Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
6338 conjugacy classes of subgroups.
The subgroup lattice has 382 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 | D7×#564 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #11744208 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | D7×#557 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #11744095 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | D7×#541 | C2 | 1 | 12 | yes | maximal |
| 7 | #11743570 | C2 | 1 | 12 | yes | maximal, complemented |
| 8 | D7×#533 | C2 | 1 | 3 | yes | maximal |
| 9 | #11743338 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C7×#564 | C22 | 1 | 4 | yes | complemented |
| 11 | C7×#557 | C22 | 1 | 12 | yes | complemented |
| 12 | C7×#541 | C22 | 1 | 12 | yes | — |
| 13 | C7×#533 | C22 | 1 | 3 | yes | — |
| 14 | #90422 | C22 | 1 | 12 | yes | — |
| 15 | #90419 | C22 | 1 | 6 | yes | — |
| 16 | D7×C4⋊Q8 | C22 | 1 | 12 | yes | — |
| 17 | D7×C4⋊Q8 | C22 | 1 | 6 | yes | — |
| 18 | #90412 | C22 | 1 | 24 | yes | complemented |
| 19 | #90412 | C22 | 1 | 12 | yes | complemented |
| 20 | D7×#126 | C22 | 1 | 16 | yes | — |
| 21 | #90392 | C22 | 1 | 48 | yes | — |
| 22 | #90388 | C22 | 1 | 12 | yes | — |
| 23 | #90387 | C22 | 1 | 48 | yes | — |
| 24 | #90379 | C22 | 1 | 6 | yes | — |
| 25 | D7×#125 | C22 | 1 | 12 | yes | — |
| 26 | D7×#125 | C22 | 1 | 48 | yes | — |
| 27 | D7×#125 | C22 | 1 | 6 | yes | — |
| 28 | C7⋊#564 | C22 | 1 | 48 | yes | complemented |
| 29 | C7⋊#564 | C22 | 1 | 12 | yes | complemented |
| 30 | #90376 | C22 | 1 | 24 | yes | complemented |
| 31 | #90376 | C22 | 1 | 48 | yes | complemented |
| 32 | D7×C22⋊Q8 | C22 | 1 | 12 | yes | — |
| 33 | #90316 | C22 | 1 | 24 | yes | — |
| 34 | #90313 | C22 | 1 | 12 | yes | — |
| 35 | #90274 | C22 | 1 | 24 | yes | — |
| 36 | #90269 | C22 | 1 | 12 | yes | — |
| 37 | C4×Q8×D7 | C22 | 1 | 24 | yes | — |
| 38 | C4×Q8×D7 | C22 | 1 | 12 | yes | — |
| 39 | #90261 | C22 | 1 | 12 | yes | complemented |
| 40 | #90260 | C22 | 1 | 24 | yes | complemented |
| 41 | #90258 | C22 | 1 | 24 | yes | complemented |
| 42 | #90258 | C22 | 1 | 12 | yes | complemented |
| 43 | D7×#117 | C22 | 1 | 6 | yes | — |
| 44 | #90209 | C22 | 1 | 12 | yes | — |
| 45 | #90208 | C22 | 1 | 6 | yes | — |
| 46 | C2×C42×D7 | C22 | 1 | 1 | yes | characteristic |
| 47 | #90161 | C22 | 1 | 3 | yes | — |
| 48 | C2×#3556 | — | 7 | 1 | no | maximal, Sylow |
| 49 | C2×Q8×D7 | C23 | 1 | 12 | yes | — |
| 50 | C22×C4×D7 | C23 | 1 | 3 | yes | — |
| 51 | C7×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 52 | C7×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 53 | C7×#126 | C23 | 1 | 16 | yes | — |
| 54 | C7×#125 | C23 | 1 | 12 | yes | — |
| 55 | C7×#125 | C23 | 1 | 48 | yes | — |
| 56 | C7×#125 | C23 | 1 | 6 | yes | — |
| 57 | C7×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 58 | C4×C7×Q8 | C23 | 1 | 24 | yes | — |
| 59 | C4×C7×Q8 | C23 | 1 | 12 | yes | — |
| 60 | C7×#117 | C23 | 1 | 6 | yes | — |
| 61 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 62 | #6509 | C23 | 1 | 12 | yes | — |
| 63 | Q8×Dic7 | C23 | 1 | 12 | yes | — |
| 64 | Q8×Dic7 | C23 | 1 | 24 | yes | — |
| 65 | #6507 | C23 | 1 | 12 | yes | — |
| 66 | #6507 | C23 | 1 | 24 | yes | — |
| 67 | #6489 | C23 | 1 | 6 | yes | — |
| 68 | #6487 | C23 | 1 | 12 | yes | — |
| 69 | C2×C4×Dic7 | C23 | 1 | 3 | yes | — |
| 70 | #6461 | C23 | 1 | 48 | yes | — |
| 71 | #6460 | C23 | 1 | 12 | yes | — |
| 72 | #6459 | C23 | 1 | 24 | yes | — |
| 73 | #6455 | C23 | 1 | 12 | yes | — |
| 74 | D7×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 75 | D7×C4⋊C4 | C23 | 1 | 24 | yes | — |
| 76 | D7×C4⋊C4 | C23 | 1 | 48 | yes | — |
| 77 | D7×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 78 | #6453 | C23 | 1 | 48 | yes | — |
| 79 | #6453 | C23 | 1 | 24 | yes | — |
| 80 | #6453 | C23 | 1 | 12 | yes | — |
| 81 | #6453 | C23 | 1 | 48 | yes | — |
| 82 | #6452 | C23 | 1 | 48 | yes | — |
| 83 | #6452 | C23 | 1 | 48 | yes | — |
| 84 | #6452 | C23 | 1 | 48 | yes | — |
| 85 | #6452 | C23 | 1 | 48 | yes | — |
| 86 | #6452 | C23 | 1 | 48 | yes | — |
| 87 | #6452 | C23 | 1 | 24 | yes | — |
| 88 | #6451 | C23 | 1 | 12 | yes | — |
| 89 | #6451 | C23 | 1 | 48 | yes | — |
| 90 | #6451 | C23 | 1 | 12 | yes | — |
| 91 | #6450 | C23 | 1 | 24 | yes | — |
| 92 | #6450 | C23 | 1 | 48 | yes | — |
| 93 | #6450 | C23 | 1 | 12 | yes | — |
| 94 | #6450 | C23 | 1 | 24 | yes | — |
| 95 | D7×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 96 | #6442 | C23 | 1 | 48 | yes | — |
| 97 | #6441 | C23 | 1 | 24 | yes | — |
| 98 | #6440 | C23 | 1 | 12 | yes | — |
| 99 | #6439 | C23 | 1 | 16 | yes | — |
| 100 | #6435 | C23 | 1 | 12 | yes | — |
| 101 | C42×D7 | C23 | 1 | 1 | yes | characteristic |
| 102 | C42×D7 | C23 | 1 | 16 | yes | — |
| 103 | C42×D7 | C23 | 1 | 12 | yes | — |
| 104 | C42×D7 | C23 | 1 | 1 | yes | characteristic |
| 105 | C42×D7 | C23 | 1 | 3 | yes | — |
| 106 | C42×D7 | C23 | 1 | 3 | yes | — |
| 107 | #6433 | C23 | 1 | 6 | yes | — |
| 108 | #6433 | C23 | 1 | 48 | yes | — |
| 109 | #6433 | C23 | 1 | 12 | yes | — |
| 110 | #6432 | C23 | 1 | 12 | yes | — |
| 111 | #6432 | C23 | 1 | 6 | yes | — |
| 112 | C4×Dic14 | C23 | 1 | 48 | yes | — |
| 113 | C4×Dic14 | C23 | 1 | 24 | yes | — |
| 114 | C4×Dic14 | C23 | 1 | 24 | yes | — |
| 115 | C4×Dic14 | C23 | 1 | 12 | yes | — |
| 116 | #3556 | — | 7 | 4 | no | — |
| 117 | #3556 | — | 7 | 12 | no | — |
| 118 | #3556 | — | 7 | 12 | no | — |
| 119 | #3556 | — | 7 | 3 | no | — |
| 120 | #3556 | D7 | 1 | 1 | yes | characteristic, direct product factor |
| 121 | C2×#564 | — | 7 | 4 | no | — |
| 122 | C2×#557 | — | 7 | 12 | no | — |
| 123 | C2×#541 | — | 7 | 12 | no | — |
| 124 | C2×#533 | — | 7 | 3 | no | — |
| 125 | C23×D7 | C24 | 1 | 1 | yes | characteristic |
| 126 | C2×C7×Q8 | C24 | 1 | 12 | yes | — |
| 127 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 128 | C22×Dic7 | C24 | 1 | 3 | yes | — |
| 129 | Q8×D7 | — | 2 | 48 | no | — |
| 130 | C2×C4×D7 | — | 2 | 12 | no | — |
| 131 | C2×C4×D7 | C24 | 1 | 24 | yes | — |
| 132 | C2×C4×D7 | C24 | 1 | 3 | yes | — |
| 133 | C2×C4×D7 | C24 | 1 | 3 | yes | — |
| 134 | C2×C4×D7 | C24 | 1 | 3 | yes | — |
| 135 | C2×C4×D7 | C24 | 1 | 3 | yes | — |
| 136 | C2×Dic14 | C24 | 1 | 12 | yes | — |
| 137 | C2×Dic14 | C24 | 1 | 24 | yes | — |
| 138 | C7×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 139 | C7×C4⋊C4 | C24 | 1 | 48 | yes | — |
| 140 | C7×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 141 | C7×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 142 | C7×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 143 | C42×C7 | C24 | 1 | 3 | yes | — |
| 144 | C42×C7 | C24 | 1 | 12 | yes | — |
| 145 | C42×C7 | C24 | 1 | 16 | yes | — |
| 146 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 147 | C22⋊Dic7 | C24 | 1 | 12 | yes | — |
| 148 | (C2×D7)⋊C4 | C24 | 1 | 24 | yes | — |
| 149 | C4⋊Dic7 | C24 | 1 | 12 | yes | — |
| 150 | C4⋊Dic7 | C24 | 1 | 48 | yes | — |
| 151 | C4⋊Dic7 | C24 | 1 | 24 | yes | — |
| 152 | C4⋊Dic7 | C24 | 1 | 12 | yes | — |
| 153 | Dic7⋊C4 | C24 | 1 | 24 | yes | — |
| 154 | Dic7⋊C4 | C24 | 1 | 24 | yes | — |
| 155 | Dic7⋊C4 | C24 | 1 | 48 | yes | — |
| 156 | Dic7⋊C4 | C24 | 1 | 48 | yes | — |
| 157 | Dic7⋊C4 | C24 | 1 | 24 | yes | — |
| 158 | Dic7⋊C4 | C24 | 1 | 24 | yes | — |
| 159 | C4×Dic7 | C24 | 1 | 6 | yes | — |
| 160 | C4×Dic7 | C24 | 1 | 12 | yes | — |
| 161 | C4×Dic7 | C24 | 1 | 24 | yes | — |
| 162 | C4×Dic7 | C24 | 1 | 48 | yes | — |
| 163 | C4×Dic7 | C24 | 1 | 3 | yes | — |
| 164 | C4×Dic7 | C24 | 1 | 3 | yes | — |
| 165 | #564 | — | 7 | 48 | no | — |
| 166 | #564 | — | 7 | 12 | no | — |
| 167 | #564 | C2×D7 | 1 | 4 | yes | complemented |
| 168 | #557 | — | 7 | 24 | no | — |
| 169 | #557 | — | 7 | 12 | no | — |
| 170 | #557 | — | 7 | 48 | no | — |
| 171 | #557 | — | 7 | 24 | no | — |
| 172 | #557 | — | 7 | 24 | no | — |
| 173 | #557 | — | 7 | 12 | no | — |
| 174 | #557 | — | 7 | 24 | no | — |
| 175 | #557 | — | 7 | 12 | no | — |
| 176 | #557 | C2×D7 | 1 | 12 | yes | complemented |
| 177 | #541 | — | 7 | 12 | no | — |
| 178 | #541 | — | 7 | 48 | no | — |
| 179 | #541 | — | 7 | 48 | no | — |
| 180 | #541 | — | 7 | 12 | no | — |
| 181 | #541 | — | 7 | 24 | no | — |
| 182 | #541 | — | 7 | 24 | no | — |
| 183 | #541 | — | 7 | 12 | no | — |
| 184 | #541 | C2×D7 | 1 | 12 | yes | — |
| 185 | #533 | — | 7 | 6 | no | — |
| 186 | #533 | — | 7 | 6 | no | — |
| 187 | #533 | — | 7 | 12 | no | — |
| 188 | #533 | — | 7 | 12 | no | — |
| 189 | #533 | — | 7 | 6 | no | — |
| 190 | #533 | — | 7 | 3 | no | — |
| 191 | #533 | C2×D7 | 1 | 3 | yes | — |
| 192 | C2×C4⋊Q8 | — | 7 | 6 | no | — |
| 193 | C2×C4⋊Q8 | — | 7 | 12 | no | — |
| 194 | C2×#126 | — | 7 | 16 | no | — |
| 195 | C2×#125 | — | 7 | 6 | no | — |
| 196 | C2×#125 | — | 7 | 12 | no | — |
| 197 | C2×#125 | — | 7 | 48 | no | — |
| 198 | C2×C22⋊Q8 | — | 7 | 12 | no | — |
| 199 | C2×C4×Q8 | — | 7 | 12 | no | — |
| 200 | C2×C4×Q8 | — | 7 | 24 | no | — |
| 201 | C2×#117 | — | 7 | 6 | no | — |
| 202 | C22×C42 | — | 7 | 1 | no | — |
| 203 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 204 | C22×D7 | — | 2 | 6 | no | — |
| 205 | C22×D7 | C25 | 1 | 1 | yes | characteristic |
| 206 | C22×D7 | C25 | 1 | 1 | yes | characteristic |
| 207 | C7×Q8 | — | 2 | 24 | no | — |
| 208 | C2×C4×C7 | — | 2 | 6 | no | — |
| 209 | C2×C4×C7 | C25 | 1 | 24 | yes | — |
| 210 | C2×C4×C7 | C25 | 1 | 3 | yes | — |
| 211 | C2×C4×C7 | C25 | 1 | 3 | yes | — |
| 212 | C2×Dic7 | — | 2 | 6 | no | — |
| 213 | C2×Dic7 | C25 | 1 | 24 | yes | — |
| 214 | C2×Dic7 | C25 | 1 | 3 | yes | — |
| 215 | C2×Dic7 | C25 | 1 | 3 | yes | — |
| 216 | C4×D7 | — | 2 | 6 | no | — |
| 217 | C4×D7 | — | 2 | 48 | no | — |
| 218 | C4×D7 | — | 2 | 6 | no | — |
| 219 | C4×D7 | — | 2 | 6 | no | — |
| 220 | C4×D7 | 2−1+4 | 1 | 12 | yes | — |
| 221 | Dic14 | — | 2 | 24 | no | — |
| 222 | Dic14 | — | 2 | 48 | no | — |
| 223 | C22×Q8 | — | 7 | 12 | no | — |
| 224 | C23×C4 | — | 7 | 3 | no | — |
| 225 | C4⋊Q8 | — | 7 | 12 | no | — |
| 226 | C4⋊Q8 | — | 7 | 24 | no | — |
| 227 | C4⋊Q8 | — | 7 | 12 | no | — |
| 228 | C4⋊Q8 | — | 7 | 12 | no | — |
| 229 | C4⋊Q8 | — | 7 | 48 | no | — |
| 230 | C4⋊Q8 | — | 7 | 6 | no | — |
| 231 | C4⋊Q8 | — | 7 | 12 | no | — |
| 232 | C4⋊Q8 | C22×D7 | 1 | 6 | yes | — |
| 233 | C4⋊Q8 | C22×D7 | 1 | 12 | yes | — |
| 234 | #126 | — | 7 | 48 | no | — |
| 235 | #126 | — | 7 | 48 | no | — |
| 236 | #126 | — | 7 | 16 | no | — |
| 237 | #126 | C22×D7 | 1 | 16 | yes | — |
| 238 | #125 | — | 7 | 24 | no | — |
| 239 | #125 | — | 7 | 12 | no | — |
| 240 | #125 | — | 7 | 48 | no | — |
| 241 | #125 | — | 7 | 24 | no | — |
| 242 | #125 | — | 7 | 48 | no | — |
| 243 | #125 | — | 7 | 48 | no | — |
| 244 | #125 | — | 7 | 48 | no | — |
| 245 | #125 | — | 7 | 48 | no | — |
| 246 | #125 | — | 7 | 48 | no | — |
| 247 | #125 | — | 7 | 48 | no | — |
| 248 | #125 | — | 7 | 6 | no | — |
| 249 | #125 | — | 7 | 12 | no | — |
| 250 | #125 | — | 7 | 48 | no | — |
| 251 | #125 | C22×D7 | 1 | 6 | yes | — |
| 252 | #125 | C22×D7 | 1 | 12 | yes | — |
| 253 | #125 | C22×D7 | 1 | 48 | yes | — |
| 254 | C22⋊Q8 | — | 7 | 12 | no | — |
| 255 | C22⋊Q8 | — | 7 | 12 | no | — |
| 256 | C22⋊Q8 | — | 7 | 24 | no | — |
| 257 | C22⋊Q8 | — | 7 | 12 | no | — |
| 258 | C22⋊Q8 | — | 7 | 24 | no | — |
| 259 | C22⋊Q8 | C22×D7 | 1 | 12 | yes | — |
| 260 | C4×Q8 | — | 7 | 12 | no | — |
| 261 | C4×Q8 | — | 7 | 24 | no | — |
| 262 | C4×Q8 | — | 7 | 24 | no | — |
| 263 | C4×Q8 | — | 7 | 12 | no | — |
| 264 | C4×Q8 | — | 7 | 48 | no | — |
| 265 | C4×Q8 | — | 7 | 24 | no | — |
| 266 | C4×Q8 | — | 7 | 24 | no | — |
| 267 | C4×Q8 | — | 7 | 12 | no | — |
| 268 | C4×Q8 | — | 7 | 48 | no | — |
| 269 | C4×Q8 | — | 7 | 24 | no | — |
| 270 | C4×Q8 | C22×D7 | 1 | 12 | yes | — |
| 271 | C4×Q8 | C22×D7 | 1 | 24 | yes | — |
| 272 | #117 | — | 7 | 6 | no | — |
| 273 | #117 | — | 7 | 12 | no | — |
| 274 | #117 | — | 7 | 12 | no | — |
| 275 | #117 | — | 7 | 12 | no | — |
| 276 | #117 | C22×D7 | 1 | 6 | yes | — |
| 277 | C2×C4⋊C4 | — | 7 | 12 | no | — |
| 278 | C2×C4⋊C4 | — | 7 | 12 | no | — |
| 279 | C2×C4⋊C4 | — | 7 | 24 | no | — |
| 280 | C2×C4⋊C4 | — | 7 | 48 | no | — |
| 281 | C2×C22⋊C4 | — | 7 | 12 | no | — |
| 282 | C2×C42 | — | 7 | 3 | no | — |
| 283 | C2×C42 | — | 7 | 12 | no | — |
| 284 | C2×C42 | — | 7 | 3 | no | — |
| 285 | C2×C42 | — | 7 | 16 | no | — |
| 286 | C2×C42 | — | 7 | 1 | no | — |
| 287 | C2×C42 | — | 7 | 1 | no | — |
| 288 | C2×C42 | — | 7 | 3 | no | — |
| 289 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 290 | C22×C7 | — | 2 | 3 | no | — |
| 291 | C22×C7 | C26 | 1 | 1 | yes | characteristic |
| 292 | C2×D7 | — | 2 | 3 | no | — |
| 293 | C2×D7 | — | 4 | 4 | no | — |
| 294 | C2×D7 | C2×2−1+4 | 1 | 6 | yes | — |
| 295 | C4×C7 | — | 2 | 24 | no | — |
| 296 | C4×C7 | — | 2 | 3 | no | — |
| 297 | C4×C7 | C2×2−1+4 | 1 | 6 | yes | — |
| 298 | Dic7 | — | 2 | 24 | no | — |
| 299 | Dic7 | — | 2 | 3 | no | — |
| 300 | Dic7 | C2×2−1+4 | 1 | 6 | yes | — |
| 301 | C24 | — | 7 | 1 | no | — |
| 302 | C2×Q8 | — | 7 | 24 | no | — |
| 303 | C2×Q8 | — | 7 | 12 | no | — |
| 304 | C2×Q8 | — | 14 | 48 | no | — |
| 305 | C2×Q8 | C23×D7 | 1 | 12 | yes | — |
| 306 | C22×C4 | — | 7 | 3 | no | — |
| 307 | C22×C4 | — | 7 | 3 | no | — |
| 308 | C22×C4 | — | 7 | 24 | no | — |
| 309 | C22×C4 | — | 7 | 3 | no | — |
| 310 | C22×C4 | — | 7 | 3 | no | — |
| 311 | C22×C4 | — | 7 | 3 | no | — |
| 312 | C22×C4 | — | 14 | 12 | no | — |
| 313 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 314 | C4⋊C4 | — | 7 | 24 | no | — |
| 315 | C4⋊C4 | — | 7 | 24 | no | — |
| 316 | C4⋊C4 | — | 7 | 24 | no | — |
| 317 | C4⋊C4 | — | 7 | 24 | no | — |
| 318 | C4⋊C4 | — | 7 | 48 | no | — |
| 319 | C4⋊C4 | — | 7 | 48 | no | — |
| 320 | C4⋊C4 | — | 7 | 12 | no | — |
| 321 | C4⋊C4 | — | 7 | 12 | no | — |
| 322 | C4⋊C4 | — | 7 | 24 | no | — |
| 323 | C4⋊C4 | — | 7 | 48 | no | — |
| 324 | C4⋊C4 | C23×D7 | 1 | 12 | yes | — |
| 325 | C4⋊C4 | C23×D7 | 1 | 12 | yes | — |
| 326 | C4⋊C4 | C23×D7 | 1 | 24 | yes | — |
| 327 | C4⋊C4 | C23×D7 | 1 | 48 | yes | — |
| 328 | C22⋊C4 | — | 7 | 12 | no | — |
| 329 | C22⋊C4 | — | 7 | 24 | no | — |
| 330 | C22⋊C4 | C23×D7 | 1 | 12 | yes | — |
| 331 | C42 | — | 7 | 3 | no | — |
| 332 | C42 | — | 7 | 6 | no | — |
| 333 | C42 | — | 7 | 3 | no | — |
| 334 | C42 | — | 7 | 24 | no | — |
| 335 | C42 | — | 7 | 12 | no | — |
| 336 | C42 | — | 7 | 48 | no | — |
| 337 | C42 | C23×D7 | 1 | 3 | yes | — |
| 338 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 339 | C42 | C23×D7 | 1 | 12 | yes | — |
| 340 | C42 | C23×D7 | 1 | 16 | yes | — |
| 341 | C2×C7 | — | 4 | 1 | no | — |
| 342 | C2×C7 | C22×2−1+4 | 1 | 3 | yes | — |
| 343 | D7 | — | 4 | 1 | no | — |
| 344 | D7 | #3556 | 1 | 4 | yes | direct product factor |
| 345 | C23 | — | 7 | 1 | no | — |
| 346 | C23 | — | 7 | 1 | no | — |
| 347 | C23 | — | 14 | 6 | no | — |
| 348 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 349 | Q8 | — | 2 | 24 | no | — |
| 350 | Q8 | — | 14 | 48 | no | — |
| 351 | Q8 | — | 14 | 24 | no | — |
| 352 | C2×C4 | — | 2 | 6 | no | — |
| 353 | C2×C4 | — | 7 | 3 | no | — |
| 354 | C2×C4 | — | 7 | 12 | no | — |
| 355 | C2×C4 | — | 7 | 24 | no | — |
| 356 | C2×C4 | — | 7 | 3 | no | — |
| 357 | C2×C4 | — | 14 | 6 | no | — |
| 358 | C2×C4 | — | 14 | 6 | no | — |
| 359 | C2×C4 | — | 14 | 48 | no | — |
| 360 | C2×C4 | — | 14 | 6 | no | — |
| 361 | C2×C4 | — | 14 | 6 | no | — |
| 362 | C2×C4 | C24×D7 | 1 | 24 | yes | — |
| 363 | C2×C4 | C24×D7 | 1 | 3 | yes | — |
| 364 | C2×C4 | C24×D7 | 1 | 3 | yes | — |
| 365 | C7 | C2×#3556 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 366 | C22 | — | 2 | 3 | no | — |
| 367 | C22 | — | 7 | 6 | no | — |
| 368 | C22 | — | 14 | 3 | no | — |
| 369 | C22 | — | 28 | 4 | no | — |
| 370 | C22 | C25×D7 | 1 | 1 | yes | characteristic |
| 371 | C4 | — | 2 | 3 | no | — |
| 372 | C4 | — | 2 | 24 | no | — |
| 373 | C4 | — | 7 | 6 | no | — |
| 374 | C4 | — | 14 | 3 | no | — |
| 375 | C4 | — | 14 | 24 | no | — |
| 376 | C4 | D7×2−1+4 | 1 | 6 | yes | — |
| 377 | C2 | — | 4 | 1 | no | — |
| 378 | C2 | — | 7 | 4 | no | — |
| 379 | C2 | — | 28 | 1 | no | — |
| 380 | C2 | C2×D7×2−1+4 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D7 |
| commutator, socle, cosocle | C22×C7 | C26 |
| Fitting | C7×#3556 | C2 |
| prime radical | C23×D7 | C24 |
| hypercenter | #3556 | D7 |
| hypocenter | C7 | C2×#3556 |
| 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. D7×#564 | C2 | semidirect |
| 3. #11744208 | C2 | semidirect |
| 4. D7×#557 | C2 | semidirect |
| 5. #11744095 | C2 | semidirect |
| 7. #11743570 | C2 | semidirect |
| 9. #11743338 | C2 | semidirect |
| 10. C7×#564 | C22 | semidirect |
| 11. C7×#557 | C22 | semidirect |
| 18. #90412 | C22 | semidirect |
| 19. #90412 | C22 | semidirect |
| 28. C7⋊#564 | C22 | semidirect |
| 29. C7⋊#564 | C22 | semidirect |
| 30. #90376 | C22 | semidirect |
| 31. #90376 | C22 | semidirect |
| 39. #90261 | C22 | semidirect |
| 40. #90260 | C22 | semidirect |
| 41. #90258 | C22 | semidirect |
| 42. #90258 | C22 | semidirect |
| 120. #3556 | D7 | direct (N × H) |
| 167. #564 | C2×D7 | semidirect |
| 176. #557 | C2×D7 | semidirect |
| 344. D7 | #3556 | direct (N × H) |
| 365. C7 | C2×#3556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3556 | 2 |
| D7×#564 | 2 |
| #11744208 | 2 |
| D7×#557 | 2 |
| #11744095 | 2 |
| D7×#541 | 2 |
| #11743570 | 2 |
| D7×#533 | 2 |
| #11743338 | 2 |
| C2×#3556 | 7 |