← #13367674
Subgroups — #13367674
Order 1792.
846 conjugacy classes of subgroups.
The subgroup lattice has 286 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11735912 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11735903 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C7×#1744 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11727545 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11727149 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11726449 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | C2×#6467 | C22 | 1 | 4 | yes | — |
| 8 | C2×#6464 | C22 | 1 | 4 | yes | — |
| 9 | #90168 | C22 | 1 | 2 | yes | — |
| 10 | C2×C4×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C4×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 12 | C43×C7 | C22 | 1 | 1 | yes | characteristic |
| 13 | #89882 | C22 | 1 | 4 | yes | — |
| 14 | C2×#6379 | C22 | 1 | 8 | yes | — |
| 15 | #89696 | C22 | 1 | 2 | yes | — |
| 16 | #89471 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #89468 | C4 | 1 | 4 | yes | complemented |
| 18 | #89467 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #89465 | C4 | 1 | 2 | yes | complemented |
| 20 | #89460 | — | 2 | 2 | no | — |
| 21 | #89460 | — | 2 | 2 | no | — |
| 22 | C8×D28 | — | 2 | 2 | no | — |
| 23 | C8×D28 | — | 2 | 2 | no | — |
| 24 | C7×#336 | C22 | 1 | 4 | yes | — |
| 25 | #89347 | C22 | 1 | 4 | yes | — |
| 26 | #22280 | — | 7 | 1 | no | maximal, Sylow |
| 27 | C2×#1157 | C23 | 1 | 4 | yes | — |
| 28 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 29 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 30 | C2×C42×C7 | — | 2 | 1 | no | — |
| 31 | C2×C42×C7 | — | 2 | 1 | no | — |
| 32 | C2×C42×C7 | C23 | 1 | 2 | yes | — |
| 33 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 34 | #6493 | — | 2 | 2 | no | — |
| 35 | #6493 | — | 2 | 2 | no | — |
| 36 | C2×#1136 | C23 | 1 | 4 | yes | — |
| 37 | C2×Dic28 | C2×C4 | 1 | 4 | yes | — |
| 38 | #6467 | — | 4 | 8 | no | — |
| 39 | C2×D56 | C2×C4 | 1 | 4 | yes | — |
| 40 | C2×#1132 | C2×C4 | 1 | 8 | yes | — |
| 41 | #6464 | — | 4 | 8 | no | — |
| 42 | C2×#1131 | — | 2 | 4 | no | — |
| 43 | C2×C8×D7 | — | 2 | 4 | no | — |
| 44 | #6438 | C2×C4 | 1 | 4 | yes | — |
| 45 | #6437 | C2×C4 | 1 | 2 | yes | — |
| 46 | C4×D28 | — | 2 | 2 | no | — |
| 47 | C4×D28 | — | 2 | 2 | no | — |
| 48 | #6432 | C2×C4 | 1 | 2 | yes | — |
| 49 | C4×C7×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C4×C7×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C4×C7×C8 | C2×C4 | 1 | 2 | yes | — |
| 52 | C4×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 53 | C4×C7×C8 | D4 | 1 | 2 | yes | — |
| 54 | C4×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 55 | (C2×D7)⋊C8 | — | 2 | 4 | no | — |
| 56 | (C2×D7)⋊C8 | — | 2 | 4 | no | — |
| 57 | #6379 | — | 4 | 8 | no | — |
| 58 | C4⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 59 | C4⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 60 | #3147 | — | 7 | 1 | no | — |
| 61 | #2931 | — | 7 | 2 | no | — |
| 62 | #1962 | — | 7 | 2 | no | — |
| 63 | #1876 | — | 7 | 8 | no | — |
| 64 | #1837 | — | 7 | 1 | no | — |
| 65 | #1744 | D7 | 1 | 1 | yes | characteristic, complemented |
| 66 | C22×C4×C7 | — | 2 | 2 | no | — |
| 67 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 68 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 69 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 70 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 71 | #1157 | — | 2 | 8 | no | — |
| 72 | #1157 | — | 2 | 8 | no | — |
| 73 | C2×D28 | — | 2 | 2 | no | — |
| 74 | C2×D28 | — | 2 | 2 | no | — |
| 75 | C2×D28 | C22×C4 | 1 | 4 | yes | — |
| 76 | C2×C4×D7 | — | 2 | 4 | no | — |
| 77 | C2×Dic14 | C22×C4 | 1 | 4 | yes | — |
| 78 | C2×C7×C8 | — | 2 | 4 | no | — |
| 79 | C2×C7×C8 | — | 2 | 4 | no | — |
| 80 | C2×C7×C8 | C22×C4 | 1 | 2 | yes | — |
| 81 | C2×C7×C8 | C22×C4 | 1 | 2 | yes | — |
| 82 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 83 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 84 | C42×C7 | — | 2 | 4 | no | — |
| 85 | C42×C7 | — | 2 | 4 | no | — |
| 86 | C42×C7 | — | 4 | 2 | no | — |
| 87 | C42×C7 | C22×C4 | 1 | 1 | yes | characteristic |
| 88 | C42×C7 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 92 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 93 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 94 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 95 | #1136 | — | 2 | 8 | no | — |
| 96 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 97 | Dic28 | — | 4 | 4 | no | — |
| 98 | D56 | — | 4 | 4 | no | — |
| 99 | #1132 | — | 4 | 8 | no | — |
| 100 | #1131 | — | 4 | 8 | no | — |
| 101 | C8×D7 | — | 4 | 8 | no | — |
| 102 | C2×#135 | — | 7 | 4 | no | — |
| 103 | C2×#131 | — | 7 | 4 | no | — |
| 104 | #532 | — | 7 | 2 | no | — |
| 105 | #495 | — | 7 | 4 | no | — |
| 106 | #494 | — | 7 | 1 | no | — |
| 107 | #493 | — | 7 | 1 | no | — |
| 108 | #492 | — | 7 | 2 | no | — |
| 109 | #436 | — | 14 | 2 | no | — |
| 110 | #436 | — | 14 | 2 | no | — |
| 111 | C8×D4 | — | 14 | 2 | no | — |
| 112 | C8×D4 | — | 14 | 2 | no | — |
| 113 | #423 | — | 7 | 2 | no | — |
| 114 | C2×#104 | — | 7 | 8 | no | — |
| 115 | #408 | — | 7 | 4 | no | — |
| 116 | C2×C4×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 117 | C2×C4×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 118 | C43 | C2×D7 | 1 | 1 | yes | characteristic |
| 119 | #341 | — | 7 | 4 | no | — |
| 120 | #336 | C2×D7 | 1 | 4 | yes | — |
| 121 | C23×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 122 | C22×D7 | — | 2 | 4 | no | — |
| 123 | C2×C4×C7 | — | 2 | 2 | no | — |
| 124 | C2×C4×C7 | — | 2 | 2 | no | — |
| 125 | C2×C4×C7 | — | 2 | 4 | no | — |
| 126 | C2×C4×C7 | — | 4 | 2 | no | — |
| 127 | C2×C4×C7 | — | 4 | 2 | no | — |
| 128 | C2×C4×C7 | C4×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×C4×C7 | C4×D4 | 1 | 1 | yes | characteristic |
| 130 | C2×C4×C7 | C4×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C7 | C4×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×C4×C7 | C23×C4 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C7 | H(5,𝔽2) | 1 | 4 | yes | — |
| 135 | C22⋊D7 | — | 4 | 8 | no | — |
| 136 | C2×Dic7 | — | 2 | 4 | no | — |
| 137 | D28 | — | 2 | 8 | no | — |
| 138 | D28 | — | 4 | 4 | no | — |
| 139 | D28 | — | 4 | 4 | no | — |
| 140 | C4×D7 | — | 4 | 4 | no | — |
| 141 | C4×D7 | — | 4 | 4 | no | — |
| 142 | Dic14 | — | 2 | 8 | no | — |
| 143 | C7×C8 | — | 2 | 2 | no | — |
| 144 | C7×C8 | — | 2 | 2 | no | — |
| 145 | C7×C8 | — | 2 | 2 | no | — |
| 146 | C7×C8 | — | 2 | 2 | no | — |
| 147 | C7⋊C8 | — | 4 | 4 | no | — |
| 148 | C2×#41 | — | 7 | 4 | no | — |
| 149 | #135 | — | 28 | 8 | no | — |
| 150 | C2×Q16 | — | 7 | 4 | no | — |
| 151 | C2×SD16 | — | 7 | 8 | no | — |
| 152 | C2×D8 | — | 7 | 4 | no | — |
| 153 | #131 | — | 28 | 8 | no | — |
| 154 | C2×M16 | — | 7 | 4 | no | — |
| 155 | C2×M16 | — | 14 | 4 | no | — |
| 156 | C22×C8 | — | 14 | 4 | no | — |
| 157 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 158 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 159 | C4⋊Q8 | — | 7 | 2 | no | — |
| 160 | #127 | — | 7 | 2 | no | — |
| 161 | #124 | — | 7 | 4 | no | — |
| 162 | #121 | — | 14 | 2 | no | — |
| 163 | #121 | — | 14 | 2 | no | — |
| 164 | C4×D4 | — | 14 | 2 | no | — |
| 165 | C4×D4 | — | 14 | 2 | no | — |
| 166 | C2×C42 | — | 2 | 1 | no | — |
| 167 | C2×C42 | — | 2 | 1 | no | — |
| 168 | C2×C42 | C22×D7 | 1 | 2 | yes | — |
| 169 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 170 | C4⋊C8 | — | 14 | 2 | no | — |
| 171 | C4⋊C8 | — | 14 | 2 | no | — |
| 172 | #104 | — | 28 | 8 | no | — |
| 173 | C22⋊C8 | — | 14 | 4 | no | — |
| 174 | C22⋊C8 | — | 14 | 4 | no | — |
| 175 | C4×C8 | C4×D7 | 1 | 1 | yes | characteristic |
| 176 | C4×C8 | C4×D7 | 1 | 1 | yes | characteristic |
| 177 | C4×C8 | C4×D7 | 1 | 2 | yes | — |
| 178 | C4×C8 | D28 | 1 | 1 | yes | characteristic |
| 179 | C4×C8 | D28 | 1 | 2 | yes | — |
| 180 | C4×C8 | D28 | 1 | 1 | yes | characteristic |
| 181 | C22×C7 | — | 2 | 1 | no | — |
| 182 | C22×C7 | — | 2 | 1 | no | — |
| 183 | C22×C7 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 184 | C22×C7 | #540 | 1 | 2 | yes | — |
| 185 | C2×D7 | — | 4 | 4 | no | — |
| 186 | C2×D7 | — | 4 | 4 | no | — |
| 187 | C2×D7 | — | 4 | 4 | no | — |
| 188 | C4×C7 | — | 2 | 1 | no | — |
| 189 | C4×C7 | — | 2 | 1 | no | — |
| 190 | C4×C7 | — | 4 | 4 | no | — |
| 191 | C4×C7 | #443 | 1 | 2 | yes | — |
| 192 | C4×C7 | #444 | 1 | 2 | yes | — |
| 193 | C4×C7 | #518 | 1 | 2 | yes | — |
| 194 | C4×C7 | #535 | 1 | 2 | yes | — |
| 195 | Dic7 | — | 4 | 4 | no | — |
| 196 | #41 | — | 14 | 8 | no | — |
| 197 | #41 | — | 14 | 8 | no | — |
| 198 | C2×Q8 | — | 7 | 4 | no | — |
| 199 | C2×D4 | — | 7 | 4 | no | — |
| 200 | C2×D4 | — | 14 | 4 | no | — |
| 201 | C2×D4 | — | 14 | 2 | no | — |
| 202 | C2×D4 | — | 14 | 2 | no | — |
| 203 | C22×C4 | — | 2 | 2 | no | — |
| 204 | C22×C4 | — | 14 | 4 | no | — |
| 205 | C22×C4 | #1157 | 1 | 1 | yes | characteristic |
| 206 | C22×C4 | #1157 | 1 | 1 | yes | characteristic |
| 207 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 208 | Q16 | — | 28 | 4 | no | — |
| 209 | SD16 | — | 28 | 8 | no | — |
| 210 | D8 | — | 28 | 4 | no | — |
| 211 | M16 | — | 14 | 8 | no | — |
| 212 | M16 | — | 28 | 8 | no | — |
| 213 | C2×C8 | — | 2 | 4 | no | — |
| 214 | C2×C8 | — | 2 | 4 | no | — |
| 215 | C2×C8 | — | 14 | 4 | no | — |
| 216 | C2×C8 | — | 28 | 8 | no | — |
| 217 | C2×C8 | C2×C4×D7 | 1 | 2 | yes | — |
| 218 | C2×C8 | C2×C4×D7 | 1 | 2 | yes | — |
| 219 | C2×C8 | C2×D28 | 1 | 2 | yes | — |
| 220 | C2×C8 | C2×D28 | 1 | 2 | yes | — |
| 221 | C4⋊C4 | — | 14 | 2 | no | — |
| 222 | C4⋊C4 | — | 14 | 2 | no | — |
| 223 | C22⋊C4 | — | 14 | 4 | no | — |
| 224 | C22⋊C4 | — | 14 | 4 | no | — |
| 225 | C42 | — | 2 | 4 | no | — |
| 226 | C42 | — | 2 | 4 | no | — |
| 227 | C42 | — | 4 | 2 | no | — |
| 228 | C42 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 229 | C42 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 230 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 231 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 232 | C2×C7 | — | 2 | 2 | no | — |
| 233 | C2×C7 | #2328 | 1 | 1 | yes | characteristic |
| 234 | C2×C7 | C2×#443 | 1 | 1 | yes | characteristic |
| 235 | C2×C7 | C2×#444 | 1 | 1 | yes | characteristic |
| 236 | D7 | — | 8 | 4 | no | — |
| 237 | C23 | — | 14 | 4 | no | — |
| 238 | C23 | C2×#1157 | 1 | 1 | yes | characteristic |
| 239 | Q8 | — | 14 | 8 | no | — |
| 240 | D4 | — | 14 | 8 | no | — |
| 241 | D4 | — | 28 | 8 | no | — |
| 242 | D4 | — | 28 | 4 | no | — |
| 243 | D4 | — | 28 | 4 | no | — |
| 244 | C2×C4 | — | 2 | 2 | no | — |
| 245 | C2×C4 | — | 2 | 2 | no | — |
| 246 | C2×C4 | — | 2 | 4 | no | — |
| 247 | C2×C4 | — | 4 | 2 | no | — |
| 248 | C2×C4 | — | 4 | 2 | no | — |
| 249 | C2×C4 | — | 14 | 4 | no | — |
| 250 | C2×C4 | — | 28 | 4 | no | — |
| 251 | C2×C4 | — | 28 | 4 | no | — |
| 252 | C2×C4 | C4×D28 | 1 | 1 | yes | characteristic |
| 253 | C2×C4 | C4×D28 | 1 | 1 | yes | characteristic |
| 254 | C2×C4 | C4×D28 | 1 | 1 | yes | characteristic |
| 255 | C2×C4 | C4×D28 | 1 | 1 | yes | characteristic |
| 256 | C2×C4 | C22×C4×D7 | 1 | 1 | yes | characteristic |
| 257 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 258 | C2×C4 | #6553 | 1 | 4 | yes | — |
| 259 | C8 | — | 2 | 2 | no | — |
| 260 | C8 | — | 2 | 2 | no | — |
| 261 | C8 | — | 2 | 2 | no | — |
| 262 | C8 | — | 2 | 2 | no | — |
| 263 | C8 | — | 28 | 4 | no | — |
| 264 | C7 | #22280 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 265 | C22 | — | 2 | 1 | no | — |
| 266 | C22 | — | 2 | 1 | no | — |
| 267 | C22 | — | 28 | 4 | no | — |
| 268 | C22 | — | 28 | 4 | no | — |
| 269 | C22 | — | 28 | 4 | no | — |
| 270 | C22 | C2×C4×D28 | 1 | 1 | yes | characteristic |
| 271 | C22 | #90226 | 1 | 2 | yes | — |
| 272 | C4 | — | 2 | 1 | no | — |
| 273 | C4 | — | 2 | 1 | no | — |
| 274 | C4 | — | 4 | 4 | no | — |
| 275 | C4 | — | 28 | 4 | no | — |
| 276 | C4 | #89472 | 1 | 2 | yes | — |
| 277 | C4 | #89489 | 1 | 2 | yes | — |
| 278 | C4 | #90212 | 1 | 2 | yes | — |
| 279 | C4 | #90216 | 1 | 2 | yes | — |
| 280 | C2 | — | 2 | 2 | no | — |
| 281 | C2 | — | 56 | 4 | no | — |
| 282 | C2 | #11730834 | 1 | 1 | yes | characteristic |
| 283 | C2 | C2×#89472 | 1 | 1 | yes | characteristic |
| 284 | C2 | C2×#89489 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta