← #14223177
Subgroups — #14223177
Order 1792.
2134 conjugacy classes of subgroups.
The subgroup lattice has 342 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C7×#3498 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11742897 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11741544 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #11740825 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #11740729 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11740727 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11740604 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×#89843 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11739956 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×C7×H(5,𝔽2) | C22 | 1 | 2 | yes | — |
| 11 | C7×#550 | — | 2 | 2 | no | — |
| 12 | C7×D42 | — | 2 | 6 | no | — |
| 13 | C7×#535 | C22 | 1 | 6 | yes | — |
| 14 | C7×#532 | C22 | 1 | 3 | yes | — |
| 15 | C2×C7×#127 | C22 | 1 | 3 | yes | — |
| 16 | C4×C7×#41 | C22 | 1 | 1 | yes | characteristic |
| 17 | #90518 | C22 | 1 | 2 | yes | — |
| 18 | C2×#6511 | C22 | 1 | 2 | yes | — |
| 19 | #90260 | — | 2 | 2 | no | — |
| 20 | #90230 | — | 2 | 6 | no | — |
| 21 | #90210 | C22 | 1 | 6 | yes | complemented |
| 22 | #90161 | C22 | 1 | 3 | yes | complemented |
| 23 | C2×#6433 | C22 | 1 | 3 | yes | complemented |
| 24 | #90005 | C22 | 1 | 12 | yes | complemented |
| 25 | #90004 | C22 | 1 | 12 | yes | complemented |
| 26 | #89987 | C22 | 1 | 12 | yes | complemented |
| 27 | C2×#6406 | C22 | 1 | 12 | yes | complemented |
| 28 | #89854 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #89854 | C22 | 1 | 3 | yes | complemented |
| 30 | #89843 | C22 | 1 | 3 | yes | complemented |
| 31 | #89843 | C22 | 1 | 3 | yes | complemented |
| 32 | #89843 | C22 | 1 | 6 | yes | complemented |
| 33 | #89843 | C22 | 1 | 12 | yes | complemented |
| 34 | #89842 | C22 | 1 | 12 | yes | complemented |
| 35 | #89828 | C22 | 1 | 12 | yes | complemented |
| 36 | #89827 | C22 | 1 | 12 | yes | complemented |
| 37 | #89769 | C22 | 1 | 6 | yes | complemented |
| 38 | C4×#1136 | C22 | 1 | 3 | yes | complemented |
| 39 | C2×#6377 | C22 | 1 | 3 | yes | complemented |
| 40 | #60626 | — | 7 | 1 | no | maximal, Sylow |
| 41 | C7×H(5,𝔽2) | — | 2 | 16 | no | — |
| 42 | C2×C7×#41 | — | 2 | 2 | no | — |
| 43 | C2×C7×#41 | C23 | 1 | 6 | yes | — |
| 44 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 45 | C22×C7×D4 | — | 2 | 6 | no | — |
| 46 | C22×C7×D4 | — | 2 | 6 | no | — |
| 47 | C22×C7×D4 | C23 | 1 | 6 | yes | — |
| 48 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 49 | C7×#127 | — | 2 | 6 | no | — |
| 50 | C7×#127 | C23 | 1 | 3 | yes | — |
| 51 | C7×#127 | C23 | 1 | 6 | yes | — |
| 52 | C7×#124 | C23 | 1 | 6 | yes | — |
| 53 | C7×#121 | — | 2 | 6 | no | — |
| 54 | C7×#121 | — | 2 | 12 | no | — |
| 55 | C7×#120 | — | 2 | 12 | no | — |
| 56 | C4×C7×Q8 | D4 | 1 | 2 | yes | — |
| 57 | C4×C7×D4 | — | 2 | 6 | no | — |
| 58 | C4×C7×D4 | D4 | 1 | 6 | yes | — |
| 59 | C7×#117 | C23 | 1 | 3 | yes | — |
| 60 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 61 | #6511 | — | 2 | 8 | no | — |
| 62 | Q8×Dic7 | — | 2 | 2 | no | — |
| 63 | D4×Dic7 | — | 2 | 6 | no | — |
| 64 | #6489 | C23 | 1 | 6 | yes | — |
| 65 | C2×C4⋊Dic7 | C23 | 1 | 6 | yes | — |
| 66 | #6487 | — | 2 | 6 | no | — |
| 67 | C2×Dic7⋊C4 | — | 2 | 6 | no | — |
| 68 | C2×#1136 | C23 | 1 | 6 | yes | — |
| 69 | C22×C7⋊C8 | C23 | 1 | 6 | yes | — |
| 70 | #6453 | — | 2 | 6 | no | — |
| 71 | #6451 | — | 2 | 6 | no | — |
| 72 | #6441 | — | 2 | 12 | no | — |
| 73 | #6433 | — | 2 | 6 | no | — |
| 74 | #6433 | C23 | 1 | 3 | yes | — |
| 75 | #6433 | C23 | 1 | 6 | yes | — |
| 76 | #6433 | C23 | 1 | 1 | yes | characteristic |
| 77 | #6432 | C23 | 1 | 6 | yes | — |
| 78 | C4×Dic14 | — | 2 | 6 | no | — |
| 79 | #6409 | C23 | 1 | 12 | yes | — |
| 80 | #6409 | C23 | 1 | 4 | yes | — |
| 81 | #6406 | C23 | 1 | 12 | yes | — |
| 82 | #6406 | C23 | 1 | 24 | yes | — |
| 83 | #6406 | C23 | 1 | 12 | yes | — |
| 84 | #6377 | C23 | 1 | 1 | yes | characteristic |
| 85 | #6377 | C23 | 1 | 3 | yes | — |
| 86 | #6377 | C23 | 1 | 6 | yes | — |
| 87 | C4×C7⋊C8 | C23 | 1 | 6 | yes | — |
| 88 | #3504 | — | 7 | 1 | no | — |
| 89 | #3498 | D7 | 1 | 1 | yes | characteristic |
| 90 | #3142 | — | 7 | 3 | no | — |
| 91 | #3138 | — | 7 | 3 | no | — |
| 92 | #3136 | — | 7 | 12 | no | — |
| 93 | #3135 | — | 7 | 3 | no | — |
| 94 | C2×#490 | — | 7 | 3 | no | — |
| 95 | #2897 | — | 7 | 4 | no | — |
| 96 | #2875 | — | 7 | 1 | no | — |
| 97 | C24×C7 | — | 2 | 6 | no | — |
| 98 | C7×#41 | — | 2 | 24 | no | — |
| 99 | C7×#41 | — | 4 | 8 | no | — |
| 100 | C7×#41 | #41 | 1 | 8 | yes | — |
| 101 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C7×Q8 | C24 | 1 | 2 | yes | — |
| 103 | C2×C7×D4 | — | 2 | 6 | no | — |
| 104 | C2×C7×D4 | — | 2 | 6 | no | — |
| 105 | C2×C7×D4 | — | 2 | 6 | no | — |
| 106 | C2×C7×D4 | — | 2 | 12 | no | — |
| 107 | C2×C7×D4 | — | 2 | 24 | no | — |
| 108 | C2×C7×D4 | — | 4 | 24 | no | — |
| 109 | C2×C7×D4 | — | 8 | 12 | no | — |
| 110 | C2×C7×D4 | C2×D4 | 1 | 3 | yes | — |
| 111 | C2×C7×D4 | C24 | 1 | 6 | yes | — |
| 112 | C22×C4×C7 | — | 2 | 6 | no | — |
| 113 | C22×C4×C7 | C2×D4 | 1 | 6 | yes | — |
| 114 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 115 | C22×Dic7 | — | 2 | 6 | no | — |
| 116 | C2×Dic14 | — | 2 | 6 | no | — |
| 117 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 118 | C7×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 119 | C7×C22⋊C4 | — | 2 | 12 | no | — |
| 120 | C7×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 121 | C42×C7 | C2×D4 | 1 | 6 | yes | — |
| 122 | C42×C7 | C24 | 1 | 3 | yes | — |
| 123 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 124 | C22⋊Dic7 | — | 2 | 6 | no | — |
| 125 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 126 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 127 | C4⋊Dic7 | C24 | 1 | 2 | yes | — |
| 128 | C4⋊Dic7 | C24 | 1 | 6 | yes | — |
| 129 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 130 | Dic7⋊C4 | — | 2 | 6 | no | — |
| 131 | Dic7⋊C4 | — | 2 | 12 | no | — |
| 132 | C4×Dic7 | — | 2 | 6 | no | — |
| 133 | #1136 | — | 2 | 12 | no | — |
| 134 | C2×C7⋊C8 | — | 2 | 12 | no | — |
| 135 | C2×C7⋊C8 | C24 | 1 | 2 | yes | — |
| 136 | C2×C7⋊C8 | C24 | 1 | 6 | yes | — |
| 137 | C2×H(5,𝔽2) | C2×D7 | 1 | 2 | yes | — |
| 138 | C2×#131 | — | 7 | 2 | no | — |
| 139 | #557 | — | 14 | 2 | no | — |
| 140 | #554 | — | 14 | 6 | no | — |
| 141 | #550 | — | 2 | 2 | no | — |
| 142 | D42 | — | 2 | 6 | no | — |
| 143 | #544 | — | 7 | 6 | no | — |
| 144 | #535 | C2×D7 | 1 | 6 | yes | — |
| 145 | #533 | — | 7 | 3 | no | — |
| 146 | #532 | C2×D7 | 1 | 3 | yes | — |
| 147 | C2×#127 | C2×D7 | 1 | 3 | yes | — |
| 148 | C2×#125 | — | 7 | 3 | no | — |
| 149 | #520 | — | 7 | 2 | no | — |
| 150 | C4×#41 | C2×D7 | 1 | 1 | yes | characteristic |
| 151 | #491 | — | 7 | 1 | no | — |
| 152 | #491 | — | 7 | 3 | no | — |
| 153 | #490 | — | 7 | 3 | no | — |
| 154 | #490 | — | 7 | 12 | no | — |
| 155 | #490 | — | 7 | 6 | no | — |
| 156 | #490 | — | 7 | 3 | no | — |
| 157 | #489 | — | 7 | 12 | no | — |
| 158 | #488 | — | 7 | 12 | no | — |
| 159 | #486 | — | 7 | 12 | no | — |
| 160 | #418 | — | 7 | 12 | no | — |
| 161 | #417 | — | 7 | 12 | no | — |
| 162 | #416 | — | 7 | 12 | no | — |
| 163 | C2×#102 | — | 7 | 12 | no | — |
| 164 | #405 | — | 7 | 6 | no | — |
| 165 | C4×M16 | — | 7 | 3 | no | — |
| 166 | C2×#97 | — | 7 | 3 | no | — |
| 167 | C23×C7 | — | 2 | 6 | no | — |
| 168 | C23×C7 | — | 4 | 12 | no | — |
| 169 | C23×C7 | — | 8 | 12 | no | — |
| 170 | C23×C7 | C22×D4 | 1 | 3 | yes | — |
| 171 | C7×Q8 | — | 2 | 4 | no | — |
| 172 | C7×Q8 | #124 | 1 | 4 | yes | — |
| 173 | C7×D4 | — | 2 | 12 | no | — |
| 174 | C7×D4 | — | 4 | 12 | no | — |
| 175 | C7×D4 | — | 4 | 12 | no | — |
| 176 | C7×D4 | — | 4 | 12 | no | — |
| 177 | C7×D4 | — | 8 | 12 | no | — |
| 178 | C7×D4 | #124 | 1 | 12 | yes | — |
| 179 | C2×C4×C7 | — | 2 | 2 | no | — |
| 180 | C2×C4×C7 | — | 4 | 6 | no | — |
| 181 | C2×C4×C7 | — | 4 | 12 | no | — |
| 182 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 183 | C2×C4×C7 | C22×D4 | 1 | 6 | yes | — |
| 184 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 185 | C2×C4×C7 | C2×#41 | 1 | 12 | yes | — |
| 186 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 187 | C2×Dic7 | — | 2 | 2 | no | — |
| 188 | C2×Dic7 | — | 2 | 6 | no | — |
| 189 | C2×Dic7 | — | 8 | 6 | no | — |
| 190 | Dic14 | — | 8 | 6 | no | — |
| 191 | C7⋊C8 | — | 2 | 2 | no | — |
| 192 | C7⋊C8 | — | 2 | 6 | no | — |
| 193 | H(5,𝔽2) | — | 2 | 16 | no | — |
| 194 | C2×#41 | — | 2 | 2 | no | — |
| 195 | C2×#41 | C22×D7 | 1 | 6 | yes | — |
| 196 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 197 | C22×D4 | — | 2 | 6 | no | — |
| 198 | C22×D4 | — | 2 | 6 | no | — |
| 199 | C22×D4 | C22×D7 | 1 | 6 | yes | — |
| 200 | #131 | — | 14 | 8 | no | — |
| 201 | C2×M16 | — | 7 | 6 | no | — |
| 202 | C22×C8 | — | 7 | 6 | no | — |
| 203 | C4⋊Q8 | — | 7 | 6 | no | — |
| 204 | C4⋊Q8 | — | 14 | 6 | no | — |
| 205 | C4⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 206 | #127 | — | 2 | 6 | no | — |
| 207 | #127 | C22×D7 | 1 | 3 | yes | — |
| 208 | #127 | C22×D7 | 1 | 6 | yes | — |
| 209 | #125 | — | 7 | 3 | no | — |
| 210 | #125 | — | 7 | 6 | no | — |
| 211 | #125 | — | 7 | 1 | no | — |
| 212 | #125 | — | 14 | 6 | no | — |
| 213 | #125 | — | 14 | 6 | no | — |
| 214 | #124 | C22×D7 | 1 | 6 | yes | — |
| 215 | C22⋊Q8 | — | 14 | 6 | no | — |
| 216 | C22⋊Q8 | — | 14 | 12 | no | — |
| 217 | #121 | — | 2 | 6 | no | — |
| 218 | #121 | — | 2 | 12 | no | — |
| 219 | #120 | — | 2 | 12 | no | — |
| 220 | C4×Q8 | — | 14 | 2 | no | — |
| 221 | C4×Q8 | — | 14 | 6 | no | — |
| 222 | C4×Q8 | C22⋊D7 | 1 | 2 | yes | — |
| 223 | C4×D4 | — | 2 | 6 | no | — |
| 224 | C4×D4 | — | 14 | 6 | no | — |
| 225 | C4×D4 | C22⋊D7 | 1 | 6 | yes | — |
| 226 | #117 | — | 7 | 6 | no | — |
| 227 | #117 | C22×D7 | 1 | 3 | yes | — |
| 228 | C2×C4⋊C4 | — | 7 | 6 | no | — |
| 229 | C2×C4⋊C4 | — | 14 | 6 | no | — |
| 230 | C2×C42 | C22×D7 | 1 | 3 | yes | — |
| 231 | #103 | — | 7 | 4 | no | — |
| 232 | #103 | — | 7 | 12 | no | — |
| 233 | #102 | — | 7 | 12 | no | — |
| 234 | #102 | — | 7 | 24 | no | — |
| 235 | #102 | — | 7 | 12 | no | — |
| 236 | #97 | — | 7 | 1 | no | — |
| 237 | #97 | — | 7 | 3 | no | — |
| 238 | #97 | — | 7 | 6 | no | — |
| 239 | C4×C8 | — | 7 | 6 | no | — |
| 240 | C22×C7 | — | 2 | 6 | no | — |
| 241 | C22×C7 | — | 4 | 12 | no | — |
| 242 | C22×C7 | — | 4 | 6 | no | — |
| 243 | C22×C7 | — | 16 | 12 | no | — |
| 244 | C22×C7 | C2×#124 | 1 | 6 | yes | — |
| 245 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 246 | C4×C7 | — | 2 | 6 | no | — |
| 247 | C4×C7 | — | 2 | 2 | no | — |
| 248 | C4×C7 | — | 4 | 2 | no | — |
| 249 | C4×C7 | C2×#124 | 1 | 6 | yes | — |
| 250 | C4×C7 | C22×#41 | 1 | 2 | yes | — |
| 251 | Dic7 | — | 4 | 2 | no | — |
| 252 | Dic7 | — | 4 | 6 | no | — |
| 253 | C24 | — | 2 | 6 | no | — |
| 254 | #41 | — | 2 | 24 | no | — |
| 255 | #41 | — | 4 | 8 | no | — |
| 256 | #41 | #1159 | 1 | 8 | yes | — |
| 257 | C2×Q8 | — | 14 | 6 | no | — |
| 258 | C2×Q8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 259 | C2×Q8 | C23×D7 | 1 | 2 | yes | — |
| 260 | C2×D4 | — | 2 | 6 | no | — |
| 261 | C2×D4 | — | 2 | 24 | no | — |
| 262 | C2×D4 | — | 2 | 6 | no | — |
| 263 | C2×D4 | — | 2 | 6 | no | — |
| 264 | C2×D4 | — | 2 | 12 | no | — |
| 265 | C2×D4 | — | 4 | 24 | no | — |
| 266 | C2×D4 | — | 8 | 12 | no | — |
| 267 | C2×D4 | C2×C22⋊D7 | 1 | 3 | yes | — |
| 268 | C2×D4 | C23×D7 | 1 | 6 | yes | — |
| 269 | C22×C4 | — | 2 | 6 | no | — |
| 270 | C22×C4 | — | 14 | 6 | no | — |
| 271 | C22×C4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 272 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 273 | M16 | — | 14 | 12 | no | — |
| 274 | C2×C8 | — | 7 | 6 | no | — |
| 275 | C2×C8 | — | 7 | 2 | no | — |
| 276 | C2×C8 | — | 14 | 12 | no | — |
| 277 | C4⋊C4 | — | 2 | 2 | no | — |
| 278 | C4⋊C4 | — | 7 | 6 | no | — |
| 279 | C4⋊C4 | — | 7 | 2 | no | — |
| 280 | C4⋊C4 | — | 14 | 6 | no | — |
| 281 | C4⋊C4 | — | 14 | 12 | no | — |
| 282 | C4⋊C4 | — | 14 | 2 | no | — |
| 283 | C4⋊C4 | — | 14 | 6 | no | — |
| 284 | C4⋊C4 | — | 14 | 6 | no | — |
| 285 | C4⋊C4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 286 | C22⋊C4 | — | 2 | 12 | no | — |
| 287 | C22⋊C4 | — | 14 | 6 | no | — |
| 288 | C22⋊C4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 289 | C42 | — | 14 | 6 | no | — |
| 290 | C42 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 291 | C42 | C23×D7 | 1 | 3 | yes | — |
| 292 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 293 | C2×C7 | — | 2 | 6 | no | — |
| 294 | C2×C7 | — | 8 | 6 | no | — |
| 295 | C2×C7 | C22×#124 | 1 | 1 | yes | characteristic |
| 296 | C2×C7 | #3585 | 1 | 2 | yes | — |
| 297 | C23 | — | 2 | 6 | no | — |
| 298 | C23 | — | 4 | 12 | no | — |
| 299 | C23 | — | 8 | 12 | no | — |
| 300 | C23 | C22×C22⋊D7 | 1 | 3 | yes | — |
| 301 | Q8 | — | 2 | 4 | no | — |
| 302 | Q8 | — | 56 | 6 | no | — |
| 303 | Q8 | #6499 | 1 | 4 | yes | — |
| 304 | D4 | — | 2 | 12 | no | — |
| 305 | D4 | — | 4 | 12 | no | — |
| 306 | D4 | — | 4 | 12 | no | — |
| 307 | D4 | — | 4 | 12 | no | — |
| 308 | D4 | — | 8 | 12 | no | — |
| 309 | D4 | #6499 | 1 | 12 | yes | — |
| 310 | C2×C4 | — | 2 | 2 | no | — |
| 311 | C2×C4 | — | 4 | 6 | no | — |
| 312 | C2×C4 | — | 4 | 12 | no | — |
| 313 | C2×C4 | — | 14 | 2 | no | — |
| 314 | C2×C4 | — | 14 | 6 | no | — |
| 315 | C2×C4 | — | 56 | 6 | no | — |
| 316 | C2×C4 | C2×#1159 | 1 | 12 | yes | — |
| 317 | C2×C4 | C22×C22⋊D7 | 1 | 2 | yes | — |
| 318 | C2×C4 | C22×C22⋊D7 | 1 | 6 | yes | — |
| 319 | C2×C4 | C22×C22⋊D7 | 1 | 3 | yes | — |
| 320 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 321 | C8 | — | 14 | 2 | no | — |
| 322 | C8 | — | 14 | 6 | no | — |
| 323 | C7 | #60626 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 324 | C22 | — | 2 | 6 | no | — |
| 325 | C22 | — | 4 | 6 | no | — |
| 326 | C22 | — | 4 | 12 | no | — |
| 327 | C22 | — | 16 | 12 | no | — |
| 328 | C22 | C2×#6499 | 1 | 6 | yes | — |
| 329 | C22 | C23×C22⋊D7 | 1 | 1 | yes | characteristic |
| 330 | C4 | — | 2 | 2 | no | — |
| 331 | C4 | — | 2 | 6 | no | — |
| 332 | C4 | — | 4 | 2 | no | — |
| 333 | C4 | — | 28 | 6 | no | — |
| 334 | C4 | — | 28 | 2 | no | — |
| 335 | C4 | C2×#6499 | 1 | 6 | yes | — |
| 336 | C4 | C22×#1159 | 1 | 2 | yes | — |
| 337 | C2 | — | 2 | 6 | no | — |
| 338 | C2 | — | 8 | 6 | no | — |
| 339 | C2 | C22×#6499 | 1 | 1 | yes | characteristic |
| 340 | C2 | #11744345 | 1 | 2 | yes | — |
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