← C137×#20010 #46869396
Subgroups — C137×#20010 #46869396
Order 35072.
566 conjugacy classes of subgroups.
The subgroup lattice has 254 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #3395×C137 | C2 | 1 | 2 | yes | maximal |
| 2 | #3383×C137 | C2 | 1 | 2 | yes | maximal |
| 3 | #1713×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #1674×C137 | C2 | 1 | 2 | yes | maximal |
| 5 | #1670×C137 | C2 | 1 | 2 | yes | maximal |
| 6 | #1648×C137 | C2 | 1 | 4 | yes | maximal |
| 7 | C8×Q16×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C8×Q16×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #557×C137 | C22 | 1 | 4 | yes | — |
| 10 | #500×C137 | C22 | 1 | 2 | yes | — |
| 11 | #500×C137 | C22 | 1 | 2 | yes | — |
| 12 | #499×C137 | — | 2 | 2 | no | — |
| 13 | #494×C137 | — | 2 | 2 | no | — |
| 14 | #494×C137 | C22 | 1 | 2 | yes | — |
| 15 | #479×C137 | — | 2 | 4 | no | — |
| 16 | #475×C137 | C22 | 1 | 4 | yes | — |
| 17 | #462×C137 | — | 2 | 4 | no | — |
| 18 | #462×C137 | C22 | 1 | 4 | yes | — |
| 19 | C8×Q8×C137 | C22 | 1 | 2 | yes | — |
| 20 | C8×Q8×C137 | C22 | 1 | 2 | yes | — |
| 21 | C4×Q16×C137 | — | 2 | 2 | no | — |
| 22 | C4×Q16×C137 | — | 2 | 2 | no | — |
| 23 | C4×Q16×C137 | C22 | 1 | 1 | yes | characteristic |
| 24 | C4×Q16×C137 | C22 | 1 | 1 | yes | characteristic |
| 25 | #335×C137 | C22 | 1 | 1 | yes | characteristic |
| 26 | #335×C137 | C22 | 1 | 1 | yes | characteristic |
| 27 | #332×C137 | C22 | 1 | 4 | yes | — |
| 28 | Q8⋊C8×C137 | C22 | 1 | 2 | yes | — |
| 29 | Q8⋊C8×C137 | C22 | 1 | 2 | yes | — |
| 30 | C82×C137 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×Q16×C137 | — | 2 | 4 | no | — |
| 32 | C2×Q16×C137 | — | 2 | 2 | no | — |
| 33 | C2×Q16×C137 | — | 2 | 2 | no | — |
| 34 | C2×Q16×C137 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×Q16×C137 | D4 | 1 | 1 | yes | characteristic |
| 36 | C4⋊Q8×C137 | — | 2 | 4 | no | — |
| 37 | C4⋊Q8×C137 | C23 | 1 | 4 | yes | — |
| 38 | #125×C137 | — | 2 | 4 | no | — |
| 39 | #125×C137 | — | 4 | 4 | no | — |
| 40 | C4×Q8×C137 | — | 2 | 4 | no | — |
| 41 | C4×Q8×C137 | — | 2 | 4 | no | — |
| 42 | C4×Q8×C137 | C23 | 1 | 2 | yes | — |
| 43 | C4×Q8×C137 | C23 | 1 | 2 | yes | — |
| 44 | #107×C137 | — | 2 | 2 | no | — |
| 45 | #107×C137 | — | 2 | 2 | no | — |
| 46 | #107×C137 | — | 4 | 2 | no | — |
| 47 | #107×C137 | D4 | 1 | 1 | yes | characteristic |
| 48 | #107×C137 | D4 | 1 | 1 | yes | characteristic |
| 49 | #106×C137 | — | 2 | 4 | no | — |
| 50 | C4⋊C8×C137 | — | 2 | 2 | no | — |
| 51 | C4⋊C8×C137 | — | 2 | 2 | no | — |
| 52 | C4⋊C8×C137 | C23 | 1 | 2 | yes | — |
| 53 | C4⋊C8×C137 | C23 | 1 | 2 | yes | — |
| 54 | #103×C137 | — | 2 | 4 | no | — |
| 55 | #103×C137 | — | 2 | 4 | no | — |
| 56 | #103×C137 | D4 | 1 | 2 | yes | — |
| 57 | #103×C137 | D4 | 1 | 2 | yes | — |
| 58 | C4×C8×C137 | — | 2 | 2 | no | — |
| 59 | C4×C8×C137 | — | 2 | 2 | no | — |
| 60 | C4×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 61 | C4×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 62 | C4×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×Q8×C137 | — | 2 | 4 | no | — |
| 64 | C2×Q8×C137 | C2×D4 | 1 | 2 | yes | — |
| 65 | C2×Q8×C137 | C2×D4 | 1 | 2 | yes | — |
| 66 | Q16×C137 | — | 2 | 2 | no | — |
| 67 | Q16×C137 | — | 4 | 4 | no | — |
| 68 | Q16×C137 | — | 8 | 2 | no | — |
| 69 | Q16×C137 | — | 8 | 4 | no | — |
| 70 | Q16×C137 | Q16 | 1 | 4 | yes | complemented |
| 71 | C2×C8×C137 | — | 2 | 1 | no | — |
| 72 | C2×C8×C137 | — | 2 | 2 | no | — |
| 73 | C2×C8×C137 | — | 2 | 2 | no | — |
| 74 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 78 | C4⋊C4×C137 | — | 2 | 2 | no | — |
| 79 | C4⋊C4×C137 | — | 2 | 2 | no | — |
| 80 | C4⋊C4×C137 | — | 2 | 4 | no | — |
| 81 | C4⋊C4×C137 | — | 2 | 4 | no | — |
| 82 | C4⋊C4×C137 | — | 4 | 4 | no | — |
| 83 | C4⋊C4×C137 | — | 4 | 4 | no | — |
| 84 | C4⋊C4×C137 | — | 4 | 4 | no | — |
| 85 | C4⋊C4×C137 | C2×D4 | 1 | 2 | yes | — |
| 86 | C4⋊C4×C137 | C2×D4 | 1 | 2 | yes | — |
| 87 | C42×C137 | — | 2 | 2 | no | — |
| 88 | C42×C137 | — | 2 | 2 | no | — |
| 89 | C42×C137 | — | 4 | 4 | no | — |
| 90 | C42×C137 | C24 | 1 | 1 | yes | characteristic |
| 91 | Q8×C137 | — | 2 | 2 | no | — |
| 92 | Q8×C137 | — | 2 | 2 | no | — |
| 93 | Q8×C137 | — | 2 | 2 | no | — |
| 94 | Q8×C137 | — | 4 | 4 | no | — |
| 95 | Q8×C137 | — | 4 | 4 | no | — |
| 96 | Q8×C137 | C2×Q16 | 1 | 4 | yes | — |
| 97 | C2×C4×C137 | — | 2 | 2 | no | — |
| 98 | C2×C4×C137 | — | 2 | 2 | no | — |
| 99 | C2×C4×C137 | — | 2 | 2 | no | — |
| 100 | C2×C4×C137 | — | 2 | 2 | no | — |
| 101 | C2×C4×C137 | — | 4 | 4 | no | — |
| 102 | C2×C4×C137 | C22×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×C4×C137 | C22×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C137 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 105 | C8×C137 | — | 2 | 2 | no | — |
| 106 | C8×C137 | — | 2 | 1 | no | — |
| 107 | C8×C137 | — | 2 | 1 | no | — |
| 108 | C8×C137 | — | 4 | 2 | no | — |
| 109 | C8×C137 | — | 4 | 2 | no | — |
| 110 | C8×C137 | C2×Q16 | 1 | 2 | yes | — |
| 111 | C8×C137 | #135 | 1 | 2 | yes | — |
| 112 | C22×C137 | D42 | 1 | 1 | yes | characteristic |
| 113 | C4×C137 | — | 2 | 4 | no | — |
| 114 | C4×C137 | — | 2 | 1 | no | — |
| 115 | C4×C137 | — | 4 | 2 | no | — |
| 116 | C4×C137 | — | 4 | 2 | no | — |
| 117 | C4×C137 | — | 4 | 2 | no | — |
| 118 | C4×C137 | — | 8 | 4 | no | — |
| 119 | C4×C137 | C22×Q16 | 1 | 1 | yes | characteristic |
| 120 | C4×C137 | C2×#135 | 1 | 1 | yes | characteristic |
| 121 | C4×C137 | #576 | 1 | 1 | yes | characteristic |
| 122 | C4×C137 | #578 | 1 | 1 | yes | characteristic |
| 123 | C2×C137 | D4×Q16 | 1 | 1 | yes | characteristic |
| 124 | C2×C137 | #3287 | 1 | 1 | yes | characteristic |
| 125 | C2×C137 | #3293 | 1 | 1 | yes | characteristic |
| 126 | #20010 | C137 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 127 | C137 | #20010 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 128 | #3395 | C2×C137 | 1 | 2 | yes | — |
| 129 | #3383 | C2×C137 | 1 | 2 | yes | — |
| 130 | #1713 | C2×C137 | 1 | 1 | yes | characteristic |
| 131 | #1674 | C2×C137 | 1 | 2 | yes | — |
| 132 | #1670 | C2×C137 | 1 | 2 | yes | — |
| 133 | #1648 | C2×C137 | 1 | 4 | yes | — |
| 134 | C8×Q16 | C2×C137 | 1 | 1 | yes | characteristic |
| 135 | C8×Q16 | C2×C137 | 1 | 1 | yes | characteristic |
| 136 | #557 | C22×C137 | 1 | 4 | yes | — |
| 137 | #500 | C22×C137 | 1 | 2 | yes | — |
| 138 | #500 | C22×C137 | 1 | 2 | yes | — |
| 139 | #499 | — | 2 | 2 | no | — |
| 140 | #494 | — | 2 | 2 | no | — |
| 141 | #494 | C22×C137 | 1 | 2 | yes | — |
| 142 | #479 | — | 2 | 4 | no | — |
| 143 | #475 | C22×C137 | 1 | 4 | yes | — |
| 144 | #462 | — | 2 | 4 | no | — |
| 145 | #462 | C22×C137 | 1 | 4 | yes | — |
| 146 | C8×Q8 | C22×C137 | 1 | 2 | yes | — |
| 147 | C8×Q8 | C22×C137 | 1 | 2 | yes | — |
| 148 | C4×Q16 | — | 2 | 2 | no | — |
| 149 | C4×Q16 | — | 2 | 2 | no | — |
| 150 | C4×Q16 | C22×C137 | 1 | 1 | yes | characteristic |
| 151 | C4×Q16 | C22×C137 | 1 | 1 | yes | characteristic |
| 152 | #335 | C22×C137 | 1 | 1 | yes | characteristic |
| 153 | #335 | C22×C137 | 1 | 1 | yes | characteristic |
| 154 | #332 | C22×C137 | 1 | 4 | yes | — |
| 155 | Q8⋊C8 | C22×C137 | 1 | 2 | yes | — |
| 156 | Q8⋊C8 | C22×C137 | 1 | 2 | yes | — |
| 157 | C82 | C22×C137 | 1 | 1 | yes | characteristic |
| 158 | C2×Q16 | — | 2 | 4 | no | — |
| 159 | C2×Q16 | — | 2 | 2 | no | — |
| 160 | C2×Q16 | — | 2 | 2 | no | — |
| 161 | C2×Q16 | D4×C137 | 1 | 1 | yes | characteristic |
| 162 | C2×Q16 | D4×C137 | 1 | 1 | yes | characteristic |
| 163 | C4⋊Q8 | — | 2 | 4 | no | — |
| 164 | C4⋊Q8 | C23×C137 | 1 | 4 | yes | — |
| 165 | #125 | — | 2 | 4 | no | — |
| 166 | #125 | — | 4 | 4 | no | — |
| 167 | C4×Q8 | — | 2 | 4 | no | — |
| 168 | C4×Q8 | — | 2 | 4 | no | — |
| 169 | C4×Q8 | C23×C137 | 1 | 2 | yes | — |
| 170 | C4×Q8 | C23×C137 | 1 | 2 | yes | — |
| 171 | #107 | — | 2 | 2 | no | — |
| 172 | #107 | — | 2 | 2 | no | — |
| 173 | #107 | — | 4 | 2 | no | — |
| 174 | #107 | D4×C137 | 1 | 1 | yes | characteristic |
| 175 | #107 | D4×C137 | 1 | 1 | yes | characteristic |
| 176 | #106 | — | 2 | 4 | no | — |
| 177 | C4⋊C8 | — | 2 | 2 | no | — |
| 178 | C4⋊C8 | — | 2 | 2 | no | — |
| 179 | C4⋊C8 | C23×C137 | 1 | 2 | yes | — |
| 180 | C4⋊C8 | C23×C137 | 1 | 2 | yes | — |
| 181 | #103 | — | 2 | 4 | no | — |
| 182 | #103 | — | 2 | 4 | no | — |
| 183 | #103 | D4×C137 | 1 | 2 | yes | — |
| 184 | #103 | D4×C137 | 1 | 2 | yes | — |
| 185 | C4×C8 | — | 2 | 2 | no | — |
| 186 | C4×C8 | — | 2 | 2 | no | — |
| 187 | C4×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 188 | C4×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 189 | C4×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 190 | C2×Q8 | — | 2 | 4 | no | — |
| 191 | C2×Q8 | C2×D4×C137 | 1 | 2 | yes | — |
| 192 | C2×Q8 | C2×D4×C137 | 1 | 2 | yes | — |
| 193 | Q16 | — | 2 | 2 | no | — |
| 194 | Q16 | — | 4 | 4 | no | — |
| 195 | Q16 | — | 8 | 2 | no | — |
| 196 | Q16 | — | 8 | 4 | no | — |
| 197 | Q16 | Q16×C137 | 1 | 4 | yes | complemented |
| 198 | C2×C8 | — | 2 | 1 | no | — |
| 199 | C2×C8 | — | 2 | 2 | no | — |
| 200 | C2×C8 | — | 2 | 2 | no | — |
| 201 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 202 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 203 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 204 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 205 | C4⋊C4 | — | 2 | 2 | no | — |
| 206 | C4⋊C4 | — | 2 | 2 | no | — |
| 207 | C4⋊C4 | — | 2 | 4 | no | — |
| 208 | C4⋊C4 | — | 2 | 4 | no | — |
| 209 | C4⋊C4 | — | 4 | 4 | no | — |
| 210 | C4⋊C4 | — | 4 | 4 | no | — |
| 211 | C4⋊C4 | — | 4 | 4 | no | — |
| 212 | C4⋊C4 | C2×D4×C137 | 1 | 2 | yes | — |
| 213 | C4⋊C4 | C2×D4×C137 | 1 | 2 | yes | — |
| 214 | C42 | — | 2 | 2 | no | — |
| 215 | C42 | — | 2 | 2 | no | — |
| 216 | C42 | — | 4 | 4 | no | — |
| 217 | C42 | C24×C137 | 1 | 1 | yes | characteristic |
| 218 | Q8 | — | 2 | 2 | no | — |
| 219 | Q8 | — | 2 | 2 | no | — |
| 220 | Q8 | — | 2 | 2 | no | — |
| 221 | Q8 | — | 4 | 4 | no | — |
| 222 | Q8 | — | 4 | 4 | no | — |
| 223 | Q8 | C2×Q16×C137 | 1 | 4 | yes | — |
| 224 | C2×C4 | — | 2 | 2 | no | — |
| 225 | C2×C4 | — | 2 | 2 | no | — |
| 226 | C2×C4 | — | 2 | 2 | no | — |
| 227 | C2×C4 | — | 2 | 2 | no | — |
| 228 | C2×C4 | — | 4 | 4 | no | — |
| 229 | C2×C4 | C22×D4×C137 | 1 | 1 | yes | characteristic |
| 230 | C2×C4 | C22×D4×C137 | 1 | 1 | yes | characteristic |
| 231 | C2×C4 | H(5,𝔽2)×C137 | 1 | 1 | yes | characteristic |
| 232 | C8 | — | 2 | 2 | no | — |
| 233 | C8 | — | 2 | 1 | no | — |
| 234 | C8 | — | 2 | 1 | no | — |
| 235 | C8 | — | 4 | 2 | no | — |
| 236 | C8 | — | 4 | 2 | no | — |
| 237 | C8 | C2×Q16×C137 | 1 | 2 | yes | — |
| 238 | C8 | #135×C137 | 1 | 2 | yes | — |
| 239 | C22 | D42×C137 | 1 | 1 | yes | characteristic |
| 240 | C4 | — | 2 | 1 | no | — |
| 241 | C4 | — | 2 | 4 | no | — |
| 242 | C4 | — | 4 | 2 | no | — |
| 243 | C4 | — | 4 | 2 | no | — |
| 244 | C4 | — | 4 | 2 | no | — |
| 245 | C4 | — | 8 | 4 | no | — |
| 246 | C4 | C22×Q16×C137 | 1 | 1 | yes | characteristic |
| 247 | C4 | C2×#135×C137 | 1 | 1 | yes | characteristic |
| 248 | C4 | #576×C137 | 1 | 1 | yes | characteristic |
| 249 | C4 | #578×C137 | 1 | 1 | yes | characteristic |
| 250 | C2 | D4×Q16×C137 | 1 | 1 | yes | characteristic |
| 251 | C2 | #3287×C137 | 1 | 1 | yes | characteristic |
| 252 | C2 | #3293×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