Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2064 conjugacy classes of subgroups.
The subgroup lattice has 520 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×Q8×D28 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11742870 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×Q8×M16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11737418 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #11737415 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #11737370 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11737369 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11736505 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11736500 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11735973 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C4×#6471 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C22×Q8×D7 | — | 2 | 1 | no | — |
| 13 | C2×C4×C7×Q8 | C22 | 1 | 1 | yes | characteristic |
| 14 | #90508 | — | 2 | 1 | no | — |
| 15 | C2×#6471 | C22 | 1 | 3 | yes | — |
| 16 | #90276 | C22 | 1 | 3 | yes | complemented |
| 17 | #90275 | C22 | 1 | 3 | yes | complemented |
| 18 | #90271 | — | 2 | 3 | no | — |
| 19 | #90268 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | Q8×D28 | — | 2 | 1 | no | — |
| 21 | Q8×D28 | — | 2 | 3 | no | — |
| 22 | Q8×D28 | C22 | 1 | 2 | yes | — |
| 23 | Q8×D28 | C22 | 1 | 6 | yes | — |
| 24 | C4×#1161 | — | 2 | 1 | no | — |
| 25 | #90261 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #90205 | — | 2 | 3 | no | — |
| 27 | C2×#6460 | — | 2 | 3 | no | — |
| 28 | #90168 | C22 | 1 | 3 | yes | — |
| 29 | C4×#1157 | C22 | 1 | 3 | yes | — |
| 30 | C2×C4×D28 | C22 | 1 | 3 | yes | — |
| 31 | C2×#6432 | C22 | 1 | 3 | yes | — |
| 32 | C7×#446 | C22 | 1 | 6 | yes | complemented |
| 33 | C7×C8×Q8 | C22 | 1 | 2 | yes | complemented |
| 34 | C7×#423 | C22 | 1 | 3 | yes | — |
| 35 | C4×C7×M16 | C22 | 1 | 3 | yes | — |
| 36 | #89905 | C22 | 1 | 3 | yes | — |
| 37 | #89905 | C22 | 1 | 6 | yes | — |
| 38 | #89903 | C22 | 1 | 1 | yes | characteristic |
| 39 | #89893 | C22 | 1 | 3 | yes | — |
| 40 | #89623 | C22 | 1 | 6 | yes | complemented |
| 41 | #89622 | C22 | 1 | 6 | yes | complemented |
| 42 | #89618 | C22 | 1 | 6 | yes | complemented |
| 43 | #89616 | C22 | 1 | 12 | yes | — |
| 44 | #89615 | C22 | 1 | 6 | yes | — |
| 45 | #89614 | C22 | 1 | 6 | yes | complemented |
| 46 | #89613 | C22 | 1 | 6 | yes | — |
| 47 | #89486 | C22 | 1 | 12 | yes | complemented |
| 48 | #89483 | C22 | 1 | 6 | yes | — |
| 49 | #89482 | C22 | 1 | 6 | yes | — |
| 50 | #89466 | C22 | 1 | 6 | yes | complemented |
| 51 | C4×D56 | C22 | 1 | 6 | yes | — |
| 52 | C4×#1132 | C22 | 1 | 6 | yes | — |
| 53 | #89453 | C22 | 1 | 6 | yes | complemented |
| 54 | #61317 | — | 7 | 1 | no | maximal, Sylow |
| 55 | C22×C7×Q8 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×#1161 | — | 2 | 1 | no | — |
| 57 | C2×Q8×D7 | — | 2 | 6 | no | — |
| 58 | C2×Q8×D7 | — | 2 | 2 | no | — |
| 59 | C2×Q8×D7 | — | 4 | 8 | no | — |
| 60 | C2×#1157 | C23 | 1 | 3 | yes | — |
| 61 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×C4×D7 | — | 2 | 3 | no | — |
| 63 | C22×Dic14 | — | 2 | 3 | no | — |
| 64 | C2×C7×M16 | C23 | 1 | 3 | yes | — |
| 65 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 66 | C4×C7×Q8 | D4 | 1 | 1 | yes | characteristic |
| 67 | C4×C7×Q8 | D4 | 1 | 3 | yes | — |
| 68 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 69 | C4×C7×Q8 | C23 | 1 | 3 | yes | — |
| 70 | C2×C7×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 71 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 72 | #6510 | — | 2 | 3 | no | — |
| 73 | #6509 | — | 2 | 3 | no | — |
| 74 | Q8×Dic7 | — | 2 | 1 | no | — |
| 75 | #6493 | — | 2 | 3 | no | — |
| 76 | #6493 | — | 2 | 3 | no | — |
| 77 | C4×C22⋊D7 | — | 2 | 3 | no | — |
| 78 | C4×C22⋊D7 | — | 2 | 3 | no | — |
| 79 | C2×(C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 80 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×C4⋊Dic7 | — | 2 | 3 | no | — |
| 82 | C2×C4⋊Dic7 | C23 | 1 | 3 | yes | — |
| 83 | #6471 | — | 2 | 12 | no | — |
| 84 | C2×D56 | C23 | 1 | 6 | yes | — |
| 85 | C2×#1132 | C23 | 1 | 6 | yes | — |
| 86 | #6461 | — | 2 | 6 | no | — |
| 87 | #6460 | — | 2 | 6 | no | — |
| 88 | #6460 | — | 2 | 6 | no | — |
| 89 | #6460 | — | 2 | 12 | no | — |
| 90 | #6458 | — | 2 | 3 | no | — |
| 91 | #6457 | — | 2 | 6 | no | — |
| 92 | #6456 | — | 2 | 3 | no | — |
| 93 | #6455 | — | 2 | 3 | no | — |
| 94 | #6453 | — | 2 | 3 | no | — |
| 95 | #6438 | C23 | 1 | 6 | yes | — |
| 96 | #6437 | C23 | 1 | 3 | yes | — |
| 97 | C4×D28 | — | 2 | 3 | no | — |
| 98 | C4×D28 | — | 2 | 3 | no | — |
| 99 | C4×D28 | — | 2 | 3 | no | — |
| 100 | C4×D28 | — | 2 | 3 | no | — |
| 101 | C4×D28 | C23 | 1 | 6 | yes | — |
| 102 | C4×D28 | C23 | 1 | 3 | yes | — |
| 103 | C4×D28 | C23 | 1 | 6 | yes | — |
| 104 | C4×D28 | C23 | 1 | 3 | yes | — |
| 105 | #6435 | — | 2 | 3 | no | — |
| 106 | C42×D7 | — | 2 | 3 | no | — |
| 107 | #6432 | — | 2 | 3 | no | — |
| 108 | #6432 | — | 2 | 3 | no | — |
| 109 | #6432 | C23 | 1 | 3 | yes | — |
| 110 | #6432 | C23 | 1 | 6 | yes | — |
| 111 | #6432 | C23 | 1 | 6 | yes | — |
| 112 | C4×Dic14 | C23 | 1 | 3 | yes | — |
| 113 | C4×Dic14 | C23 | 1 | 3 | yes | — |
| 114 | C7×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 115 | C7×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 116 | C7×#97 | C23 | 1 | 6 | yes | — |
| 117 | C4×C7×C8 | C23 | 1 | 6 | yes | — |
| 118 | #6395 | C23 | 1 | 12 | yes | — |
| 119 | #6395 | C23 | 1 | 2 | yes | — |
| 120 | #6395 | C23 | 1 | 2 | yes | — |
| 121 | #6395 | C23 | 1 | 6 | yes | — |
| 122 | #6392 | C23 | 1 | 6 | yes | — |
| 123 | #6391 | C23 | 1 | 6 | yes | — |
| 124 | #6390 | C23 | 1 | 12 | yes | — |
| 125 | #6390 | C23 | 1 | 6 | yes | — |
| 126 | #3480 | — | 7 | 1 | no | — |
| 127 | C2×D4×Q8 | — | 7 | 1 | no | — |
| 128 | #3373 | — | 7 | 6 | no | — |
| 129 | #3367 | — | 7 | 6 | no | — |
| 130 | #3359 | — | 7 | 2 | no | — |
| 131 | #3358 | — | 7 | 2 | no | — |
| 132 | #3141 | — | 7 | 3 | no | — |
| 133 | #3079 | — | 7 | 3 | no | — |
| 134 | #3036 | — | 7 | 3 | no | — |
| 135 | Q8×M16 | D7 | 1 | 1 | yes | characteristic, complemented |
| 136 | C4×AGL(1,ℤ/8) | — | 7 | 3 | no | — |
| 137 | C23×D7 | — | 2 | 1 | no | — |
| 138 | C2×C7×Q8 | — | 2 | 4 | no | — |
| 139 | C2×C7×Q8 | C2×D4 | 1 | 3 | yes | — |
| 140 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C22×C4×C7 | C2×D4 | 1 | 3 | yes | — |
| 142 | C22×C4×C7 | C2×D4 | 1 | 3 | yes | — |
| 143 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 144 | C2×C22⋊D7 | — | 2 | 3 | no | — |
| 145 | C22×Dic7 | — | 2 | 3 | no | — |
| 146 | #1161 | — | 4 | 4 | no | — |
| 147 | Q8×D7 | — | 4 | 24 | no | — |
| 148 | Q8×D7 | — | 4 | 8 | no | — |
| 149 | #1157 | — | 2 | 6 | no | — |
| 150 | #1157 | — | 2 | 6 | no | — |
| 151 | C2×D28 | — | 2 | 1 | no | — |
| 152 | C2×D28 | — | 2 | 2 | no | — |
| 153 | C2×D28 | — | 2 | 3 | no | — |
| 154 | C2×D28 | — | 2 | 3 | no | — |
| 155 | C2×D28 | #41 | 1 | 4 | yes | complemented |
| 156 | C2×D28 | C24 | 1 | 3 | yes | — |
| 157 | C2×D28 | C24 | 1 | 2 | yes | — |
| 158 | C2×C4×D7 | — | 2 | 3 | no | — |
| 159 | C2×C4×D7 | — | 2 | 3 | no | — |
| 160 | C2×C4×D7 | — | 2 | 6 | no | — |
| 161 | C2×C4×D7 | — | 2 | 6 | no | — |
| 162 | C2×C4×D7 | — | 2 | 3 | no | — |
| 163 | C2×C4×D7 | — | 4 | 12 | no | — |
| 164 | C2×Dic14 | — | 2 | 6 | no | — |
| 165 | C2×Dic14 | — | 2 | 6 | no | — |
| 166 | C2×Dic14 | — | 4 | 12 | no | — |
| 167 | C2×Dic14 | C24 | 1 | 3 | yes | — |
| 168 | C7×M16 | — | 2 | 6 | no | — |
| 169 | C7×M16 | — | 2 | 2 | no | — |
| 170 | C2×C7×C8 | C24 | 1 | 2 | yes | — |
| 171 | C2×C7×C8 | C24 | 1 | 6 | yes | — |
| 172 | C7×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 173 | C7×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 174 | C7×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 175 | C42×C7 | C2×D4 | 1 | 3 | yes | — |
| 176 | C42×C7 | C2×D4 | 1 | 3 | yes | — |
| 177 | C42×C7 | C24 | 1 | 3 | yes | — |
| 178 | C42×C7 | C24 | 1 | 3 | yes | — |
| 179 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 180 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 181 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 182 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 183 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 184 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 185 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 186 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 187 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 188 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 189 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 190 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 191 | C4⋊Dic7 | C24 | 1 | 1 | yes | characteristic |
| 192 | C4⋊Dic7 | C24 | 1 | 1 | yes | characteristic |
| 193 | C4⋊Dic7 | C24 | 1 | 6 | yes | — |
| 194 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 195 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 196 | C4×Dic7 | — | 2 | 3 | no | — |
| 197 | C4×Dic7 | — | 2 | 3 | no | — |
| 198 | C4×Dic7 | — | 2 | 1 | no | — |
| 199 | D56 | — | 2 | 12 | no | — |
| 200 | #1132 | — | 2 | 12 | no | — |
| 201 | C23×Q8 | — | 14 | 1 | no | — |
| 202 | C2×AGL(1,ℤ/8) | — | 7 | 3 | no | — |
| 203 | #559 | — | 7 | 3 | no | — |
| 204 | #557 | — | 7 | 1 | no | — |
| 205 | #556 | — | 7 | 3 | no | — |
| 206 | #553 | — | 14 | 3 | no | — |
| 207 | #550 | — | 7 | 1 | no | — |
| 208 | D4×Q8 | — | 7 | 2 | no | — |
| 209 | D4×Q8 | — | 7 | 6 | no | — |
| 210 | D4×Q8 | — | 14 | 1 | no | — |
| 211 | D4×Q8 | — | 14 | 3 | no | — |
| 212 | #548 | — | 14 | 1 | no | — |
| 213 | #532 | — | 7 | 3 | no | — |
| 214 | C2×C4⋊Q8 | — | 7 | 3 | no | — |
| 215 | #529 | — | 14 | 3 | no | — |
| 216 | C2×C22⋊Q8 | — | 14 | 3 | no | — |
| 217 | C4×#41 | — | 7 | 3 | no | — |
| 218 | C4×#41 | — | 14 | 1 | no | — |
| 219 | C2×C4×Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 220 | C2×C4×D4 | — | 7 | 3 | no | — |
| 221 | #489 | — | 7 | 12 | no | — |
| 222 | #487 | — | 7 | 6 | no | — |
| 223 | #486 | — | 7 | 6 | no | — |
| 224 | #477 | — | 7 | 6 | no | — |
| 225 | #476 | — | 7 | 6 | no | — |
| 226 | #475 | — | 7 | 6 | no | — |
| 227 | #474 | — | 7 | 6 | no | — |
| 228 | #463 | — | 7 | 12 | no | — |
| 229 | #461 | — | 7 | 6 | no | — |
| 230 | #459 | — | 7 | 6 | no | — |
| 231 | #446 | C2×D7 | 1 | 6 | yes | complemented |
| 232 | C8×Q8 | C2×D7 | 1 | 2 | yes | complemented |
| 233 | #442 | — | 7 | 6 | no | — |
| 234 | #440 | — | 7 | 6 | no | — |
| 235 | C4×SD16 | — | 7 | 6 | no | — |
| 236 | C4×D8 | — | 7 | 6 | no | — |
| 237 | #428 | — | 7 | 3 | no | — |
| 238 | #423 | C2×D7 | 1 | 3 | yes | — |
| 239 | #418 | — | 7 | 1 | no | — |
| 240 | #417 | — | 7 | 6 | no | — |
| 241 | #417 | — | 7 | 3 | no | — |
| 242 | C4×M16 | C2×D7 | 1 | 3 | yes | — |
| 243 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 244 | C22×D7 | — | 2 | 4 | no | — |
| 245 | C22×D7 | — | 2 | 2 | no | — |
| 246 | C22×D7 | — | 2 | 3 | no | — |
| 247 | C22×D7 | — | 4 | 2 | no | — |
| 248 | C22×D7 | — | 4 | 2 | no | — |
| 249 | C7×Q8 | — | 2 | 6 | no | — |
| 250 | C7×Q8 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 251 | C2×C4×C7 | — | 2 | 6 | no | — |
| 252 | C2×C4×C7 | — | 4 | 3 | no | — |
| 253 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 254 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 255 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 256 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 258 | C2×C4×C7 | C2×#41 | 1 | 2 | yes | — |
| 259 | C2×C4×C7 | 2−1+4 | 1 | 2 | yes | — |
| 260 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 261 | C22⋊D7 | — | 4 | 6 | no | — |
| 262 | C2×Dic7 | — | 2 | 1 | no | — |
| 263 | C2×Dic7 | — | 2 | 1 | no | — |
| 264 | C2×Dic7 | — | 2 | 3 | no | — |
| 265 | C2×Dic7 | — | 2 | 6 | no | — |
| 266 | C2×Dic7 | — | 4 | 6 | no | — |
| 267 | D28 | — | 2 | 4 | no | — |
| 268 | D28 | — | 2 | 3 | no | — |
| 269 | D28 | — | 2 | 2 | no | — |
| 270 | D28 | — | 2 | 3 | no | — |
| 271 | D28 | — | 4 | 6 | no | — |
| 272 | D28 | — | 8 | 3 | no | — |
| 273 | D28 | C2×#41 | 1 | 4 | yes | — |
| 274 | C4×D7 | — | 4 | 12 | no | — |
| 275 | C4×D7 | — | 4 | 6 | no | — |
| 276 | C4×D7 | — | 4 | 12 | no | — |
| 277 | C4×D7 | — | 4 | 6 | no | — |
| 278 | C4×D7 | — | 8 | 3 | no | — |
| 279 | Dic14 | — | 2 | 3 | no | — |
| 280 | Dic14 | — | 2 | 3 | no | — |
| 281 | Dic14 | — | 4 | 12 | no | — |
| 282 | Dic14 | — | 4 | 12 | no | — |
| 283 | C7×C8 | — | 2 | 6 | no | — |
| 284 | C7×C8 | — | 2 | 2 | no | — |
| 285 | C2×#41 | — | 7 | 3 | no | — |
| 286 | C2×#41 | — | 14 | 1 | no | — |
| 287 | C22×Q8 | — | 14 | 6 | no | — |
| 288 | C22×Q8 | — | 14 | 2 | no | — |
| 289 | C22×Q8 | — | 14 | 3 | no | — |
| 290 | C22×Q8 | — | 28 | 8 | no | — |
| 291 | C22×Q8 | D28 | 1 | 1 | yes | characteristic |
| 292 | C22×D4 | — | 7 | 1 | no | — |
| 293 | C23×C4 | — | 14 | 3 | no | — |
| 294 | AGL(1,ℤ/8) | — | 14 | 12 | no | — |
| 295 | C2×SD16 | — | 7 | 6 | no | — |
| 296 | C2×D8 | — | 7 | 6 | no | — |
| 297 | C2×M16 | C22×D7 | 1 | 3 | yes | — |
| 298 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 299 | C4⋊Q8 | — | 7 | 6 | no | — |
| 300 | C4⋊Q8 | — | 7 | 6 | no | — |
| 301 | C4⋊Q8 | — | 7 | 3 | no | — |
| 302 | C4⋊Q8 | — | 14 | 3 | no | — |
| 303 | C4⋊Q8 | — | 14 | 3 | no | — |
| 304 | #127 | — | 7 | 3 | no | — |
| 305 | #126 | — | 14 | 6 | no | — |
| 306 | #125 | — | 14 | 3 | no | — |
| 307 | #124 | — | 7 | 6 | no | — |
| 308 | #124 | — | 14 | 3 | no | — |
| 309 | #123 | — | 14 | 6 | no | — |
| 310 | C22⋊Q8 | — | 14 | 3 | no | — |
| 311 | C22⋊Q8 | — | 14 | 6 | no | — |
| 312 | C22⋊Q8 | — | 14 | 6 | no | — |
| 313 | C22⋊Q8 | — | 14 | 12 | no | — |
| 314 | #121 | — | 14 | 3 | no | — |
| 315 | #121 | — | 14 | 3 | no | — |
| 316 | #121 | — | 14 | 3 | no | — |
| 317 | C4×Q8 | — | 7 | 3 | no | — |
| 318 | C4×Q8 | — | 7 | 3 | no | — |
| 319 | C4×Q8 | — | 14 | 1 | no | — |
| 320 | C4×Q8 | D28 | 1 | 1 | yes | characteristic |
| 321 | C4×Q8 | D28 | 1 | 3 | yes | — |
| 322 | C4×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 323 | C4×Q8 | C22×D7 | 1 | 3 | yes | — |
| 324 | C4×D4 | — | 7 | 6 | no | — |
| 325 | C4×D4 | — | 7 | 6 | no | — |
| 326 | C4×D4 | — | 7 | 3 | no | — |
| 327 | C4×D4 | — | 7 | 3 | no | — |
| 328 | C4×D4 | — | 14 | 3 | no | — |
| 329 | C4×D4 | — | 14 | 3 | no | — |
| 330 | C4×D4 | — | 14 | 3 | no | — |
| 331 | C4×D4 | — | 14 | 3 | no | — |
| 332 | C4×D4 | — | 14 | 3 | no | — |
| 333 | C4×D4 | — | 14 | 3 | no | — |
| 334 | C4×D4 | — | 14 | 3 | no | — |
| 335 | #117 | — | 7 | 1 | no | — |
| 336 | #117 | — | 14 | 3 | no | — |
| 337 | #117 | — | 14 | 3 | no | — |
| 338 | C2×C4⋊C4 | — | 7 | 3 | no | — |
| 339 | C2×C4⋊C4 | — | 14 | 3 | no | — |
| 340 | C2×C4⋊C4 | D28 | 1 | 3 | yes | — |
| 341 | C2×C22⋊C4 | — | 14 | 3 | no | — |
| 342 | C2×C42 | — | 14 | 3 | no | — |
| 343 | C2×C42 | C22×D7 | 1 | 3 | yes | — |
| 344 | #107 | — | 7 | 6 | no | — |
| 345 | #106 | — | 7 | 6 | no | — |
| 346 | C4⋊C8 | C22×D7 | 1 | 6 | yes | — |
| 347 | C4⋊C8 | C22×D7 | 1 | 6 | yes | — |
| 348 | #103 | — | 7 | 6 | no | — |
| 349 | #103 | — | 7 | 12 | no | — |
| 350 | #102 | — | 7 | 6 | no | — |
| 351 | #102 | — | 7 | 12 | no | — |
| 352 | #102 | — | 7 | 2 | no | — |
| 353 | #102 | — | 7 | 2 | no | — |
| 354 | #97 | C22×D7 | 1 | 6 | yes | — |
| 355 | C4×C8 | C22×D7 | 1 | 6 | yes | — |
| 356 | C22×C7 | — | 2 | 1 | no | — |
| 357 | C22×C7 | — | 2 | 1 | no | — |
| 358 | C22×C7 | #548 | 1 | 2 | yes | — |
| 359 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 360 | C2×D7 | — | 2 | 4 | no | — |
| 361 | C2×D7 | — | 4 | 8 | no | — |
| 362 | C2×D7 | — | 4 | 2 | no | — |
| 363 | C2×D7 | — | 4 | 2 | no | — |
| 364 | C2×D7 | — | 4 | 3 | no | — |
| 365 | C2×D7 | — | 4 | 3 | no | — |
| 366 | C2×D7 | — | 4 | 3 | no | — |
| 367 | C4×C7 | — | 2 | 3 | no | — |
| 368 | C4×C7 | — | 2 | 3 | no | — |
| 369 | C4×C7 | — | 2 | 3 | no | — |
| 370 | C4×C7 | #548 | 1 | 2 | yes | — |
| 371 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 372 | C4×C7 | C22×#41 | 1 | 1 | yes | characteristic |
| 373 | C4×C7 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 374 | Dic7 | — | 4 | 1 | no | — |
| 375 | Dic7 | — | 4 | 3 | no | — |
| 376 | Dic7 | — | 4 | 6 | no | — |
| 377 | Dic7 | — | 4 | 1 | no | — |
| 378 | C24 | — | 14 | 1 | no | — |
| 379 | #41 | — | 14 | 6 | no | — |
| 380 | #41 | — | 14 | 6 | no | — |
| 381 | #41 | — | 28 | 4 | no | — |
| 382 | C2×Q8 | — | 2 | 4 | no | — |
| 383 | C2×Q8 | — | 7 | 3 | no | — |
| 384 | C2×Q8 | — | 14 | 6 | no | — |
| 385 | C2×Q8 | — | 14 | 6 | no | — |
| 386 | C2×Q8 | — | 28 | 12 | no | — |
| 387 | C2×Q8 | — | 28 | 24 | no | — |
| 388 | C2×Q8 | — | 28 | 8 | no | — |
| 389 | C2×Q8 | C2×D28 | 1 | 3 | yes | — |
| 390 | C2×Q8 | C2×D28 | 1 | 1 | yes | characteristic |
| 391 | C2×D4 | — | 7 | 4 | no | — |
| 392 | C2×D4 | — | 7 | 2 | no | — |
| 393 | C2×D4 | — | 7 | 3 | no | — |
| 394 | C2×D4 | — | 14 | 3 | no | — |
| 395 | C2×D4 | — | 14 | 1 | no | — |
| 396 | C2×D4 | — | 14 | 3 | no | — |
| 397 | C2×D4 | — | 14 | 3 | no | — |
| 398 | C2×D4 | — | 14 | 2 | no | — |
| 399 | C22×C4 | — | 14 | 3 | no | — |
| 400 | C22×C4 | — | 14 | 3 | no | — |
| 401 | C22×C4 | — | 14 | 3 | no | — |
| 402 | C22×C4 | — | 14 | 6 | no | — |
| 403 | C22×C4 | — | 14 | 6 | no | — |
| 404 | C22×C4 | — | 14 | 3 | no | — |
| 405 | C22×C4 | — | 28 | 12 | no | — |
| 406 | C22×C4 | C2×D28 | 1 | 3 | yes | — |
| 407 | C22×C4 | C2×D28 | 1 | 3 | yes | — |
| 408 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 409 | SD16 | — | 14 | 12 | no | — |
| 410 | D8 | — | 14 | 12 | no | — |
| 411 | M16 | — | 2 | 2 | no | — |
| 412 | M16 | — | 2 | 6 | no | — |
| 413 | C2×C8 | C23×D7 | 1 | 2 | yes | — |
| 414 | C2×C8 | C23×D7 | 1 | 6 | yes | — |
| 415 | C4⋊C4 | — | 7 | 6 | no | — |
| 416 | C4⋊C4 | — | 7 | 1 | no | — |
| 417 | C4⋊C4 | — | 7 | 1 | no | — |
| 418 | C4⋊C4 | — | 14 | 3 | no | — |
| 419 | C4⋊C4 | — | 14 | 3 | no | — |
| 420 | C4⋊C4 | — | 14 | 3 | no | — |
| 421 | C4⋊C4 | — | 14 | 6 | no | — |
| 422 | C4⋊C4 | — | 14 | 6 | no | — |
| 423 | C4⋊C4 | — | 14 | 3 | no | — |
| 424 | C4⋊C4 | — | 14 | 3 | no | — |
| 425 | C4⋊C4 | C2×D28 | 1 | 3 | yes | — |
| 426 | C4⋊C4 | C2×D28 | 1 | 3 | yes | — |
| 427 | C4⋊C4 | C2×D28 | 1 | 6 | yes | — |
| 428 | C22⋊C4 | — | 14 | 1 | no | — |
| 429 | C22⋊C4 | — | 14 | 6 | no | — |
| 430 | C22⋊C4 | — | 14 | 6 | no | — |
| 431 | C22⋊C4 | — | 14 | 3 | no | — |
| 432 | C22⋊C4 | — | 14 | 3 | no | — |
| 433 | C22⋊C4 | — | 14 | 6 | no | — |
| 434 | C22⋊C4 | — | 14 | 6 | no | — |
| 435 | C42 | — | 14 | 1 | no | — |
| 436 | C42 | — | 14 | 3 | no | — |
| 437 | C42 | — | 14 | 3 | no | — |
| 438 | C42 | C2×D28 | 1 | 3 | yes | — |
| 439 | C42 | C2×D28 | 1 | 3 | yes | — |
| 440 | C42 | C23×D7 | 1 | 3 | yes | — |
| 441 | C42 | C23×D7 | 1 | 3 | yes | — |
| 442 | C2×C7 | — | 2 | 2 | no | — |
| 443 | C2×C7 | C2×#548 | 1 | 1 | yes | characteristic |
| 444 | C2×C7 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 445 | C2×C7 | #3586 | 1 | 1 | yes | characteristic |
| 446 | D7 | — | 4 | 4 | no | — |
| 447 | D7 | — | 8 | 3 | no | — |
| 448 | C23 | — | 14 | 4 | no | — |
| 449 | C23 | — | 14 | 2 | no | — |
| 450 | C23 | — | 14 | 3 | no | — |
| 451 | C23 | — | 28 | 2 | no | — |
| 452 | C23 | — | 28 | 2 | no | — |
| 453 | C23 | C22×D28 | 1 | 1 | yes | characteristic |
| 454 | Q8 | — | 2 | 6 | no | — |
| 455 | Q8 | — | 14 | 3 | no | — |
| 456 | Q8 | — | 14 | 3 | no | — |
| 457 | Q8 | — | 28 | 12 | no | — |
| 458 | Q8 | — | 28 | 12 | no | — |
| 459 | Q8 | #6471 | 1 | 4 | yes | complemented |
| 460 | D4 | — | 7 | 4 | no | — |
| 461 | D4 | — | 14 | 4 | no | — |
| 462 | D4 | — | 14 | 2 | no | — |
| 463 | D4 | — | 14 | 3 | no | — |
| 464 | D4 | — | 14 | 3 | no | — |
| 465 | D4 | — | 28 | 6 | no | — |
| 466 | D4 | — | 28 | 6 | no | — |
| 467 | D4 | — | 56 | 3 | no | — |
| 468 | C2×C4 | — | 2 | 6 | no | — |
| 469 | C2×C4 | — | 4 | 3 | no | — |
| 470 | C2×C4 | — | 14 | 1 | no | — |
| 471 | C2×C4 | — | 14 | 1 | no | — |
| 472 | C2×C4 | — | 14 | 3 | no | — |
| 473 | C2×C4 | — | 14 | 6 | no | — |
| 474 | C2×C4 | — | 28 | 12 | no | — |
| 475 | C2×C4 | — | 28 | 6 | no | — |
| 476 | C2×C4 | — | 28 | 12 | no | — |
| 477 | C2×C4 | — | 28 | 6 | no | — |
| 478 | C2×C4 | — | 28 | 6 | no | — |
| 479 | C2×C4 | — | 56 | 3 | no | — |
| 480 | C2×C4 | C22×D28 | 1 | 3 | yes | — |
| 481 | C2×C4 | C22×D28 | 1 | 3 | yes | — |
| 482 | C2×C4 | C22×D28 | 1 | 3 | yes | — |
| 483 | C2×C4 | C22×D28 | 1 | 3 | yes | — |
| 484 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 485 | C2×C4 | #6551 | 1 | 2 | yes | — |
| 486 | C2×C4 | D7×#41 | 1 | 2 | yes | — |
| 487 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 488 | C8 | — | 2 | 2 | no | — |
| 489 | C8 | — | 2 | 6 | no | — |
| 490 | C7 | #61317 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 491 | C22 | — | 2 | 1 | no | — |
| 492 | C22 | — | 2 | 1 | no | — |
| 493 | C22 | — | 14 | 4 | no | — |
| 494 | C22 | — | 28 | 8 | no | — |
| 495 | C22 | — | 28 | 2 | no | — |
| 496 | C22 | — | 28 | 2 | no | — |
| 497 | C22 | — | 28 | 3 | no | — |
| 498 | C22 | — | 28 | 3 | no | — |
| 499 | C22 | — | 28 | 3 | no | — |
| 500 | C22 | #90267 | 1 | 2 | yes | — |
| 501 | C22 | C23×D28 | 1 | 1 | yes | characteristic |
| 502 | C4 | — | 2 | 3 | no | — |
| 503 | C4 | — | 2 | 3 | no | — |
| 504 | C4 | — | 2 | 3 | no | — |
| 505 | C4 | — | 28 | 3 | no | — |
| 506 | C4 | — | 28 | 6 | no | — |
| 507 | C4 | — | 28 | 1 | no | — |
| 508 | C4 | — | 28 | 1 | no | — |
| 509 | C4 | #90267 | 1 | 2 | yes | — |
| 510 | C4 | C2×#6471 | 1 | 6 | yes | — |
| 511 | C4 | C2×#6551 | 1 | 1 | yes | characteristic |
| 512 | C4 | C2×D7×#41 | 1 | 1 | yes | characteristic |
| 513 | C2 | — | 2 | 2 | no | — |
| 514 | C2 | — | 28 | 4 | no | — |
| 515 | C2 | — | 56 | 3 | no | — |
| 516 | C2 | C2×#90267 | 1 | 1 | yes | characteristic |
| 517 | C2 | C22×#6471 | 1 | 1 | yes | characteristic |
| 518 | C2 | #11744236 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D28 | C2 | semidirect |
| 2. #11742870 | C2 | semidirect |
| 3. C7×Q8×M16 | C2 | semidirect |
| 4. #11737418 | C2 | semidirect |
| 5. #11737415 | C2 | semidirect |
| 6. #11737370 | C2 | semidirect |
| 7. #11737369 | C2 | semidirect |
| 8. #11736505 | C2 | semidirect |
| 9. #11736500 | C2 | semidirect |
| 10. #11735973 | C2 | semidirect |
| 11. C4×#6471 | C2 | semidirect |
| 16. #90276 | C22 | semidirect |
| 17. #90275 | C22 | semidirect |
| 19. #90268 | C22 | semidirect |
| 25. #90261 | C22 | semidirect |
| 32. C7×#446 | C22 | semidirect |
| 33. C7×C8×Q8 | C22 | semidirect |
| 40. #89623 | C22 | semidirect |
| 41. #89622 | C22 | semidirect |
| 42. #89618 | C22 | semidirect |
| 45. #89614 | C22 | semidirect |
| 47. #89486 | C22 | semidirect |
| 50. #89466 | C22 | semidirect |
| 53. #89453 | C22 | semidirect |
| 135. Q8×M16 | D7 | semidirect |
| 155. C2×D28 | #41 | semidirect |
| 231. #446 | C2×D7 | semidirect |
| 232. C8×Q8 | C2×D7 | semidirect |
| 250. C7×Q8 | AGL(1,ℤ/8) | semidirect |
| 459. Q8 | #6471 | semidirect |
| 490. C7 | #61317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D28 | 2 |
| #11742870 | 2 |
| C7×Q8×M16 | 2 |
| #11737418 | 2 |
| #11737415 | 2 |
| #11737370 | 2 |
| #11737369 | 2 |
| #11736505 | 2 |
| #11736500 | 2 |
| #11735973 | 2 |
| C4×#6471 | 2 |
| #61317 | 7 |