← C137×#11976 #46861362
Subgroups — C137×#11976 #46861362
Order 35072.
292 conjugacy classes of subgroups.
The subgroup lattice has 226 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #3160×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #2163×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #1567×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #1365×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #1364×C137 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #533×C137 | — | 2 | 1 | no | — |
| 7 | #500×C137 | C22 | 1 | 1 | yes | characteristic |
| 8 | #500×C137 | C22 | 1 | 1 | yes | characteristic |
| 9 | #499×C137 | — | 2 | 1 | no | — |
| 10 | #499×C137 | C4 | 1 | 2 | yes | — |
| 11 | #498×C137 | — | 2 | 1 | no | — |
| 12 | #427×C137 | — | 2 | 1 | no | — |
| 13 | #427×C137 | C4 | 1 | 2 | yes | — |
| 14 | #423×C137 | — | 2 | 1 | no | — |
| 15 | C2×C4×C8×C137 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4⋊C16×C137 | C22 | 1 | 2 | yes | — |
| 17 | C22⋊C16×C137 | — | 2 | 1 | no | — |
| 18 | #346×C137 | — | 2 | 1 | no | — |
| 19 | #335×C137 | — | 2 | 1 | no | — |
| 20 | #335×C137 | C22 | 1 | 2 | yes | — |
| 21 | C2×M16×C137 | — | 4 | 1 | no | — |
| 22 | C22×C8×C137 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | C22×C8×C137 | D4 | 1 | 1 | yes | characteristic |
| 24 | C4⋊Q8×C137 | — | 2 | 1 | no | — |
| 25 | C4⋊Q8×C137 | — | 2 | 1 | no | — |
| 26 | #125×C137 | — | 2 | 2 | no | — |
| 27 | C22⋊Q8×C137 | — | 4 | 1 | no | — |
| 28 | C22⋊Q8×C137 | — | 4 | 1 | no | — |
| 29 | C4×Q8×C137 | — | 4 | 1 | no | — |
| 30 | C4×Q8×C137 | — | 4 | 1 | no | — |
| 31 | #117×C137 | — | 2 | 2 | no | — |
| 32 | C2×C42×C137 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×C16×C137 | — | 2 | 2 | no | — |
| 34 | #107×C137 | — | 2 | 1 | no | — |
| 35 | #107×C137 | — | 2 | 1 | no | — |
| 36 | #107×C137 | C2×C4 | 1 | 2 | yes | — |
| 37 | #107×C137 | C2×C4 | 1 | 2 | yes | — |
| 38 | #106×C137 | — | 2 | 2 | no | — |
| 39 | #106×C137 | — | 2 | 2 | no | — |
| 40 | C4⋊C8×C137 | — | 2 | 2 | no | — |
| 41 | C4⋊C8×C137 | — | 4 | 1 | no | — |
| 42 | C4×C8×C137 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C4×C8×C137 | D4 | 1 | 1 | yes | characteristic |
| 44 | C4×C8×C137 | D4 | 1 | 1 | yes | characteristic |
| 45 | C4×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×Q8×C137 | — | 4 | 1 | no | — |
| 47 | C2×Q8×C137 | — | 4 | 1 | no | — |
| 48 | C22×C4×C137 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 49 | C22×C4×C137 | D8 | 1 | 1 | yes | characteristic |
| 50 | C22×C4×C137 | SD16 | 1 | 1 | yes | characteristic |
| 51 | M16×C137 | — | 8 | 2 | no | — |
| 52 | C2×C8×C137 | — | 2 | 2 | no | — |
| 53 | C2×C8×C137 | — | 2 | 2 | no | — |
| 54 | C2×C8×C137 | — | 4 | 2 | no | — |
| 55 | C2×C8×C137 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 56 | C2×C8×C137 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 57 | C2×C8×C137 | C22×C4 | 1 | 1 | yes | characteristic |
| 58 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 59 | C4⋊C4×C137 | — | 2 | 2 | no | — |
| 60 | C4⋊C4×C137 | — | 2 | 2 | no | — |
| 61 | C4⋊C4×C137 | — | 4 | 2 | no | — |
| 62 | C4⋊C4×C137 | — | 4 | 2 | no | — |
| 63 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 64 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 65 | C22⋊C4×C137 | — | 4 | 2 | no | — |
| 66 | C42×C137 | — | 4 | 2 | no | — |
| 67 | C42×C137 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 68 | C42×C137 | D8 | 1 | 1 | yes | characteristic |
| 69 | C42×C137 | SD16 | 1 | 1 | yes | characteristic |
| 70 | C42×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C16×C137 | — | 4 | 2 | no | — |
| 72 | C23×C137 | #102 | 1 | 1 | yes | characteristic |
| 73 | Q8×C137 | — | 8 | 2 | no | — |
| 74 | Q8×C137 | — | 8 | 1 | no | — |
| 75 | Q8×C137 | — | 8 | 1 | no | — |
| 76 | C2×C4×C137 | — | 2 | 1 | no | — |
| 77 | C2×C4×C137 | — | 2 | 1 | no | — |
| 78 | C2×C4×C137 | — | 2 | 1 | no | — |
| 79 | C2×C4×C137 | — | 2 | 1 | no | — |
| 80 | C2×C4×C137 | — | 4 | 1 | no | — |
| 81 | C2×C4×C137 | — | 4 | 2 | no | — |
| 82 | C2×C4×C137 | — | 4 | 2 | no | — |
| 83 | C2×C4×C137 | #102 | 1 | 1 | yes | characteristic |
| 84 | C2×C4×C137 | #102 | 1 | 1 | yes | characteristic |
| 85 | C2×C4×C137 | #102 | 1 | 1 | yes | characteristic |
| 86 | C2×C4×C137 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 87 | C2×C4×C137 | C2×D8 | 1 | 1 | yes | characteristic |
| 88 | C2×C4×C137 | C2×SD16 | 1 | 1 | yes | characteristic |
| 89 | C8×C137 | — | 2 | 1 | no | — |
| 90 | C8×C137 | — | 2 | 1 | no | — |
| 91 | C8×C137 | — | 8 | 2 | no | — |
| 92 | C8×C137 | #101 | 1 | 2 | yes | — |
| 93 | C8×C137 | #137 | 1 | 2 | yes | — |
| 94 | C22×C137 | — | 2 | 1 | no | — |
| 95 | C22×C137 | — | 2 | 1 | no | — |
| 96 | C22×C137 | — | 2 | 1 | no | — |
| 97 | C22×C137 | C2×#102 | 1 | 1 | yes | characteristic |
| 98 | C4×C137 | — | 2 | 1 | no | — |
| 99 | C4×C137 | — | 2 | 1 | no | — |
| 100 | C4×C137 | — | 2 | 1 | no | — |
| 101 | C4×C137 | — | 2 | 1 | no | — |
| 102 | C4×C137 | — | 8 | 2 | no | — |
| 103 | C4×C137 | — | 8 | 2 | no | — |
| 104 | C4×C137 | C2×#101 | 1 | 1 | yes | characteristic |
| 105 | C4×C137 | #419 | 1 | 1 | yes | characteristic |
| 106 | C4×C137 | #509 | 1 | 1 | yes | characteristic |
| 107 | C4×C137 | #510 | 1 | 1 | yes | characteristic |
| 108 | C2×C137 | — | 4 | 1 | no | — |
| 109 | C2×C137 | #1546 | 1 | 1 | yes | characteristic |
| 110 | C2×C137 | #2139 | 1 | 1 | yes | characteristic |
| 111 | C2×C137 | #2148 | 1 | 1 | yes | characteristic |
| 112 | #11976 | C137 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 113 | C137 | #11976 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 114 | #3160 | C2×C137 | 1 | 1 | yes | characteristic |
| 115 | #2163 | C2×C137 | 1 | 1 | yes | characteristic |
| 116 | #1567 | C2×C137 | 1 | 1 | yes | characteristic |
| 117 | #1365 | C2×C137 | 1 | 2 | yes | complemented |
| 118 | #1364 | C2×C137 | 1 | 2 | yes | complemented |
| 119 | #533 | — | 2 | 1 | no | — |
| 120 | #500 | C22×C137 | 1 | 1 | yes | characteristic |
| 121 | #500 | C22×C137 | 1 | 1 | yes | characteristic |
| 122 | #499 | — | 2 | 1 | no | — |
| 123 | #499 | C4×C137 | 1 | 2 | yes | — |
| 124 | #498 | — | 2 | 1 | no | — |
| 125 | #427 | — | 2 | 1 | no | — |
| 126 | #427 | C4×C137 | 1 | 2 | yes | — |
| 127 | #423 | — | 2 | 1 | no | — |
| 128 | C2×C4×C8 | C22×C137 | 1 | 1 | yes | characteristic |
| 129 | C4⋊C16 | C22×C137 | 1 | 2 | yes | — |
| 130 | C22⋊C16 | — | 2 | 1 | no | — |
| 131 | #346 | — | 2 | 1 | no | — |
| 132 | #335 | — | 2 | 1 | no | — |
| 133 | #335 | C22×C137 | 1 | 2 | yes | — |
| 134 | C2×M16 | — | 4 | 1 | no | — |
| 135 | C22×C8 | C2×C4×C137 | 1 | 1 | yes | characteristic |
| 136 | C22×C8 | D4×C137 | 1 | 1 | yes | characteristic |
| 137 | C4⋊Q8 | — | 2 | 1 | no | — |
| 138 | C4⋊Q8 | — | 2 | 1 | no | — |
| 139 | #125 | — | 2 | 2 | no | — |
| 140 | C22⋊Q8 | — | 4 | 1 | no | — |
| 141 | C22⋊Q8 | — | 4 | 1 | no | — |
| 142 | C4×Q8 | — | 4 | 1 | no | — |
| 143 | C4×Q8 | — | 4 | 1 | no | — |
| 144 | #117 | — | 2 | 2 | no | — |
| 145 | C2×C42 | D4×C137 | 1 | 1 | yes | characteristic |
| 146 | C2×C16 | — | 2 | 2 | no | — |
| 147 | #107 | — | 2 | 1 | no | — |
| 148 | #107 | — | 2 | 1 | no | — |
| 149 | #107 | C2×C4×C137 | 1 | 2 | yes | — |
| 150 | #107 | C2×C4×C137 | 1 | 2 | yes | — |
| 151 | #106 | — | 2 | 2 | no | — |
| 152 | #106 | — | 2 | 2 | no | — |
| 153 | C4⋊C8 | — | 2 | 2 | no | — |
| 154 | C4⋊C8 | — | 4 | 1 | no | — |
| 155 | C4×C8 | C2×C4×C137 | 1 | 1 | yes | characteristic |
| 156 | C4×C8 | D4×C137 | 1 | 1 | yes | characteristic |
| 157 | C4×C8 | D4×C137 | 1 | 1 | yes | characteristic |
| 158 | C4×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 159 | C2×Q8 | — | 4 | 1 | no | — |
| 160 | C2×Q8 | — | 4 | 1 | no | — |
| 161 | C22×C4 | C22⋊C4×C137 | 1 | 1 | yes | characteristic |
| 162 | C22×C4 | D8×C137 | 1 | 1 | yes | characteristic |
| 163 | C22×C4 | SD16×C137 | 1 | 1 | yes | characteristic |
| 164 | M16 | — | 8 | 2 | no | — |
| 165 | C2×C8 | — | 2 | 2 | no | — |
| 166 | C2×C8 | — | 2 | 2 | no | — |
| 167 | C2×C8 | — | 4 | 2 | no | — |
| 168 | C2×C8 | C22⋊C4×C137 | 1 | 1 | yes | characteristic |
| 169 | C2×C8 | C22⋊C4×C137 | 1 | 1 | yes | characteristic |
| 170 | C2×C8 | C22×C4×C137 | 1 | 1 | yes | characteristic |
| 171 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 172 | C4⋊C4 | — | 2 | 2 | no | — |
| 173 | C4⋊C4 | — | 2 | 2 | no | — |
| 174 | C4⋊C4 | — | 4 | 2 | no | — |
| 175 | C4⋊C4 | — | 4 | 2 | no | — |
| 176 | C4⋊C4 | — | 4 | 1 | no | — |
| 177 | C4⋊C4 | — | 4 | 1 | no | — |
| 178 | C22⋊C4 | — | 4 | 2 | no | — |
| 179 | C42 | — | 4 | 2 | no | — |
| 180 | C42 | C22⋊C4×C137 | 1 | 1 | yes | characteristic |
| 181 | C42 | D8×C137 | 1 | 1 | yes | characteristic |
| 182 | C42 | SD16×C137 | 1 | 1 | yes | characteristic |
| 183 | C42 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 184 | C16 | — | 4 | 2 | no | — |
| 185 | C23 | #102×C137 | 1 | 1 | yes | characteristic |
| 186 | Q8 | — | 8 | 2 | no | — |
| 187 | Q8 | — | 8 | 1 | no | — |
| 188 | Q8 | — | 8 | 1 | no | — |
| 189 | C2×C4 | — | 2 | 1 | no | — |
| 190 | C2×C4 | — | 2 | 1 | no | — |
| 191 | C2×C4 | — | 2 | 1 | no | — |
| 192 | C2×C4 | — | 2 | 1 | no | — |
| 193 | C2×C4 | — | 4 | 1 | no | — |
| 194 | C2×C4 | — | 4 | 2 | no | — |
| 195 | C2×C4 | — | 4 | 2 | no | — |
| 196 | C2×C4 | #102×C137 | 1 | 1 | yes | characteristic |
| 197 | C2×C4 | #102×C137 | 1 | 1 | yes | characteristic |
| 198 | C2×C4 | #102×C137 | 1 | 1 | yes | characteristic |
| 199 | C2×C4 | C2×C22⋊C4×C137 | 1 | 1 | yes | characteristic |
| 200 | C2×C4 | C2×D8×C137 | 1 | 1 | yes | characteristic |
| 201 | C2×C4 | C2×SD16×C137 | 1 | 1 | yes | characteristic |
| 202 | C8 | — | 2 | 1 | no | — |
| 203 | C8 | — | 2 | 1 | no | — |
| 204 | C8 | — | 8 | 2 | no | — |
| 205 | C8 | #101×C137 | 1 | 2 | yes | — |
| 206 | C8 | #137×C137 | 1 | 2 | yes | — |
| 207 | C22 | — | 2 | 1 | no | — |
| 208 | C22 | — | 2 | 1 | no | — |
| 209 | C22 | — | 2 | 1 | no | — |
| 210 | C22 | C2×#102×C137 | 1 | 1 | yes | characteristic |
| 211 | C4 | — | 2 | 1 | no | — |
| 212 | C4 | — | 2 | 1 | no | — |
| 213 | C4 | — | 2 | 1 | no | — |
| 214 | C4 | — | 2 | 1 | no | — |
| 215 | C4 | — | 8 | 2 | no | — |
| 216 | C4 | — | 8 | 2 | no | — |
| 217 | C4 | C2×#101×C137 | 1 | 1 | yes | characteristic |
| 218 | C4 | #419×C137 | 1 | 1 | yes | characteristic |
| 219 | C4 | #509×C137 | 1 | 1 | yes | characteristic |
| 220 | C4 | #510×C137 | 1 | 1 | yes | characteristic |
| 221 | C2 | — | 4 | 1 | no | — |
| 222 | C2 | #1546×C137 | 1 | 1 | yes | characteristic |
| 223 | C2 | #2139×C137 | 1 | 1 | yes | characteristic |
| 224 | C2 | #2148×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