← #28355985
Subgroups — #28355985
Order 13851.
824 conjugacy classes of subgroups.
The subgroup lattice has 246 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C32×C9×C19⋊C3 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | #17987444 | C3 | 1 | 6 | yes | maximal, complemented |
| 3 | #17987441 | C3 | 1 | 2 | yes | maximal, complemented |
| 4 | #17987440 | C3 | 1 | 2 | yes | maximal, complemented |
| 5 | #17987437 | C3 | 1 | 6 | yes | maximal, complemented |
| 6 | #17987436 | C3 | 1 | 6 | yes | maximal, complemented |
| 7 | #17987435 | C3 | 1 | 2 | yes | maximal, complemented |
| 8 | #17987420 | C3 | 1 | 1 | yes | maximal, characteristic |
| 9 | #17987419 | C3 | 1 | 1 | yes | maximal, characteristic |
| 10 | #17987418 | C3 | 1 | 1 | yes | maximal, characteristic |
| 11 | C9×#10587023 | C3 | 1 | 3 | yes | maximal, complemented |
| 12 | C9×#10587022 | C3 | 1 | 3 | yes | maximal, complemented |
| 13 | C9×#10587025 | C3 | 1 | 2 | yes | maximal, complemented |
| 14 | #17987403 | C3 | 1 | 3 | yes | maximal, complemented |
| 15 | C9×C19×3−1+2 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C33×C19⋊C3 | C32 | 1 | 1 | yes | characteristic |
| 17 | C3×#10587025 | C32 | 1 | 2 | yes | — |
| 18 | C3×#10587022 | C32 | 1 | 3 | yes | — |
| 19 | C3×#10587023 | C32 | 1 | 3 | yes | — |
| 20 | C32×#4294 | C32 | 1 | 2 | yes | — |
| 21 | C3×C9×C19⋊C3 | — | 3 | 9 | no | — |
| 22 | C3×C9×C19⋊C3 | C32 | 1 | 1 | yes | characteristic |
| 23 | C3×C9×C19⋊C3 | C32 | 1 | 1 | yes | characteristic |
| 24 | C3×C9×C19⋊C3 | C32 | 1 | 2 | yes | — |
| 25 | C3×C9×C19⋊C3 | C32 | 1 | 2 | yes | — |
| 26 | C3×C9×C19⋊C3 | C32 | 1 | 2 | yes | — |
| 27 | C3×C9×C19⋊C3 | C32 | 1 | 1 | yes | characteristic |
| 28 | #13095307 | C32 | 1 | 6 | yes | complemented |
| 29 | #13095306 | C32 | 1 | 6 | yes | complemented |
| 30 | #13095305 | C32 | 1 | 6 | yes | complemented |
| 31 | #13095305 | C32 | 1 | 6 | yes | complemented |
| 32 | #13095305 | C32 | 1 | 6 | yes | complemented |
| 33 | #13095305 | C32 | 1 | 12 | yes | complemented |
| 34 | #13095305 | C32 | 1 | 6 | yes | complemented |
| 35 | #13095305 | C32 | 1 | 6 | yes | complemented |
| 36 | #13095305 | C32 | 1 | 6 | yes | complemented |
| 37 | #13095305 | C32 | 1 | 6 | yes | complemented |
| 38 | C32⋊#4294 | C32 | 1 | 2 | yes | — |
| 39 | C32⋊#4294 | C32 | 1 | 2 | yes | — |
| 40 | #13095303 | C32 | 1 | 3 | yes | — |
| 41 | #13095303 | C32 | 1 | 3 | yes | — |
| 42 | #13095303 | C32 | 1 | 3 | yes | — |
| 43 | #13095303 | C32 | 1 | 3 | yes | — |
| 44 | #13095303 | C32 | 1 | 3 | yes | — |
| 45 | #13095303 | C32 | 1 | 3 | yes | — |
| 46 | #13095303 | C32 | 1 | 3 | yes | — |
| 47 | C9×#4294 | C32 | 1 | 6 | yes | complemented |
| 48 | C3×C19×3−1+2 | C32 | 1 | 1 | yes | characteristic |
| 49 | C32×C9×C19 | C32 | 1 | 1 | yes | characteristic |
| 50 | C19×C9⋊C9 | C32 | 1 | 6 | yes | complemented |
| 51 | C19×C32⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 52 | C19×C32⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 53 | C92×C19 | C32 | 1 | 3 | yes | complemented |
| 54 | #10624872 | — | 19 | 1 | no | maximal, Sylow |
| 55 | C33×C19 | C33 | 1 | 1 | yes | characteristic |
| 56 | C32×C19⋊C3 | — | 3 | 3 | no | — |
| 57 | C32×C19⋊C3 | — | 3 | 3 | no | — |
| 58 | C32×C19⋊C3 | — | 3 | 3 | no | — |
| 59 | C32×C19⋊C3 | — | 3 | 3 | no | — |
| 60 | C32×C19⋊C3 | C33 | 1 | 1 | yes | characteristic |
| 61 | C32×C19⋊C3 | C33 | 1 | 1 | yes | characteristic |
| 62 | C32×C19⋊C3 | C33 | 1 | 1 | yes | characteristic |
| 63 | C19×3−1+2 | — | 3 | 3 | no | — |
| 64 | C3×C9×C19 | — | 3 | 3 | no | — |
| 65 | C3×C9×C19 | C33 | 1 | 3 | yes | — |
| 66 | C3×C9×C19 | C33 | 1 | 3 | yes | — |
| 67 | C3×C9×C19 | C33 | 1 | 3 | yes | — |
| 68 | C3×C9×C19 | C33 | 1 | 2 | yes | — |
| 69 | C3×C9×C19 | C33 | 1 | 1 | yes | characteristic |
| 70 | #10587025 | — | 3 | 6 | no | — |
| 71 | C3×#4294 | — | 3 | 6 | no | — |
| 72 | C3×#4294 | C33 | 1 | 6 | yes | — |
| 73 | C3×#4294 | C33 | 1 | 6 | yes | — |
| 74 | C3×#4294 | C33 | 1 | 6 | yes | — |
| 75 | C3×#4294 | C33 | 1 | 2 | yes | — |
| 76 | C3×#4294 | C33 | 1 | 2 | yes | — |
| 77 | C3×#4294 | C33 | 1 | 2 | yes | — |
| 78 | #10587023 | — | 3 | 9 | no | — |
| 79 | #10587022 | — | 3 | 9 | no | — |
| 80 | C9×C19⋊C3 | — | 3 | 6 | no | — |
| 81 | C9×C19⋊C3 | — | 3 | 3 | no | — |
| 82 | C9×C19⋊C3 | — | 3 | 3 | no | — |
| 83 | C9×C19⋊C3 | — | 3 | 6 | no | — |
| 84 | C9×C19⋊C3 | — | 3 | 6 | no | — |
| 85 | C9×C19⋊C3 | 3−1+2 | 1 | 9 | yes | complemented |
| 86 | C33×C9 | — | 19 | 1 | no | — |
| 87 | #6895 | — | 19 | 6 | no | — |
| 88 | #6894 | — | 19 | 2 | no | — |
| 89 | #6894 | — | 19 | 6 | no | — |
| 90 | #6894 | — | 19 | 6 | no | — |
| 91 | #6894 | — | 19 | 2 | no | — |
| 92 | #6894 | — | 19 | 2 | no | — |
| 93 | #6891 | — | 19 | 1 | no | — |
| 94 | #6891 | — | 19 | 1 | no | — |
| 95 | #6891 | — | 19 | 1 | no | — |
| 96 | C9×3−1+2 | — | 19 | 2 | no | — |
| 97 | C9×3−1+2 | — | 19 | 3 | no | — |
| 98 | C9×3−1+2 | — | 19 | 3 | no | — |
| 99 | C9×3−1+2 | C19⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 100 | #6887 | — | 19 | 3 | no | — |
| 101 | C32×C19 | — | 3 | 1 | no | — |
| 102 | C32×C19 | — | 3 | 1 | no | — |
| 103 | C32×C19 | — | 3 | 1 | no | — |
| 104 | C32×C19 | #737 | 1 | 3 | yes | — |
| 105 | C32×C19 | C34 | 1 | 1 | yes | characteristic |
| 106 | C3×C19⋊C3 | — | 3 | 27 | no | — |
| 107 | C3×C19⋊C3 | — | 3 | 1 | no | — |
| 108 | C3×C19⋊C3 | — | 3 | 1 | no | — |
| 109 | C3×C19⋊C3 | — | 3 | 1 | no | — |
| 110 | C3×C19⋊C3 | — | 3 | 1 | no | — |
| 111 | C3×C19⋊C3 | — | 3 | 1 | no | — |
| 112 | C3×C19⋊C3 | — | 3 | 1 | no | — |
| 113 | C3×C19⋊C3 | — | 3 | 1 | no | — |
| 114 | C3×C19⋊C3 | — | 3 | 1 | no | — |
| 115 | C3×C19⋊C3 | — | 3 | 1 | no | — |
| 116 | C3×C19⋊C3 | C3×3−1+2 | 1 | 3 | yes | — |
| 117 | C3×C19⋊C3 | #737 | 1 | 3 | yes | — |
| 118 | C3×C19⋊C3 | #737 | 1 | 3 | yes | — |
| 119 | C9×C19 | — | 3 | 2 | no | — |
| 120 | C9×C19 | — | 3 | 3 | no | — |
| 121 | C9×C19 | — | 3 | 3 | no | — |
| 122 | C9×C19 | — | 3 | 3 | no | — |
| 123 | C9×C19 | C3×3−1+2 | 1 | 3 | yes | — |
| 124 | #4294 | — | 3 | 2 | no | — |
| 125 | #4294 | — | 3 | 2 | no | — |
| 126 | #4294 | — | 3 | 6 | no | — |
| 127 | #4294 | — | 3 | 6 | no | — |
| 128 | #4294 | — | 3 | 6 | no | — |
| 129 | #4294 | C3×3−1+2 | 1 | 6 | yes | — |
| 130 | C34 | — | 19 | 1 | no | — |
| 131 | C3×3−1+2 | — | 19 | 2 | no | — |
| 132 | C3×3−1+2 | — | 19 | 3 | no | — |
| 133 | C3×3−1+2 | — | 19 | 3 | no | — |
| 134 | C3×3−1+2 | C3×C19⋊C3 | 1 | 1 | yes | characteristic |
| 135 | C32×C9 | — | 19 | 1 | no | — |
| 136 | C32×C9 | — | 19 | 2 | no | — |
| 137 | C32×C9 | — | 19 | 2 | no | — |
| 138 | C32×C9 | — | 19 | 2 | no | — |
| 139 | C32×C9 | — | 19 | 2 | no | — |
| 140 | C32×C9 | — | 19 | 1 | no | — |
| 141 | C32×C9 | — | 19 | 1 | no | — |
| 142 | C32×C9 | — | 57 | 9 | no | — |
| 143 | C32×C9 | C3×C19⋊C3 | 1 | 1 | yes | characteristic |
| 144 | C9⋊C9 | — | 19 | 6 | no | — |
| 145 | C9⋊C9 | — | 19 | 6 | no | — |
| 146 | C9⋊C9 | — | 19 | 6 | no | — |
| 147 | C9⋊C9 | — | 19 | 12 | no | — |
| 148 | C9⋊C9 | — | 19 | 6 | no | — |
| 149 | C9⋊C9 | — | 19 | 6 | no | — |
| 150 | C9⋊C9 | — | 19 | 6 | no | — |
| 151 | C9⋊C9 | — | 19 | 6 | no | — |
| 152 | C9⋊C9 | — | 19 | 6 | no | — |
| 153 | C9⋊C9 | — | 19 | 6 | no | — |
| 154 | C9⋊C9 | C3×C19⋊C3 | 1 | 6 | yes | complemented |
| 155 | C32⋊C9 | — | 19 | 2 | no | — |
| 156 | C32⋊C9 | — | 19 | 2 | no | — |
| 157 | C32⋊C9 | — | 19 | 3 | no | — |
| 158 | C32⋊C9 | — | 19 | 3 | no | — |
| 159 | C32⋊C9 | — | 19 | 3 | no | — |
| 160 | C32⋊C9 | — | 19 | 3 | no | — |
| 161 | C32⋊C9 | — | 19 | 3 | no | — |
| 162 | C32⋊C9 | — | 19 | 3 | no | — |
| 163 | C32⋊C9 | — | 19 | 3 | no | — |
| 164 | C32⋊C9 | C3×C19⋊C3 | 1 | 1 | yes | characteristic |
| 165 | C32⋊C9 | C3×C19⋊C3 | 1 | 1 | yes | characteristic |
| 166 | C92 | — | 19 | 6 | no | — |
| 167 | C92 | C3×C19⋊C3 | 1 | 3 | yes | complemented |
| 168 | C3×C19 | — | 3 | 3 | no | — |
| 169 | C3×C19 | C32×3−1+2 | 1 | 1 | yes | characteristic |
| 170 | C3×C19 | C3×#737 | 1 | 1 | yes | characteristic |
| 171 | C3×C19 | C3×#737 | 1 | 1 | yes | characteristic |
| 172 | C3×C19 | C3×#737 | 1 | 1 | yes | characteristic |
| 173 | C19⋊C3 | — | 3 | 3 | no | — |
| 174 | C19⋊C3 | — | 3 | 3 | no | — |
| 175 | C19⋊C3 | — | 3 | 3 | no | — |
| 176 | C33 | — | 19 | 1 | no | — |
| 177 | C33 | — | 19 | 1 | no | — |
| 178 | C33 | — | 19 | 1 | no | — |
| 179 | C33 | — | 57 | 3 | no | — |
| 180 | C33 | — | 57 | 3 | no | — |
| 181 | C33 | — | 57 | 3 | no | — |
| 182 | C33 | — | 57 | 3 | no | — |
| 183 | C33 | C32×C19⋊C3 | 1 | 1 | yes | characteristic |
| 184 | 3−1+2 | — | 3 | 3 | no | — |
| 185 | 3−1+2 | — | 57 | 9 | no | — |
| 186 | 3−1+2 | — | 57 | 9 | no | — |
| 187 | 3−1+2 | — | 57 | 6 | no | — |
| 188 | C3×C9 | — | 3 | 3 | no | — |
| 189 | C3×C9 | — | 19 | 2 | no | — |
| 190 | C3×C9 | — | 19 | 9 | no | — |
| 191 | C3×C9 | — | 19 | 6 | no | — |
| 192 | C3×C9 | — | 19 | 6 | no | — |
| 193 | C3×C9 | — | 19 | 6 | no | — |
| 194 | C3×C9 | — | 19 | 2 | no | — |
| 195 | C3×C9 | — | 19 | 2 | no | — |
| 196 | C3×C9 | — | 57 | 6 | no | — |
| 197 | C3×C9 | — | 57 | 6 | no | — |
| 198 | C3×C9 | — | 57 | 6 | no | — |
| 199 | C3×C9 | — | 57 | 6 | no | — |
| 200 | C3×C9 | — | 57 | 3 | no | — |
| 201 | C3×C9 | — | 57 | 3 | no | — |
| 202 | C3×C9 | C32×C19⋊C3 | 1 | 3 | yes | — |
| 203 | C3×C9 | C32×C19⋊C3 | 1 | 3 | yes | — |
| 204 | C3×C9 | C32×C19⋊C3 | 1 | 3 | yes | — |
| 205 | C3×C9 | C32×C19⋊C3 | 1 | 2 | yes | — |
| 206 | C3×C9 | C32×C19⋊C3 | 1 | 1 | yes | characteristic |
| 207 | C19 | #10624872 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 208 | C32 | — | 3 | 1 | no | — |
| 209 | C32 | — | 3 | 1 | no | — |
| 210 | C32 | — | 3 | 1 | no | — |
| 211 | C32 | — | 19 | 3 | no | — |
| 212 | C32 | — | 19 | 3 | no | — |
| 213 | C32 | — | 19 | 3 | no | — |
| 214 | C32 | — | 57 | 27 | no | — |
| 215 | C32 | — | 57 | 1 | no | — |
| 216 | C32 | — | 57 | 1 | no | — |
| 217 | C32 | — | 57 | 1 | no | — |
| 218 | C32 | — | 57 | 1 | no | — |
| 219 | C32 | — | 57 | 1 | no | — |
| 220 | C32 | — | 57 | 1 | no | — |
| 221 | C32 | — | 57 | 1 | no | — |
| 222 | C32 | — | 57 | 1 | no | — |
| 223 | C32 | — | 57 | 1 | no | — |
| 224 | C32 | #13095332 | 1 | 3 | yes | — |
| 225 | C32 | C33×C19⋊C3 | 1 | 1 | yes | characteristic |
| 226 | C9 | — | 3 | 2 | no | — |
| 227 | C9 | — | 3 | 3 | no | — |
| 228 | C9 | — | 3 | 3 | no | — |
| 229 | C9 | — | 3 | 3 | no | — |
| 230 | C9 | — | 19 | 6 | no | — |
| 231 | C9 | — | 57 | 2 | no | — |
| 232 | C9 | — | 57 | 2 | no | — |
| 233 | C9 | — | 57 | 6 | no | — |
| 234 | C9 | — | 57 | 6 | no | — |
| 235 | C9 | — | 57 | 6 | no | — |
| 236 | C9 | 3−1+2×C19⋊C3 | 1 | 3 | yes | — |
| 237 | C3 | — | 3 | 3 | no | — |
| 238 | C3 | — | 57 | 3 | no | — |
| 239 | C3 | — | 57 | 3 | no | — |
| 240 | C3 | — | 57 | 3 | no | — |
| 241 | C3 | C3×3−1+2×C19⋊C3 | 1 | 1 | yes | characteristic |
| 242 | C3 | C19⋊C3×#737 | 1 | 1 | yes | characteristic |
| 243 | C3 | C19⋊C3×#737 | 1 | 1 | yes | characteristic |
| 244 | C3 | C3×#13095332 | 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