← #26216902
Subgroups — #26216902
Order 12032.
718 conjugacy classes of subgroups.
The subgroup lattice has 256 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20252025 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×#15689080 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #20243559 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20243529 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20243429 | C2 | 1 | 2 | yes | maximal |
| 6 | #20243425 | C2 | 1 | 2 | yes | maximal |
| 7 | #20243293 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20243289 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C47×#1838 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×#10625324 | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×C8×D47 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#13093981 | C22 | 1 | 1 | yes | characteristic |
| 13 | #15689183 | — | 2 | 8 | no | — |
| 14 | C2×#13093959 | C22 | 1 | 4 | yes | — |
| 15 | C2×#13093959 | C22 | 1 | 4 | yes | — |
| 16 | #15689147 | C22 | 1 | 2 | yes | — |
| 17 | #15689086 | C22 | 1 | 4 | yes | — |
| 18 | #15689080 | C4 | 1 | 8 | yes | — |
| 19 | M16×Dic47 | C22 | 1 | 4 | yes | — |
| 20 | C2×#13093934 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C4×C47⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C8×Dic47 | C22 | 1 | 1 | yes | characteristic |
| 23 | #15688888 | C22 | 1 | 2 | yes | — |
| 24 | #15688888 | C22 | 1 | 2 | yes | — |
| 25 | C47×#423 | C22 | 1 | 2 | yes | — |
| 26 | C2×#97×C47 | C22 | 1 | 1 | yes | characteristic |
| 27 | C47×#341 | C22 | 1 | 2 | yes | — |
| 28 | C47×#341 | C22 | 1 | 2 | yes | — |
| 29 | C22×C4×D47 | C23 | 1 | 1 | yes | characteristic |
| 30 | C2×#10625329 | C23 | 1 | 4 | yes | — |
| 31 | C2×#10625324 | — | 2 | 4 | no | — |
| 32 | C2×#10625324 | C2×C4 | 1 | 4 | yes | — |
| 33 | C22×C47⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 34 | C22×C47⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×C8×D47 | — | 2 | 4 | no | — |
| 36 | C2×C8×D47 | C2×C4 | 1 | 4 | yes | — |
| 37 | #13093981 | C2×C4 | 1 | 4 | yes | — |
| 38 | #13093981 | D4 | 1 | 4 | yes | — |
| 39 | C2×Dic47⋊C4 | Q8 | 1 | 2 | yes | — |
| 40 | C2×(C2×D47)⋊C4 | Q8 | 1 | 2 | yes | — |
| 41 | C2×C4×Dic47 | C23 | 1 | 1 | yes | characteristic |
| 42 | #13093959 | — | 2 | 8 | no | — |
| 43 | #13093959 | — | 2 | 8 | no | — |
| 44 | C4⋊(C47⋊C8) | — | 2 | 4 | no | — |
| 45 | (C2×D47)⋊C8 | — | 2 | 8 | no | — |
| 46 | #13093934 | — | 2 | 4 | no | — |
| 47 | #13093934 | C2×C4 | 1 | 4 | yes | — |
| 48 | C4×C47⋊C8 | C2×C4 | 1 | 4 | yes | — |
| 49 | C8×Dic47 | — | 2 | 4 | no | — |
| 50 | C8×Dic47 | C2×C4 | 1 | 4 | yes | — |
| 51 | C2×M16×C47 | C23 | 1 | 4 | yes | — |
| 52 | C22×C8×C47 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×C8×C47 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C42×C47 | C23 | 1 | 1 | yes | characteristic |
| 55 | C4⋊C8×C47 | — | 2 | 4 | no | — |
| 56 | #97×C47 | C2×C4 | 1 | 4 | yes | — |
| 57 | C23×D47 | C2×Q8 | 1 | 1 | yes | characteristic |
| 58 | C22×C4×C47 | C2×Q8 | 1 | 2 | yes | — |
| 59 | C22×C4×C47 | C24 | 1 | 1 | yes | characteristic |
| 60 | C22×Dic47 | C2×Q8 | 1 | 1 | yes | characteristic |
| 61 | C22×Dic47 | C2×Q8 | 1 | 2 | yes | — |
| 62 | C2×C4×D47 | — | 2 | 2 | no | — |
| 63 | C2×C4×D47 | — | 2 | 2 | no | — |
| 64 | C2×C4×D47 | C22×C4 | 1 | 2 | yes | — |
| 65 | C2×C4×D47 | C2×D4 | 1 | 2 | yes | — |
| 66 | M16×C47 | — | 2 | 4 | no | — |
| 67 | M16×C47 | — | 2 | 4 | no | — |
| 68 | C2×C8×C47 | — | 2 | 2 | no | — |
| 69 | C2×C8×C47 | — | 2 | 2 | no | — |
| 70 | C2×C8×C47 | — | 2 | 4 | no | — |
| 71 | C2×C8×C47 | C22×C4 | 1 | 2 | yes | — |
| 72 | C2×C8×C47 | C22×C4 | 1 | 2 | yes | — |
| 73 | C42×C47 | C22×C4 | 1 | 2 | yes | — |
| 74 | C42×C47 | C2×D4 | 1 | 2 | yes | — |
| 75 | (C2×D47)⋊C4 | C4⋊C4 | 1 | 8 | yes | — |
| 76 | Dic47⋊C4 | C4⋊C4 | 1 | 8 | yes | — |
| 77 | C4×Dic47 | C22×C4 | 1 | 2 | yes | — |
| 78 | C4×Dic47 | C2×D4 | 1 | 2 | yes | — |
| 79 | #10625329 | — | 2 | 4 | no | — |
| 80 | #10625329 | — | 2 | 4 | no | — |
| 81 | C2×C47⋊C8 | — | 2 | 4 | no | — |
| 82 | C2×C47⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 83 | C2×C47⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 84 | C2×C47⋊C8 | #41 | 1 | 4 | yes | — |
| 85 | C2×C47⋊C8 | #41 | 1 | 4 | yes | — |
| 86 | #10625324 | — | 2 | 8 | no | — |
| 87 | C8×D47 | — | 2 | 8 | no | — |
| 88 | C23×C47 | C22×Q8 | 1 | 1 | yes | characteristic |
| 89 | C22×D47 | — | 2 | 2 | no | — |
| 90 | C22×D47 | — | 4 | 2 | no | — |
| 91 | C22×D47 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 92 | C2×C4×C47 | — | 4 | 2 | no | — |
| 93 | C2×C4×C47 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 94 | C2×C4×C47 | C23×C4 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×C47 | C22×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C4×C47 | C2×#41 | 1 | 2 | yes | — |
| 97 | C2×C4×C47 | C2×#41 | 1 | 2 | yes | — |
| 98 | C2×Dic47 | — | 2 | 2 | no | — |
| 99 | C2×Dic47 | — | 4 | 2 | no | — |
| 100 | C2×Dic47 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 101 | C2×Dic47 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 102 | C4×D47 | — | 2 | 2 | no | — |
| 103 | C4×D47 | — | 2 | 2 | no | — |
| 104 | C4×D47 | — | 2 | 4 | no | — |
| 105 | C8×C47 | — | 2 | 2 | no | — |
| 106 | C8×C47 | — | 2 | 2 | no | — |
| 107 | C8×C47 | — | 4 | 4 | no | — |
| 108 | C47⋊C8 | — | 4 | 4 | no | — |
| 109 | C47⋊C8 | #117 | 1 | 4 | yes | — |
| 110 | C47⋊C8 | #117 | 1 | 4 | yes | — |
| 111 | #20828 | — | 47 | 1 | no | maximal, Sylow |
| 112 | C22×C47 | — | 2 | 2 | no | — |
| 113 | C22×C47 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 114 | C22×C47 | #533 | 1 | 2 | yes | — |
| 115 | C2×D47 | — | 2 | 4 | no | — |
| 116 | C2×D47 | — | 2 | 2 | no | — |
| 117 | C2×D47 | — | 4 | 4 | no | — |
| 118 | C4×C47 | — | 2 | 4 | no | — |
| 119 | C4×C47 | C2×#117 | 1 | 1 | yes | characteristic |
| 120 | C4×C47 | C2×#117 | 1 | 1 | yes | characteristic |
| 121 | C4×C47 | #532 | 1 | 2 | yes | — |
| 122 | Dic47 | — | 2 | 4 | no | — |
| 123 | Dic47 | — | 2 | 2 | no | — |
| 124 | #2921 | — | 47 | 2 | no | — |
| 125 | C2×#405 | — | 47 | 1 | no | — |
| 126 | #1848 | — | 47 | 2 | no | — |
| 127 | #1838 | — | 47 | 1 | no | — |
| 128 | #1838 | D47 | 1 | 1 | yes | characteristic, complemented |
| 129 | #1811 | — | 47 | 2 | no | — |
| 130 | #1810 | — | 47 | 2 | no | — |
| 131 | #1778 | — | 47 | 2 | no | — |
| 132 | C4×#108 | — | 47 | 2 | no | — |
| 133 | C2×C47 | — | 2 | 2 | no | — |
| 134 | C2×C47 | #2285 | 1 | 1 | yes | characteristic |
| 135 | C2×C47 | #2916 | 1 | 2 | yes | — |
| 136 | D47 | — | 4 | 2 | no | — |
| 137 | C22×M16 | — | 47 | 1 | no | — |
| 138 | C23×C8 | — | 47 | 1 | no | — |
| 139 | C2×#117 | — | 47 | 1 | no | — |
| 140 | #433 | — | 94 | 8 | no | — |
| 141 | C2×#108 | — | 47 | 4 | no | — |
| 142 | C2×#108 | — | 47 | 4 | no | — |
| 143 | #423 | — | 47 | 2 | no | — |
| 144 | #423 | C2×D47 | 1 | 2 | yes | — |
| 145 | #407 | — | 47 | 4 | no | — |
| 146 | #405 | — | 47 | 8 | no | — |
| 147 | C4×M16 | — | 47 | 4 | no | — |
| 148 | C2×#97 | — | 47 | 1 | no | — |
| 149 | C2×#97 | C2×D47 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×C8 | — | 47 | 1 | no | — |
| 151 | C2×C4×C8 | — | 47 | 1 | no | — |
| 152 | #341 | — | 47 | 2 | no | — |
| 153 | #341 | — | 47 | 2 | no | — |
| 154 | #341 | C2×D47 | 1 | 2 | yes | — |
| 155 | #341 | C2×D47 | 1 | 2 | yes | — |
| 156 | C47 | #20828 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 157 | C23×C4 | — | 47 | 1 | no | — |
| 158 | C2×M16 | — | 47 | 4 | no | — |
| 159 | C2×M16 | — | 47 | 4 | no | — |
| 160 | C2×M16 | — | 94 | 4 | no | — |
| 161 | C2×M16 | C22×D47 | 1 | 4 | yes | — |
| 162 | C22×C8 | — | 47 | 1 | no | — |
| 163 | C22×C8 | — | 47 | 1 | no | — |
| 164 | C22×C8 | — | 47 | 4 | no | — |
| 165 | C22×C8 | — | 94 | 4 | no | — |
| 166 | C22×C8 | C22×D47 | 1 | 1 | yes | characteristic |
| 167 | C22×C8 | C22×D47 | 1 | 1 | yes | characteristic |
| 168 | #117 | — | 47 | 4 | no | — |
| 169 | #117 | — | 47 | 4 | no | — |
| 170 | C2×C4⋊C4 | — | 47 | 2 | no | — |
| 171 | C2×C22⋊C4 | — | 47 | 2 | no | — |
| 172 | C2×C42 | — | 47 | 1 | no | — |
| 173 | C2×C42 | C22×D47 | 1 | 1 | yes | characteristic |
| 174 | #108 | — | 94 | 8 | no | — |
| 175 | #108 | — | 94 | 8 | no | — |
| 176 | C4⋊C8 | — | 2 | 4 | no | — |
| 177 | C4⋊C8 | — | 94 | 4 | no | — |
| 178 | C22⋊C8 | — | 94 | 8 | no | — |
| 179 | #97 | — | 47 | 4 | no | — |
| 180 | #97 | — | 94 | 4 | no | — |
| 181 | #97 | C4×D47 | 1 | 4 | yes | — |
| 182 | C4×C8 | — | 47 | 4 | no | — |
| 183 | C4×C8 | — | 47 | 4 | no | — |
| 184 | C4×C8 | — | 94 | 4 | no | — |
| 185 | C24 | — | 47 | 1 | no | — |
| 186 | C22×C4 | — | 47 | 1 | no | — |
| 187 | C22×C4 | — | 47 | 2 | no | — |
| 188 | C22×C4 | — | 47 | 2 | no | — |
| 189 | C22×C4 | — | 47 | 2 | no | — |
| 190 | C22×C4 | — | 94 | 2 | no | — |
| 191 | C22×C4 | — | 94 | 2 | no | — |
| 192 | C22×C4 | Q8×D47 | 1 | 2 | yes | — |
| 193 | C22×C4 | C23×D47 | 1 | 1 | yes | characteristic |
| 194 | M16 | — | 2 | 4 | no | — |
| 195 | M16 | — | 2 | 4 | no | — |
| 196 | M16 | — | 94 | 8 | no | — |
| 197 | M16 | — | 94 | 4 | no | — |
| 198 | M16 | — | 94 | 4 | no | — |
| 199 | C2×C8 | — | 2 | 2 | no | — |
| 200 | C2×C8 | — | 2 | 2 | no | — |
| 201 | C2×C8 | — | 2 | 4 | no | — |
| 202 | C2×C8 | — | 47 | 2 | no | — |
| 203 | C2×C8 | — | 47 | 2 | no | — |
| 204 | C2×C8 | — | 47 | 4 | no | — |
| 205 | C2×C8 | — | 47 | 4 | no | — |
| 206 | C2×C8 | — | 94 | 8 | no | — |
| 207 | C2×C8 | — | 94 | 4 | no | — |
| 208 | C2×C8 | C2×C4×D47 | 1 | 2 | yes | — |
| 209 | C2×C8 | C2×C4×D47 | 1 | 2 | yes | — |
| 210 | C4⋊C4 | — | 47 | 8 | no | — |
| 211 | C22⋊C4 | — | 47 | 8 | no | — |
| 212 | C42 | — | 47 | 2 | no | — |
| 213 | C42 | — | 47 | 2 | no | — |
| 214 | C42 | C2×C4×D47 | 1 | 2 | yes | — |
| 215 | C42 | D4×D47 | 1 | 2 | yes | — |
| 216 | C23 | — | 47 | 2 | no | — |
| 217 | C23 | — | 94 | 2 | no | — |
| 218 | C23 | — | 188 | 2 | no | — |
| 219 | C23 | C2×Q8×D47 | 1 | 1 | yes | characteristic |
| 220 | C2×C4 | — | 4 | 2 | no | — |
| 221 | C2×C4 | — | 47 | 4 | no | — |
| 222 | C2×C4 | — | 47 | 2 | no | — |
| 223 | C2×C4 | — | 94 | 2 | no | — |
| 224 | C2×C4 | — | 94 | 2 | no | — |
| 225 | C2×C4 | — | 94 | 2 | no | — |
| 226 | C2×C4 | — | 94 | 4 | no | — |
| 227 | C2×C4 | — | 188 | 2 | no | — |
| 228 | C2×C4 | C4⋊C4×D47 | 1 | 4 | yes | — |
| 229 | C2×C4 | C22×C4×D47 | 1 | 1 | yes | characteristic |
| 230 | C2×C4 | C2×D4×D47 | 1 | 1 | yes | characteristic |
| 231 | C2×C4 | #41×D47 | 1 | 2 | yes | — |
| 232 | C2×C4 | #41×D47 | 1 | 2 | yes | — |
| 233 | C8 | — | 2 | 2 | no | — |
| 234 | C8 | — | 2 | 2 | no | — |
| 235 | C8 | — | 4 | 4 | no | — |
| 236 | C8 | — | 47 | 4 | no | — |
| 237 | C8 | — | 47 | 4 | no | — |
| 238 | C8 | — | 188 | 4 | no | — |
| 239 | C22 | — | 2 | 2 | no | — |
| 240 | C22 | — | 94 | 2 | no | — |
| 241 | C22 | — | 94 | 4 | no | — |
| 242 | C22 | — | 188 | 4 | no | — |
| 243 | C22 | C2×C4⋊C4×D47 | 1 | 1 | yes | characteristic |
| 244 | C22 | #15689679 | 1 | 2 | yes | — |
| 245 | C4 | — | 2 | 4 | no | — |
| 246 | C4 | — | 94 | 2 | no | — |
| 247 | C4 | — | 94 | 4 | no | — |
| 248 | C4 | #117×D47 | 1 | 1 | yes | characteristic |
| 249 | C4 | #117×D47 | 1 | 1 | yes | characteristic |
| 250 | C4 | #15689672 | 1 | 2 | yes | — |
| 251 | C2 | — | 2 | 2 | no | — |
| 252 | C2 | — | 188 | 2 | no | — |
| 253 | C2 | #20245794 | 1 | 1 | yes | characteristic |
| 254 | C2 | #20251998 | 1 | 2 | yes | — |
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