← C137×#20006 #46869392
Subgroups — C137×#20006 #46869392
Order 35072.
586 conjugacy classes of subgroups.
The subgroup lattice has 262 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #3380×C137 | C2 | 1 | 2 | yes | maximal |
| 2 | #3338×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #1713×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #1676×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #1675×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #1632×C137 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C8×Q16×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C8×D8×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #554×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 | C22 | 1 | 2 | yes | — |
| 14 | #484×C137 | — | 2 | 4 | no | — |
| 15 | #478×C137 | — | 2 | 4 | no | — |
| 16 | #477×C137 | C22 | 1 | 4 | yes | — |
| 17 | #476×C137 | C22 | 1 | 4 | yes | — |
| 18 | #467×C137 | — | 2 | 2 | no | — |
| 19 | C8×Q8×C137 | C22 | 1 | 2 | yes | — |
| 20 | C4×Q16×C137 | C22 | 1 | 1 | yes | characteristic |
| 21 | C4×D8×C137 | — | 2 | 2 | no | — |
| 22 | C4×D8×C137 | C22 | 1 | 1 | yes | characteristic |
| 23 | C8×D4×C137 | C22 | 1 | 2 | yes | — |
| 24 | C2×#107×C137 | — | 2 | 2 | no | — |
| 25 | #335×C137 | C22 | 1 | 1 | yes | characteristic |
| 26 | #335×C137 | C22 | 1 | 1 | yes | characteristic |
| 27 | #333×C137 | C22 | 1 | 4 | yes | — |
| 28 | Q8⋊C8×C137 | C22 | 1 | 2 | yes | — |
| 29 | D4⋊C8×C137 | C22 | 1 | 2 | yes | — |
| 30 | C82×C137 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×Q16×C137 | — | 4 | 2 | no | — |
| 32 | C2×Q16×C137 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×D8×C137 | D4 | 1 | 1 | yes | characteristic |
| 34 | C22×C8×C137 | — | 2 | 2 | no | — |
| 35 | C4⋊Q8×C137 | C23 | 1 | 4 | yes | — |
| 36 | #125×C137 | — | 2 | 4 | no | — |
| 37 | C22⋊Q8×C137 | — | 2 | 4 | no | — |
| 38 | C22⋊Q8×C137 | — | 4 | 4 | no | — |
| 39 | C4×Q8×C137 | C23 | 1 | 2 | yes | — |
| 40 | C4×D4×C137 | — | 2 | 4 | no | — |
| 41 | C4×D4×C137 | C23 | 1 | 2 | yes | — |
| 42 | C2×C4⋊C4×C137 | — | 2 | 4 | no | — |
| 43 | #107×C137 | — | 2 | 2 | no | — |
| 44 | #107×C137 | — | 2 | 2 | no | — |
| 45 | #107×C137 | — | 2 | 2 | no | — |
| 46 | #107×C137 | — | 2 | 2 | no | — |
| 47 | #107×C137 | — | 2 | 4 | no | — |
| 48 | #107×C137 | D4 | 1 | 1 | yes | characteristic |
| 49 | #107×C137 | D4 | 1 | 1 | yes | characteristic |
| 50 | #106×C137 | — | 2 | 4 | 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 | D4 | 1 | 2 | yes | — |
| 56 | #102×C137 | — | 2 | 4 | no | — |
| 57 | #102×C137 | D4 | 1 | 2 | yes | — |
| 58 | C22⋊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×D4×C137 | C2×D4 | 1 | 2 | yes | — |
| 66 | C22×C4×C137 | — | 2 | 2 | no | — |
| 67 | C22×C4×C137 | — | 4 | 4 | no | — |
| 68 | Q16×C137 | — | 2 | 2 | no | — |
| 69 | Q16×C137 | — | 8 | 4 | no | — |
| 70 | D8×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 | — | 4 | 4 | no | — |
| 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 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 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 | C2×D4 | 1 | 2 | yes | — |
| 85 | C4⋊C4×C137 | C2×D4 | 1 | 2 | yes | — |
| 86 | C22⋊C4×C137 | — | 2 | 2 | no | — |
| 87 | C22⋊C4×C137 | — | 4 | 4 | no | — |
| 88 | C42×C137 | — | 2 | 2 | no | — |
| 89 | C42×C137 | C24 | 1 | 1 | yes | characteristic |
| 90 | C23×C137 | — | 2 | 2 | no | — |
| 91 | Q8×C137 | — | 2 | 2 | no | — |
| 92 | Q8×C137 | — | 2 | 2 | no | — |
| 93 | Q8×C137 | — | 8 | 4 | no | — |
| 94 | D4×C137 | — | 2 | 2 | no | — |
| 95 | D4×C137 | C2×Q16 | 1 | 4 | yes | — |
| 96 | C2×C4×C137 | — | 2 | 2 | no | — |
| 97 | C2×C4×C137 | — | 2 | 2 | no | — |
| 98 | C2×C4×C137 | — | 2 | 2 | no | — |
| 99 | C2×C4×C137 | — | 4 | 2 | no | — |
| 100 | C2×C4×C137 | — | 4 | 2 | no | — |
| 101 | C2×C4×C137 | — | 4 | 4 | no | — |
| 102 | C2×C4×C137 | — | 16 | 4 | no | — |
| 103 | C2×C4×C137 | C22×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C137 | C22×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C137 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 106 | C8×C137 | — | 2 | 2 | no | — |
| 107 | C8×C137 | — | 2 | 1 | no | — |
| 108 | C8×C137 | — | 2 | 1 | no | — |
| 109 | C8×C137 | — | 4 | 2 | no | — |
| 110 | C8×C137 | — | 4 | 2 | no | — |
| 111 | C8×C137 | C2×Q16 | 1 | 2 | yes | — |
| 112 | C8×C137 | #135 | 1 | 2 | yes | — |
| 113 | C22×C137 | — | 2 | 4 | no | — |
| 114 | C22×C137 | — | 4 | 2 | no | — |
| 115 | C22×C137 | — | 4 | 2 | no | — |
| 116 | C22×C137 | D42 | 1 | 1 | yes | characteristic |
| 117 | C4×C137 | — | 2 | 1 | no | — |
| 118 | C4×C137 | — | 4 | 2 | no | — |
| 119 | C4×C137 | — | 4 | 2 | no | — |
| 120 | C4×C137 | — | 4 | 2 | no | — |
| 121 | C4×C137 | — | 8 | 4 | no | — |
| 122 | C4×C137 | C22×Q16 | 1 | 1 | yes | characteristic |
| 123 | C4×C137 | C2×#135 | 1 | 1 | yes | characteristic |
| 124 | C4×C137 | #578 | 1 | 1 | yes | characteristic |
| 125 | C4×C137 | #578 | 1 | 1 | yes | characteristic |
| 126 | C2×C137 | — | 4 | 4 | no | — |
| 127 | C2×C137 | #3283 | 1 | 1 | yes | characteristic |
| 128 | C2×C137 | D4×Q16 | 1 | 1 | yes | characteristic |
| 129 | C2×C137 | #3292 | 1 | 1 | yes | characteristic |
| 130 | #20006 | C137 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 131 | C137 | #20006 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 132 | #3380 | C2×C137 | 1 | 2 | yes | — |
| 133 | #3338 | C2×C137 | 1 | 2 | yes | complemented |
| 134 | #1713 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 135 | #1676 | C2×C137 | 1 | 2 | yes | complemented |
| 136 | #1675 | C2×C137 | 1 | 2 | yes | complemented |
| 137 | #1632 | C2×C137 | 1 | 4 | yes | complemented |
| 138 | C8×Q16 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 139 | C8×D8 | C2×C137 | 1 | 1 | yes | characteristic |
| 140 | #554 | C22×C137 | 1 | 4 | yes | — |
| 141 | #500 | C22×C137 | 1 | 2 | yes | — |
| 142 | #500 | C22×C137 | 1 | 2 | yes | — |
| 143 | #499 | — | 2 | 2 | no | — |
| 144 | #494 | C22×C137 | 1 | 2 | yes | — |
| 145 | #484 | — | 2 | 4 | no | — |
| 146 | #478 | — | 2 | 4 | no | — |
| 147 | #477 | C22×C137 | 1 | 4 | yes | — |
| 148 | #476 | C22×C137 | 1 | 4 | yes | — |
| 149 | #467 | — | 2 | 2 | no | — |
| 150 | C8×Q8 | C22×C137 | 1 | 2 | yes | — |
| 151 | C4×Q16 | C22×C137 | 1 | 1 | yes | characteristic |
| 152 | C4×D8 | — | 2 | 2 | no | — |
| 153 | C4×D8 | C22×C137 | 1 | 1 | yes | characteristic |
| 154 | C8×D4 | C22×C137 | 1 | 2 | yes | — |
| 155 | C2×#107 | — | 2 | 2 | no | — |
| 156 | #335 | C22×C137 | 1 | 1 | yes | characteristic |
| 157 | #335 | C22×C137 | 1 | 1 | yes | characteristic |
| 158 | #333 | C22×C137 | 1 | 4 | yes | — |
| 159 | Q8⋊C8 | C22×C137 | 1 | 2 | yes | — |
| 160 | D4⋊C8 | C22×C137 | 1 | 2 | yes | — |
| 161 | C82 | C22×C137 | 1 | 1 | yes | characteristic |
| 162 | C2×Q16 | — | 4 | 2 | no | — |
| 163 | C2×Q16 | D4×C137 | 1 | 1 | yes | characteristic |
| 164 | C2×D8 | D4×C137 | 1 | 1 | yes | characteristic |
| 165 | C22×C8 | — | 2 | 2 | no | — |
| 166 | C4⋊Q8 | C23×C137 | 1 | 4 | yes | — |
| 167 | #125 | — | 2 | 4 | no | — |
| 168 | C22⋊Q8 | — | 2 | 4 | no | — |
| 169 | C22⋊Q8 | — | 4 | 4 | no | — |
| 170 | C4×Q8 | C23×C137 | 1 | 2 | yes | — |
| 171 | C4×D4 | — | 2 | 4 | no | — |
| 172 | C4×D4 | C23×C137 | 1 | 2 | yes | — |
| 173 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 174 | #107 | — | 2 | 2 | no | — |
| 175 | #107 | — | 2 | 2 | no | — |
| 176 | #107 | — | 2 | 2 | no | — |
| 177 | #107 | — | 2 | 2 | no | — |
| 178 | #107 | — | 2 | 4 | no | — |
| 179 | #107 | D4×C137 | 1 | 1 | yes | characteristic |
| 180 | #107 | D4×C137 | 1 | 1 | yes | characteristic |
| 181 | #106 | — | 2 | 4 | no | — |
| 182 | C4⋊C8 | — | 2 | 2 | no | — |
| 183 | C4⋊C8 | C23×C137 | 1 | 2 | yes | — |
| 184 | C4⋊C8 | C23×C137 | 1 | 2 | yes | — |
| 185 | #103 | — | 2 | 4 | no | — |
| 186 | #103 | D4×C137 | 1 | 2 | yes | — |
| 187 | #102 | — | 2 | 4 | no | — |
| 188 | #102 | D4×C137 | 1 | 2 | yes | — |
| 189 | C22⋊C8 | — | 2 | 2 | no | — |
| 190 | C4×C8 | — | 2 | 2 | no | — |
| 191 | C4×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 192 | C4×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 193 | C4×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 194 | C2×Q8 | — | 2 | 4 | no | — |
| 195 | C2×Q8 | C2×D4×C137 | 1 | 2 | yes | — |
| 196 | C2×D4 | C2×D4×C137 | 1 | 2 | yes | — |
| 197 | C22×C4 | — | 2 | 2 | no | — |
| 198 | C22×C4 | — | 4 | 4 | no | — |
| 199 | Q16 | — | 2 | 2 | no | — |
| 200 | Q16 | — | 8 | 4 | no | — |
| 201 | D8 | Q16×C137 | 1 | 4 | yes | complemented |
| 202 | C2×C8 | — | 2 | 1 | no | — |
| 203 | C2×C8 | — | 2 | 2 | no | — |
| 204 | C2×C8 | — | 2 | 2 | no | — |
| 205 | C2×C8 | — | 4 | 4 | no | — |
| 206 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 207 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 208 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 209 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 210 | C4⋊C4 | — | 2 | 2 | no | — |
| 211 | C4⋊C4 | — | 2 | 4 | no | — |
| 212 | C4⋊C4 | — | 2 | 4 | no | — |
| 213 | C4⋊C4 | — | 4 | 4 | no | — |
| 214 | C4⋊C4 | — | 4 | 4 | no | — |
| 215 | C4⋊C4 | C2×D4×C137 | 1 | 2 | yes | — |
| 216 | C4⋊C4 | C2×D4×C137 | 1 | 2 | yes | — |
| 217 | C22⋊C4 | — | 2 | 2 | no | — |
| 218 | C22⋊C4 | — | 4 | 4 | no | — |
| 219 | C42 | — | 2 | 2 | no | — |
| 220 | C42 | C24×C137 | 1 | 1 | yes | characteristic |
| 221 | C23 | — | 2 | 2 | no | — |
| 222 | Q8 | — | 2 | 2 | no | — |
| 223 | Q8 | — | 2 | 2 | no | — |
| 224 | Q8 | — | 8 | 4 | no | — |
| 225 | D4 | — | 2 | 2 | no | — |
| 226 | D4 | C2×Q16×C137 | 1 | 4 | yes | — |
| 227 | C2×C4 | — | 2 | 2 | no | — |
| 228 | C2×C4 | — | 2 | 2 | no | — |
| 229 | C2×C4 | — | 2 | 2 | no | — |
| 230 | C2×C4 | — | 4 | 2 | no | — |
| 231 | C2×C4 | — | 4 | 2 | no | — |
| 232 | C2×C4 | — | 4 | 4 | no | — |
| 233 | C2×C4 | — | 16 | 4 | no | — |
| 234 | C2×C4 | C22×D4×C137 | 1 | 1 | yes | characteristic |
| 235 | C2×C4 | C22×D4×C137 | 1 | 1 | yes | characteristic |
| 236 | C2×C4 | H(5,𝔽2)×C137 | 1 | 1 | yes | characteristic |
| 237 | C8 | — | 2 | 2 | no | — |
| 238 | C8 | — | 2 | 1 | no | — |
| 239 | C8 | — | 2 | 1 | no | — |
| 240 | C8 | — | 4 | 2 | no | — |
| 241 | C8 | — | 4 | 2 | no | — |
| 242 | C8 | C2×Q16×C137 | 1 | 2 | yes | — |
| 243 | C8 | #135×C137 | 1 | 2 | yes | — |
| 244 | C22 | — | 2 | 4 | no | — |
| 245 | C22 | — | 4 | 2 | no | — |
| 246 | C22 | — | 4 | 2 | no | — |
| 247 | C22 | D42×C137 | 1 | 1 | yes | characteristic |
| 248 | C4 | — | 2 | 1 | no | — |
| 249 | C4 | — | 4 | 2 | no | — |
| 250 | C4 | — | 4 | 2 | no | — |
| 251 | C4 | — | 4 | 2 | no | — |
| 252 | C4 | — | 8 | 4 | no | — |
| 253 | C4 | C22×Q16×C137 | 1 | 1 | yes | characteristic |
| 254 | C4 | C2×#135×C137 | 1 | 1 | yes | characteristic |
| 255 | C4 | #578×C137 | 1 | 1 | yes | characteristic |
| 256 | C4 | #578×C137 | 1 | 1 | yes | characteristic |
| 257 | C2 | — | 4 | 4 | no | — |
| 258 | C2 | #3283×C137 | 1 | 1 | yes | characteristic |
| 259 | C2 | D4×Q16×C137 | 1 | 1 | yes | characteristic |
| 260 | C2 | #3292×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