes | complemented |
| 71 | #90254 | C22 | 1 | 12 | yes | complemented |
| 72 | #90253 | C22 | 1 | 12 | yes | complemented |
| 73 | #90251 | C22 | 1 | 24 | yes | — |
| 74 | #90250 | C22 | 1 | 12 | yes | complemented |
| 75 | #90249 | C22 | 1 | 12 | yes | complemented |
| 76 | #90248 | C22 | 1 | 6 | yes | complemented |
| 77 | #90248 | C22 | 1 | 6 | yes | complemented |
| 78 | #90244 | C22 | 1 | 12 | yes | complemented |
| 79 | #90239 | C22 | 1 | 6 | yes | complemented |
| 80 | #90239 | C22 | 1 | 6 | yes | complemented |
| 81 | #90239 | C22 | 1 | 12 | yes | complemented |
| 82 | #90238 | C22 | 1 | 12 | yes | — |
| 83 | #90238 | C22 | 1 | 12 | yes | — |
| 84 | #90229 | C22 | 1 | 4 | yes | — |
| 85 | #90229 | C22 | 1 | 12 | yes | — |
| 86 | #90226 | C22 | 1 | 12 | yes | complemented |
| 87 | #90225 | C22 | 1 | 12 | yes | complemented |
| 88 | #90224 | C22 | 1 | 12 | yes | complemented |
| 89 | #90223 | C22 | 1 | 12 | yes | complemented |
| 90 | #90223 | C22 | 1 | 12 | yes | complemented |
| 91 | #90221 | C22 | 1 | 12 | yes | complemented |
| 92 | #90219 | C22 | 1 | 12 | yes | complemented |
| 93 | #90219 | C22 | 1 | 12 | yes | complemented |
| 94 | #90216 | C22 | 1 | 6 | yes | — |
| 95 | #90215 | C22 | 1 | 6 | yes | — |
| 96 | #90210 | C22 | 1 | 6 | yes | — |
| 97 | #90208 | C22 | 1 | 6 | yes | — |
| 98 | #90205 | C22 | 1 | 12 | yes | complemented |
| 99 | #90205 | C22 | 1 | 12 | yes | complemented |
| 100 | #90204 | C22 | 1 | 12 | yes | complemented |
| 101 | #90198 | C22 | 1 | 12 | yes | complemented |
| 102 | #90195 | C22 | 1 | 6 | yes | — |
| 103 | C2×#6456 | C22 | 1 | 3 | yes | — |
| 104 | C2×#6455 | C22 | 1 | 3 | yes | — |
| 105 | #90170 | C22 | 1 | 12 | yes | complemented |
| 106 | #90168 | C22 | 1 | 12 | yes | complemented |
| 107 | C4×#1157 | C22 | 1 | 6 | yes | — |
| 108 | C4×#1157 | C22 | 1 | 12 | yes | complemented |
| 109 | C4×#1157 | C22 | 1 | 12 | yes | complemented |
| 110 | C2×C4×D28 | C22 | 1 | 3 | yes | — |
| 111 | C2×C42×D7 | C22 | 1 | 3 | yes | — |
| 112 | #62793 | — | 7 | 1 | no | maximal, Sylow |
| 113 | C7×2−1+4 | — | 2 | 8 | no | — |
| 114 | C2×C7×#41 | C23 | 1 | 6 | yes | — |
| 115 | C2×C7×#41 | C23 | 1 | 4 | yes | — |
| 116 | C22×C7×Q8 | C23 | 1 | 4 | yes | — |
| 117 | C22×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 118 | #6551 | — | 2 | 8 | no | — |
| 119 | C2×#1161 | — | 2 | 8 | no | — |
| 120 | C2×#1161 | C23 | 1 | 4 | yes | — |
| 121 | C2×#1161 | C23 | 1 | 4 | yes | — |
| 122 | C2×#1161 | C23 | 1 | 4 | yes | — |
| 123 | C2×Q8×D7 | C23 | 1 | 4 | yes | — |
| 124 | C2×#1157 | C23 | 1 | 6 | yes | — |
| 125 | C2×#1157 | C23 | 1 | 12 | yes | — |
| 126 | C2×#1157 | C23 | 1 | 12 | yes | — |
| 127 | C22×D28 | C23 | 1 | 3 | yes | — |
| 128 | C22×C4×D7 | C23 | 1 | 3 | yes | — |
| 129 | C22×C4×D7 | C23 | 1 | 3 | yes | — |
| 130 | C22×C4×D7 | C23 | 1 | 3 | yes | — |
| 131 | C4×C7×Q8 | C23 | 1 | 4 | yes | — |
| 132 | C4×C7×Q8 | C23 | 1 | 12 | yes | — |
| 133 | C4×C7×Q8 | C23 | 1 | 4 | yes | — |
| 134 | C4×C7×Q8 | C23 | 1 | 4 | yes | — |
| 135 | C4×C7×Q8 | C23 | 1 | 4 | yes | — |
| 136 | C4×C7×Q8 | C23 | 1 | 6 | yes | — |
| 137 | C4×C7×Q8 | C23 | 1 | 6 | yes | — |
| 138 | C4×C7×D4 | C23 | 1 | 4 | yes | — |
| 139 | C4×C7×D4 | C23 | 1 | 12 | yes | — |
| 140 | C4×C7×D4 | C23 | 1 | 6 | yes | — |
| 141 | C4×C7×D4 | C23 | 1 | 6 | yes | — |
| 142 | C4×C7×D4 | C23 | 1 | 12 | yes | — |
| 143 | C7×#117 | C23 | 1 | 6 | yes | — |
| 144 | C7×#117 | C23 | 1 | 12 | yes | — |
| 145 | C7×#117 | C23 | 1 | 12 | yes | — |
| 146 | C2×C7×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 147 | C2×C7×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 148 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 149 | C2×C42×C7 | C23 | 1 | 12 | yes | — |
| 150 | #6510 | C23 | 1 | 12 | yes | — |
| 151 | #6510 | C23 | 1 | 6 | yes | — |
| 152 | #6509 | C23 | 1 | 12 | yes | — |
| 153 | #6509 | C23 | 1 | 6 | yes | — |
| 154 | #6509 | C23 | 1 | 6 | 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 | 4 | yes | — |
| 159 | #6507 | C23 | 1 | 6 | yes | — |
| 160 | #6503 | C23 | 1 | 6 | yes | — |
| 161 | #6503 | C23 | 1 | 12 | yes | — |
| 162 | #6502 | C23 | 1 | 4 | yes | — |
| 163 | #6502 | C23 | 1 | 12 | yes | — |
| 164 | #6501 | C23 | 1 | 6 | yes | — |
| 165 | #6501 | C23 | 1 | 6 | yes | — |
| 166 | #6501 | C23 | 1 | 12 | yes | — |
| 167 | #6500 | C23 | 1 | 12 | yes | — |
| 168 | #6499 | C23 | 1 | 6 | yes | — |
| 169 | #6498 | C23 | 1 | 4 | yes | — |
| 170 | #6493 | C23 | 1 | 24 | yes | — |
| 171 | #6493 | C23 | 1 | 12 | yes | — |
| 172 | #6493 | C23 | 1 | 12 | yes | — |
| 173 | #6493 | C23 | 1 | 12 | yes | — |
| 174 | #6492 | C23 | 1 | 24 | yes | — |
| 175 | C4×C22⋊D7 | C23 | 1 | 4 | yes | — |
| 176 | C4×C22⋊D7 | C23 | 1 | 12 | yes | — |
| 177 | C4×C22⋊D7 | C23 | 1 | 4 | yes | — |
| 178 | C4×C22⋊D7 | C23 | 1 | 12 | yes | — |
| 179 | C4×C22⋊D7 | C23 | 1 | 12 | yes | — |
| 180 | C4×C22⋊D7 | C23 | 1 | 12 | yes | — |
| 181 | C4×C22⋊D7 | C23 | 1 | 12 | yes | — |
| 182 | C4×C22⋊D7 | C23 | 1 | 12 | yes | — |
| 183 | C4×C22⋊D7 | C23 | 1 | 12 | yes | — |
| 184 | C4×C22⋊D7 | C23 | 1 | 12 | yes | — |
| 185 | C2×(C2×D7)⋊C4 | C23 | 1 | 6 | yes | — |
| 186 | #6489 | C23 | 1 | 6 | yes | — |
| 187 | #6489 | C23 | 1 | 4 | yes | — |
| 188 | #6489 | C23 | 1 | 12 | yes | — |
| 189 | C2×C4⋊Dic7 | C23 | 1 | 3 | yes | — |
| 190 | #6487 | C23 | 1 | 12 | yes | — |
| 191 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 192 | C2×C4×Dic7 | C23 | 1 | 3 | yes | — |
| 193 | C2×C4×Dic7 | C23 | 1 | 3 | yes | — |
| 194 | #6461 | C23 | 1 | 24 | yes | — |
| 195 | #6461 | C23 | 1 | 12 | yes | — |
| 196 | #6461 | C23 | 1 | 4 | yes | — |
| 197 | #6460 | C23 | 1 | 6 | yes | — |
| 198 | #6460 | C23 | 1 | 6 | yes | — |
| 199 | #6459 | C23 | 1 | 12 | yes | — |
| 200 | #6459 | C23 | 1 | 12 | yes | — |
| 201 | #6458 | C23 | 1 | 12 | yes | — |
| 202 | #6458 | C23 | 1 | 6 | yes | — |
| 203 | #6458 | C23 | 1 | 6 | yes | — |
| 204 | #6458 | C23 | 1 | 12 | yes | — |
| 205 | #6457 | C23 | 1 | 24 | yes | — |
| 206 | #6457 | C23 | 1 | 12 | yes | — |
| 207 | #6457 | C23 | 1 | 12 | yes | — |
| 208 | #6456 | C23 | 1 | 12 | yes | — |
| 209 | #6456 | C23 | 1 | 12 | yes | — |
| 210 | #6456 | C23 | 1 | 12 | yes | — |
| 211 | #6455 | C23 | 1 | 12 | yes | — |
| 212 | #6455 | C23 | 1 | 12 | yes | — |
| 213 | #6455 | C23 | 1 | 12 | yes | — |
| 214 | D7×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 215 | #6453 | C23 | 1 | 12 | yes | — |
| 216 | #6453 | C23 | 1 | 6 | yes | — |
| 217 | #6453 | C23 | 1 | 6 | yes | — |
| 218 | #6452 | C23 | 1 | 12 | yes | — |
| 219 | #6452 | C23 | 1 | 4 | yes | — |
| 220 | #6451 | C23 | 1 | 6 | yes | — |
| 221 | #6451 | C23 | 1 | 6 | yes | — |
| 222 | #6451 | C23 | 1 | 12 | yes | — |
| 223 | #6450 | C23 | 1 | 12 | yes | — |
| 224 | #6449 | C23 | 1 | 4 | yes | — |
| 225 | #6448 | C23 | 1 | 4 | yes | — |
| 226 | #6448 | C23 | 1 | 12 | yes | — |
| 227 | #6448 | C23 | 1 | 24 | yes | — |
| 228 | #6447 | C23 | 1 | 12 | yes | — |
| 229 | #6447 | C23 | 1 | 12 | yes | — |
| 230 | #6447 | C23 | 1 | 24 | yes | — |
| 231 | #6446 | C23 | 1 | 12 | yes | — |
| 232 | #6446 | C23 | 1 | 12 | yes | — |
| 233 | #6445 | C23 | 1 | 12 | yes | — |
| 234 | #6442 | C23 | 1 | 4 | yes | — |
| 235 | #6442 | C23 | 1 | 12 | yes | — |
| 236 | #6441 | C23 | 1 | 4 | yes | — |
| 237 | #6441 | C23 | 1 | 12 | yes | — |
| 238 | #6439 | C23 | 1 | 24 | yes | — |
| 239 | #6438 | C23 | 1 | 24 | yes | — |
| 240 | #6438 | C23 | 1 | 12 | yes | — |
| 241 | #6437 | C23 | 1 | 12 | yes | — |
| 242 | C4×D28 | C23 | 1 | 12 | yes | — |
| 243 | C4×D28 | C23 | 1 | 12 | yes | — |
| 244 | C4×D28 | C23 | 1 | 6 | yes | — |
| 245 | C4×D28 | C23 | 1 | 6 | yes | — |
| 246 | C4×D28 | C23 | 1 | 12 | yes | — |
| 247 | C4×D28 | C23 | 1 | 12 | yes | — |
| 248 | C4×D28 | C23 | 1 | 12 | yes | — |
| 249 | C4×D28 | C23 | 1 | 12 | yes | — |
| 250 | #6435 | C23 | 1 | 12 | yes | — |
| 251 | #6435 | C23 | 1 | 4 | yes | — |
| 252 | #6435 | C23 | 1 | 12 | yes | — |
| 253 | #6435 | C23 | 1 | 12 | yes | — |
| 254 | #6435 | C23 | 1 | 12 | yes | — |
| 255 | C42×D7 | C23 | 1 | 6 | yes | — |
| 256 | C42×D7 | C23 | 1 | 6 | yes | — |
| 257 | C42×D7 | C23 | 1 | 6 | yes | — |
| 258 | C42×D7 | C23 | 1 | 6 | yes | — |
| 259 | C42×D7 | C23 | 1 | 12 | yes | — |
| 260 | #6433 | C23 | 1 | 12 | yes | — |
| 261 | #6432 | C23 | 1 | 12 | yes | — |
| 262 | C4×Dic14 | C23 | 1 | 6 | yes | — |
| 263 | C4×Dic14 | C23 | 1 | 6 | yes | — |
| 264 | C4×Dic14 | C23 | 1 | 4 | yes | — |
| 265 | C4×Dic14 | C23 | 1 | 12 | yes | — |
| 266 | C4×Dic14 | C23 | 1 | 12 | yes | — |
| 267 | C4×Dic14 | C23 | 1 | 12 | yes | — |
| 268 | #3524 | — | 7 | 4 | no | — |
| 269 | #3524 | — | 7 | 4 | no | — |
| 270 | #3518 | — | 7 | 4 | no | — |
| 271 | #3517 | — | 7 | 4 | no | — |
| 272 | #3506 | — | 7 | 6 | no | — |
| 273 | #3502 | — | 7 | 1 | no | — |
| 274 | #3497 | — | 7 | 1 | no | — |
| 275 | #3493 | — | 7 | 6 | no | — |
| 276 | #3487 | — | 7 | 1 | no | — |
| 277 | #3487 | — | 7 | 1 | no | — |
| 278 | #3483 | — | 7 | 4 | no | — |
| 279 | #3482 | — | 7 | 4 | no | — |
| 280 | #3480 | — | 7 | 4 | no | — |
| 281 | #3480 | — | 7 | 4 | no | — |
| 282 | #3460 | — | 7 | 6 | no | — |
| 283 | #3444 | — | 7 | 6 | no | — |
| 284 | C4×2−1+4 | — | 7 | 1 | no | — |
| 285 | C4×2−1+4 | D7 | 1 | 1 | yes | characteristic, complemented |
| 286 | C2×C4×#41 | — | 7 | 1 | no | — |
| 287 | C23×D7 | C24 | 1 | 3 | yes | — |
| 288 | C7×#41 | — | 2 | 16 | no | — |
| 289 | C7×#41 | — | 2 | 24 | no | — |
| 290 | C2×C7×Q8 | — | 2 | 16 | no | — |
| 291 | C2×C7×Q8 | #41 | 1 | 8 | yes | complemented |
| 292 | C2×C7×Q8 | C24 | 1 | 6 | yes | — |
| 293 | C2×C7×Q8 | C24 | 1 | 4 | yes | — |
| 294 | C2×C7×D4 | C24 | 1 | 4 | yes | — |
| 295 | C2×C7×D4 | C24 | 1 | 6 | yes | — |
| 296 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 297 | C22×C4×C7 | C24 | 1 | 12 | yes | — |
| 298 | C22×C4×C7 | C24 | 1 | 4 | yes | — |
| 299 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 300 | C22×C4×C7 | C24 | 1 | 12 | yes | — |
| 301 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 302 | C2×C22⋊D7 | C24 | 1 | 4 | yes | — |
| 303 | C2×C22⋊D7 | C24 | 1 | 4 | yes | — |
| 304 | C2×C22⋊D7 | C24 | 1 | 12 | yes | — |
| 305 | C2×C22⋊D7 | C24 | 1 | 12 | yes | — |
| 306 | C2×C22⋊D7 | C24 | 1 | 12 | yes | — |
| 307 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 308 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 309 | C22×Dic7 | C24 | 1 | 3 | yes | — |
| 310 | #1161 | — | 2 | 16 | no | — |
| 311 | #1161 | — | 2 | 16 | no | — |
| 312 | #1161 | — | 2 | 16 | no | — |
| 313 | Q8×D7 | — | 2 | 16 | no | — |
| 314 | #1157 | — | 2 | 24 | no | — |
| 315 | #1157 | — | 4 | 24 | no | — |
| 316 | #1157 | — | 4 | 24 | no | — |
| 317 | C2×D28 | — | 2 | 12 | no | — |
| 318 | C2×D28 | C24 | 1 | 6 | yes | — |
| 319 | C2×D28 | C24 | 1 | 12 | yes | — |
| 320 | C2×D28 | C24 | 1 | 12 | yes | — |
| 321 | C2×D28 | C24 | 1 | 12 | yes | — |
| 322 | C2×C4×D7 | — | 2 | 12 | no | — |
| 323 | C2×C4×D7 | — | 4 | 6 | no | — |
| 324 | C2×C4×D7 | — | 4 | 6 | no | — |
| 325 | C2×C4×D7 | C24 | 1 | 4 | yes | — |
| 326 | C2×C4×D7 | C24 | 1 | 6 | yes | — |
| 327 | C2×C4×D7 | C24 | 1 | 6 | yes | — |
| 328 | C2×C4×D7 | C24 | 1 | 6 | yes | — |
| 329 | C2×C4×D7 | C24 | 1 | 6 | yes | — |
| 330 | C2×C4×D7 | C24 | 1 | 12 | yes | — |
| 331 | C2×C4×D7 | C24 | 1 | 6 | yes | — |
| 332 | C2×C4×D7 | C24 | 1 | 6 | yes | — |
| 333 | C2×C4×D7 | C24 | 1 | 12 | yes | — |
| 334 | C2×Dic14 | C24 | 1 | 4 | yes | — |
| 335 | C2×Dic14 | C24 | 1 | 6 | yes | — |
| 336 | C2×Dic14 | C24 | 1 | 12 | yes | — |
| 337 | C7×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 338 | C7×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 339 | C7×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 340 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 341 | C7×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 342 | C7×C22⋊C4 | C24 | 1 | 4 | yes | — |
| 343 | C7×C22⋊C4 | C24 | 1 | 4 | yes | — |
| 344 | C7×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 345 | C42×C7 | C24 | 1 | 12 | yes | — |
| 346 | C42×C7 | C24 | 1 | 6 | yes | — |
| 347 | C42×C7 | C24 | 1 | 6 | yes | — |
| 348 | C42×C7 | C24 | 1 | 4 | yes | — |
| 349 | C42×C7 | C24 | 1 | 12 | yes | — |
| 350 | C22⋊Dic7 | C24 | 1 | 4 | yes | — |
| 351 | C22⋊Dic7 | C24 | 1 | 4 | yes | — |
| 352 | C22⋊Dic7 | C24 | 1 | 4 | yes | — |
| 353 | C22⋊Dic7 | C24 | 1 | 12 | yes | — |
| 354 | C22⋊Dic7 | C24 | 1 | 4 | yes | — |
| 355 | (C2×D7)⋊C4 | C24 | 1 | 4 | yes | — |
| 356 | (C2×D7)⋊C4 | C24 | 1 | 4 | yes | — |
| 357 | (C2×D7)⋊C4 | C24 | 1 | 4 | yes | — |
| 358 | (C2×D7)⋊C4 | C24 | 1 | 4 | yes | — |
| 359 | (C2×D7)⋊C4 | C24 | 1 | 12 | yes | — |
| 360 | (C2×D7)⋊C4 | C24 | 1 | 12 | yes | — |
| 361 | (C2×D7)⋊C4 | C24 | 1 | 12 | yes | — |
| 362 | (C2×D7)⋊C4 | C24 | 1 | 12 | yes | — |
| 363 | (C2×D7)⋊C4 | C24 | 1 | 12 | yes | — |
| 364 | (C2×D7)⋊C4 | C24 | 1 | 12 | yes | — |
| 365 | (C2×D7)⋊C4 | C24 | 1 | 24 | yes | — |
| 366 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 367 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 368 | C4⋊Dic7 | C24 | 1 | 12 | yes | — |
| 369 | C4⋊Dic7 | C24 | 1 | 6 | yes | — |
| 370 | C4⋊Dic7 | C24 | 1 | 6 | yes | — |
| 371 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 372 | C4⋊Dic7 | C24 | 1 | 12 | yes | — |
| 373 | Dic7⋊C4 | C24 | 1 | 4 | yes | — |
| 374 | Dic7⋊C4 | C24 | 1 | 4 | yes | — |
| 375 | Dic7⋊C4 | C24 | 1 | 4 | yes | — |
| 376 | Dic7⋊C4 | C24 | 1 | 4 | yes | — |
| 377 | Dic7⋊C4 | C24 | 1 | 12 | yes | — |
| 378 | Dic7⋊C4 | C24 | 1 | 12 | yes | — |
| 379 | Dic7⋊C4 | C24 | 1 | 4 | yes | — |
| 380 | Dic7⋊C4 | C24 | 1 | 4 | yes | — |
| 381 | Dic7⋊C4 | C24 | 1 | 12 | yes | — |
| 382 | Dic7⋊C4 | C24 | 1 | 12 | yes | — |
| 383 | C4×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 384 | C4×Dic7 | C24 | 1 | 4 | yes | — |
| 385 | C4×Dic7 | C24 | 1 | 6 | yes | — |
| 386 | C4×Dic7 | C24 | 1 | 6 | yes | — |
| 387 | C4×Dic7 | C24 | 1 | 6 | yes | — |
| 388 | C4×Dic7 | C24 | 1 | 12 | yes | — |
| 389 | C4×Dic7 | C24 | 1 | 12 | yes | — |
| 390 | C4×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 391 | C4×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 392 | C4×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 393 | C4×Dic7 | C24 | 1 | 6 | yes | — |
| 394 | C2×2−1+4 | — | 7 | 1 | no | — |
| 395 | C2×2−1+4 | C2×D7 | 1 | 1 | yes | characteristic |
| 396 | C22×#41 | — | 7 | 1 | no | — |
| 397 | #559 | — | 7 | 12 | no | — |
| 398 | #559 | — | 7 | 12 | no | — |
| 399 | Q82 | — | 7 | 4 | no | — |
| 400 | #557 | — | 7 | 4 | no | — |
| 401 | #557 | — | 7 | 4 | no | — |
| 402 | #557 | — | 7 | 4 | no | — |
| 403 | #556 | — | 7 | 12 | no | — |
| 404 | #556 | — | 7 | 12 | no | — |
| 405 | #556 | — | 7 | 12 | no | — |
| 406 | #555 | — | 7 | 12 | no | — |
| 407 | #555 | — | 7 | 12 | no | — |
| 408 | #555 | — | 7 | 12 | no | — |
| 409 | #553 | — | 7 | 12 | no | — |
| 410 | #553 | — | 7 | 12 | no | — |
| 411 | #553 | — | 7 | 12 | no | — |
| 412 | #553 | — | 7 | 12 | no | — |
| 413 | #552 | — | 7 | 12 | no | — |
| 414 | #552 | — | 7 | 12 | no | — |
| 415 | #550 | — | 7 | 4 | no | — |
| 416 | #550 | — | 7 | 4 | no | — |
| 417 | #550 | — | 7 | 4 | no | — |
| 418 | #550 | — | 7 | 4 | no | — |
| 419 | #550 | — | 7 | 4 | no | — |
| 420 | #550 | — | 7 | 12 | no | — |
| 421 | D4×Q8 | — | 7 | 4 | no | — |
| 422 | #548 | — | 7 | 4 | no | — |
| 423 | #548 | — | 7 | 4 | no | — |
| 424 | #548 | — | 7 | 4 | no | — |
| 425 | #548 | — | 7 | 4 | no | — |
| 426 | #548 | — | 7 | 4 | no | — |
| 427 | #548 | — | 7 | 4 | no | — |
| 428 | #547 | — | 7 | 12 | no | — |
| 429 | #544 | — | 7 | 6 | no | — |
| 430 | #542 | — | 7 | 12 | no | — |
| 431 | #542 | — | 7 | 12 | no | — |
| 432 | #540 | — | 7 | 12 | no | — |
| 433 | #540 | — | 7 | 12 | no | — |
| 434 | #538 | — | 7 | 24 | no | — |
| 435 | #537 | — | 7 | 6 | no | — |
| 436 | #535 | — | 7 | 6 | no | — |
| 437 | #535 | — | 7 | 6 | no | — |
| 438 | #533 | — | 7 | 6 | no | — |
| 439 | #533 | — | 7 | 6 | no | — |
| 440 | #533 | — | 7 | 6 | no | — |
| 441 | #532 | — | 7 | 6 | no | — |
| 442 | #532 | — | 7 | 6 | no | — |
| 443 | #532 | — | 7 | 6 | no | — |
| 444 | #532 | — | 7 | 12 | no | — |
| 445 | #532 | — | 7 | 12 | no | — |
| 446 | #529 | — | 7 | 6 | no | — |
| 447 | #529 | — | 7 | 6 | no | — |
| 448 | #529 | — | 7 | 12 | no | — |
| 449 | #529 | — | 7 | 4 | no | — |
| 450 | #529 | — | 7 | 12 | no | — |
| 451 | #529 | — | 7 | 6 | no | — |
| 452 | #529 | — | 7 | 6 | no | — |
| 453 | #529 | — | 7 | 12 | no | — |
| 454 | #529 | — | 7 | 12 | no | — |
| 455 | #529 | — | 7 | 12 | no | — |
| 456 | #525 | — | 7 | 6 | no | — |
| 457 | #525 | — | 7 | 12 | no | — |
| 458 | #525 | — | 7 | 12 | no | — |
| 459 | #525 | — | 7 | 6 | no | — |
| 460 | #520 | — | 7 | 4 | no | — |
| 461 | #520 | — | 7 | 6 | no | — |
| 462 | #520 | C2×D7 | 1 | 6 | yes | — |
| 463 | #520 | C2×D7 | 1 | 4 | yes | complemented |
| 464 | #519 | — | 7 | 1 | no | — |
| 465 | #519 | — | 7 | 4 | no | — |
| 466 | #519 | C2×D7 | 1 | 1 | yes | characteristic |
| 467 | #519 | C2×D7 | 1 | 4 | yes | complemented |
| 468 | C4×#41 | — | 7 | 4 | no | — |
| 469 | C4×#41 | — | 7 | 4 | no | — |
| 470 | C4×#41 | — | 7 | 4 | no | — |
| 471 | C4×#41 | — | 7 | 4 | no | — |
| 472 | C4×#41 | — | 7 | 4 | no | — |
| 473 | C4×#41 | — | 7 | 6 | no | — |
| 474 | C4×#41 | — | 7 | 12 | no | — |
| 475 | C4×#41 | — | 7 | 12 | no | — |
| 476 | C4×#41 | C2×D7 | 1 | 6 | yes | — |
| 477 | C4×#41 | C2×D7 | 1 | 4 | yes | complemented |
| 478 | C2×C4×Q8 | — | 7 | 1 | no | — |
| 479 | C2×C4×Q8 | — | 7 | 4 | no | — |
| 480 | C2×C4×Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 481 | C2×C4×Q8 | C2×D7 | 1 | 4 | yes | complemented |
| 482 | C2×C4×D4 | — | 7 | 3 | no | — |
| 483 | C2×C4×D4 | — | 7 | 3 | no | — |
| 484 | C2×#117 | — | 7 | 3 | no | — |
| 485 | C22×C42 | — | 7 | 3 | no | — |
| 486 | C23×C7 | C25 | 1 | 4 | yes | — |
| 487 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 488 | C22×D7 | — | 2 | 6 | no | — |
| 489 | C22×D7 | — | 4 | 3 | no | — |
| 490 | C22×D7 | — | 4 | 3 | no | — |
| 491 | C22×D7 | C25 | 1 | 6 | yes | — |
| 492 | C22×D7 | C25 | 1 | 4 | yes | — |
| 493 | C7×Q8 | — | 2 | 12 | no | — |
| 494 | C7×Q8 | C2×#41 | 1 | 16 | yes | — |
| 495 | C7×D4 | — | 2 | 8 | no | — |
| 496 | C7×D4 | — | 2 | 12 | no | — |
| 497 | C2×C4×C7 | — | 2 | 24 | no | — |
| 498 | C2×C4×C7 | — | 2 | 2 | no | — |
| 499 | C2×C4×C7 | — | 2 | 8 | no | — |
| 500 | C2×C4×C7 | — | 4 | 3 | no | — |
| 501 | C2×C4×C7 | — | 4 | 12 | no | — |
| 502 | C2×C4×C7 | C2×#41 | 1 | 12 | yes | — |
| 503 | C2×C4×C7 | C25 | 1 | 6 | yes | — |
| 504 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 505 | C2×C4×C7 | C25 | 1 | 4 | yes | — |
| 506 | C2×C4×C7 | C25 | 1 | 4 | yes | — |
| 507 | C2×C4×C7 | C25 | 1 | 4 | yes | — |
| 508 | C2×C4×C7 | C25 | 1 | 6 | yes | — |
| 509 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 510 | C22⋊D7 | — | 2 | 8 | no | — |
| 511 | C22⋊D7 | — | 2 | 8 | no | — |
| 512 | C22⋊D7 | — | 4 | 12 | no | — |
| 513 | C22⋊D7 | — | 4 | 12 | no | — |
| 514 | C22⋊D7 | — | 4 | 12 | no | — |
| 515 | C2×Dic7 | — | 2 | 2 | no | — |
| 516 | C2×Dic7 | — | 2 | 2 | no | — |
| 517 | C2×Dic7 | — | 4 | 3 | no | — |
| 518 | C2×Dic7 | C25 | 1 | 1 | yes | characteristic |
| 519 | C2×Dic7 | C25 | 1 | 1 | yes | characteristic |
| 520 | C2×Dic7 | C25 | 1 | 1 | yes | characteristic |
| 521 | C2×Dic7 | C25 | 1 | 4 | yes | — |
| 522 | C2×Dic7 | C25 | 1 | 4 | yes | — |
| 523 | C2×Dic7 | C25 | 1 | 4 | yes | — |
| 524 | C2×Dic7 | C25 | 1 | 6 | yes | — |
| 525 | C2×Dic7 | C25 | 1 | 1 | yes | characteristic |
| 526 | D28 | — | 2 | 24 | no | — |
| 527 | D28 | — | 2 | 12 | no | — |
| 528 | D28 | — | 4 | 12 | no | — |
| 529 | D28 | — | 4 | 12 | no | — |
| 530 | C4×D7 | — | 2 | 12 | no | — |
| 531 | C4×D7 | — | 2 | 12 | no | — |
| 532 | C4×D7 | — | 2 | 24 | no | — |
| 533 | C4×D7 | — | 2 | 12 | no | — |
| 534 | C4×D7 | — | 2 | 8 | no | — |
| 535 | C4×D7 | — | 2 | 12 | no | — |
| 536 | C4×D7 | — | 4 | 6 | no | — |
| 537 | C4×D7 | — | 4 | 6 | no | — |
| 538 | C4×D7 | — | 4 | 12 | no | — |
| 539 | Dic14 | — | 2 | 12 | no | — |
| 540 | Dic14 | — | 2 | 8 | no | — |
| 541 | Dic14 | — | 4 | 12 | no | — |
| 542 | 2−1+4 | — | 2 | 8 | no | — |
| 543 | 2−1+4 | — | 14 | 8 | no | — |
| 544 | C2×#41 | — | 7 | 4 | no | — |
| 545 | C2×#41 | — | 7 | 4 | no | — |
| 546 | C2×#41 | — | 7 | 4 | no | — |
| 547 | C2×#41 | — | 7 | 6 | no | — |
| 548 | C2×#41 | — | 7 | 12 | no | — |
| 549 | C2×#41 | — | 7 | 12 | no | — |
| 550 | C2×#41 | — | 14 | 8 | no | — |
| 551 | C2×#41 | C22×D7 | 1 | 6 | yes | — |
| 552 | C2×#41 | C22×D7 | 1 | 4 | yes | — |
| 553 | C22×Q8 | — | 7 | 4 | no | — |
| 554 | C22×Q8 | C22×D7 | 1 | 4 | yes | — |
| 555 | C22×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 556 | C22×D4 | — | 7 | 3 | no | — |
| 557 | C23×C4 | — | 7 | 3 | no | — |
| 558 | C23×C4 | — | 7 | 3 | no | — |
| 559 | C23×C4 | — | 7 | 3 | no | — |
| 560 | C4⋊Q8 | — | 7 | 6 | no | — |
| 561 | C4⋊Q8 | — | 7 | 6 | no | — |
| 562 | C4⋊Q8 | — | 7 | 6 | no | — |
| 563 | C4⋊Q8 | — | 7 | 12 | no | — |
| 564 | C4⋊Q8 | — | 7 | 12 | no | — |
| 565 | #127 | — | 7 | 6 | no | — |
| 566 | #127 | — | 7 | 12 | no | — |
| 567 | #127 | — | 7 | 12 | no | — |
| 568 | #126 | — | 7 | 4 | no | — |
| 569 | #126 | — | 7 | 12 | no | — |
| 570 | #126 | — | 7 | 24 | no | — |
| 571 | #126 | — | 7 | 4 | no | — |
| 572 | #126 | — | 7 | 12 | no | — |
| 573 | #126 | — | 7 | 24 | no | — |
| 574 | #125 | — | 7 | 4 | no | — |
| 575 | #125 | — | 7 | 12 | no | — |
| 576 | #125 | — | 7 | 6 | no | — |
| 577 | #125 | — | 7 | 6 | no | — |
| 578 | #125 | — | 7 | 12 | no | — |
| 579 | #125 | — | 7 | 12 | no | — |
| 580 | #124 | — | 7 | 6 | no | — |
| 581 | #124 | — | 7 | 12 | no | — |
| 582 | #124 | — | 7 | 6 | no | — |
| 583 | #124 | — | 7 | 4 | no | — |
| 584 | #124 | — | 7 | 12 | no | — |
| 585 | #124 | — | 7 | 24 | no | — |
| 586 | #124 | — | 7 | 12 | no | — |
| 587 | #124 | — | 7 | 24 | no | — |
| 588 | #123 | — | 7 | 4 | no | — |
| 589 | #123 | — | 7 | 24 | no | — |
| 590 | #123 | — | 7 | 12 | no | — |
| 591 | #123 | — | 7 | 12 | no | — |
| 592 | #123 | — | 7 | 24 | no | — |
| 593 | #123 | — | 7 | 4 | no | — |
| 594 | #123 | — | 7 | 12 | no | — |
| 595 | #123 | — | 7 | 12 | no | — |
| 596 | C22⋊Q8 | — | 7 | 6 | no | — |
| 597 | C22⋊Q8 | — | 7 | 6 | no | — |
| 598 | C22⋊Q8 | — | 7 | 12 | no | — |
| 599 | C22⋊Q8 | — | 7 | 12 | no | — |
| 600 | C22⋊Q8 | — | 7 | 12 | no | — |
| 601 | C22⋊Q8 | — | 7 | 12 | no | — |
| 602 | C22⋊Q8 | — | 7 | 6 | no | — |
| 603 | C22⋊Q8 | — | 7 | 6 | no | — |
| 604 | C22⋊Q8 | — | 7 | 4 | no | — |
| 605 | C22⋊Q8 | — | 7 | 12 | no | — |
| 606 | #121 | — | 7 | 4 | no | — |
| 607 | #121 | — | 7 | 12 | no | — |
| 608 | #121 | — | 7 | 6 | no | — |
| 609 | #121 | — | 7 | 6 | no | — |
| 610 | #121 | — | 7 | 12 | no | — |
| 611 | #121 | — | 7 | 12 | no | — |
| 612 | #121 | — | 7 | 12 | no | — |
| 613 | #121 | — | 7 | 12 | no | — |
| 614 | #121 | — | 7 | 24 | no | — |
| 615 | #121 | — | 7 | 6 | no | — |
| 616 | #121 | — | 7 | 6 | no | — |
| 617 | #121 | — | 7 | 12 | no | — |
| 618 | #121 | — | 7 | 12 | no | — |
| 619 | #121 | — | 7 | 12 | no | — |
| 620 | #121 | — | 7 | 12 | no | — |
| 621 | #121 | — | 7 | 24 | no | — |
| 622 | #120 | — | 7 | 12 | no | — |
| 623 | #120 | — | 7 | 12 | no | — |
| 624 | C4×Q8 | — | 7 | 4 | no | — |
| 625 | C4×Q8 | — | 7 | 4 | no | — |
| 626 | C4×Q8 | — | 7 | 4 | no | — |
| 627 | C4×Q8 | — | 7 | 4 | no | — |
| 628 | C4×Q8 | — | 7 | 12 | no | — |
| 629 | C4×Q8 | — | 7 | 6 | no | — |
| 630 | C4×Q8 | — | 7 | 4 | no | — |
| 631 | C4×Q8 | — | 7 | 6 | no | — |
| 632 | C4×Q8 | — | 7 | 12 | no | — |
| 633 | C4×Q8 | — | 7 | 12 | no | — |
| 634 | C4×Q8 | — | 7 | 12 | no | — |
| 635 | C4×Q8 | C22×D7 | 1 | 4 | yes | — |
| 636 | C4×Q8 | C22×D7 | 1 | 4 | yes | — |
| 637 | C4×Q8 | C22×D7 | 1 | 6 | yes | — |
| 638 | C4×Q8 | C22×D7 | 1 | 4 | yes | — |
| 639 | C4×Q8 | C22×D7 | 1 | 12 | yes | — |
| 640 | C4×Q8 | C22×D7 | 1 | 6 | yes | — |
| 641 | C4×Q8 | C22×D7 | 1 | 4 | yes | — |
| 642 | C4×D4 | — | 7 | 4 | no | — |
| 643 | C4×D4 | — | 7 | 4 | no | — |
| 644 | C4×D4 | — | 7 | 12 | no | — |
| 645 | C4×D4 | — | 7 | 12 | no | — |
| 646 | C4×D4 | — | 7 | 12 | no | — |
| 647 | C4×D4 | — | 7 | 12 | no | — |
| 648 | C4×D4 | — | 7 | 12 | no | — |
| 649 | C4×D4 | — | 7 | 12 | no | — |
| 650 | C4×D4 | — | 7 | 12 | no | — |
| 651 | C4×D4 | — | 7 | 12 | no | — |
| 652 | C4×D4 | — | 7 | 12 | no | — |
| 653 | C4×D4 | — | 7 | 12 | no | — |
| 654 | C4×D4 | — | 7 | 12 | no | — |
| 655 | C4×D4 | — | 7 | 12 | no | — |
| 656 | C4×D4 | — | 7 | 12 | no | — |
| 657 | C4×D4 | — | 7 | 6 | no | — |
| 658 | C4×D4 | — | 7 | 6 | no | — |
| 659 | C4×D4 | — | 7 | 12 | no | — |
| 660 | C4×D4 | — | 7 | 12 | no | — |
| 661 | C4×D4 | — | 7 | 12 | no | — |
| 662 | C4×D4 | — | 7 | 12 | no | — |
| 663 | C4×D4 | C22×D7 | 1 | 4 | yes | — |
| 664 | C4×D4 | C22×D7 | 1 | 6 | yes | — |
| 665 | C4×D4 | C22×D7 | 1 | 12 | yes | — |
| 666 | C4×D4 | C22×D7 | 1 | 6 | yes | — |
| 667 | C4×D4 | C22×D7 | 1 | 12 | yes | — |
| 668 | #117 | — | 7 | 4 | no | — |
| 669 | #117 | — | 7 | 6 | no | — |
| 670 | #117 | — | 7 | 12 | no | — |
| 671 | #117 | — | 7 | 12 | no | — |
| 672 | #117 | — | 7 | 12 | no | — |
| 673 | #117 | — | 7 | 12 | no | — |
| 674 | #117 | — | 7 | 4 | no | — |
| 675 | #117 | — | 7 | 12 | no | — |
| 676 | #117 | — | 7 | 12 | no | — |
| 677 | #117 | — | 7 | 12 | no | — |
| 678 | #117 | — | 7 | 12 | no | — |
| 679 | #117 | C22×D7 | 1 | 6 | yes | — |
| 680 | #117 | C22×D7 | 1 | 12 | yes | — |
| 681 | #117 | C22×D7 | 1 | 12 | yes | — |
| 682 | C2×C4⋊C4 | — | 7 | 3 | no | — |
| 683 | C2×C4⋊C4 | — | 7 | 12 | no | — |
| 684 | C2×C4⋊C4 | C22×D7 | 1 | 3 | yes | — |
| 685 | C2×C4⋊C4 | C22×D7 | 1 | 12 | yes | — |
| 686 | C2×C22⋊C4 | — | 7 | 6 | no | — |
| 687 | C2×C42 | — | 7 | 3 | no | — |
| 688 | C2×C42 | — | 7 | 3 | no | — |
| 689 | C2×C42 | — | 7 | 1 | no | — |
| 690 | C2×C42 | — | 7 | 12 | no | — |
| 691 | C2×C42 | — | 7 | 6 | no | — |
| 692 | C2×C42 | — | 7 | 6 | no | — |
| 693 | C2×C42 | — | 7 | 6 | no | — |
| 694 | C2×C42 | — | 7 | 6 | no | — |
| 695 | C2×C42 | C22×D7 | 1 | 3 | yes | — |
| 696 | C2×C42 | C22×D7 | 1 | 12 | yes | — |
| 697 | C22×C7 | — | 2 | 1 | no | — |
| 698 | C22×C7 | — | 2 | 1 | no | — |
| 699 | C22×C7 | — | 2 | 4 | no | — |
| 700 | C22×C7 | — | 2 | 4 | no | — |
| 701 | C22×C7 | — | 2 | 4 | no | — |
| 702 | C22×C7 | C22×#41 | 1 | 2 | yes | — |
| 703 | C22×C7 | C26 | 1 | 1 | yes | characteristic |
| 704 | C2×D7 | — | 2 | 4 | no | — |
| 705 | C2×D7 | — | 2 | 6 | no | — |
| 706 | C2×D7 | — | 2 | 6 | no | — |
| 707 | C2×D7 | — | 2 | 6 | no | — |
| 708 | C2×D7 | — | 2 | 4 | no | — |
| 709 | C2×D7 | — | 2 | 4 | no | — |
| 710 | C2×D7 | — | 4 | 12 | no | — |
| 711 | C4×C7 | — | 2 | 4 | no | — |
| 712 | C4×C7 | — | 2 | 4 | no | — |
| 713 | C4×C7 | — | 2 | 4 | no | — |
| 714 | C4×C7 | — | 2 | 6 | no | — |
| 715 | C4×C7 | — | 2 | 1 | no | — |
| 716 | C4×C7 | C22×#41 | 1 | 12 | yes | — |
| 717 | C4×C7 | #585 | 1 | 2 | yes | — |
| 718 | Dic7 | — | 2 | 4 | no | — |
| 719 | Dic7 | — | 2 | 1 | no | — |
| 720 | Dic7 | — | 2 | 1 | no | — |
| 721 | Dic7 | — | 2 | 4 | no | — |
| 722 | Dic7 | — | 2 | 4 | no | — |
| 723 | Dic7 | — | 2 | 6 | no | — |
| 724 | Dic7 | — | 2 | 1 | no | — |
| 725 | Dic7 | #585 | 1 | 2 | yes | — |
| 726 | C24 | — | 7 | 3 | no | — |
| 727 | #41 | — | 2 | 16 | no | — |
| 728 | #41 | — | 2 | 24 | no | — |
| 729 | #41 | — | 14 | 16 | no | — |
| 730 | #41 | — | 14 | 16 | no | — |
| 731 | #41 | — | 14 | 16 | no | — |
| 732 | #41 | — | 14 | 24 | no | — |
| 733 | #41 | — | 28 | 24 | no | — |
| 734 | #41 | — | 28 | 24 | no | — |
| 735 | C2×Q8 | — | 2 | 16 | no | — |
| 736 | C2×Q8 | — | 7 | 6 | no | — |
| 737 | C2×Q8 | — | 7 | 4 | no | — |
| 738 | C2×Q8 | — | 7 | 12 | no | — |
| 739 | C2×Q8 | — | 14 | 16 | no | — |
| 740 | C2×Q8 | #1157 | 1 | 8 | yes | complemented |
| 741 | C2×Q8 | C23×D7 | 1 | 6 | yes | — |
| 742 | C2×Q8 | C23×D7 | 1 | 4 | yes | — |
| 743 | C2×D4 | — | 7 | 4 | no | — |
| 744 | C2×D4 | — | 7 | 4 | no | — |
| 745 | C2×D4 | — | 7 | 12 | no | — |
| 746 | C2×D4 | — | 7 | 12 | no | — |
| 747 | C2×D4 | — | 7 | 12 | no | — |
| 748 | C2×D4 | — | 7 | 12 | no | — |
| 749 | C2×D4 | — | 7 | 6 | no | — |
| 750 | C2×D4 | — | 7 | 12 | no | — |
| 751 | C2×D4 | — | 7 | 12 | no | — |
| 752 | C2×D4 | — | 14 | 12 | no | — |
| 753 | C2×D4 | C23×D7 | 1 | 4 | yes | — |
| 754 | C2×D4 | C23×D7 | 1 | 6 | yes | — |
| 755 | C22×C4 | — | 7 | 1 | no | — |
| 756 | C22×C4 | — | 7 | 1 | no | — |
| 757 | C22×C4 | — | 7 | 3 | no | — |
| 758 | C22×C4 | — | 7 | 6 | no | — |
| 759 | C22×C4 | — | 7 | 6 | no | — |
| 760 | C22×C4 | — | 7 | 6 | no | — |
| 761 | C22×C4 | — | 7 | 12 | no | — |
| 762 | C22×C4 | — | 7 | 4 | no | — |
| 763 | C22×C4 | — | 7 | 6 | no | — |
| 764 | C22×C4 | — | 7 | 6 | no | — |
| 765 | C22×C4 | — | 7 | 6 | no | — |
| 766 | C22×C4 | — | 7 | 12 | no | — |
| 767 | C22×C4 | — | 14 | 12 | no | — |
| 768 | C22×C4 | — | 28 | 6 | no | — |
| 769 | C22×C4 | — | 28 | 6 | no | — |
| 770 | C22×C4 | C23×D7 | 1 | 12 | yes | — |
| 771 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 772 | C22×C4 | C23×D7 | 1 | 4 | yes | — |
| 773 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 774 | C22×C4 | C23×D7 | 1 | 12 | yes | — |
| 775 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 776 | C4⋊C4 | — | 7 | 12 | no | — |
| 777 | C4⋊C4 | — | 7 | 4 | no | — |
| 778 | C4⋊C4 | — | 7 | 4 | no | — |
| 779 | C4⋊C4 | — | 7 | 4 | no | — |
| 780 | C4⋊C4 | — | 7 | 4 | no | — |
| 781 | C4⋊C4 | — | 7 | 4 | no | — |
| 782 | C4⋊C4 | — | 7 | 4 | no | — |
| 783 | C4⋊C4 | — | 7 | 12 | no | — |
| 784 | C4⋊C4 | — | 7 | 12 | no | — |
| 785 | C4⋊C4 | — | 7 | 12 | no | — |
| 786 | C4⋊C4 | — | 7 | 6 | no | — |
| 787 | C4⋊C4 | — | 7 | 12 | no | — |
| 788 | C4⋊C4 | — | 7 | 4 | no | — |
| 789 | C4⋊C4 | — | 7 | 6 | no | — |
| 790 | C4⋊C4 | — | 7 | 4 | no | — |
| 791 | C4⋊C4 | — | 7 | 4 | no | — |
| 792 | C4⋊C4 | — | 7 | 12 | no | — |
| 793 | C4⋊C4 | C23×D7 | 1 | 12 | yes | — |
| 794 | C4⋊C4 | C23×D7 | 1 | 6 | yes | — |
| 795 | C4⋊C4 | C23×D7 | 1 | 12 | yes | — |
| 796 | C4⋊C4 | C23×D7 | 1 | 6 | yes | — |
| 797 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 798 | C22⋊C4 | — | 7 | 4 | no | — |
| 799 | C22⋊C4 | — | 7 | 4 | no | — |
| 800 | C22⋊C4 | — | 7 | 4 | no | — |
| 801 | C22⋊C4 | — | 7 | 4 | no | — |
| 802 | C22⋊C4 | — | 7 | 12 | no | — |
| 803 | C22⋊C4 | — | 7 | 24 | no | — |
| 804 | C22⋊C4 | — | 7 | 4 | no | — |
| 805 | C22⋊C4 | — | 7 | 4 | no | — |
| 806 | C22⋊C4 | — | 7 | 12 | no | — |
| 807 | C22⋊C4 | — | 7 | 4 | no | — |
| 808 | C22⋊C4 | — | 7 | 4 | no | — |
| 809 | C22⋊C4 | — | 7 | 12 | no | — |
| 810 | C22⋊C4 | — | 7 | 12 | no | — |
| 811 | C22⋊C4 | — | 7 | 12 | no | — |
| 812 | C22⋊C4 | — | 7 | 12 | no | — |
| 813 | C22⋊C4 | — | 7 | 12 | no | — |
| 814 | C22⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 815 | C22⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 816 | C22⋊C4 | C23×D7 | 1 | 12 | yes | — |
| 817 | C42 | — | 7 | 1 | no | — |
| 818 | C42 | — | 7 | 1 | no | — |
| 819 | C42 | — | 7 | 6 | no | — |
| 820 | C42 | — | 7 | 6 | no | — |
| 821 | C42 | — | 7 | 6 | no | — |
| 822 | C42 | — | 7 | 6 | no | — |
| 823 | C42 | — | 7 | 12 | no | — |
| 824 | C42 | — | 7 | 12 | no | — |
| 825 | C42 | — | 7 | 1 | no | — |
| 826 | C42 | — | 7 | 1 | no | — |
| 827 | C42 | — | 7 | 4 | no | — |
| 828 | C42 | C23×D7 | 1 | 6 | yes | — |
| 829 | C42 | C23×D7 | 1 | 12 | yes | — |
| 830 | C42 | C23×D7 | 1 | 12 | yes | — |
| 831 | C42 | C23×D7 | 1 | 6 | yes | — |
| 832 | C42 | C23×D7 | 1 | 4 | yes | — |
| 833 | C2×C7 | — | 2 | 2 | no | — |
| 834 | C2×C7 | — | 4 | 4 | no | — |
| 835 | C2×C7 | C23×#41 | 1 | 1 | yes | characteristic |
| 836 | C2×C7 | C2×#585 | 1 | 1 | yes | characteristic |
| 837 | C2×C7 | C2×#585 | 1 | 1 | yes | characteristic |
| 838 | D7 | — | 4 | 4 | no | — |
| 839 | D7 | — | 4 | 6 | no | — |
| 840 | C23 | — | 7 | 6 | no | — |
| 841 | C23 | — | 7 | 4 | no | — |
| 842 | C23 | — | 14 | 6 | no | — |
| 843 | C23 | — | 28 | 3 | no | — |
| 844 | C23 | — | 28 | 3 | no | — |
| 845 | C23 | C24×D7 | 1 | 4 | yes | — |
| 846 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 847 | Q8 | — | 2 | 12 | no | — |
| 848 | Q8 | — | 14 | 8 | no | — |
| 849 | Q8 | — | 14 | 12 | no | — |
| 850 | Q8 | — | 28 | 12 | no | — |
| 851 | Q8 | C2×#1157 | 1 | 16 | yes | — |
| 852 | D4 | — | 2 | 8 | no | — |
| 853 | D4 | — | 2 | 12 | no | — |
| 854 | D4 | — | 14 | 8 | no | — |
| 855 | D4 | — | 14 | 8 | no | — |
| 856 | D4 | — | 14 | 24 | no | — |
| 857 | D4 | — | 14 | 12 | no | — |
| 858 | D4 | — | 28 | 12 | no | — |
| 859 | D4 | — | 28 | 12 | no | — |
| 860 | D4 | — | 28 | 12 | no | — |
| 861 | D4 | — | 28 | 12 | no | — |
| 862 | D4 | — | 28 | 12 | no | — |
| 863 | C2×C4 | — | 2 | 24 | no | — |
| 864 | C2×C4 | — | 2 | 2 | no | — |
| 865 | C2×C4 | — | 2 | 8 | no | — |
| 866 | C2×C4 | — | 4 | 3 | no | — |
| 867 | C2×C4 | — | 4 | 12 | no | — |
| 868 | C2×C4 | — | 7 | 1 | no | — |
| 869 | C2×C4 | — | 7 | 1 | no | — |
| 870 | C2×C4 | — | 7 | 1 | no | — |
| 871 | C2×C4 | — | 7 | 1 | no | — |
| 872 | C2×C4 | — | 7 | 4 | no | — |
| 873 | C2×C4 | — | 7 | 4 | no | — |
| 874 | C2×C4 | — | 7 | 6 | no | — |
| 875 | C2×C4 | — | 7 | 4 | no | — |
| 876 | C2×C4 | — | 14 | 12 | no | — |
| 877 | C2×C4 | — | 14 | 2 | no | — |
| 878 | C2×C4 | — | 14 | 2 | no | — |
| 879 | C2×C4 | — | 14 | 12 | no | — |
| 880 | C2×C4 | — | 14 | 12 | no | — |
| 881 | C2×C4 | — | 14 | 24 | no | — |
| 882 | C2×C4 | — | 14 | 12 | no | — |
| 883 | C2×C4 | — | 14 | 8 | no | — |
| 884 | C2×C4 | — | 28 | 6 | no | — |
| 885 | C2×C4 | — | 28 | 6 | no | — |
| 886 | C2×C4 | — | 28 | 12 | no | — |
| 887 | C2×C4 | — | 28 | 3 | no | — |
| 888 | C2×C4 | C2×#1157 | 1 | 12 | yes | — |
| 889 | C2×C4 | C24×D7 | 1 | 6 | yes | — |
| 890 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 891 | C2×C4 | C24×D7 | 1 | 4 | yes | — |
| 892 | C2×C4 | C24×D7 | 1 | 4 | yes | — |
| 893 | C2×C4 | C24×D7 | 1 | 4 | yes | — |
| 894 | C2×C4 | C24×D7 | 1 | 6 | yes | — |
| 895 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 896 | C7 | #62793 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 897 | C22 | — | 2 | 1 | no | — |
| 898 | C22 | — | 2 | 1 | no | — |
| 899 | C22 | — | 2 | 4 | no | — |
| 900 | C22 | — | 2 | 4 | no | — |
| 901 | C22 | — | 2 | 4 | no | — |
| 902 | C22 | — | 14 | 4 | no | — |
| 903 | C22 | — | 14 | 6 | no | — |
| 904 | C22 | — | 14 | 6 | no | — |
| 905 | C22 | — | 14 | 4 | no | — |
| 906 | C22 | — | 14 | 6 | no | — |
| 907 | C22 | — | 14 | 4 | no | — |
| 908 | C22 | — | 28 | 12 | no | — |
| 909 | C22 | C22×#1157 | 1 | 2 | yes | — |
| 910 | C22 | C25×D7 | 1 | 1 | yes | characteristic |
| 911 | C4 | — | 2 | 4 | no | — |
| 912 | C4 | — | 2 | 1 | no | — |
| 913 | C4 | — | 2 | 4 | no | — |
| 914 | C4 | — | 2 | 6 | no | — |
| 915 | C4 | — | 2 | 4 | no | — |
| 916 | C4 | — | 7 | 2 | no | — |
| 917 | C4 | — | 14 | 1 | no | — |
| 918 | C4 | — | 14 | 1 | no | — |
| 919 | C4 | — | 14 | 4 | no | — |
| 920 | C4 | — | 14 | 6 | no | — |
| 921 | C4 | — | 14 | 4 | no | — |
| 922 | C4 | — | 14 | 1 | no | — |
| 923 | C4 | — | 14 | 4 | no | — |
| 924 | C4 | C22×#1157 | 1 | 12 | yes | — |
| 925 | C4 | #90620 | 1 | 2 | yes | — |
| 926 | C2 | — | 2 | 2 | no | — |
| 927 | C2 | — | 4 | 4 | no | — |
| 928 | C2 | — | 28 | 6 | no | — |
| 929 | C2 | — | 28 | 4 | no | — |
| 930 | C2 | C23×#1157 | 1 | 1 | yes | characteristic |
| 931 | C2 | C2×#90620 | 1 | 1 | yes | characteristic |
| 932 | C2 | D7×#585 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C26 |
| Frattini | C22 | C25×D7 |
| Fitting | C4×C7×2−1+4 | C2 |
| hypercenter | C4×2−1+4 | D7 |
| hypocenter | C7 | #62793 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ C4×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C7×2−1+4 | C2 | semidirect |
| 2. #11744359 | C2 | semidirect |
| 3. #11744358 | C2 | semidirect |
| 4. #11742966 | C2 | semidirect |
| 5. #11742964 | C2 | semidirect |
| 6. #11742959 | C2 | semidirect |
| 7. #11742956 | C2 | semidirect |
| 8. #11742947 | C2 | semidirect |
| 9. #11742946 | C2 | semidirect |
| 10. #11742943 | C2 | semidirect |
| 11. #11742942 | C2 | semidirect |
| 12. #11742913 | C2 | semidirect |
| 13. #11742910 | C2 | semidirect |
| 14. #11742906 | C2 | semidirect |
| 15. #11742904 | C2 | semidirect |
| 16. #11742885 | C2 | semidirect |
| 17. #11742870 | C2 | semidirect |
| 18. C4×#6551 | C2 | semidirect |
| 19. C2×C4×#1161 | C2 | semidirect |
| 24. C7×#520 | C22 | semidirect |
| 26. C7×#519 | C22 | semidirect |
| 28. C4×C7×#41 | C22 | semidirect |
| 30. C2×C4×C7×Q8 | C22 | semidirect |
| 33. #90525 | C22 | semidirect |
| 36. #90522 | C22 | semidirect |
| 41. #90508 | C22 | semidirect |
| 42. Q8×C22⋊D7 | C22 | semidirect |
| 45. #90276 | C22 | semidirect |
| 46. #90275 | C22 | semidirect |
| 47. #90273 | C22 | semidirect |
| 48. #90272 | C22 | semidirect |
| 49. #90271 | C22 | semidirect |
| 50. #90271 | C22 | semidirect |
| 51. #90271 | C22 | semidirect |
| 52. #90269 | C22 | semidirect |
| 53. #90269 | C22 | semidirect |
| 58. #90265 | C22 | semidirect |
| 63. C4×#1161 | C22 | semidirect |
| 64. #90263 | C22 | semidirect |
| 65. C4×Q8×D7 | C22 | semidirect |
| 66. #90261 | C22 | semidirect |
| 67. #90260 | C22 | semidirect |
| 68. #90260 | C22 | semidirect |
| 69. #90259 | C22 | semidirect |
| 70. Q8×Dic14 | C22 | semidirect |
| 71. #90254 | C22 | semidirect |
| 72. #90253 | C22 | semidirect |
| 74. #90250 | C22 | semidirect |
| 75. #90249 | C22 | semidirect |
| 76. #90248 | C22 | semidirect |
| 77. #90248 | C22 | semidirect |
| 78. #90244 | C22 | semidirect |
| 79. #90239 | C22 | semidirect |
| 80. #90239 | C22 | semidirect |
| 81. #90239 | C22 | semidirect |
| 86. #90226 | C22 | semidirect |
| 87. #90225 | C22 | semidirect |
| 88. #90224 | C22 | semidirect |
| 89. #90223 | C22 | semidirect |
| 90. #90223 | C22 | semidirect |
| 91. #90221 | C22 | semidirect |
| 92. #90219 | C22 | semidirect |
| 93. #90219 | C22 | semidirect |
| 98. #90205 | C22 | semidirect |
| 99. #90205 | C22 | semidirect |
| 100. #90204 | C22 | semidirect |
| 101. #90198 | C22 | semidirect |
| 105. #90170 | C22 | semidirect |
| 106. #90168 | C22 | semidirect |
| 108. C4×#1157 | C22 | semidirect |
| 109. C4×#1157 | C22 | semidirect |
| 285. C4×2−1+4 | D7 | semidirect |
| 291. C2×C7×Q8 | #41 | semidirect |
| 463. #520 | C2×D7 | semidirect |
| 467. #519 | C2×D7 | semidirect |
| 477. C4×#41 | C2×D7 | semidirect |
| 481. C2×C4×Q8 | C2×D7 | semidirect |
| 740. C2×Q8 | #1157 | semidirect |
| 896. C7 | #62793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.