Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1078 conjugacy classes of subgroups.
The subgroup lattice has 566 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11743320 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11740752 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11736795 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11735944 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1530 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11728565 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11727552 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11726106 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11726104 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | C7×#532 | C22 | 1 | 1 | yes | characteristic |
| 11 | #90521 | — | 2 | 2 | no | — |
| 12 | C2×#6467 | — | 2 | 2 | no | — |
| 13 | #90425 | — | 2 | 1 | no | — |
| 14 | #90408 | — | 2 | 1 | no | — |
| 15 | #90374 | C22 | 1 | 4 | yes | — |
| 16 | #90298 | — | 2 | 2 | no | — |
| 17 | #90298 | — | 2 | 2 | no | — |
| 18 | #90254 | — | 2 | 1 | no | — |
| 19 | #90254 | — | 2 | 1 | no | — |
| 20 | D4×D28 | — | 2 | 1 | no | — |
| 21 | D4×D28 | — | 2 | 1 | no | — |
| 22 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 23 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 24 | #90168 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C7×#432 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C7×#97 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #90010 | — | 2 | 2 | no | — |
| 28 | #89855 | — | 2 | 1 | no | — |
| 29 | #89844 | — | 2 | 1 | no | — |
| 30 | #89830 | C22 | 1 | 2 | yes | complemented |
| 31 | #89827 | C22 | 1 | 2 | yes | complemented |
| 32 | #89698 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #89615 | — | 2 | 1 | no | — |
| 34 | #89613 | — | 2 | 1 | no | — |
| 35 | #89506 | — | 2 | 2 | no | — |
| 36 | #89487 | — | 2 | 1 | no | — |
| 37 | #89487 | C22 | 1 | 2 | yes | complemented |
| 38 | #89486 | C22 | 1 | 2 | yes | complemented |
| 39 | #89484 | — | 2 | 1 | no | — |
| 40 | #89484 | C22 | 1 | 2 | yes | complemented |
| 41 | #89484 | C22 | 1 | 2 | yes | complemented |
| 42 | C7×#329 | C22 | 1 | 4 | yes | complemented |
| 43 | #89259 | C22 | 1 | 4 | yes | complemented |
| 44 | #89259 | C22 | 1 | 4 | yes | complemented |
| 45 | #19052 | — | 7 | 1 | no | maximal, Sylow |
| 46 | C2×C7×#41 | D4 | 1 | 2 | yes | — |
| 47 | C2×D4×D7 | — | 2 | 2 | no | — |
| 48 | C2×D4×D7 | — | 2 | 2 | no | — |
| 49 | C2×#1157 | — | 2 | 1 | no | — |
| 50 | C2×#1157 | D4 | 1 | 2 | yes | — |
| 51 | C2×#1157 | D4 | 1 | 2 | yes | — |
| 52 | C22×D28 | — | 2 | 2 | no | — |
| 53 | C22×C7×C8 | — | 2 | 1 | no | — |
| 54 | C7×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 55 | C7×#127 | D4 | 1 | 1 | yes | characteristic |
| 56 | C7×#124 | C23 | 1 | 2 | yes | — |
| 57 | C7×#121 | — | 2 | 1 | no | — |
| 58 | C7×#121 | — | 2 | 1 | no | — |
| 59 | C4×C7×D4 | — | 2 | 1 | no | — |
| 60 | C4×C7×D4 | — | 2 | 1 | no | — |
| 61 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 62 | #6510 | — | 2 | 4 | no | — |
| 63 | C2×#1143 | — | 2 | 2 | no | — |
| 64 | #6503 | — | 2 | 4 | no | — |
| 65 | #6501 | — | 2 | 2 | no | — |
| 66 | #6501 | — | 2 | 2 | no | — |
| 67 | #6500 | — | 2 | 4 | no | — |
| 68 | #6500 | — | 2 | 4 | no | — |
| 69 | C2×#1141 | — | 2 | 2 | no | — |
| 70 | #6493 | — | 2 | 2 | no | — |
| 71 | #6493 | — | 2 | 2 | no | — |
| 72 | #6493 | — | 2 | 1 | no | — |
| 73 | #6493 | — | 2 | 1 | no | — |
| 74 | #6493 | — | 2 | 1 | no | — |
| 75 | #6493 | — | 2 | 1 | no | — |
| 76 | #6493 | — | 2 | 1 | no | — |
| 77 | #6493 | — | 2 | 1 | no | — |
| 78 | #6489 | — | 2 | 2 | no | — |
| 79 | C2×Dic28 | — | 2 | 2 | no | — |
| 80 | #6467 | — | 4 | 8 | no | — |
| 81 | C2×D56 | — | 2 | 2 | no | — |
| 82 | C2×D56 | — | 2 | 2 | no | — |
| 83 | C2×#1132 | — | 2 | 2 | no | — |
| 84 | C2×#1132 | — | 2 | 2 | no | — |
| 85 | C2×#1132 | — | 2 | 2 | no | — |
| 86 | #6458 | — | 2 | 2 | no | — |
| 87 | #6458 | — | 2 | 2 | no | — |
| 88 | #6455 | — | 2 | 2 | no | — |
| 89 | #6455 | — | 2 | 2 | no | — |
| 90 | #6448 | — | 2 | 4 | no | — |
| 91 | #6448 | — | 2 | 4 | no | — |
| 92 | #6445 | — | 2 | 4 | no | — |
| 93 | #6445 | — | 2 | 4 | no | — |
| 94 | #6438 | — | 2 | 1 | no | — |
| 95 | #6438 | C23 | 1 | 2 | yes | — |
| 96 | #6438 | C23 | 1 | 2 | yes | — |
| 97 | #6437 | D4 | 1 | 1 | yes | characteristic |
| 98 | #6437 | D4 | 1 | 1 | yes | characteristic |
| 99 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 100 | C4×D28 | — | 2 | 1 | no | — |
| 101 | C4×D28 | — | 2 | 1 | no | — |
| 102 | C4×D28 | — | 2 | 1 | no | — |
| 103 | C4×D28 | — | 2 | 1 | no | — |
| 104 | C4×D28 | — | 2 | 1 | no | — |
| 105 | C4×D28 | — | 2 | 1 | no | — |
| 106 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 107 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 108 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 109 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 110 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 111 | C7×#97 | — | 2 | 1 | no | — |
| 112 | C7×#97 | C23 | 1 | 2 | yes | — |
| 113 | C7×#97 | C23 | 1 | 2 | yes | — |
| 114 | #6409 | — | 2 | 2 | no | — |
| 115 | #6406 | — | 2 | 2 | no | — |
| 116 | C22⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 117 | #6395 | — | 2 | 2 | no | — |
| 118 | #6390 | — | 2 | 2 | no | — |
| 119 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 120 | #6377 | C23 | 1 | 2 | yes | — |
| 121 | #3549 | — | 7 | 1 | no | — |
| 122 | #3214 | — | 7 | 1 | no | — |
| 123 | #3214 | — | 7 | 1 | no | — |
| 124 | #3150 | — | 7 | 1 | no | — |
| 125 | #1659 | — | 7 | 4 | no | — |
| 126 | #1655 | — | 7 | 4 | no | — |
| 127 | #1536 | — | 7 | 1 | no | — |
| 128 | #1530 | — | 7 | 1 | no | — |
| 129 | #1530 | D7 | 1 | 1 | yes | characteristic, complemented |
| 130 | C23×D7 | — | 2 | 4 | no | — |
| 131 | C7×#41 | — | 8 | 2 | no | — |
| 132 | C2×C7×Q8 | C2×D4 | 1 | 2 | yes | — |
| 133 | C2×C7×D4 | — | 2 | 2 | no | — |
| 134 | C2×C7×D4 | — | 2 | 1 | no | — |
| 135 | C2×C7×D4 | — | 2 | 1 | no | — |
| 136 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 137 | C22×C4×C7 | — | 2 | 2 | no | — |
| 138 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 142 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 143 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 144 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 145 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 146 | D4×D7 | — | 8 | 4 | no | — |
| 147 | D4×D7 | — | 8 | 4 | no | — |
| 148 | #1157 | — | 4 | 4 | no | — |
| 149 | #1157 | — | 4 | 4 | no | — |
| 150 | #1157 | — | 8 | 2 | no | — |
| 151 | C2×D28 | — | 2 | 1 | no | — |
| 152 | C2×D28 | — | 2 | 1 | no | — |
| 153 | C2×D28 | — | 2 | 1 | no | — |
| 154 | C2×D28 | — | 2 | 1 | no | — |
| 155 | C2×D28 | — | 2 | 1 | no | — |
| 156 | C2×D28 | — | 2 | 1 | no | — |
| 157 | C2×D28 | — | 2 | 1 | no | — |
| 158 | C2×D28 | — | 2 | 4 | no | — |
| 159 | C2×D28 | — | 8 | 4 | no | — |
| 160 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 161 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 162 | C2×C4×D7 | — | 2 | 2 | no | — |
| 163 | C2×C4×D7 | — | 2 | 2 | no | — |
| 164 | C2×C4×D7 | — | 4 | 1 | no | — |
| 165 | C2×Dic14 | — | 2 | 1 | no | — |
| 166 | C2×Dic14 | C2×D4 | 1 | 2 | yes | — |
| 167 | C2×Dic14 | C2×D4 | 1 | 2 | yes | — |
| 168 | C2×C7×C8 | — | 2 | 4 | no | — |
| 169 | C2×C7×C8 | — | 2 | 2 | no | — |
| 170 | C2×C7×C8 | — | 2 | 2 | no | — |
| 171 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 172 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 173 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 174 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 175 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 179 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 180 | #1143 | — | 8 | 2 | no | — |
| 181 | #1141 | — | 8 | 2 | no | — |
| 182 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 183 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 184 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 185 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 186 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 187 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 188 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 189 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 190 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 191 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 192 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 193 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 194 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 195 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 196 | C4×Dic7 | — | 2 | 4 | no | — |
| 197 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 198 | Dic28 | — | 4 | 4 | no | — |
| 199 | D56 | — | 4 | 4 | no | — |
| 200 | D56 | — | 8 | 2 | no | — |
| 201 | #1132 | — | 4 | 4 | no | — |
| 202 | #1132 | — | 4 | 4 | no | — |
| 203 | #1132 | — | 8 | 2 | no | — |
| 204 | C2×#135 | — | 14 | 2 | no | — |
| 205 | H(3,𝔽4) | — | 7 | 4 | no | — |
| 206 | #555 | — | 14 | 1 | no | — |
| 207 | #555 | — | 14 | 1 | no | — |
| 208 | #555 | — | 14 | 1 | no | — |
| 209 | D42 | — | 14 | 1 | no | — |
| 210 | D42 | — | 14 | 1 | no | — |
| 211 | D42 | — | 14 | 1 | no | — |
| 212 | #535 | — | 14 | 2 | no | — |
| 213 | #535 | — | 14 | 2 | no | — |
| 214 | #535 | — | 14 | 2 | no | — |
| 215 | #532 | — | 7 | 1 | no | — |
| 216 | #532 | — | 7 | 1 | no | — |
| 217 | #532 | — | 7 | 1 | no | — |
| 218 | #532 | C2×D7 | 1 | 1 | yes | characteristic |
| 219 | #497 | — | 7 | 2 | no | — |
| 220 | #497 | — | 14 | 1 | no | — |
| 221 | #496 | — | 7 | 2 | no | — |
| 222 | #496 | — | 7 | 2 | no | — |
| 223 | #496 | — | 7 | 2 | no | — |
| 224 | #496 | — | 14 | 1 | no | — |
| 225 | #489 | — | 7 | 2 | no | — |
| 226 | #489 | — | 7 | 2 | no | — |
| 227 | #461 | — | 14 | 1 | no | — |
| 228 | #461 | — | 14 | 1 | no | — |
| 229 | #459 | — | 14 | 1 | no | — |
| 230 | #459 | — | 14 | 1 | no | — |
| 231 | #449 | — | 14 | 2 | no | — |
| 232 | #449 | — | 14 | 2 | no | — |
| 233 | #432 | — | 7 | 1 | no | — |
| 234 | #432 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 235 | C2×#97 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 236 | #329 | — | 7 | 4 | no | — |
| 237 | #329 | — | 7 | 4 | no | — |
| 238 | #329 | C2×D7 | 1 | 4 | yes | complemented |
| 239 | C23×C7 | — | 2 | 2 | no | — |
| 240 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 241 | C22×D7 | — | 2 | 2 | no | — |
| 242 | C22×D7 | — | 2 | 2 | no | — |
| 243 | C22×D7 | — | 4 | 1 | no | — |
| 244 | C22×D7 | — | 8 | 4 | no | — |
| 245 | C22×D7 | — | 8 | 4 | no | — |
| 246 | C22×D7 | — | 8 | 4 | no | — |
| 247 | C7×Q8 | — | 4 | 2 | no | — |
| 248 | C7×D4 | — | 4 | 2 | no | — |
| 249 | C7×D4 | — | 4 | 2 | no | — |
| 250 | C7×D4 | — | 4 | 2 | no | — |
| 251 | C7×D4 | — | 8 | 2 | no | — |
| 252 | C2×C4×C7 | — | 2 | 2 | no | — |
| 253 | C2×C4×C7 | — | 2 | 2 | no | — |
| 254 | C2×C4×C7 | — | 4 | 1 | no | — |
| 255 | C2×C4×C7 | — | 4 | 1 | no | — |
| 256 | C2×C4×C7 | — | 4 | 4 | no | — |
| 257 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 262 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 263 | C22⋊D7 | — | 8 | 2 | no | — |
| 264 | C22⋊D7 | — | 8 | 2 | no | — |
| 265 | C22⋊D7 | — | 8 | 4 | no | — |
| 266 | C22⋊D7 | — | 8 | 4 | no | — |
| 267 | C22⋊D7 | — | 8 | 2 | no | — |
| 268 | C2×Dic7 | — | 2 | 2 | no | — |
| 269 | C2×Dic7 | — | 2 | 2 | no | — |
| 270 | C2×Dic7 | — | 4 | 1 | no | — |
| 271 | D28 | — | 4 | 2 | no | — |
| 272 | D28 | — | 4 | 2 | no | — |
| 273 | D28 | — | 4 | 2 | no | — |
| 274 | D28 | — | 4 | 2 | no | — |
| 275 | D28 | — | 4 | 2 | no | — |
| 276 | D28 | — | 4 | 2 | no | — |
| 277 | D28 | — | 4 | 1 | no | — |
| 278 | D28 | — | 4 | 1 | no | — |
| 279 | D28 | — | 4 | 1 | no | — |
| 280 | D28 | — | 4 | 1 | no | — |
| 281 | D28 | — | 4 | 2 | no | — |
| 282 | D28 | — | 8 | 4 | no | — |
| 283 | C4×D7 | — | 4 | 4 | no | — |
| 284 | C4×D7 | — | 4 | 4 | no | — |
| 285 | C4×D7 | — | 8 | 2 | no | — |
| 286 | Dic14 | — | 4 | 2 | no | — |
| 287 | Dic14 | — | 4 | 2 | no | — |
| 288 | Dic14 | — | 4 | 2 | no | — |
| 289 | C7×C8 | — | 2 | 4 | no | — |
| 290 | C7×C8 | — | 4 | 2 | no | — |
| 291 | C7⋊C8 | — | 4 | 2 | no | — |
| 292 | C2×#41 | — | 7 | 2 | no | — |
| 293 | C2×#41 | — | 7 | 2 | no | — |
| 294 | C2×#41 | — | 14 | 1 | no | — |
| 295 | C2×#41 | D28 | 1 | 2 | yes | — |
| 296 | C22×D4 | — | 14 | 2 | no | — |
| 297 | C22×D4 | — | 14 | 2 | no | — |
| 298 | C22×D4 | — | 14 | 2 | no | — |
| 299 | #135 | — | 28 | 8 | no | — |
| 300 | C2×Q16 | — | 14 | 2 | no | — |
| 301 | C2×SD16 | — | 14 | 2 | no | — |
| 302 | C2×SD16 | — | 14 | 2 | no | — |
| 303 | C2×SD16 | — | 14 | 2 | no | — |
| 304 | C2×SD16 | — | 14 | 2 | no | — |
| 305 | C2×D8 | — | 14 | 2 | no | — |
| 306 | C2×D8 | — | 14 | 2 | no | — |
| 307 | C2×D8 | — | 14 | 2 | no | — |
| 308 | C22×C8 | — | 2 | 1 | no | — |
| 309 | C4⋊Q8 | — | 7 | 1 | no | — |
| 310 | C4⋊Q8 | — | 7 | 1 | no | — |
| 311 | C4⋊Q8 | — | 7 | 1 | no | — |
| 312 | C4⋊Q8 | D28 | 1 | 1 | yes | characteristic |
| 313 | #127 | — | 7 | 1 | no | — |
| 314 | #127 | — | 7 | 1 | no | — |
| 315 | #127 | — | 7 | 1 | no | — |
| 316 | #127 | — | 14 | 4 | no | — |
| 317 | #127 | D28 | 1 | 1 | yes | characteristic |
| 318 | #124 | — | 7 | 2 | no | — |
| 319 | #124 | — | 7 | 2 | no | — |
| 320 | #124 | — | 14 | 4 | no | — |
| 321 | #124 | — | 14 | 4 | no | — |
| 322 | #124 | — | 14 | 4 | no | — |
| 323 | #124 | — | 14 | 1 | no | — |
| 324 | #124 | C22×D7 | 1 | 2 | yes | — |
| 325 | #121 | — | 2 | 1 | no | — |
| 326 | #121 | — | 2 | 1 | no | — |
| 327 | #121 | — | 14 | 2 | no | — |
| 328 | #121 | — | 14 | 2 | no | — |
| 329 | #121 | — | 14 | 2 | no | — |
| 330 | #121 | — | 14 | 2 | no | — |
| 331 | #121 | — | 14 | 2 | no | — |
| 332 | #121 | — | 14 | 2 | no | — |
| 333 | #121 | — | 14 | 1 | no | — |
| 334 | #121 | — | 14 | 1 | no | — |
| 335 | #121 | — | 14 | 1 | no | — |
| 336 | #121 | — | 14 | 1 | no | — |
| 337 | #121 | — | 14 | 1 | no | — |
| 338 | #121 | — | 14 | 1 | no | — |
| 339 | #120 | — | 14 | 4 | no | — |
| 340 | #120 | — | 14 | 4 | no | — |
| 341 | #120 | — | 14 | 4 | no | — |
| 342 | #120 | — | 14 | 4 | no | — |
| 343 | C4×D4 | — | 2 | 1 | no | — |
| 344 | C4×D4 | — | 2 | 1 | no | — |
| 345 | C4×D4 | — | 14 | 1 | no | — |
| 346 | C4×D4 | — | 14 | 1 | no | — |
| 347 | C4×D4 | — | 14 | 1 | no | — |
| 348 | C4×D4 | — | 14 | 1 | no | — |
| 349 | C4×D4 | — | 14 | 1 | no | — |
| 350 | C4×D4 | — | 14 | 1 | no | — |
| 351 | #117 | — | 14 | 2 | no | — |
| 352 | #117 | — | 14 | 2 | no | — |
| 353 | #117 | — | 14 | 2 | no | — |
| 354 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 355 | C4⋊C8 | — | 2 | 1 | no | — |
| 356 | C4⋊C8 | — | 14 | 1 | no | — |
| 357 | #103 | — | 14 | 2 | no | — |
| 358 | #103 | — | 14 | 2 | no | — |
| 359 | #102 | — | 14 | 2 | no | — |
| 360 | #102 | — | 14 | 2 | no | — |
| 361 | C22⋊C8 | — | 2 | 1 | no | — |
| 362 | C22⋊C8 | — | 14 | 1 | no | — |
| 363 | #97 | — | 2 | 1 | no | — |
| 364 | #97 | — | 7 | 2 | no | — |
| 365 | #97 | C22×D7 | 1 | 2 | yes | — |
| 366 | #97 | C22×D7 | 1 | 2 | yes | — |
| 367 | C22×C7 | — | 2 | 1 | no | — |
| 368 | C22×C7 | — | 2 | 1 | no | — |
| 369 | C22×C7 | — | 2 | 1 | no | — |
| 370 | C22×C7 | — | 4 | 2 | no | — |
| 371 | C22×C7 | — | 4 | 2 | no | — |
| 372 | C22×C7 | — | 4 | 2 | no | — |
| 373 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 374 | C2×D7 | — | 4 | 2 | no | — |
| 375 | C2×D7 | — | 4 | 2 | no | — |
| 376 | C2×D7 | — | 4 | 2 | no | — |
| 377 | C2×D7 | — | 4 | 2 | no | — |
| 378 | C2×D7 | — | 4 | 2 | no | — |
| 379 | C2×D7 | — | 4 | 2 | no | — |
| 380 | C2×D7 | — | 8 | 1 | no | — |
| 381 | C2×D7 | — | 8 | 1 | no | — |
| 382 | C2×D7 | — | 8 | 1 | no | — |
| 383 | C2×D7 | — | 16 | 8 | no | — |
| 384 | C4×C7 | — | 2 | 1 | no | — |
| 385 | C4×C7 | — | 2 | 1 | no | — |
| 386 | C4×C7 | — | 2 | 1 | no | — |
| 387 | C4×C7 | — | 2 | 1 | no | — |
| 388 | C4×C7 | — | 2 | 1 | no | — |
| 389 | C4×C7 | — | 4 | 2 | no | — |
| 390 | C4×C7 | #453 | 1 | 2 | yes | — |
| 391 | Dic7 | — | 4 | 2 | no | — |
| 392 | Dic7 | — | 4 | 2 | no | — |
| 393 | Dic7 | — | 8 | 1 | no | — |
| 394 | C24 | — | 14 | 4 | no | — |
| 395 | #41 | — | 8 | 2 | no | — |
| 396 | #41 | — | 28 | 4 | no | — |
| 397 | #41 | — | 28 | 4 | no | — |
| 398 | #41 | — | 56 | 2 | no | — |
| 399 | C2×Q8 | — | 7 | 2 | no | — |
| 400 | C2×Q8 | — | 7 | 2 | no | — |
| 401 | C2×Q8 | — | 14 | 1 | no | — |
| 402 | C2×Q8 | C2×D28 | 1 | 2 | yes | — |
| 403 | C2×D4 | — | 2 | 2 | no | — |
| 404 | C2×D4 | — | 2 | 1 | no | — |
| 405 | C2×D4 | — | 2 | 1 | no | — |
| 406 | C2×D4 | — | 7 | 2 | no | — |
| 407 | C2×D4 | — | 7 | 2 | no | — |
| 408 | C2×D4 | — | 14 | 4 | no | — |
| 409 | C2×D4 | — | 14 | 4 | no | — |
| 410 | C2×D4 | — | 14 | 4 | no | — |
| 411 | C2×D4 | — | 14 | 2 | no | — |
| 412 | C2×D4 | — | 14 | 2 | no | — |
| 413 | C2×D4 | — | 14 | 1 | no | — |
| 414 | C2×D4 | — | 14 | 1 | no | — |
| 415 | C2×D4 | — | 14 | 1 | no | — |
| 416 | C2×D4 | — | 14 | 1 | no | — |
| 417 | C2×D4 | — | 14 | 1 | no | — |
| 418 | C2×D4 | — | 14 | 1 | no | — |
| 419 | C2×D4 | — | 14 | 1 | no | — |
| 420 | C2×D4 | — | 28 | 1 | no | — |
| 421 | C2×D4 | — | 56 | 4 | no | — |
| 422 | C2×D4 | — | 56 | 4 | no | — |
| 423 | C2×D4 | — | 56 | 4 | no | — |
| 424 | C2×D4 | C2×D28 | 1 | 2 | yes | — |
| 425 | C22×C4 | — | 2 | 2 | no | — |
| 426 | C22×C4 | — | 14 | 2 | no | — |
| 427 | C22×C4 | — | 14 | 2 | no | — |
| 428 | C22×C4 | — | 28 | 1 | no | — |
| 429 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 430 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 431 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 432 | Q16 | — | 28 | 4 | no | — |
| 433 | SD16 | — | 28 | 4 | no | — |
| 434 | SD16 | — | 28 | 4 | no | — |
| 435 | SD16 | — | 56 | 2 | no | — |
| 436 | SD16 | — | 56 | 2 | no | — |
| 437 | D8 | — | 28 | 4 | no | — |
| 438 | D8 | — | 56 | 2 | no | — |
| 439 | D8 | — | 56 | 2 | no | — |
| 440 | C2×C8 | — | 2 | 4 | no | — |
| 441 | C2×C8 | — | 2 | 2 | no | — |
| 442 | C2×C8 | — | 2 | 2 | no | — |
| 443 | C2×C8 | — | 14 | 2 | no | — |
| 444 | C4⋊C4 | — | 2 | 1 | no | — |
| 445 | C4⋊C4 | — | 2 | 1 | no | — |
| 446 | C4⋊C4 | — | 14 | 1 | no | — |
| 447 | C4⋊C4 | — | 14 | 1 | no | — |
| 448 | C4⋊C4 | — | 14 | 1 | no | — |
| 449 | C4⋊C4 | — | 14 | 1 | no | — |
| 450 | C4⋊C4 | — | 14 | 1 | no | — |
| 451 | C4⋊C4 | — | 14 | 1 | no | — |
| 452 | C22⋊C4 | — | 2 | 2 | no | — |
| 453 | C22⋊C4 | — | 2 | 2 | no | — |
| 454 | C22⋊C4 | — | 14 | 4 | no | — |
| 455 | C22⋊C4 | — | 14 | 4 | no | — |
| 456 | C22⋊C4 | — | 14 | 4 | no | — |
| 457 | C22⋊C4 | — | 14 | 2 | no | — |
| 458 | C22⋊C4 | — | 14 | 2 | no | — |
| 459 | C22⋊C4 | — | 14 | 2 | no | — |
| 460 | C22⋊C4 | — | 14 | 2 | no | — |
| 461 | C22⋊C4 | — | 28 | 1 | no | — |
| 462 | C22⋊C4 | — | 28 | 1 | no | — |
| 463 | C42 | — | 14 | 4 | no | — |
| 464 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 465 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 466 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 467 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 468 | C2×C7 | — | 4 | 1 | no | — |
| 469 | C2×C7 | — | 8 | 2 | no | — |
| 470 | C2×C7 | C2×#453 | 1 | 1 | yes | characteristic |
| 471 | C2×C7 | #3019 | 1 | 1 | yes | characteristic |
| 472 | C2×C7 | #3019 | 1 | 1 | yes | characteristic |
| 473 | D7 | — | 8 | 2 | no | — |
| 474 | D7 | — | 8 | 2 | no | — |
| 475 | D7 | — | 16 | 1 | no | — |
| 476 | C23 | — | 2 | 2 | no | — |
| 477 | C23 | — | 14 | 2 | no | — |
| 478 | C23 | — | 14 | 2 | no | — |
| 479 | C23 | — | 28 | 1 | no | — |
| 480 | C23 | — | 56 | 4 | no | — |
| 481 | C23 | — | 56 | 4 | no | — |
| 482 | C23 | — | 56 | 4 | no | — |
| 483 | C23 | #6445 | 1 | 1 | yes | characteristic |
| 484 | Q8 | — | 4 | 2 | no | — |
| 485 | Q8 | — | 28 | 2 | no | — |
| 486 | Q8 | — | 28 | 2 | no | — |
| 487 | Q8 | — | 28 | 2 | no | — |
| 488 | D4 | — | 4 | 2 | no | — |
| 489 | D4 | — | 4 | 2 | no | — |
| 490 | D4 | — | 4 | 2 | no | — |
| 491 | D4 | — | 8 | 2 | no | — |
| 492 | D4 | — | 28 | 2 | no | — |
| 493 | D4 | — | 28 | 2 | no | — |
| 494 | D4 | — | 28 | 2 | no | — |
| 495 | D4 | — | 28 | 2 | no | — |
| 496 | D4 | — | 28 | 2 | no | — |
| 497 | D4 | — | 28 | 2 | no | — |
| 498 | D4 | — | 28 | 1 | no | — |
| 499 | D4 | — | 28 | 1 | no | — |
| 500 | D4 | — | 28 | 1 | no | — |
| 501 | D4 | — | 28 | 1 | no | — |
| 502 | D4 | — | 28 | 2 | no | — |
| 503 | D4 | — | 56 | 4 | no | — |
| 504 | D4 | — | 56 | 2 | no | — |
| 505 | D4 | — | 56 | 2 | no | — |
| 506 | D4 | — | 56 | 4 | no | — |
| 507 | D4 | — | 56 | 4 | no | — |
| 508 | D4 | — | 56 | 2 | no | — |
| 509 | C2×C4 | — | 2 | 2 | no | — |
| 510 | C2×C4 | — | 2 | 2 | no | — |
| 511 | C2×C4 | — | 4 | 1 | no | — |
| 512 | C2×C4 | — | 4 | 1 | no | — |
| 513 | C2×C4 | — | 4 | 4 | no | — |
| 514 | C2×C4 | — | 14 | 2 | no | — |
| 515 | C2×C4 | — | 14 | 2 | no | — |
| 516 | C2×C4 | — | 28 | 4 | no | — |
| 517 | C2×C4 | — | 28 | 4 | no | — |
| 518 | C2×C4 | — | 28 | 1 | no | — |
| 519 | C2×C4 | — | 56 | 2 | no | — |
| 520 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 521 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 522 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 523 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 524 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 526 | C8 | — | 2 | 4 | no | — |
| 527 | C8 | — | 4 | 2 | no | — |
| 528 | C8 | — | 28 | 2 | no | — |
| 529 | C7 | #19052 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 530 | C22 | — | 2 | 1 | no | — |
| 531 | C22 | — | 2 | 1 | no | — |
| 532 | C22 | — | 2 | 1 | no | — |
| 533 | C22 | — | 4 | 2 | no | — |
| 534 | C22 | — | 4 | 2 | no | — |
| 535 | C22 | — | 4 | 2 | no | — |
| 536 | C22 | — | 28 | 2 | no | — |
| 537 | C22 | — | 28 | 2 | no | — |
| 538 | C22 | — | 28 | 2 | no | — |
| 539 | C22 | — | 28 | 2 | no | — |
| 540 | C22 | — | 28 | 2 | no | — |
| 541 | C22 | — | 28 | 2 | no | — |
| 542 | C22 | — | 56 | 1 | no | — |
| 543 | C22 | — | 56 | 1 | no | — |
| 544 | C22 | — | 56 | 1 | no | — |
| 545 | C22 | — | 112 | 8 | no | — |
| 546 | C22 | C2×#6445 | 1 | 1 | yes | characteristic |
| 547 | C4 | — | 2 | 1 | no | — |
| 548 | C4 | — | 2 | 1 | no | — |
| 549 | C4 | — | 2 | 1 | no | — |
| 550 | C4 | — | 2 | 1 | no | — |
| 551 | C4 | — | 2 | 1 | no | — |
| 552 | C4 | — | 4 | 2 | no | — |
| 553 | C4 | — | 28 | 2 | no | — |
| 554 | C4 | — | 28 | 2 | no | — |
| 555 | C4 | — | 56 | 1 | no | — |
| 556 | C4 | #89594 | 1 | 2 | yes | — |
| 557 | C2 | — | 4 | 1 | no | — |
| 558 | C2 | — | 8 | 2 | no | — |
| 559 | C2 | — | 56 | 2 | no | — |
| 560 | C2 | — | 56 | 2 | no | — |
| 561 | C2 | — | 112 | 1 | no | — |
| 562 | C2 | #11736145 | 1 | 1 | yes | characteristic |
| 563 | C2 | C2×#89594 | 1 | 1 | yes | characteristic |
| 564 | C2 | #11736438 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#6445 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#1530 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #1530 | D7 |
| hypocenter | C7 | #19052 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #1530 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11743320 | C2 | semidirect |
| 2. #11740752 | C2 | semidirect |
| 3. #11736795 | C2 | semidirect |
| 4. #11735944 | C2 | semidirect |
| 5. C7×#1530 | C2 | semidirect |
| 6. #11728565 | C2 | semidirect |
| 7. #11727552 | C2 | semidirect |
| 8. #11726106 | C2 | semidirect |
| 9. #11726104 | C2 | semidirect |
| 24. #90168 | C22 | semidirect |
| 25. C7×#432 | C22 | semidirect |
| 26. C2×C7×#97 | C22 | semidirect |
| 30. #89830 | C22 | semidirect |
| 31. #89827 | C22 | semidirect |
| 32. #89698 | C22 | semidirect |
| 37. #89487 | C22 | semidirect |
| 38. #89486 | C22 | semidirect |
| 40. #89484 | C22 | semidirect |
| 41. #89484 | C22 | semidirect |
| 42. C7×#329 | C22 | semidirect |
| 43. #89259 | C22 | semidirect |
| 44. #89259 | C22 | semidirect |
| 129. #1530 | D7 | semidirect |
| 234. #432 | C2×D7 | semidirect |
| 235. C2×#97 | C2×D7 | semidirect |
| 238. #329 | C2×D7 | semidirect |
| 529. C7 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743320 | 2 |
| #11740752 | 2 |
| #11736795 | 2 |
| #11735944 | 2 |
| C7×#1530 | 2 |
| #11728565 | 2 |
| #11727552 | 2 |
| #11726106 | 2 |
| #11726104 | 2 |
| #19052 | 7 |