← #16827908
Subgroups — #16827908
Order 3712.
564 conjugacy classes of subgroups.
The subgroup lattice has 248 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×#90772 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×M16×D29 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #117×D29 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #14271121 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14271120 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #14271119 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #14271118 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #14271117 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #14271115 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C4×#90772 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C29×#405 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×C4×D29 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×M16×C29 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C8×C29 | C22 | 1 | 1 | yes | characteristic |
| 15 | C29×#117 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11745288 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#90777 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×#6597 | C22 | 1 | 1 | yes | characteristic |
| 19 | M16×D29 | C4 | 1 | 8 | yes | complemented |
| 20 | C2×#90772 | C4 | 1 | 8 | yes | complemented |
| 21 | C2×#90772 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#90772 | C22 | 1 | 2 | yes | — |
| 23 | C2×#90772 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#90772 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#90772 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×C8×D29 | C22 | 1 | 2 | yes | — |
| 27 | #11745254 | C4 | 1 | 2 | yes | — |
| 28 | C4⋊C4×D29 | C4 | 1 | 2 | yes | — |
| 29 | C22⋊C4×D29 | C4 | 1 | 2 | yes | — |
| 30 | #11745239 | C4 | 1 | 2 | yes | — |
| 31 | #11745234 | C22 | 1 | 2 | yes | — |
| 32 | C42×D29 | C22 | 1 | 2 | yes | — |
| 33 | C29×#97 | C22 | 1 | 2 | yes | complemented |
| 34 | C4×C8×C29 | C22 | 1 | 2 | yes | complemented |
| 35 | #11745163 | C22 | 1 | 2 | yes | complemented |
| 36 | #11745163 | C22 | 1 | 2 | yes | complemented |
| 37 | C8×Dic29 | C22 | 1 | 2 | yes | complemented |
| 38 | C8×Dic29 | C22 | 1 | 2 | yes | complemented |
| 39 | #11745151 | C22 | 1 | 2 | yes | complemented |
| 40 | C4×#6597 | C22 | 1 | 2 | yes | complemented |
| 41 | C23×D29 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C22×C4×C29 | C23 | 1 | 1 | yes | characteristic |
| 43 | C22×Dic29 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C2×C4×D29 | C2×C4 | 1 | 4 | yes | — |
| 45 | C2×C4×D29 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C2×C4×D29 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C2×C4×D29 | C2×C4 | 1 | 4 | yes | — |
| 48 | C2×C4×D29 | C2×C4 | 1 | 4 | yes | — |
| 49 | C2×C4×D29 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C4×D29 | C23 | 1 | 1 | yes | characteristic |
| 51 | M16×C29 | C2×C4 | 1 | 4 | yes | complemented |
| 52 | C2×C8×C29 | C2×C4 | 1 | 4 | yes | complemented |
| 53 | C2×C8×C29 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C8×C29 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×C8×C29 | C23 | 1 | 2 | yes | — |
| 56 | C4⋊C4×C29 | C2×C4 | 1 | 2 | yes | — |
| 57 | C22⋊C4×C29 | C2×C4 | 1 | 2 | yes | — |
| 58 | C42×C29 | C23 | 1 | 2 | yes | — |
| 59 | C22⋊Dic29 | C2×C4 | 1 | 2 | yes | — |
| 60 | #90781 | C2×C4 | 1 | 4 | yes | — |
| 61 | C4⋊Dic29 | C2×C4 | 1 | 2 | yes | — |
| 62 | #90779 | C2×C4 | 1 | 4 | yes | — |
| 63 | C4×Dic29 | C2×C4 | 1 | 4 | yes | — |
| 64 | C4×Dic29 | C23 | 1 | 2 | yes | — |
| 65 | #90777 | C2×C4 | 1 | 4 | yes | complemented |
| 66 | C2×#6597 | C2×C4 | 1 | 4 | yes | complemented |
| 67 | C2×#6597 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×#6597 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×#6597 | C23 | 1 | 2 | yes | — |
| 70 | #90772 | C2×C4 | 1 | 4 | yes | — |
| 71 | #90772 | C2×C4 | 1 | 4 | yes | — |
| 72 | #90772 | C2×C4 | 1 | 8 | yes | — |
| 73 | #90772 | C2×C4 | 1 | 4 | yes | complemented |
| 74 | #90772 | C2×C4 | 1 | 4 | yes | complemented |
| 75 | C8×D29 | C2×C4 | 1 | 8 | yes | complemented |
| 76 | C23×C29 | C22×C4 | 1 | 1 | yes | characteristic |
| 77 | C22×D29 | — | 4 | 2 | no | — |
| 78 | C22×D29 | C42 | 1 | 4 | yes | — |
| 79 | C22×D29 | C22×C4 | 1 | 1 | yes | characteristic |
| 80 | C22×D29 | C22×C4 | 1 | 1 | yes | characteristic |
| 81 | C2×C4×C29 | C22×C4 | 1 | 4 | yes | — |
| 82 | C2×C4×C29 | C22×C4 | 1 | 1 | yes | characteristic |
| 83 | C2×C4×C29 | C22×C4 | 1 | 2 | yes | — |
| 84 | C2×C4×C29 | C22×C4 | 1 | 2 | yes | — |
| 85 | C2×C4×C29 | C24 | 1 | 1 | yes | characteristic |
| 86 | C2×Dic29 | C42 | 1 | 4 | yes | — |
| 87 | C2×Dic29 | C22×C4 | 1 | 4 | yes | — |
| 88 | C2×Dic29 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | C2×Dic29 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | C4×D29 | — | 4 | 4 | no | — |
| 91 | C4×D29 | C42 | 1 | 4 | yes | — |
| 92 | C4×D29 | C42 | 1 | 4 | yes | — |
| 93 | C4×D29 | C22×C4 | 1 | 2 | yes | — |
| 94 | C4×D29 | C22×C4 | 1 | 2 | yes | — |
| 95 | C4×D29 | C22×C4 | 1 | 2 | yes | — |
| 96 | C4×D29 | C22×C4 | 1 | 2 | yes | — |
| 97 | C8×C29 | C22×C4 | 1 | 4 | yes | — |
| 98 | C8×C29 | C22×C4 | 1 | 2 | yes | — |
| 99 | C8×C29 | C22×C4 | 1 | 2 | yes | — |
| 100 | #6597 | C22×C4 | 1 | 4 | yes | — |
| 101 | #6597 | C22×C4 | 1 | 2 | yes | — |
| 102 | #6597 | C22×C4 | 1 | 2 | yes | — |
| 103 | #2873 | — | 29 | 1 | no | maximal, Sylow |
| 104 | C22×C29 | — | 2 | 2 | no | — |
| 105 | C22×C29 | C2×C42 | 1 | 2 | yes | — |
| 106 | C22×C29 | C23×C4 | 1 | 1 | yes | characteristic |
| 107 | C2×D29 | — | 2 | 2 | no | — |
| 108 | C2×D29 | — | 2 | 2 | no | — |
| 109 | C2×D29 | — | 4 | 4 | no | — |
| 110 | C2×D29 | C2×C42 | 1 | 2 | yes | — |
| 111 | C2×D29 | C2×C42 | 1 | 2 | yes | — |
| 112 | C4×C29 | — | 2 | 4 | no | — |
| 113 | C4×C29 | C2×C42 | 1 | 2 | yes | — |
| 114 | C4×C29 | C23×C4 | 1 | 1 | yes | characteristic |
| 115 | C4×C29 | C23×C4 | 1 | 1 | yes | characteristic |
| 116 | Dic29 | — | 2 | 4 | no | — |
| 117 | Dic29 | C2×C42 | 1 | 2 | yes | — |
| 118 | Dic29 | C2×C42 | 1 | 2 | yes | — |
| 119 | C22×M16 | — | 29 | 1 | no | — |
| 120 | C22×M16 | — | 29 | 1 | no | — |
| 121 | C2×#117 | — | 29 | 1 | no | — |
| 122 | #405 | — | 29 | 1 | no | — |
| 123 | #405 | — | 29 | 1 | no | — |
| 124 | #405 | — | 29 | 1 | no | — |
| 125 | #405 | — | 29 | 2 | no | — |
| 126 | #405 | — | 29 | 2 | no | — |
| 127 | #405 | D29 | 1 | 1 | yes | characteristic, complemented |
| 128 | C4×M16 | — | 29 | 2 | no | — |
| 129 | C4×M16 | — | 29 | 2 | no | — |
| 130 | C2×C29 | — | 2 | 2 | no | — |
| 131 | C2×C29 | C22×C42 | 1 | 1 | yes | characteristic |
| 132 | C2×C29 | #568 | 1 | 2 | yes | — |
| 133 | D29 | — | 2 | 2 | no | — |
| 134 | D29 | — | 2 | 2 | no | — |
| 135 | C23×C4 | — | 29 | 1 | no | — |
| 136 | C2×M16 | — | 29 | 1 | no | — |
| 137 | C2×M16 | — | 29 | 8 | no | — |
| 138 | C2×M16 | — | 29 | 8 | no | — |
| 139 | C2×M16 | — | 29 | 1 | no | — |
| 140 | C2×M16 | — | 29 | 2 | no | — |
| 141 | C2×M16 | — | 29 | 1 | no | — |
| 142 | C2×M16 | — | 29 | 1 | no | — |
| 143 | C2×M16 | — | 29 | 1 | no | — |
| 144 | C2×M16 | C2×D29 | 1 | 1 | yes | characteristic |
| 145 | C22×C8 | — | 29 | 1 | no | — |
| 146 | C22×C8 | — | 29 | 2 | no | — |
| 147 | C22×C8 | C2×D29 | 1 | 1 | yes | characteristic |
| 148 | #117 | — | 29 | 1 | no | — |
| 149 | #117 | — | 29 | 2 | no | — |
| 150 | #117 | — | 29 | 2 | no | — |
| 151 | #117 | — | 29 | 2 | no | — |
| 152 | #117 | C2×D29 | 1 | 1 | yes | characteristic |
| 153 | C2×C4⋊C4 | — | 29 | 2 | no | — |
| 154 | C2×C22⋊C4 | — | 29 | 2 | no | — |
| 155 | C2×C42 | — | 29 | 2 | no | — |
| 156 | #97 | — | 29 | 2 | no | — |
| 157 | #97 | — | 29 | 2 | no | — |
| 158 | #97 | — | 29 | 2 | no | — |
| 159 | #97 | C2×D29 | 1 | 2 | yes | complemented |
| 160 | C4×C8 | — | 29 | 2 | no | — |
| 161 | C4×C8 | — | 29 | 2 | no | — |
| 162 | C4×C8 | — | 29 | 2 | no | — |
| 163 | C4×C8 | C2×D29 | 1 | 2 | yes | complemented |
| 164 | C29 | #2873 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 165 | C24 | — | 29 | 1 | no | — |
| 166 | C22×C4 | — | 29 | 1 | no | — |
| 167 | C22×C4 | — | 29 | 1 | no | — |
| 168 | C22×C4 | — | 29 | 1 | no | — |
| 169 | C22×C4 | — | 29 | 4 | no | — |
| 170 | C22×C4 | — | 29 | 4 | no | — |
| 171 | C22×C4 | — | 29 | 1 | no | — |
| 172 | C22×C4 | — | 29 | 1 | no | — |
| 173 | C22×C4 | — | 29 | 4 | no | — |
| 174 | C22×C4 | C22×D29 | 1 | 1 | yes | characteristic |
| 175 | M16 | — | 29 | 4 | no | — |
| 176 | M16 | — | 29 | 8 | no | — |
| 177 | M16 | — | 29 | 4 | no | — |
| 178 | M16 | — | 29 | 4 | no | — |
| 179 | M16 | — | 29 | 4 | no | — |
| 180 | M16 | — | 29 | 4 | no | — |
| 181 | M16 | C4×D29 | 1 | 4 | yes | complemented |
| 182 | C2×C8 | — | 29 | 4 | no | — |
| 183 | C2×C8 | — | 29 | 1 | no | — |
| 184 | C2×C8 | — | 29 | 2 | no | — |
| 185 | C2×C8 | — | 29 | 1 | no | — |
| 186 | C2×C8 | — | 29 | 8 | no | — |
| 187 | C2×C8 | C4×D29 | 1 | 4 | yes | complemented |
| 188 | C2×C8 | C22×D29 | 1 | 1 | yes | characteristic |
| 189 | C2×C8 | C22×D29 | 1 | 2 | yes | — |
| 190 | C2×C8 | C22×D29 | 1 | 1 | yes | characteristic |
| 191 | C4⋊C4 | — | 29 | 4 | no | — |
| 192 | C4⋊C4 | — | 29 | 2 | no | — |
| 193 | C4⋊C4 | C4×D29 | 1 | 2 | yes | — |
| 194 | C22⋊C4 | — | 29 | 2 | no | — |
| 195 | C22⋊C4 | — | 29 | 4 | no | — |
| 196 | C22⋊C4 | C4×D29 | 1 | 2 | yes | — |
| 197 | C42 | — | 29 | 4 | no | — |
| 198 | C42 | — | 29 | 2 | no | — |
| 199 | C42 | C22×D29 | 1 | 2 | yes | — |
| 200 | C23 | — | 29 | 1 | no | — |
| 201 | C23 | — | 29 | 1 | no | — |
| 202 | C23 | — | 29 | 4 | no | — |
| 203 | C23 | — | 116 | 2 | no | — |
| 204 | C23 | C2×C4×D29 | 1 | 1 | yes | characteristic |
| 205 | C2×C4 | — | 29 | 1 | no | — |
| 206 | C2×C4 | — | 29 | 1 | no | — |
| 207 | C2×C4 | — | 29 | 4 | no | — |
| 208 | C2×C4 | — | 29 | 2 | no | — |
| 209 | C2×C4 | — | 29 | 2 | no | — |
| 210 | C2×C4 | — | 29 | 2 | no | — |
| 211 | C2×C4 | — | 29 | 2 | no | — |
| 212 | C2×C4 | — | 29 | 4 | no | — |
| 213 | C2×C4 | — | 29 | 4 | no | — |
| 214 | C2×C4 | — | 29 | 4 | no | — |
| 215 | C2×C4 | — | 116 | 4 | no | — |
| 216 | C2×C4 | C2×C4×D29 | 1 | 4 | yes | — |
| 217 | C2×C4 | C2×C4×D29 | 1 | 2 | yes | — |
| 218 | C2×C4 | C2×C4×D29 | 1 | 2 | yes | — |
| 219 | C2×C4 | C2×C4×D29 | 1 | 1 | yes | characteristic |
| 220 | C2×C4 | C23×D29 | 1 | 1 | yes | characteristic |
| 221 | C8 | — | 29 | 2 | no | — |
| 222 | C8 | — | 29 | 2 | no | — |
| 223 | C8 | — | 29 | 4 | no | — |
| 224 | C8 | C2×C4×D29 | 1 | 4 | yes | — |
| 225 | C8 | C2×C4×D29 | 1 | 2 | yes | — |
| 226 | C8 | C2×C4×D29 | 1 | 2 | yes | — |
| 227 | C22 | — | 2 | 2 | no | — |
| 228 | C22 | — | 29 | 2 | no | — |
| 229 | C22 | — | 29 | 2 | no | — |
| 230 | C22 | — | 58 | 2 | no | — |
| 231 | C22 | — | 58 | 2 | no | — |
| 232 | C22 | — | 116 | 4 | no | — |
| 233 | C22 | C42×D29 | 1 | 2 | yes | — |
| 234 | C22 | C22×C4×D29 | 1 | 1 | yes | characteristic |
| 235 | C4 | — | 2 | 4 | no | — |
| 236 | C4 | — | 29 | 2 | no | — |
| 237 | C4 | — | 29 | 2 | no | — |
| 238 | C4 | — | 58 | 4 | no | — |
| 239 | C4 | C42×D29 | 1 | 2 | yes | — |
| 240 | C4 | C22×C4×D29 | 1 | 1 | yes | characteristic |
| 241 | C4 | C22×C4×D29 | 1 | 1 | yes | characteristic |
| 242 | C2 | — | 2 | 2 | no | — |
| 243 | C2 | — | 58 | 2 | no | — |
| 244 | C2 | — | 58 | 2 | no | — |
| 245 | C2 | C2×C42×D29 | 1 | 1 | yes | characteristic |
| 246 | C2 | #14271928 | 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