← #31997685
Subgroups — #31997685
Order 18176.
778 conjugacy classes of subgroups.
The subgroup lattice has 260 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22596902 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×#17985956 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22588481 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22588479 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22588477 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22588476 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22588065 | C2 | 1 | 2 | yes | maximal |
| 8 | #341×D71 | C2 | 1 | 2 | yes | maximal |
| 9 | C71×#1838 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×#11765848 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×M16×D71 | C22 | 1 | 4 | yes | — |
| 12 | C22×C8×D71 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#14556085 | C22 | 1 | 1 | yes | characteristic |
| 14 | #17986024 | — | 2 | 8 | no | — |
| 15 | #17986023 | C22 | 1 | 2 | yes | — |
| 16 | #17986022 | C22 | 1 | 4 | yes | — |
| 17 | #17985956 | C4 | 1 | 8 | yes | — |
| 18 | C2×#14556038 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×C71⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C8×Dic71 | C22 | 1 | 1 | yes | characteristic |
| 21 | #17985764 | C22 | 1 | 2 | yes | — |
| 22 | #17985764 | C22 | 1 | 2 | yes | — |
| 23 | #17985763 | C22 | 1 | 4 | yes | — |
| 24 | #17985763 | C22 | 1 | 4 | yes | — |
| 25 | #423×C71 | C22 | 1 | 2 | yes | — |
| 26 | C2×#97×C71 | C22 | 1 | 1 | yes | characteristic |
| 27 | #341×C71 | C22 | 1 | 2 | yes | — |
| 28 | #341×C71 | C22 | 1 | 2 | yes | — |
| 29 | C22×C4×D71 | C23 | 1 | 1 | yes | characteristic |
| 30 | C2×#11765849 | C23 | 1 | 4 | yes | — |
| 31 | C2×#11765848 | — | 2 | 4 | no | — |
| 32 | C2×#11765848 | — | 2 | 4 | no | — |
| 33 | C2×#11765848 | C2×C4 | 1 | 4 | yes | — |
| 34 | M16×D71 | — | 2 | 8 | no | — |
| 35 | M16×D71 | — | 2 | 8 | no | — |
| 36 | C22×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 37 | C22×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×C8×D71 | — | 2 | 4 | no | — |
| 39 | C2×C8×D71 | — | 2 | 4 | no | — |
| 40 | C2×C8×D71 | C2×C4 | 1 | 4 | yes | — |
| 41 | #14556085 | C2×C4 | 1 | 4 | yes | — |
| 42 | #14556085 | D4 | 1 | 4 | yes | — |
| 43 | C2×Dic71⋊C4 | Q8 | 1 | 2 | yes | — |
| 44 | C2×(C2×D71)⋊C4 | Q8 | 1 | 2 | yes | — |
| 45 | C2×C4×Dic71 | C23 | 1 | 1 | yes | characteristic |
| 46 | C4⋊(C71⋊C8) | — | 2 | 4 | no | — |
| 47 | Dic71⋊C8 | — | 2 | 8 | no | — |
| 48 | #14556038 | C2×C4 | 1 | 4 | yes | — |
| 49 | C4×C71⋊C8 | C2×C4 | 1 | 4 | yes | — |
| 50 | C8×Dic71 | C2×C4 | 1 | 4 | yes | — |
| 51 | C2×M16×C71 | C23 | 1 | 4 | yes | — |
| 52 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 55 | C4⋊C8×C71 | — | 2 | 4 | no | — |
| 56 | #97×C71 | C2×C4 | 1 | 4 | yes | — |
| 57 | C23×D71 | C2×Q8 | 1 | 1 | yes | characteristic |
| 58 | C22×Dic71 | C2×Q8 | 1 | 2 | yes | — |
| 59 | C22×Dic71 | C2×Q8 | 1 | 1 | yes | characteristic |
| 60 | C2×C4×D71 | C22×C4 | 1 | 2 | yes | — |
| 61 | C2×C4×D71 | C2×D4 | 1 | 2 | yes | — |
| 62 | C2×C4×D71 | #41 | 1 | 4 | yes | — |
| 63 | C2×C4×D71 | #41 | 1 | 4 | yes | — |
| 64 | #11765849 | — | 2 | 4 | no | — |
| 65 | #11765849 | — | 2 | 4 | no | — |
| 66 | #11765848 | — | 2 | 8 | no | — |
| 67 | #11765848 | — | 4 | 8 | no | — |
| 68 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 69 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 70 | C2×C71⋊C8 | — | 2 | 4 | no | — |
| 71 | C2×C71⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 72 | C2×C71⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 73 | C8×D71 | — | 2 | 8 | no | — |
| 74 | C8×D71 | — | 4 | 8 | no | — |
| 75 | Dic71⋊C4 | C4⋊C4 | 1 | 8 | yes | — |
| 76 | (C2×D71)⋊C4 | C4⋊C4 | 1 | 8 | yes | — |
| 77 | C4×Dic71 | C22×C4 | 1 | 2 | yes | — |
| 78 | C4×Dic71 | C2×D4 | 1 | 2 | yes | — |
| 79 | C22×C4×C71 | C2×Q8 | 1 | 2 | yes | — |
| 80 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 81 | M16×C71 | — | 2 | 4 | no | — |
| 82 | M16×C71 | — | 2 | 4 | no | — |
| 83 | C2×C8×C71 | — | 2 | 2 | no | — |
| 84 | C2×C8×C71 | — | 2 | 2 | no | — |
| 85 | C2×C8×C71 | — | 2 | 4 | no | — |
| 86 | C2×C8×C71 | C22×C4 | 1 | 2 | yes | — |
| 87 | C2×C8×C71 | C22×C4 | 1 | 2 | yes | — |
| 88 | C42×C71 | C22×C4 | 1 | 2 | yes | — |
| 89 | C42×C71 | C2×D4 | 1 | 2 | yes | — |
| 90 | C23×C71 | C22×Q8 | 1 | 1 | yes | characteristic |
| 91 | C22×D71 | — | 4 | 2 | no | — |
| 92 | C22×D71 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 93 | C22×D71 | #125 | 1 | 4 | yes | — |
| 94 | C2×C4×C71 | — | 4 | 2 | no | — |
| 95 | C2×C4×C71 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 96 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 97 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×C71 | C2×#41 | 1 | 2 | yes | — |
| 99 | C2×C4×C71 | C2×#41 | 1 | 2 | yes | — |
| 100 | C2×Dic71 | — | 4 | 2 | no | — |
| 101 | C2×Dic71 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 102 | C2×Dic71 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 103 | C2×Dic71 | #125 | 1 | 4 | yes | — |
| 104 | C4×D71 | #117 | 1 | 4 | yes | — |
| 105 | C4×D71 | #117 | 1 | 4 | yes | — |
| 106 | C4×D71 | #124 | 1 | 8 | yes | — |
| 107 | C8×C71 | — | 2 | 2 | no | — |
| 108 | C8×C71 | — | 2 | 2 | no | — |
| 109 | C8×C71 | — | 4 | 4 | no | — |
| 110 | C71⋊C8 | — | 2 | 2 | no | — |
| 111 | C71⋊C8 | — | 2 | 2 | no | — |
| 112 | C71⋊C8 | — | 4 | 4 | no | — |
| 113 | C22×C71 | — | 2 | 2 | no | — |
| 114 | C22×C71 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C22×C71 | C2×#125 | 1 | 2 | yes | — |
| 116 | C2×D71 | — | 2 | 4 | no | — |
| 117 | C2×D71 | — | 4 | 4 | no | — |
| 118 | C2×D71 | #382 | 1 | 4 | yes | — |
| 119 | C4×C71 | — | 2 | 4 | no | — |
| 120 | C4×C71 | C2×#117 | 1 | 1 | yes | characteristic |
| 121 | C4×C71 | C2×#117 | 1 | 1 | yes | characteristic |
| 122 | C4×C71 | C2×#124 | 1 | 2 | yes | — |
| 123 | Dic71 | — | 2 | 4 | no | — |
| 124 | Dic71 | #382 | 1 | 4 | yes | — |
| 125 | #20768 | — | 71 | 1 | no | maximal, Sylow |
| 126 | C2×C71 | — | 2 | 2 | no | — |
| 127 | C2×C71 | C2×#382 | 1 | 1 | yes | characteristic |
| 128 | C2×C71 | #2916 | 1 | 2 | yes | — |
| 129 | D71 | — | 2 | 4 | no | — |
| 130 | #2905 | — | 71 | 2 | no | — |
| 131 | C2×#405 | — | 71 | 1 | no | — |
| 132 | #1838 | — | 71 | 1 | no | — |
| 133 | #1838 | — | 71 | 2 | no | — |
| 134 | #1838 | D71 | 1 | 1 | yes | characteristic, complemented |
| 135 | #1837 | — | 71 | 2 | no | — |
| 136 | #1837 | — | 71 | 2 | no | — |
| 137 | #1738 | — | 71 | 2 | no | — |
| 138 | C2×#341 | — | 71 | 2 | no | — |
| 139 | C71 | #20768 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 140 | C22×M16 | — | 71 | 1 | no | — |
| 141 | C22×M16 | — | 71 | 4 | no | — |
| 142 | C23×C8 | — | 71 | 1 | no | — |
| 143 | C2×#117 | — | 71 | 1 | no | — |
| 144 | #424 | — | 142 | 8 | no | — |
| 145 | #423 | — | 71 | 4 | no | — |
| 146 | #423 | — | 71 | 2 | no | — |
| 147 | #423 | C2×D71 | 1 | 2 | yes | — |
| 148 | #405 | — | 71 | 8 | no | — |
| 149 | C2×#97 | — | 71 | 1 | no | — |
| 150 | C2×#97 | C2×D71 | 1 | 1 | yes | characteristic |
| 151 | C2×C4×C8 | — | 71 | 1 | no | — |
| 152 | C2×C4×C8 | — | 71 | 1 | no | — |
| 153 | #341 | — | 71 | 4 | no | — |
| 154 | #341 | — | 71 | 4 | no | — |
| 155 | #341 | — | 71 | 2 | no | — |
| 156 | #341 | — | 71 | 2 | no | — |
| 157 | #341 | C2×D71 | 1 | 2 | yes | — |
| 158 | #341 | C2×D71 | 1 | 2 | yes | — |
| 159 | C23×C4 | — | 71 | 1 | no | — |
| 160 | C2×M16 | — | 71 | 4 | no | — |
| 161 | C2×M16 | — | 71 | 4 | no | — |
| 162 | C2×M16 | — | 142 | 4 | no | — |
| 163 | C2×M16 | — | 142 | 4 | no | — |
| 164 | C2×M16 | — | 142 | 8 | no | — |
| 165 | C2×M16 | — | 142 | 8 | no | — |
| 166 | C2×M16 | C22×D71 | 1 | 4 | yes | — |
| 167 | C22×C8 | — | 71 | 1 | no | — |
| 168 | C22×C8 | — | 71 | 1 | no | — |
| 169 | C22×C8 | — | 71 | 4 | no | — |
| 170 | C22×C8 | — | 142 | 4 | no | — |
| 171 | C22×C8 | — | 142 | 4 | no | — |
| 172 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 173 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 174 | #117 | — | 71 | 4 | no | — |
| 175 | #117 | — | 71 | 4 | no | — |
| 176 | C2×C4⋊C4 | — | 71 | 2 | no | — |
| 177 | C2×C22⋊C4 | — | 71 | 2 | no | — |
| 178 | C2×C42 | — | 71 | 1 | no | — |
| 179 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 180 | C4⋊C8 | — | 2 | 4 | no | — |
| 181 | C4⋊C8 | — | 142 | 8 | no | — |
| 182 | C4⋊C8 | — | 142 | 4 | no | — |
| 183 | #97 | — | 71 | 4 | no | — |
| 184 | #97 | C4×D71 | 1 | 4 | yes | — |
| 185 | C4×C8 | — | 71 | 4 | no | — |
| 186 | C4×C8 | — | 71 | 4 | no | — |
| 187 | C24 | — | 71 | 1 | no | — |
| 188 | C22×C4 | — | 71 | 2 | no | — |
| 189 | C22×C4 | — | 71 | 1 | no | — |
| 190 | C22×C4 | — | 71 | 2 | no | — |
| 191 | C22×C4 | — | 71 | 2 | no | — |
| 192 | C22×C4 | — | 71 | 4 | no | — |
| 193 | C22×C4 | — | 71 | 4 | no | — |
| 194 | C22×C4 | Q8×D71 | 1 | 2 | yes | — |
| 195 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 196 | M16 | — | 2 | 4 | no | — |
| 197 | M16 | — | 2 | 4 | no | — |
| 198 | M16 | — | 284 | 8 | no | — |
| 199 | M16 | — | 142 | 8 | no | — |
| 200 | M16 | — | 142 | 4 | no | — |
| 201 | M16 | — | 142 | 4 | no | — |
| 202 | C2×C8 | — | 2 | 2 | no | — |
| 203 | C2×C8 | — | 2 | 2 | no | — |
| 204 | C2×C8 | — | 2 | 4 | no | — |
| 205 | C2×C8 | — | 284 | 8 | no | — |
| 206 | C2×C8 | — | 71 | 2 | no | — |
| 207 | C2×C8 | — | 71 | 2 | no | — |
| 208 | C2×C8 | — | 142 | 8 | no | — |
| 209 | C2×C8 | — | 142 | 4 | no | — |
| 210 | C2×C8 | — | 142 | 2 | no | — |
| 211 | C2×C8 | — | 142 | 2 | no | — |
| 212 | C2×C8 | C2×C4×D71 | 1 | 2 | yes | — |
| 213 | C2×C8 | C2×C4×D71 | 1 | 2 | yes | — |
| 214 | C4⋊C4 | — | 71 | 8 | no | — |
| 215 | C22⋊C4 | — | 71 | 8 | no | — |
| 216 | C42 | — | 71 | 2 | no | — |
| 217 | C42 | — | 71 | 2 | no | — |
| 218 | C42 | C2×C4×D71 | 1 | 2 | yes | — |
| 219 | C42 | D4×D71 | 1 | 2 | yes | — |
| 220 | C23 | — | 284 | 2 | no | — |
| 221 | C23 | — | 71 | 4 | no | — |
| 222 | C23 | — | 71 | 2 | no | — |
| 223 | C23 | C2×Q8×D71 | 1 | 1 | yes | characteristic |
| 224 | C2×C4 | — | 4 | 2 | no | — |
| 225 | C2×C4 | — | 284 | 2 | no | — |
| 226 | C2×C4 | — | 71 | 2 | no | — |
| 227 | C2×C4 | — | 71 | 4 | no | — |
| 228 | C2×C4 | — | 71 | 4 | no | — |
| 229 | C2×C4 | — | 71 | 4 | no | — |
| 230 | C2×C4 | — | 71 | 8 | no | — |
| 231 | C2×C4 | — | 71 | 4 | no | — |
| 232 | C2×C4 | C4⋊C4×D71 | 1 | 4 | yes | — |
| 233 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 234 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 235 | C2×C4 | #41×D71 | 1 | 2 | yes | — |
| 236 | C2×C4 | #41×D71 | 1 | 2 | yes | — |
| 237 | C8 | — | 2 | 2 | no | — |
| 238 | C8 | — | 2 | 2 | no | — |
| 239 | C8 | — | 4 | 4 | no | — |
| 240 | C8 | — | 284 | 4 | no | — |
| 241 | C8 | — | 142 | 2 | no | — |
| 242 | C8 | — | 142 | 2 | no | — |
| 243 | C22 | — | 2 | 2 | no | — |
| 244 | C22 | — | 284 | 4 | no | — |
| 245 | C22 | — | 71 | 4 | no | — |
| 246 | C22 | — | 142 | 4 | no | — |
| 247 | C22 | C2×C4⋊C4×D71 | 1 | 1 | yes | characteristic |
| 248 | C22 | #125×D71 | 1 | 2 | yes | — |
| 249 | C4 | — | 2 | 4 | no | — |
| 250 | C4 | — | 71 | 4 | no | — |
| 251 | C4 | — | 142 | 4 | no | — |
| 252 | C4 | #117×D71 | 1 | 1 | yes | characteristic |
| 253 | C4 | #117×D71 | 1 | 1 | yes | characteristic |
| 254 | C4 | #124×D71 | 1 | 2 | yes | — |
| 255 | C2 | — | 2 | 2 | no | — |
| 256 | C2 | — | 142 | 4 | no | — |
| 257 | C2 | #382×D71 | 1 | 1 | yes | characteristic |
| 258 | C2 | #22596950 | 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