← #13336999
Subgroups — #13336999
Order 1792.
774 conjugacy classes of subgroups.
The subgroup lattice has 338 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C7×#493 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11740614 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11735890 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11729513 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11729041 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11729040 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11727483 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×C7×D8 | — | 2 | 1 | no | — |
| 9 | C22×C7×D8 | — | 2 | 1 | no | — |
| 10 | C2×C7×#127 | C22 | 1 | 2 | yes | — |
| 11 | #90161 | C22 | 1 | 1 | yes | characteristic |
| 12 | C7×#493 | — | 2 | 1 | no | — |
| 13 | C7×#493 | — | 2 | 1 | no | — |
| 14 | C7×#493 | C22 | 1 | 2 | yes | — |
| 15 | C7×#493 | C22 | 1 | 2 | yes | — |
| 16 | C2×C4×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 17 | #89990 | — | 2 | 4 | no | — |
| 18 | #89874 | — | 2 | 1 | no | — |
| 19 | #89873 | — | 2 | 1 | no | — |
| 20 | #89848 | — | 2 | 2 | no | — |
| 21 | #89847 | C22 | 1 | 8 | yes | complemented |
| 22 | #89842 | — | 2 | 2 | no | — |
| 23 | #89697 | C22 | 1 | 2 | yes | — |
| 24 | #89696 | C22 | 1 | 1 | yes | characteristic |
| 25 | #89451 | — | 2 | 1 | no | — |
| 26 | #89451 | C22 | 1 | 2 | yes | complemented |
| 27 | C8×Dic14 | — | 2 | 1 | no | — |
| 28 | C8×Dic14 | C22 | 1 | 2 | yes | complemented |
| 29 | #89339 | C22 | 1 | 8 | yes | complemented |
| 30 | #89253 | C22 | 1 | 2 | yes | complemented |
| 31 | #89252 | C22 | 1 | 2 | yes | complemented |
| 32 | #19203 | — | 7 | 1 | no | maximal, Sylow |
| 33 | C22×C7×D4 | — | 2 | 2 | no | — |
| 34 | C22×C7×D4 | — | 2 | 2 | no | — |
| 35 | C22×C7×D4 | — | 2 | 2 | no | — |
| 36 | C2×C7×D8 | — | 2 | 2 | no | — |
| 37 | C2×C7×D8 | — | 2 | 2 | no | — |
| 38 | C2×C7×D8 | — | 2 | 2 | no | — |
| 39 | C2×C7×D8 | — | 2 | 2 | no | — |
| 40 | C2×C7×D8 | — | 4 | 4 | no | — |
| 41 | C2×C7×D8 | — | 4 | 4 | no | — |
| 42 | C22×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 43 | C22×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 44 | C7×#127 | — | 2 | 2 | no | — |
| 45 | C7×#127 | — | 2 | 2 | no | — |
| 46 | C7×#127 | — | 2 | 2 | no | — |
| 47 | C7×#127 | C23 | 1 | 4 | yes | — |
| 48 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×#1142 | — | 2 | 8 | no | — |
| 50 | #6489 | — | 2 | 1 | no | — |
| 51 | #6487 | — | 2 | 1 | no | — |
| 52 | #6487 | D4 | 1 | 2 | yes | — |
| 53 | C2×#1136 | — | 2 | 1 | no | — |
| 54 | #6433 | — | 2 | 1 | no | — |
| 55 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 56 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 57 | C4×Dic14 | — | 2 | 1 | no | — |
| 58 | C4×Dic14 | C23 | 1 | 2 | yes | — |
| 59 | C4×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 60 | C4×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 61 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 62 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 63 | #6406 | — | 2 | 8 | no | — |
| 64 | C22⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 65 | #6389 | — | 2 | 2 | no | — |
| 66 | Dic7⋊C8 | — | 2 | 2 | no | — |
| 67 | Dic7⋊C8 | — | 2 | 2 | no | — |
| 68 | C8×Dic7 | — | 2 | 2 | no | — |
| 69 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 70 | C4⋊(C7⋊C8) | C23 | 1 | 2 | yes | — |
| 71 | C4⋊(C7⋊C8) | C23 | 1 | 4 | yes | — |
| 72 | C4×C7⋊C8 | — | 2 | 2 | no | — |
| 73 | #3208 | — | 7 | 2 | no | — |
| 74 | C2×#493 | D7 | 1 | 1 | yes | characteristic |
| 75 | #2960 | — | 7 | 1 | no | — |
| 76 | #1688 | — | 7 | 4 | no | — |
| 77 | #1668 | — | 7 | 4 | no | — |
| 78 | #1564 | — | 7 | 1 | no | — |
| 79 | #1545 | — | 7 | 2 | no | — |
| 80 | C24×C7 | — | 4 | 2 | no | — |
| 81 | C2×C7×D4 | — | 2 | 4 | no | — |
| 82 | C2×C7×D4 | — | 2 | 4 | no | — |
| 83 | C2×C7×D4 | — | 2 | 4 | no | — |
| 84 | C2×C7×D4 | — | 4 | 2 | no | — |
| 85 | C2×C7×D4 | — | 4 | 2 | no | — |
| 86 | C2×C7×D4 | — | 4 | 2 | no | — |
| 87 | C2×C7×D4 | — | 4 | 4 | no | — |
| 88 | C2×C7×D4 | — | 4 | 4 | no | — |
| 89 | C2×C7×D4 | — | 8 | 4 | no | — |
| 90 | C2×C7×D4 | — | 8 | 4 | no | — |
| 91 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 94 | C2×Dic14 | — | 2 | 1 | no | — |
| 95 | C2×Dic14 | C2×D4 | 1 | 2 | yes | — |
| 96 | C7×D8 | — | 4 | 4 | no | — |
| 97 | C7×D8 | — | 4 | 4 | no | — |
| 98 | C7×D8 | — | 4 | 4 | no | — |
| 99 | C7×D8 | — | 4 | 4 | no | — |
| 100 | C2×C7×C8 | — | 2 | 2 | no | — |
| 101 | C2×C7×C8 | SD16 | 1 | 4 | yes | complemented |
| 102 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 109 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 110 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 111 | #1142 | — | 8 | 8 | no | — |
| 112 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 113 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 114 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 115 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 116 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 117 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 118 | C4×Dic7 | — | 2 | 2 | no | — |
| 119 | #1136 | — | 4 | 2 | no | — |
| 120 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 121 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 122 | C22×D8 | — | 2 | 1 | no | — |
| 123 | C22×D8 | — | 2 | 1 | no | — |
| 124 | #533 | — | 7 | 1 | no | — |
| 125 | C2×#127 | C2×D7 | 1 | 2 | yes | — |
| 126 | #493 | — | 2 | 1 | no | — |
| 127 | #493 | — | 2 | 1 | no | — |
| 128 | #493 | C2×D7 | 1 | 2 | yes | — |
| 129 | #493 | C2×D7 | 1 | 2 | yes | — |
| 130 | #492 | — | 14 | 2 | no | — |
| 131 | #486 | — | 14 | 2 | no | — |
| 132 | #460 | — | 7 | 8 | no | — |
| 133 | #450 | — | 14 | 4 | no | — |
| 134 | #446 | — | 7 | 2 | no | — |
| 135 | #446 | — | 14 | 1 | no | — |
| 136 | C8×Q8 | — | 7 | 2 | no | — |
| 137 | C8×Q8 | — | 14 | 1 | no | — |
| 138 | #431 | — | 7 | 2 | no | — |
| 139 | #424 | — | 14 | 1 | no | — |
| 140 | #423 | — | 7 | 1 | no | — |
| 141 | #405 | — | 14 | 1 | no | — |
| 142 | C2×C4×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 143 | #335 | — | 7 | 2 | no | — |
| 144 | #334 | — | 7 | 2 | no | — |
| 145 | #331 | — | 7 | 8 | no | — |
| 146 | C23×C7 | — | 4 | 4 | no | — |
| 147 | C23×C7 | — | 8 | 4 | no | — |
| 148 | C23×C7 | — | 8 | 4 | no | — |
| 149 | C23×C7 | — | 8 | 4 | no | — |
| 150 | C23×C7 | #121 | 1 | 1 | yes | characteristic |
| 151 | C7×D4 | — | 4 | 4 | no | — |
| 152 | C7×D4 | — | 4 | 4 | no | — |
| 153 | C7×D4 | — | 4 | 8 | no | — |
| 154 | C7×D4 | — | 8 | 4 | no | — |
| 155 | C7×D4 | — | 8 | 4 | no | — |
| 156 | C7×D4 | — | 8 | 4 | no | — |
| 157 | C7×D4 | — | 8 | 4 | no | — |
| 158 | C2×C4×C7 | — | 2 | 2 | no | — |
| 159 | C2×C4×C7 | — | 2 | 2 | no | — |
| 160 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C7 | C2×SD16 | 1 | 2 | yes | — |
| 164 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 165 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 168 | C2×Dic7 | — | 2 | 2 | no | — |
| 169 | C2×Dic7 | — | 2 | 2 | no | — |
| 170 | Dic14 | — | 2 | 4 | no | — |
| 171 | Dic14 | — | 4 | 2 | no | — |
| 172 | C7×C8 | — | 2 | 1 | no | — |
| 173 | C7×C8 | — | 2 | 1 | no | — |
| 174 | C7×C8 | C2×SD16 | 1 | 2 | yes | — |
| 175 | C7×C8 | C2×SD16 | 1 | 2 | yes | — |
| 176 | C7⋊C8 | — | 4 | 2 | no | — |
| 177 | C7⋊C8 | — | 4 | 4 | no | — |
| 178 | C22×D4 | — | 2 | 2 | no | — |
| 179 | C22×D4 | — | 2 | 2 | no | — |
| 180 | C22×D4 | — | 2 | 2 | no | — |
| 181 | C2×SD16 | — | 14 | 8 | no | — |
| 182 | C2×D8 | — | 2 | 2 | no | — |
| 183 | C2×D8 | — | 2 | 2 | no | — |
| 184 | C2×D8 | — | 2 | 2 | no | — |
| 185 | C2×D8 | — | 2 | 2 | no | — |
| 186 | C2×D8 | — | 4 | 4 | no | — |
| 187 | C2×D8 | — | 4 | 4 | no | — |
| 188 | C2×M16 | — | 14 | 1 | no | — |
| 189 | C22×C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 190 | C22×C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 191 | C4⋊Q8 | — | 7 | 1 | no | — |
| 192 | C4⋊Q8 | — | 7 | 1 | no | — |
| 193 | #127 | — | 2 | 2 | no | — |
| 194 | #127 | — | 2 | 2 | no | — |
| 195 | #127 | — | 2 | 2 | no | — |
| 196 | #127 | C22×D7 | 1 | 4 | yes | — |
| 197 | #125 | — | 14 | 1 | no | — |
| 198 | C22⋊Q8 | — | 7 | 2 | no | — |
| 199 | C22⋊Q8 | — | 14 | 1 | no | — |
| 200 | C4×Q8 | — | 7 | 2 | no | — |
| 201 | C4×Q8 | — | 14 | 1 | no | — |
| 202 | #117 | — | 14 | 1 | no | — |
| 203 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 204 | C4⋊C8 | — | 7 | 2 | no | — |
| 205 | C4⋊C8 | — | 7 | 4 | no | — |
| 206 | C4⋊C8 | — | 14 | 2 | no | — |
| 207 | C4⋊C8 | — | 14 | 2 | no | — |
| 208 | C4⋊C8 | — | 14 | 1 | no | — |
| 209 | #102 | — | 14 | 8 | no | — |
| 210 | C22⋊C8 | — | 14 | 2 | no | — |
| 211 | #97 | — | 14 | 2 | no | — |
| 212 | C4×C8 | — | 14 | 2 | no | — |
| 213 | C4×C8 | — | 14 | 2 | no | — |
| 214 | C4×C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 215 | C4×C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 216 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 217 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 218 | C22×C7 | — | 2 | 1 | no | — |
| 219 | C22×C7 | — | 2 | 1 | no | — |
| 220 | C22×C7 | — | 8 | 4 | no | — |
| 221 | C22×C7 | — | 8 | 4 | no | — |
| 222 | C22×C7 | — | 8 | 4 | no | — |
| 223 | C22×C7 | — | 16 | 8 | no | — |
| 224 | C22×C7 | #460 | 1 | 2 | yes | — |
| 225 | C22×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 226 | C4×C7 | — | 2 | 1 | no | — |
| 227 | C4×C7 | — | 2 | 1 | no | — |
| 228 | C4×C7 | #460 | 1 | 2 | yes | — |
| 229 | C4×C7 | #472 | 1 | 2 | yes | — |
| 230 | C4×C7 | C22×SD16 | 1 | 1 | yes | characteristic |
| 231 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 232 | C4×C7 | #576 | 1 | 2 | yes | — |
| 233 | Dic7 | — | 4 | 2 | no | — |
| 234 | Dic7 | — | 4 | 2 | no | — |
| 235 | C24 | — | 4 | 2 | no | — |
| 236 | C2×Q8 | — | 7 | 2 | no | — |
| 237 | C2×Q8 | — | 14 | 1 | no | — |
| 238 | C2×D4 | — | 2 | 4 | no | — |
| 239 | C2×D4 | — | 2 | 4 | no | — |
| 240 | C2×D4 | — | 2 | 4 | no | — |
| 241 | C2×D4 | — | 4 | 4 | no | — |
| 242 | C2×D4 | — | 4 | 4 | no | — |
| 243 | C2×D4 | — | 4 | 2 | no | — |
| 244 | C2×D4 | — | 4 | 2 | no | — |
| 245 | C2×D4 | — | 4 | 2 | no | — |
| 246 | C2×D4 | — | 8 | 4 | no | — |
| 247 | C2×D4 | — | 8 | 4 | no | — |
| 248 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 249 | C22×C4 | #1159 | 1 | 1 | yes | characteristic |
| 250 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 251 | SD16 | — | 56 | 8 | no | — |
| 252 | D8 | — | 4 | 4 | no | — |
| 253 | D8 | — | 4 | 4 | no | — |
| 254 | D8 | — | 4 | 4 | no | — |
| 255 | D8 | — | 4 | 4 | no | — |
| 256 | M16 | — | 28 | 2 | no | — |
| 257 | C2×C8 | — | 2 | 2 | no | — |
| 258 | C2×C8 | — | 14 | 4 | no | — |
| 259 | C2×C8 | — | 14 | 2 | no | — |
| 260 | C2×C8 | #1142 | 1 | 4 | yes | complemented |
| 261 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 262 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 263 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 264 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 265 | C4⋊C4 | — | 7 | 2 | no | — |
| 266 | C4⋊C4 | — | 14 | 2 | no | — |
| 267 | C4⋊C4 | — | 14 | 1 | no | — |
| 268 | C4⋊C4 | — | 14 | 1 | no | — |
| 269 | C4⋊C4 | — | 14 | 1 | no | — |
| 270 | C4⋊C4 | — | 14 | 2 | no | — |
| 271 | C22⋊C4 | — | 14 | 2 | no | — |
| 272 | C42 | — | 14 | 2 | no | — |
| 273 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 274 | C42 | #1159 | 1 | 1 | yes | characteristic |
| 275 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 276 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 277 | C2×C7 | — | 2 | 2 | no | — |
| 278 | C2×C7 | — | 16 | 4 | no | — |
| 279 | C2×C7 | C2×#460 | 1 | 1 | yes | characteristic |
| 280 | C2×C7 | #3058 | 1 | 1 | yes | characteristic |
| 281 | C2×C7 | C2×#472 | 1 | 1 | yes | characteristic |
| 282 | C23 | — | 4 | 4 | no | — |
| 283 | C23 | — | 8 | 4 | no | — |
| 284 | C23 | — | 8 | 4 | no | — |
| 285 | C23 | — | 8 | 4 | no | — |
| 286 | C23 | #6501 | 1 | 1 | yes | characteristic |
| 287 | Q8 | — | 14 | 4 | no | — |
| 288 | Q8 | — | 28 | 2 | no | — |
| 289 | D4 | — | 4 | 8 | no | — |
| 290 | D4 | — | 4 | 4 | no | — |
| 291 | D4 | — | 4 | 4 | no | — |
| 292 | D4 | — | 8 | 4 | no | — |
| 293 | D4 | — | 8 | 4 | no | — |
| 294 | D4 | — | 8 | 4 | no | — |
| 295 | D4 | — | 8 | 4 | no | — |
| 296 | C2×C4 | — | 2 | 2 | no | — |
| 297 | C2×C4 | — | 2 | 2 | no | — |
| 298 | C2×C4 | — | 14 | 2 | no | — |
| 299 | C2×C4 | — | 14 | 2 | no | — |
| 300 | C2×C4 | #6495 | 1 | 2 | yes | — |
| 301 | C2×C4 | C2×#1142 | 1 | 2 | yes | — |
| 302 | C2×C4 | #6501 | 1 | 1 | yes | characteristic |
| 303 | C2×C4 | #6501 | 1 | 1 | yes | characteristic |
| 304 | C2×C4 | #6501 | 1 | 1 | yes | characteristic |
| 305 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 306 | C2×C4 | C2×#1159 | 1 | 1 | yes | characteristic |
| 307 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 308 | C8 | — | 2 | 1 | no | — |
| 309 | C8 | — | 2 | 1 | no | — |
| 310 | C8 | — | 28 | 4 | no | — |
| 311 | C8 | — | 28 | 2 | no | — |
| 312 | C8 | C2×#1142 | 1 | 2 | yes | — |
| 313 | C8 | C2×#1142 | 1 | 2 | yes | — |
| 314 | C7 | #19203 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 315 | C22 | — | 2 | 1 | no | — |
| 316 | C22 | — | 2 | 1 | no | — |
| 317 | C22 | — | 8 | 4 | no | — |
| 318 | C22 | — | 8 | 4 | no | — |
| 319 | C22 | — | 8 | 4 | no | — |
| 320 | C22 | — | 16 | 8 | no | — |
| 321 | C22 | #89847 | 1 | 2 | yes | — |
| 322 | C22 | C2×#6501 | 1 | 1 | yes | characteristic |
| 323 | C4 | — | 2 | 1 | no | — |
| 324 | C4 | — | 2 | 1 | no | — |
| 325 | C4 | — | 28 | 2 | no | — |
| 326 | C4 | — | 28 | 2 | no | — |
| 327 | C4 | #89847 | 1 | 2 | yes | — |
| 328 | C4 | #89932 | 1 | 2 | yes | — |
| 329 | C4 | #90448 | 1 | 2 | yes | — |
| 330 | C4 | C2×#6495 | 1 | 1 | yes | characteristic |
| 331 | C4 | C22×#1142 | 1 | 1 | yes | characteristic |
| 332 | C2 | — | 2 | 2 | no | — |
| 333 | C2 | — | 16 | 4 | no | — |
| 334 | C2 | C2×#89847 | 1 | 1 | yes | characteristic |
| 335 | C2 | #11741281 | 1 | 1 | yes | characteristic |
| 336 | C2 | C2×#89932 | 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