← #13507341
Subgroups — #13507341
Order 1792.
508 conjugacy classes of subgroups.
The subgroup lattice has 320 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11735893 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×C7×M32 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11729187 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11729184 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11727499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11726829 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11726822 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11726807 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11726805 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #90170 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×C7×M32 | C22 | 1 | 2 | yes | — |
| 12 | C2×C4×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 13 | #89883 | C4 | 1 | 2 | yes | — |
| 14 | C8×C22⋊D7 | C22 | 1 | 2 | yes | — |
| 15 | #89698 | C4 | 1 | 1 | yes | characteristic |
| 16 | C2×#6372 | C22 | 1 | 2 | yes | — |
| 17 | C2×D7×C16 | C22 | 1 | 2 | yes | — |
| 18 | #89462 | C4 | 1 | 2 | yes | — |
| 19 | #89461 | C22 | 1 | 2 | yes | — |
| 20 | #89460 | C4 | 1 | 1 | yes | characteristic |
| 21 | C8×D28 | C22 | 1 | 1 | yes | characteristic |
| 22 | #89451 | C4 | 1 | 1 | yes | characteristic |
| 23 | C8×Dic14 | C22 | 1 | 1 | yes | characteristic |
| 24 | C7×#346 | C22 | 1 | 2 | yes | — |
| 25 | C4×C7×C16 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4×C7×C16 | C22 | 1 | 1 | yes | characteristic |
| 27 | C22⋊(C7⋊C16) | C22 | 1 | 1 | yes | characteristic |
| 28 | C22⋊(C7⋊C16) | C22 | 1 | 1 | yes | characteristic |
| 29 | (C2×D7)⋊C16 | C22 | 1 | 2 | yes | — |
| 30 | (C2×D7)⋊C16 | C22 | 1 | 2 | yes | — |
| 31 | #89297 | C22 | 1 | 2 | yes | — |
| 32 | Dic7⋊C16 | C22 | 1 | 2 | yes | — |
| 33 | Dic7⋊C16 | C22 | 1 | 2 | yes | — |
| 34 | C16×Dic7 | C22 | 1 | 2 | yes | — |
| 35 | C4⋊(C7⋊C16) | C22 | 1 | 2 | yes | — |
| 36 | #89256 | C22 | 1 | 2 | yes | — |
| 37 | #33481 | — | 7 | 1 | no | maximal, Sylow |
| 38 | C22×C7×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×C42×C7 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | #6493 | C8 | 1 | 1 | yes | characteristic |
| 42 | #6492 | C8 | 1 | 2 | yes | — |
| 43 | C4×C22⋊D7 | C2×C4 | 1 | 2 | yes | — |
| 44 | #6487 | C8 | 1 | 1 | yes | characteristic |
| 45 | C2×#1131 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×C8×D7 | C23 | 1 | 2 | yes | — |
| 47 | #6439 | C8 | 1 | 2 | yes | — |
| 48 | #6438 | C8 | 1 | 1 | yes | characteristic |
| 49 | C4×D28 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | #6435 | C2×C4 | 1 | 2 | yes | — |
| 51 | #6433 | C8 | 1 | 1 | yes | characteristic |
| 52 | C4×Dic14 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C7×M32 | — | 2 | 4 | no | — |
| 54 | C2×C7×C16 | C23 | 1 | 2 | yes | — |
| 55 | C2×C7×C16 | C23 | 1 | 2 | yes | — |
| 56 | C4×C7×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C4×C7×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 59 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22⋊(C7⋊C8) | C2×C4 | 1 | 2 | yes | — |
| 61 | (C2×D7)⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 62 | (C2×D7)⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 63 | #6389 | C2×C4 | 1 | 2 | yes | — |
| 64 | Dic7⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 65 | Dic7⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 66 | C8×Dic7 | C23 | 1 | 2 | yes | — |
| 67 | C2×C7⋊C16 | C23 | 1 | 2 | yes | — |
| 68 | C2×C7⋊C16 | C23 | 1 | 2 | yes | — |
| 69 | C4⋊(C7⋊C8) | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C4⋊(C7⋊C8) | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | #6377 | C2×C4 | 1 | 2 | yes | — |
| 72 | #6372 | — | 2 | 4 | no | — |
| 73 | D7×C16 | — | 2 | 4 | no | — |
| 74 | #2966 | — | 7 | 1 | no | — |
| 75 | #2183 | — | 7 | 2 | no | — |
| 76 | #2169 | — | 7 | 2 | no | — |
| 77 | #2168 | — | 7 | 2 | no | — |
| 78 | #2168 | — | 7 | 2 | no | — |
| 79 | #2164 | — | 7 | 2 | no | — |
| 80 | #2163 | — | 7 | 1 | no | — |
| 81 | #2108 | — | 7 | 2 | no | — |
| 82 | C4×M32 | D7 | 1 | 1 | yes | characteristic, complemented |
| 83 | C22×C4×C7 | C2×C8 | 1 | 1 | yes | characteristic |
| 84 | C22×C4×C7 | C2×C8 | 1 | 1 | yes | characteristic |
| 85 | C22×C4×C7 | C22×C4 | 1 | 1 | yes | characteristic |
| 86 | C2×C22⋊D7 | C2×C8 | 1 | 2 | yes | — |
| 87 | C2×D28 | C2×C8 | 1 | 1 | yes | characteristic |
| 88 | C2×C4×D7 | C22×C4 | 1 | 2 | yes | — |
| 89 | C2×Dic14 | C2×C8 | 1 | 1 | yes | characteristic |
| 90 | C2×C7×C8 | — | 2 | 2 | no | — |
| 91 | C2×C7×C8 | — | 2 | 2 | no | — |
| 92 | C2×C7×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 93 | C2×C7×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 94 | C2×C7×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 96 | C42×C7 | C2×C8 | 1 | 1 | yes | characteristic |
| 97 | C42×C7 | C2×C8 | 1 | 1 | yes | characteristic |
| 98 | C42×C7 | C22×C4 | 1 | 1 | yes | characteristic |
| 99 | C42×C7 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | C22⋊Dic7 | C2×C8 | 1 | 2 | yes | — |
| 101 | (C2×D7)⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 102 | (C2×D7)⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 103 | (C2×D7)⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 104 | (C2×D7)⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 105 | C4⋊Dic7 | C2×C8 | 1 | 1 | yes | characteristic |
| 106 | C4⋊Dic7 | C2×C8 | 1 | 1 | yes | characteristic |
| 107 | Dic7⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 108 | Dic7⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 109 | Dic7⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 110 | Dic7⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 111 | C4×Dic7 | C22×C4 | 1 | 2 | yes | — |
| 112 | C2×C7⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 113 | C2×C7⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 114 | #1131 | — | 2 | 4 | no | — |
| 115 | C8×D7 | — | 2 | 2 | no | — |
| 116 | C8×D7 | — | 2 | 2 | no | — |
| 117 | C7×C16 | — | 2 | 2 | no | — |
| 118 | C7×C16 | #41 | 1 | 4 | yes | — |
| 119 | C7⋊C16 | — | 2 | 2 | no | — |
| 120 | C7⋊C16 | — | 2 | 2 | no | — |
| 121 | #529 | — | 7 | 1 | no | — |
| 122 | C2×M32 | — | 7 | 2 | no | — |
| 123 | C2×M32 | C2×D7 | 1 | 2 | yes | — |
| 124 | C22×C16 | — | 7 | 2 | no | — |
| 125 | #446 | — | 7 | 1 | no | — |
| 126 | C8×Q8 | — | 7 | 1 | no | — |
| 127 | #436 | — | 7 | 1 | no | — |
| 128 | #435 | — | 7 | 2 | no | — |
| 129 | C8×D4 | — | 7 | 2 | no | — |
| 130 | C8×D4 | — | 7 | 1 | no | — |
| 131 | #433 | — | 7 | 2 | no | — |
| 132 | #432 | — | 7 | 1 | no | — |
| 133 | #405 | — | 7 | 2 | no | — |
| 134 | C2×C4×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 135 | C4⋊C16 | — | 7 | 2 | no | — |
| 136 | C4⋊C16 | — | 7 | 2 | no | — |
| 137 | C4⋊C16 | — | 7 | 2 | no | — |
| 138 | C22⋊C16 | — | 7 | 1 | no | — |
| 139 | C22⋊C16 | — | 7 | 1 | no | — |
| 140 | C22⋊C16 | — | 7 | 2 | no | — |
| 141 | C22⋊C16 | — | 7 | 2 | no | — |
| 142 | #346 | — | 7 | 2 | no | — |
| 143 | #346 | — | 7 | 2 | no | — |
| 144 | #346 | C2×D7 | 1 | 2 | yes | — |
| 145 | C4×C16 | — | 7 | 2 | no | — |
| 146 | C4×C16 | C2×D7 | 1 | 1 | yes | characteristic |
| 147 | C4×C16 | C2×D7 | 1 | 1 | yes | characteristic |
| 148 | C23×C7 | C22×C8 | 1 | 1 | yes | characteristic |
| 149 | C22×D7 | C22×C8 | 1 | 2 | yes | — |
| 150 | C2×C4×C7 | — | 2 | 1 | no | — |
| 151 | C2×C4×C7 | — | 2 | 1 | no | — |
| 152 | C2×C4×C7 | — | 4 | 1 | no | — |
| 153 | C2×C4×C7 | — | 4 | 1 | no | — |
| 154 | C2×C4×C7 | C22×C8 | 1 | 1 | yes | characteristic |
| 155 | C2×C4×C7 | C22×C8 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C7 | C22×C8 | 1 | 1 | yes | characteristic |
| 157 | C2×C4×C7 | C22×C8 | 1 | 1 | yes | characteristic |
| 158 | C2×C4×C7 | C22×C8 | 1 | 1 | yes | characteristic |
| 159 | C2×C4×C7 | C23×C4 | 1 | 1 | yes | characteristic |
| 160 | C22⋊D7 | — | 4 | 2 | no | — |
| 161 | C2×Dic7 | C22×C8 | 1 | 2 | yes | — |
| 162 | C2×Dic7 | C22×C8 | 1 | 2 | yes | — |
| 163 | C2×Dic7 | C22×C8 | 1 | 2 | yes | — |
| 164 | D28 | — | 4 | 1 | no | — |
| 165 | C4×D7 | — | 2 | 2 | no | — |
| 166 | C4×D7 | — | 2 | 2 | no | — |
| 167 | Dic14 | — | 4 | 1 | no | — |
| 168 | C7×C8 | — | 2 | 1 | no | — |
| 169 | C7×C8 | — | 2 | 1 | no | — |
| 170 | C7×C8 | #131 | 1 | 2 | yes | — |
| 171 | C7×C8 | C2×#41 | 1 | 2 | yes | — |
| 172 | C7⋊C8 | — | 2 | 2 | no | — |
| 173 | C7⋊C8 | — | 2 | 2 | no | — |
| 174 | C2×M16 | — | 7 | 2 | no | — |
| 175 | C22×C8 | — | 7 | 2 | no | — |
| 176 | C22×C8 | C4×D7 | 1 | 1 | yes | characteristic |
| 177 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 178 | #126 | — | 7 | 2 | no | — |
| 179 | #125 | — | 7 | 1 | no | — |
| 180 | #124 | — | 7 | 1 | no | — |
| 181 | #123 | — | 7 | 2 | no | — |
| 182 | C22⋊Q8 | — | 7 | 1 | no | — |
| 183 | #121 | — | 7 | 1 | no | — |
| 184 | C4×Q8 | — | 7 | 1 | no | — |
| 185 | C4×D4 | — | 7 | 2 | no | — |
| 186 | C4×D4 | — | 7 | 1 | no | — |
| 187 | #117 | — | 7 | 2 | no | — |
| 188 | C2×C42 | C4×D7 | 1 | 1 | yes | characteristic |
| 189 | M32 | — | 2 | 4 | no | — |
| 190 | M32 | — | 14 | 4 | no | — |
| 191 | C2×C16 | — | 7 | 2 | no | — |
| 192 | C2×C16 | — | 7 | 2 | no | — |
| 193 | C2×C16 | — | 14 | 4 | no | — |
| 194 | C2×C16 | C22×D7 | 1 | 2 | yes | — |
| 195 | C2×C16 | C22×D7 | 1 | 2 | yes | — |
| 196 | C4⋊C8 | — | 7 | 2 | no | — |
| 197 | C4⋊C8 | — | 7 | 2 | no | — |
| 198 | C4⋊C8 | — | 7 | 1 | no | — |
| 199 | C4⋊C8 | — | 7 | 1 | no | — |
| 200 | C22⋊C8 | — | 7 | 2 | no | — |
| 201 | C22⋊C8 | — | 7 | 2 | no | — |
| 202 | C22⋊C8 | — | 7 | 2 | no | — |
| 203 | #97 | — | 7 | 2 | no | — |
| 204 | #97 | — | 7 | 2 | no | — |
| 205 | C4×C8 | — | 7 | 2 | no | — |
| 206 | C4×C8 | C4×D7 | 1 | 1 | yes | characteristic |
| 207 | C4×C8 | C4×D7 | 1 | 1 | yes | characteristic |
| 208 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 209 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 210 | C22×C7 | — | 2 | 1 | no | — |
| 211 | C22×C7 | — | 2 | 1 | no | — |
| 212 | C22×C7 | — | 2 | 1 | no | — |
| 213 | C22×C7 | C23×C8 | 1 | 1 | yes | characteristic |
| 214 | C2×D7 | — | 2 | 2 | no | — |
| 215 | C2×D7 | — | 2 | 2 | no | — |
| 216 | C2×D7 | — | 2 | 2 | no | — |
| 217 | C4×C7 | — | 2 | 1 | no | — |
| 218 | C4×C7 | — | 2 | 1 | no | — |
| 219 | C4×C7 | — | 2 | 1 | no | — |
| 220 | C4×C7 | — | 2 | 1 | no | — |
| 221 | C4×C7 | — | 2 | 1 | no | — |
| 222 | C4×C7 | C4×#41 | 1 | 1 | yes | characteristic |
| 223 | C4×C7 | C2×#131 | 1 | 1 | yes | characteristic |
| 224 | Dic7 | — | 2 | 2 | no | — |
| 225 | Dic7 | — | 2 | 2 | no | — |
| 226 | Dic7 | — | 2 | 2 | no | — |
| 227 | C2×Q8 | — | 7 | 1 | no | — |
| 228 | C2×D4 | — | 7 | 2 | no | — |
| 229 | C2×D4 | — | 7 | 1 | no | — |
| 230 | C22×C4 | — | 7 | 2 | no | — |
| 231 | C22×C4 | C8×D7 | 1 | 1 | yes | characteristic |
| 232 | C22×C4 | C8×D7 | 1 | 1 | yes | characteristic |
| 233 | C22×C4 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 234 | M16 | — | 14 | 4 | no | — |
| 235 | C2×C8 | — | 2 | 2 | no | — |
| 236 | C2×C8 | — | 2 | 2 | no | — |
| 237 | C2×C8 | — | 7 | 2 | no | — |
| 238 | C2×C8 | — | 7 | 2 | no | — |
| 239 | C2×C8 | — | 14 | 2 | no | — |
| 240 | C2×C8 | — | 14 | 2 | no | — |
| 241 | C2×C8 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 242 | C2×C8 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 243 | C2×C8 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 244 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 245 | C4⋊C4 | — | 7 | 2 | no | — |
| 246 | C4⋊C4 | — | 7 | 2 | no | — |
| 247 | C4⋊C4 | — | 7 | 2 | no | — |
| 248 | C4⋊C4 | — | 7 | 2 | no | — |
| 249 | C4⋊C4 | — | 7 | 1 | no | — |
| 250 | C4⋊C4 | — | 7 | 1 | no | — |
| 251 | C22⋊C4 | — | 7 | 2 | no | — |
| 252 | C22⋊C4 | — | 7 | 2 | no | — |
| 253 | C22⋊C4 | — | 7 | 2 | no | — |
| 254 | C22⋊C4 | — | 7 | 2 | no | — |
| 255 | C22⋊C4 | — | 7 | 2 | no | — |
| 256 | C42 | — | 7 | 2 | no | — |
| 257 | C42 | C8×D7 | 1 | 1 | yes | characteristic |
| 258 | C42 | C8×D7 | 1 | 1 | yes | characteristic |
| 259 | C42 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 260 | C42 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 261 | C16 | — | 2 | 2 | no | — |
| 262 | C16 | — | 14 | 2 | no | — |
| 263 | C16 | — | 14 | 2 | no | — |
| 264 | C16 | #1157 | 1 | 4 | yes | — |
| 265 | C2×C7 | — | 4 | 1 | no | — |
| 266 | C2×C7 | C8×#41 | 1 | 1 | yes | characteristic |
| 267 | C2×C7 | #3407 | 1 | 1 | yes | characteristic |
| 268 | C2×C7 | #3407 | 1 | 1 | yes | characteristic |
| 269 | D7 | — | 4 | 2 | no | — |
| 270 | C23 | — | 7 | 2 | no | — |
| 271 | C23 | C2×C8×D7 | 1 | 1 | yes | characteristic |
| 272 | Q8 | — | 28 | 1 | no | — |
| 273 | D4 | — | 28 | 1 | no | — |
| 274 | D4 | — | 28 | 2 | no | — |
| 275 | C2×C4 | — | 2 | 1 | no | — |
| 276 | C2×C4 | — | 2 | 1 | no | — |
| 277 | C2×C4 | — | 4 | 1 | no | — |
| 278 | C2×C4 | — | 4 | 1 | no | — |
| 279 | C2×C4 | — | 7 | 2 | no | — |
| 280 | C2×C4 | — | 7 | 2 | no | — |
| 281 | C2×C4 | — | 7 | 2 | no | — |
| 282 | C2×C4 | — | 14 | 2 | no | — |
| 283 | C2×C4 | — | 14 | 2 | no | — |
| 284 | C2×C4 | C2×C8×D7 | 1 | 1 | yes | characteristic |
| 285 | C2×C4 | C2×C8×D7 | 1 | 1 | yes | characteristic |
| 286 | C2×C4 | C2×C8×D7 | 1 | 1 | yes | characteristic |
| 287 | C2×C4 | C2×C8×D7 | 1 | 1 | yes | characteristic |
| 288 | C2×C4 | C2×C8×D7 | 1 | 1 | yes | characteristic |
| 289 | C2×C4 | C22×C4×D7 | 1 | 1 | yes | characteristic |
| 290 | C8 | — | 2 | 1 | no | — |
| 291 | C8 | — | 2 | 1 | no | — |
| 292 | C8 | — | 14 | 2 | no | — |
| 293 | C8 | — | 14 | 2 | no | — |
| 294 | C8 | #6464 | 1 | 2 | yes | — |
| 295 | C8 | C2×#1157 | 1 | 2 | yes | — |
| 296 | C7 | #33481 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 297 | C22 | — | 2 | 1 | no | — |
| 298 | C22 | — | 2 | 1 | no | — |
| 299 | C22 | — | 2 | 1 | no | — |
| 300 | C22 | — | 14 | 2 | no | — |
| 301 | C22 | — | 14 | 2 | no | — |
| 302 | C22 | — | 14 | 2 | no | — |
| 303 | C22 | C22×C8×D7 | 1 | 1 | yes | characteristic |
| 304 | C4 | — | 2 | 1 | no | — |
| 305 | C4 | — | 2 | 1 | no | — |
| 306 | C4 | — | 2 | 1 | no | — |
| 307 | C4 | — | 2 | 1 | no | — |
| 308 | C4 | — | 2 | 1 | no | — |
| 309 | C4 | — | 14 | 2 | no | — |
| 310 | C4 | — | 14 | 2 | no | — |
| 311 | C4 | — | 14 | 2 | no | — |
| 312 | C4 | C4×#1157 | 1 | 1 | yes | characteristic |
| 313 | C4 | C2×#6464 | 1 | 1 | yes | characteristic |
| 314 | C2 | — | 4 | 1 | no | — |
| 315 | C2 | — | 28 | 2 | no | — |
| 316 | C2 | C8×#1157 | 1 | 1 | yes | characteristic |
| 317 | C2 | #11739452 | 1 | 1 | yes | characteristic |
| 318 | C2 | #11739452 | 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