← C137×#33919 #46883305
Subgroups — C137×#33919 #46883305
Order 35072.
464 conjugacy classes of subgroups.
The subgroup lattice has 266 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #3336×C137 | C2 | 1 | 2 | yes | maximal |
| 2 | #2253×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #2237×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #2236×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #2229×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #2219×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C4×Q32×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #2169×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #2159×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #552×C137 | — | 2 | 2 | no | — |
| 11 | C2×Q32×C137 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×M32×C137 | C22 | 1 | 2 | yes | — |
| 13 | #499×C137 | C22 | 1 | 2 | yes | — |
| 14 | #485×C137 | — | 2 | 2 | no | — |
| 15 | #483×C137 | — | 2 | 2 | no | — |
| 16 | #479×C137 | — | 2 | 2 | no | — |
| 17 | #467×C137 | C22 | 1 | 2 | yes | — |
| 18 | #467×C137 | C22 | 1 | 2 | yes | — |
| 19 | C4×Q16×C137 | C22 | 1 | 2 | yes | — |
| 20 | C8×D4×C137 | C22 | 1 | 1 | yes | characteristic |
| 21 | #427×C137 | C22 | 1 | 2 | yes | — |
| 22 | C2×#107×C137 | C22 | 1 | 2 | yes | — |
| 23 | #367×C137 | C22 | 1 | 2 | yes | — |
| 24 | #367×C137 | C22 | 1 | 2 | yes | — |
| 25 | #366×C137 | C22 | 1 | 1 | yes | characteristic |
| 26 | #366×C137 | C22 | 1 | 2 | yes | — |
| 27 | #366×C137 | C22 | 1 | 1 | yes | characteristic |
| 28 | #366×C137 | C22 | 1 | 1 | yes | characteristic |
| 29 | C4⋊C16×C137 | C22 | 1 | 1 | yes | characteristic |
| 30 | #358×C137 | C22 | 1 | 2 | yes | — |
| 31 | #358×C137 | C22 | 1 | 2 | yes | — |
| 32 | #358×C137 | C22 | 1 | 2 | yes | — |
| 33 | C22⋊C16×C137 | C22 | 1 | 2 | yes | — |
| 34 | C4×C16×C137 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×Q16×C137 | C23 | 1 | 2 | yes | — |
| 36 | C22×C8×C137 | C23 | 1 | 2 | yes | — |
| 37 | #126×C137 | — | 4 | 2 | no | — |
| 38 | #125×C137 | — | 2 | 2 | no | — |
| 39 | #125×C137 | — | 4 | 2 | no | — |
| 40 | #123×C137 | — | 4 | 2 | no | — |
| 41 | C22⋊Q8×C137 | — | 2 | 2 | no | — |
| 42 | C22⋊Q8×C137 | — | 2 | 2 | no | — |
| 43 | C4×Q8×C137 | — | 2 | 2 | no | — |
| 44 | C4×D4×C137 | D4 | 1 | 1 | yes | characteristic |
| 45 | #117×C137 | — | 2 | 2 | no | — |
| 46 | #117×C137 | — | 4 | 2 | no | — |
| 47 | C2×C4⋊C4×C137 | — | 2 | 2 | no | — |
| 48 | Q32×C137 | — | 2 | 2 | no | — |
| 49 | M32×C137 | — | 2 | 4 | no | — |
| 50 | C2×C16×C137 | C23 | 1 | 2 | yes | — |
| 51 | C2×C16×C137 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×C16×C137 | C23 | 1 | 1 | yes | characteristic |
| 53 | #107×C137 | — | 2 | 2 | no | — |
| 54 | #107×C137 | C23 | 1 | 2 | yes | — |
| 55 | #107×C137 | C23 | 1 | 2 | yes | — |
| 56 | #107×C137 | C23 | 1 | 2 | yes | — |
| 57 | #106×C137 | — | 2 | 2 | no | — |
| 58 | #106×C137 | — | 2 | 2 | no | — |
| 59 | C4⋊C8×C137 | D4 | 1 | 1 | yes | characteristic |
| 60 | #103×C137 | — | 2 | 2 | no | — |
| 61 | #103×C137 | — | 2 | 2 | no | — |
| 62 | #103×C137 | — | 2 | 2 | no | — |
| 63 | C22⋊C8×C137 | D4 | 1 | 2 | yes | — |
| 64 | C4×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×Q8×C137 | — | 2 | 2 | no | — |
| 66 | C2×D4×C137 | D8 | 1 | 1 | yes | characteristic |
| 67 | C22×C4×C137 | — | 4 | 2 | no | — |
| 68 | C22×C4×C137 | C2×D4 | 1 | 2 | yes | — |
| 69 | Q16×C137 | — | 2 | 2 | no | — |
| 70 | Q16×C137 | — | 2 | 2 | no | — |
| 71 | C2×C8×C137 | — | 2 | 2 | no | — |
| 72 | C2×C8×C137 | — | 2 | 2 | no | — |
| 73 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C2×C8×C137 | C2×D4 | 1 | 2 | yes | — |
| 75 | C2×C8×C137 | C24 | 1 | 1 | yes | characteristic |
| 76 | C4⋊C4×C137 | — | 2 | 2 | no | — |
| 77 | C4⋊C4×C137 | — | 2 | 2 | no | — |
| 78 | C4⋊C4×C137 | — | 2 | 2 | no | — |
| 79 | C4⋊C4×C137 | — | 4 | 2 | no | — |
| 80 | C4⋊C4×C137 | — | 4 | 2 | no | — |
| 81 | C4⋊C4×C137 | — | 4 | 2 | no | — |
| 82 | C4⋊C4×C137 | — | 4 | 2 | no | — |
| 83 | C4⋊C4×C137 | — | 4 | 2 | no | — |
| 84 | C4⋊C4×C137 | — | 4 | 2 | no | — |
| 85 | C4⋊C4×C137 | D8 | 1 | 1 | yes | characteristic |
| 86 | C22⋊C4×C137 | — | 4 | 2 | no | — |
| 87 | C22⋊C4×C137 | — | 4 | 2 | no | — |
| 88 | C22⋊C4×C137 | — | 4 | 2 | no | — |
| 89 | C22⋊C4×C137 | D8 | 1 | 2 | yes | — |
| 90 | C42×C137 | — | 4 | 2 | no | — |
| 91 | C42×C137 | — | 4 | 2 | no | — |
| 92 | C42×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C16×C137 | — | 2 | 2 | no | — |
| 94 | C16×C137 | — | 2 | 1 | no | — |
| 95 | C16×C137 | #41 | 1 | 2 | yes | — |
| 96 | C23×C137 | C2×D8 | 1 | 2 | yes | — |
| 97 | Q8×C137 | — | 4 | 2 | no | — |
| 98 | Q8×C137 | — | 4 | 2 | no | — |
| 99 | D4×C137 | — | 4 | 1 | no | — |
| 100 | C2×C4×C137 | — | 2 | 2 | no | — |
| 101 | C2×C4×C137 | — | 2 | 2 | no | — |
| 102 | C2×C4×C137 | — | 4 | 2 | no | — |
| 103 | C2×C4×C137 | — | 4 | 2 | no | — |
| 104 | C2×C4×C137 | — | 4 | 2 | no | — |
| 105 | C2×C4×C137 | — | 4 | 2 | no | — |
| 106 | C2×C4×C137 | — | 8 | 4 | no | — |
| 107 | C2×C4×C137 | C2×D8 | 1 | 1 | yes | characteristic |
| 108 | C2×C4×C137 | C2×D8 | 1 | 2 | yes | — |
| 109 | C2×C4×C137 | C2×D8 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C137 | C22×D4 | 1 | 1 | yes | characteristic |
| 111 | C8×C137 | — | 2 | 2 | no | — |
| 112 | C8×C137 | — | 2 | 1 | no | — |
| 113 | C8×C137 | C2×#41 | 1 | 1 | yes | characteristic |
| 114 | C8×C137 | 2−1+4 | 1 | 1 | yes | characteristic |
| 115 | C22×C137 | — | 2 | 2 | no | — |
| 116 | C22×C137 | — | 2 | 2 | no | — |
| 117 | C22×C137 | — | 2 | 2 | no | — |
| 118 | C22×C137 | C22×D8 | 1 | 1 | yes | characteristic |
| 119 | C4×C137 | — | 2 | 2 | no | — |
| 120 | C4×C137 | — | 2 | 1 | no | — |
| 121 | C4×C137 | — | 2 | 1 | no | — |
| 122 | C4×C137 | — | 8 | 2 | no | — |
| 123 | C4×C137 | — | 8 | 2 | no | — |
| 124 | C4×C137 | — | 8 | 2 | no | — |
| 125 | C4×C137 | — | 8 | 2 | no | — |
| 126 | C4×C137 | #547 | 1 | 1 | yes | characteristic |
| 127 | C4×C137 | #578 | 1 | 1 | yes | characteristic |
| 128 | C2×C137 | — | 4 | 2 | no | — |
| 129 | C2×C137 | #3334 | 1 | 1 | yes | characteristic |
| 130 | C2×C137 | #3414 | 1 | 1 | yes | characteristic |
| 131 | C2×C137 | #3417 | 1 | 1 | yes | characteristic |
| 132 | #33919 | C137 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 133 | C137 | #33919 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 134 | #3336 | C2×C137 | 1 | 2 | yes | — |
| 135 | #2253 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 136 | #2237 | C2×C137 | 1 | 2 | yes | complemented |
| 137 | #2236 | C2×C137 | 1 | 2 | yes | complemented |
| 138 | #2229 | C2×C137 | 1 | 2 | yes | complemented |
| 139 | #2219 | C2×C137 | 1 | 2 | yes | complemented |
| 140 | C4×Q32 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 141 | #2169 | C2×C137 | 1 | 1 | yes | characteristic |
| 142 | #2159 | C2×C137 | 1 | 2 | yes | complemented |
| 143 | #552 | — | 2 | 2 | no | — |
| 144 | C2×Q32 | C22×C137 | 1 | 1 | yes | characteristic |
| 145 | C2×M32 | C22×C137 | 1 | 2 | yes | — |
| 146 | #499 | C22×C137 | 1 | 2 | yes | — |
| 147 | #485 | — | 2 | 2 | no | — |
| 148 | #483 | — | 2 | 2 | no | — |
| 149 | #479 | — | 2 | 2 | no | — |
| 150 | #467 | C22×C137 | 1 | 2 | yes | — |
| 151 | #467 | C22×C137 | 1 | 2 | yes | — |
| 152 | C4×Q16 | C22×C137 | 1 | 2 | yes | — |
| 153 | C8×D4 | C22×C137 | 1 | 1 | yes | characteristic |
| 154 | #427 | C22×C137 | 1 | 2 | yes | — |
| 155 | C2×#107 | C22×C137 | 1 | 2 | yes | — |
| 156 | #367 | C22×C137 | 1 | 2 | yes | — |
| 157 | #367 | C22×C137 | 1 | 2 | yes | — |
| 158 | #366 | C22×C137 | 1 | 1 | yes | characteristic |
| 159 | #366 | C22×C137 | 1 | 2 | yes | — |
| 160 | #366 | C22×C137 | 1 | 1 | yes | characteristic |
| 161 | #366 | C22×C137 | 1 | 1 | yes | characteristic |
| 162 | C4⋊C16 | C22×C137 | 1 | 1 | yes | characteristic |
| 163 | #358 | C22×C137 | 1 | 2 | yes | — |
| 164 | #358 | C22×C137 | 1 | 2 | yes | — |
| 165 | #358 | C22×C137 | 1 | 2 | yes | — |
| 166 | C22⋊C16 | C22×C137 | 1 | 2 | yes | — |
| 167 | C4×C16 | C22×C137 | 1 | 1 | yes | characteristic |
| 168 | C2×Q16 | C23×C137 | 1 | 2 | yes | — |
| 169 | C22×C8 | C23×C137 | 1 | 2 | yes | — |
| 170 | #126 | — | 4 | 2 | no | — |
| 171 | #125 | — | 2 | 2 | no | — |
| 172 | #125 | — | 4 | 2 | no | — |
| 173 | #123 | — | 4 | 2 | no | — |
| 174 | C22⋊Q8 | — | 2 | 2 | no | — |
| 175 | C22⋊Q8 | — | 2 | 2 | no | — |
| 176 | C4×Q8 | — | 2 | 2 | no | — |
| 177 | C4×D4 | D4×C137 | 1 | 1 | yes | characteristic |
| 178 | #117 | — | 2 | 2 | no | — |
| 179 | #117 | — | 4 | 2 | no | — |
| 180 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 181 | Q32 | — | 2 | 2 | no | — |
| 182 | M32 | — | 2 | 4 | no | — |
| 183 | C2×C16 | C23×C137 | 1 | 1 | yes | characteristic |
| 184 | C2×C16 | C23×C137 | 1 | 2 | yes | — |
| 185 | C2×C16 | C23×C137 | 1 | 1 | yes | characteristic |
| 186 | #107 | — | 2 | 2 | no | — |
| 187 | #107 | C23×C137 | 1 | 2 | yes | — |
| 188 | #107 | C23×C137 | 1 | 2 | yes | — |
| 189 | #107 | C23×C137 | 1 | 2 | yes | — |
| 190 | #106 | — | 2 | 2 | no | — |
| 191 | #106 | — | 2 | 2 | no | — |
| 192 | C4⋊C8 | D4×C137 | 1 | 1 | yes | characteristic |
| 193 | #103 | — | 2 | 2 | no | — |
| 194 | #103 | — | 2 | 2 | no | — |
| 195 | #103 | — | 2 | 2 | no | — |
| 196 | C22⋊C8 | D4×C137 | 1 | 2 | yes | — |
| 197 | C4×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 198 | C2×Q8 | — | 2 | 2 | no | — |
| 199 | C2×D4 | D8×C137 | 1 | 1 | yes | characteristic |
| 200 | C22×C4 | — | 4 | 2 | no | — |
| 201 | C22×C4 | C2×D4×C137 | 1 | 2 | yes | — |
| 202 | Q16 | — | 2 | 2 | no | — |
| 203 | Q16 | — | 2 | 2 | no | — |
| 204 | C2×C8 | — | 2 | 2 | no | — |
| 205 | C2×C8 | — | 2 | 2 | no | — |
| 206 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 207 | C2×C8 | C2×D4×C137 | 1 | 2 | yes | — |
| 208 | C2×C8 | C24×C137 | 1 | 1 | yes | characteristic |
| 209 | C4⋊C4 | — | 2 | 2 | no | — |
| 210 | C4⋊C4 | — | 2 | 2 | no | — |
| 211 | C4⋊C4 | — | 2 | 2 | no | — |
| 212 | C4⋊C4 | — | 4 | 2 | no | — |
| 213 | C4⋊C4 | — | 4 | 2 | no | — |
| 214 | C4⋊C4 | — | 4 | 2 | no | — |
| 215 | C4⋊C4 | — | 4 | 2 | no | — |
| 216 | C4⋊C4 | — | 4 | 2 | no | — |
| 217 | C4⋊C4 | — | 4 | 2 | no | — |
| 218 | C4⋊C4 | D8×C137 | 1 | 1 | yes | characteristic |
| 219 | C22⋊C4 | — | 4 | 2 | no | — |
| 220 | C22⋊C4 | — | 4 | 2 | no | — |
| 221 | C22⋊C4 | — | 4 | 2 | no | — |
| 222 | C22⋊C4 | D8×C137 | 1 | 2 | yes | — |
| 223 | C42 | — | 4 | 2 | no | — |
| 224 | C42 | — | 4 | 2 | no | — |
| 225 | C42 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 226 | C16 | — | 2 | 2 | no | — |
| 227 | C16 | — | 2 | 1 | no | — |
| 228 | C16 | #41×C137 | 1 | 2 | yes | — |
| 229 | C23 | C2×D8×C137 | 1 | 2 | yes | — |
| 230 | Q8 | — | 4 | 2 | no | — |
| 231 | Q8 | — | 4 | 2 | no | — |
| 232 | D4 | — | 4 | 1 | no | — |
| 233 | C2×C4 | — | 2 | 2 | no | — |
| 234 | C2×C4 | — | 2 | 2 | no | — |
| 235 | C2×C4 | — | 4 | 2 | no | — |
| 236 | C2×C4 | — | 4 | 2 | no | — |
| 237 | C2×C4 | — | 4 | 2 | no | — |
| 238 | C2×C4 | — | 4 | 2 | no | — |
| 239 | C2×C4 | — | 8 | 4 | no | — |
| 240 | C2×C4 | C2×D8×C137 | 1 | 1 | yes | characteristic |
| 241 | C2×C4 | C2×D8×C137 | 1 | 2 | yes | — |
| 242 | C2×C4 | C2×D8×C137 | 1 | 1 | yes | characteristic |
| 243 | C2×C4 | C22×D4×C137 | 1 | 1 | yes | characteristic |
| 244 | C8 | — | 2 | 2 | no | — |
| 245 | C8 | — | 2 | 1 | no | — |
| 246 | C8 | C2×#41×C137 | 1 | 1 | yes | characteristic |
| 247 | C8 | 2−1+4×C137 | 1 | 1 | yes | characteristic |
| 248 | C22 | — | 2 | 2 | no | — |
| 249 | C22 | — | 2 | 2 | no | — |
| 250 | C22 | — | 2 | 2 | no | — |
| 251 | C22 | C22×D8×C137 | 1 | 1 | yes | characteristic |
| 252 | C4 | — | 2 | 2 | no | — |
| 253 | C4 | — | 2 | 1 | no | — |
| 254 | C4 | — | 2 | 1 | no | — |
| 255 | C4 | — | 8 | 2 | no | — |
| 256 | C4 | — | 8 | 2 | no | — |
| 257 | C4 | — | 8 | 2 | no | — |
| 258 | C4 | — | 8 | 2 | no | — |
| 259 | C4 | #547×C137 | 1 | 1 | yes | characteristic |
| 260 | C4 | #578×C137 | 1 | 1 | yes | characteristic |
| 261 | C2 | — | 4 | 2 | no | — |
| 262 | C2 | #3334×C137 | 1 | 1 | yes | characteristic |
| 263 | C2 | #3414×C137 | 1 | 1 | yes | characteristic |
| 264 | C2 | #3417×C137 | 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