← #14552262
Subgroups — #14552262
Order 2187.
1331 conjugacy classes of subgroups.
The subgroup lattice has 339 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C3×#6894 | C3 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×#6891 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×#6891 | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×C9×3−1+2 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C32×C32⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10624566 | C3 | 1 | 6 | yes | maximal, complemented |
| 7 | #10624566 | C3 | 1 | 6 | yes | maximal, complemented |
| 8 | #10624565 | C3 | 1 | 6 | yes | maximal, complemented |
| 9 | #10624560 | C3 | 1 | 3 | yes | maximal, complemented |
| 10 | #10624558 | C3 | 1 | 2 | yes | maximal, complemented |
| 11 | #10624558 | C3 | 1 | 2 | yes | maximal, complemented |
| 12 | #10624558 | C3 | 1 | 2 | yes | maximal, complemented |
| 13 | #10624557 | C3 | 1 | 3 | yes | maximal, complemented |
| 14 | #10624557 | C3 | 1 | 3 | yes | maximal, complemented |
| 15 | #10624547 | C3 | 1 | 1 | yes | maximal, characteristic |
| 16 | C35 | C32 | 1 | 1 | yes | characteristic |
| 17 | C32×3−1+2 | C32 | 1 | 2 | yes | — |
| 18 | C32×3−1+2 | C32 | 1 | 1 | yes | characteristic |
| 19 | C32×3−1+2 | C32 | 1 | 3 | yes | — |
| 20 | C33×C9 | C32 | 1 | 1 | yes | characteristic |
| 21 | C33×C9 | C32 | 1 | 2 | yes | — |
| 22 | #6894 | — | 3 | 18 | no | — |
| 23 | #6891 | — | 3 | 9 | no | — |
| 24 | #6891 | — | 3 | 9 | no | — |
| 25 | C9×3−1+2 | — | 3 | 9 | no | — |
| 26 | C3×C9⋊C9 | C32 | 1 | 6 | yes | complemented |
| 27 | C3×C9⋊C9 | C32 | 1 | 6 | yes | complemented |
| 28 | C3×C9⋊C9 | C32 | 1 | 6 | yes | complemented |
| 29 | C3×C9⋊C9 | C32 | 1 | 6 | yes | complemented |
| 30 | C3×C32⋊C9 | — | 3 | 9 | no | — |
| 31 | C3×C32⋊C9 | C32 | 1 | 3 | yes | — |
| 32 | C3×C32⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 33 | C3×C32⋊C9 | C32 | 1 | 2 | yes | — |
| 34 | C3×C32⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 35 | C3×C32⋊C9 | C32 | 1 | 3 | yes | — |
| 36 | C3×C32⋊C9 | C32 | 1 | 3 | yes | — |
| 37 | C3×C32⋊C9 | C32 | 1 | 3 | yes | — |
| 38 | C3×C32⋊C9 | C32 | 1 | 3 | yes | — |
| 39 | C3×C32⋊C9 | C32 | 1 | 2 | yes | — |
| 40 | C3×C32⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 41 | C3×C32⋊C9 | C32 | 1 | 3 | yes | — |
| 42 | C3×C32⋊C9 | C32 | 1 | 2 | yes | — |
| 43 | C3×C32⋊C9 | C32 | 1 | 2 | yes | — |
| 44 | C3×C32⋊C9 | C32 | 1 | 2 | yes | — |
| 45 | C3×C32⋊C9 | C32 | 1 | 3 | yes | — |
| 46 | C3×C32⋊C9 | C32 | 1 | 3 | yes | — |
| 47 | C3×C32⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 48 | C3×C32⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 49 | C3×C92 | C32 | 1 | 3 | yes | complemented |
| 50 | #6855 | C32 | 1 | 6 | yes | complemented |
| 51 | #6855 | C32 | 1 | 6 | yes | complemented |
| 52 | #6855 | C32 | 1 | 6 | yes | complemented |
| 53 | #6855 | C32 | 1 | 6 | yes | complemented |
| 54 | #6855 | C32 | 1 | 6 | yes | complemented |
| 55 | #6855 | C32 | 1 | 6 | yes | complemented |
| 56 | #6855 | C32 | 1 | 6 | yes | complemented |
| 57 | #6855 | C32 | 1 | 12 | yes | complemented |
| 58 | C34 | — | 3 | 3 | no | — |
| 59 | C34 | — | 3 | 3 | no | — |
| 60 | C34 | — | 3 | 3 | no | — |
| 61 | C34 | — | 3 | 3 | no | — |
| 62 | C34 | — | 3 | 3 | no | — |
| 63 | C34 | — | 3 | 3 | no | — |
| 64 | C34 | — | 3 | 3 | no | — |
| 65 | C34 | — | 9 | 1 | no | — |
| 66 | C34 | — | 9 | 1 | no | — |
| 67 | C34 | — | 9 | 1 | no | — |
| 68 | C34 | — | 9 | 1 | no | — |
| 69 | C34 | — | 9 | 1 | no | — |
| 70 | C34 | — | 9 | 1 | no | — |
| 71 | C34 | C33 | 1 | 1 | yes | characteristic |
| 72 | C34 | C33 | 1 | 1 | yes | characteristic |
| 73 | C34 | C33 | 1 | 1 | yes | characteristic |
| 74 | C34 | C33 | 1 | 1 | yes | characteristic |
| 75 | C3×3−1+2 | — | 3 | 3 | no | — |
| 76 | C3×3−1+2 | — | 3 | 3 | no | — |
| 77 | C3×3−1+2 | — | 3 | 3 | no | — |
| 78 | C3×3−1+2 | — | 3 | 6 | no | — |
| 79 | C3×3−1+2 | — | 3 | 6 | no | — |
| 80 | C3×3−1+2 | — | 3 | 9 | no | — |
| 81 | C3×3−1+2 | — | 3 | 6 | no | — |
| 82 | C3×3−1+2 | — | 3 | 6 | no | — |
| 83 | C3×3−1+2 | — | 3 | 9 | no | — |
| 84 | C3×3−1+2 | — | 9 | 3 | no | — |
| 85 | C3×3−1+2 | — | 9 | 3 | no | — |
| 86 | C3×3−1+2 | 3−1+2 | 1 | 9 | yes | complemented |
| 87 | C32×C9 | — | 3 | 3 | no | — |
| 88 | C32×C9 | — | 3 | 6 | no | — |
| 89 | C32×C9 | — | 3 | 3 | no | — |
| 90 | C32×C9 | — | 3 | 6 | no | — |
| 91 | C32×C9 | — | 9 | 1 | no | — |
| 92 | C32×C9 | — | 9 | 1 | no | — |
| 93 | C32×C9 | — | 9 | 2 | no | — |
| 94 | C32×C9 | — | 9 | 2 | no | — |
| 95 | C32×C9 | C33 | 1 | 2 | yes | — |
| 96 | C32×C9 | C33 | 1 | 2 | yes | — |
| 97 | C32×C9 | C33 | 1 | 2 | yes | — |
| 98 | C32×C9 | C33 | 1 | 6 | yes | — |
| 99 | C32×C9 | C33 | 1 | 6 | yes | — |
| 100 | C32×C9 | C33 | 1 | 3 | yes | — |
| 101 | C32×C9 | C33 | 1 | 6 | yes | — |
| 102 | C32×C9 | C33 | 1 | 3 | yes | — |
| 103 | C32×C9 | C33 | 1 | 1 | yes | characteristic |
| 104 | C32×C9 | C33 | 1 | 2 | yes | — |
| 105 | C32×C9 | C33 | 1 | 3 | yes | — |
| 106 | C9⋊C9 | — | 3 | 18 | no | — |
| 107 | C9⋊C9 | — | 3 | 18 | no | — |
| 108 | C9⋊C9 | — | 3 | 18 | no | — |
| 109 | C9⋊C9 | — | 3 | 18 | no | — |
| 110 | C32⋊C9 | — | 3 | 3 | no | — |
| 111 | C32⋊C9 | — | 3 | 6 | no | — |
| 112 | C32⋊C9 | — | 3 | 6 | no | — |
| 113 | C32⋊C9 | — | 3 | 6 | no | — |
| 114 | C32⋊C9 | — | 3 | 9 | no | — |
| 115 | C32⋊C9 | — | 3 | 9 | no | — |
| 116 | C32⋊C9 | — | 3 | 9 | no | — |
| 117 | C32⋊C9 | — | 3 | 3 | no | — |
| 118 | C32⋊C9 | — | 3 | 3 | no | — |
| 119 | C32⋊C9 | — | 3 | 6 | no | — |
| 120 | C32⋊C9 | — | 3 | 6 | no | — |
| 121 | C32⋊C9 | — | 3 | 9 | no | — |
| 122 | C32⋊C9 | — | 3 | 9 | no | — |
| 123 | C32⋊C9 | — | 3 | 9 | no | — |
| 124 | C32⋊C9 | — | 9 | 3 | no | — |
| 125 | C32⋊C9 | — | 9 | 3 | no | — |
| 126 | C32⋊C9 | H(3,𝔽3) | 1 | 9 | yes | — |
| 127 | C32⋊C9 | 3−1+2 | 1 | 9 | yes | complemented |
| 128 | C92 | — | 3 | 9 | no | — |
| 129 | C33 | — | 3 | 1 | no | — |
| 130 | C33 | — | 3 | 1 | no | — |
| 131 | C33 | — | 3 | 1 | no | — |
| 132 | C33 | — | 3 | 1 | no | — |
| 133 | C33 | — | 3 | 1 | no | — |
| 134 | C33 | — | 3 | 1 | no | — |
| 135 | C33 | — | 3 | 1 | no | — |
| 136 | C33 | — | 3 | 1 | no | — |
| 137 | C33 | — | 3 | 1 | no | — |
| 138 | C33 | — | 3 | 27 | no | — |
| 139 | C33 | — | 3 | 1 | no | — |
| 140 | C33 | — | 3 | 1 | no | — |
| 141 | C33 | — | 3 | 1 | no | — |
| 142 | C33 | — | 3 | 1 | no | — |
| 143 | C33 | — | 3 | 1 | no | — |
| 144 | C33 | — | 3 | 1 | no | — |
| 145 | C33 | — | 3 | 1 | no | — |
| 146 | C33 | — | 3 | 1 | no | — |
| 147 | C33 | — | 3 | 1 | no | — |
| 148 | C33 | — | 3 | 1 | no | — |
| 149 | C33 | — | 3 | 1 | no | — |
| 150 | C33 | — | 3 | 1 | no | — |
| 151 | C33 | — | 3 | 1 | no | — |
| 152 | C33 | — | 3 | 1 | no | — |
| 153 | C33 | — | 3 | 1 | no | — |
| 154 | C33 | — | 3 | 1 | no | — |
| 155 | C33 | — | 3 | 1 | no | — |
| 156 | C33 | — | 3 | 1 | no | — |
| 157 | C33 | — | 3 | 1 | no | — |
| 158 | C33 | — | 3 | 1 | no | — |
| 159 | C33 | — | 3 | 1 | no | — |
| 160 | C33 | — | 3 | 1 | no | — |
| 161 | C33 | — | 3 | 1 | no | — |
| 162 | C33 | — | 3 | 1 | no | — |
| 163 | C33 | — | 3 | 1 | no | — |
| 164 | C33 | — | 3 | 1 | no | — |
| 165 | C33 | — | 3 | 1 | no | — |
| 166 | C33 | — | 3 | 1 | no | — |
| 167 | C33 | — | 3 | 1 | no | — |
| 168 | C33 | — | 3 | 1 | no | — |
| 169 | C33 | — | 3 | 1 | no | — |
| 170 | C33 | — | 3 | 1 | no | — |
| 171 | C33 | — | 3 | 1 | no | — |
| 172 | C33 | — | 3 | 1 | no | — |
| 173 | C33 | — | 3 | 1 | no | — |
| 174 | C33 | — | 3 | 1 | no | — |
| 175 | C33 | — | 9 | 9 | no | — |
| 176 | C33 | — | 9 | 9 | no | — |
| 177 | C33 | — | 9 | 9 | no | — |
| 178 | C33 | — | 9 | 9 | no | — |
| 179 | C33 | — | 9 | 9 | no | — |
| 180 | C33 | — | 9 | 9 | no | — |
| 181 | C33 | — | 9 | 9 | no | — |
| 182 | C33 | — | 9 | 9 | no | — |
| 183 | C33 | — | 9 | 9 | no | — |
| 184 | C33 | — | 9 | 9 | no | — |
| 185 | C33 | — | 9 | 9 | no | — |
| 186 | C33 | — | 9 | 9 | no | — |
| 187 | C33 | C3×H(3,𝔽3) | 1 | 3 | yes | — |
| 188 | C33 | C3×3−1+2 | 1 | 3 | yes | — |
| 189 | C33 | C3×3−1+2 | 1 | 3 | yes | — |
| 190 | C33 | #737 | 1 | 3 | yes | — |
| 191 | C33 | #737 | 1 | 3 | yes | — |
| 192 | C33 | #737 | 1 | 3 | yes | — |
| 193 | C33 | #737 | 1 | 3 | yes | — |
| 194 | C33 | C34 | 1 | 1 | yes | characteristic |
| 195 | 3−1+2 | — | 3 | 27 | no | — |
| 196 | 3−1+2 | — | 9 | 27 | no | — |
| 197 | 3−1+2 | — | 9 | 18 | no | — |
| 198 | C3×C9 | — | 3 | 1 | no | — |
| 199 | C3×C9 | — | 3 | 3 | no | — |
| 200 | C3×C9 | — | 3 | 2 | no | — |
| 201 | C3×C9 | — | 3 | 3 | no | — |
| 202 | C3×C9 | — | 3 | 3 | no | — |
| 203 | C3×C9 | — | 3 | 3 | no | — |
| 204 | C3×C9 | — | 3 | 1 | no | — |
| 205 | C3×C9 | — | 3 | 2 | no | — |
| 206 | C3×C9 | — | 3 | 1 | no | — |
| 207 | C3×C9 | — | 3 | 2 | no | — |
| 208 | C3×C9 | — | 3 | 3 | no | — |
| 209 | C3×C9 | — | 3 | 3 | no | — |
| 210 | C3×C9 | — | 3 | 3 | no | — |
| 211 | C3×C9 | — | 3 | 6 | no | — |
| 212 | C3×C9 | — | 3 | 6 | no | — |
| 213 | C3×C9 | — | 3 | 2 | no | — |
| 214 | C3×C9 | — | 3 | 2 | no | — |
| 215 | C3×C9 | — | 3 | 2 | no | — |
| 216 | C3×C9 | — | 3 | 6 | no | — |
| 217 | C3×C9 | — | 3 | 2 | no | — |
| 218 | C3×C9 | — | 3 | 2 | no | — |
| 219 | C3×C9 | — | 3 | 2 | no | — |
| 220 | C3×C9 | — | 3 | 6 | no | — |
| 221 | C3×C9 | — | 3 | 3 | no | — |
| 222 | C3×C9 | — | 3 | 6 | no | — |
| 223 | C3×C9 | — | 3 | 6 | no | — |
| 224 | C3×C9 | — | 3 | 6 | no | — |
| 225 | C3×C9 | — | 3 | 6 | no | — |
| 226 | C3×C9 | — | 3 | 3 | no | — |
| 227 | C3×C9 | — | 3 | 6 | no | — |
| 228 | C3×C9 | — | 3 | 3 | no | — |
| 229 | C3×C9 | — | 3 | 6 | no | — |
| 230 | C3×C9 | — | 3 | 2 | no | — |
| 231 | C3×C9 | — | 3 | 2 | no | — |
| 232 | C3×C9 | — | 3 | 2 | no | — |
| 233 | C3×C9 | — | 3 | 2 | no | — |
| 234 | C3×C9 | — | 3 | 2 | no | — |
| 235 | C3×C9 | — | 3 | 2 | no | — |
| 236 | C3×C9 | — | 3 | 6 | no | — |
| 237 | C3×C9 | — | 3 | 6 | no | — |
| 238 | C3×C9 | — | 9 | 9 | no | — |
| 239 | C3×C9 | — | 9 | 18 | no | — |
| 240 | C3×C9 | C3×H(3,𝔽3) | 1 | 9 | yes | — |
| 241 | C3×C9 | C3×3−1+2 | 1 | 9 | yes | — |
| 242 | C3×C9 | C3×3−1+2 | 1 | 3 | yes | — |
| 243 | C3×C9 | C3×3−1+2 | 1 | 6 | yes | — |
| 244 | C32 | — | 3 | 3 | no | — |
| 245 | C32 | — | 3 | 3 | no | — |
| 246 | C32 | — | 3 | 3 | no | — |
| 247 | C32 | — | 3 | 3 | no | — |
| 248 | C32 | — | 3 | 3 | no | — |
| 249 | C32 | — | 3 | 3 | no | — |
| 250 | C32 | — | 3 | 3 | no | — |
| 251 | C32 | — | 3 | 3 | no | — |
| 252 | C32 | — | 3 | 3 | no | — |
| 253 | C32 | — | 3 | 3 | no | — |
| 254 | C32 | — | 3 | 3 | no | — |
| 255 | C32 | — | 3 | 3 | no | — |
| 256 | C32 | — | 3 | 3 | no | — |
| 257 | C32 | — | 3 | 3 | no | — |
| 258 | C32 | — | 3 | 3 | no | — |
| 259 | C32 | — | 3 | 3 | no | — |
| 260 | C32 | — | 3 | 3 | no | — |
| 261 | C32 | — | 3 | 3 | no | — |
| 262 | C32 | — | 3 | 3 | no | — |
| 263 | C32 | — | 3 | 3 | no | — |
| 264 | C32 | — | 3 | 3 | no | — |
| 265 | C32 | — | 3 | 3 | no | — |
| 266 | C32 | — | 3 | 3 | no | — |
| 267 | C32 | — | 3 | 3 | no | — |
| 268 | C32 | — | 9 | 81 | no | — |
| 269 | C32 | — | 9 | 1 | no | — |
| 270 | C32 | — | 9 | 1 | no | — |
| 271 | C32 | — | 9 | 1 | no | — |
| 272 | C32 | — | 9 | 1 | no | — |
| 273 | C32 | — | 9 | 1 | no | — |
| 274 | C32 | — | 9 | 1 | no | — |
| 275 | C32 | — | 9 | 1 | no | — |
| 276 | C32 | — | 9 | 1 | no | — |
| 277 | C32 | — | 9 | 1 | no | — |
| 278 | C32 | — | 9 | 1 | no | — |
| 279 | C32 | — | 9 | 1 | no | — |
| 280 | C32 | — | 9 | 1 | no | — |
| 281 | C32 | — | 9 | 1 | no | — |
| 282 | C32 | — | 9 | 1 | no | — |
| 283 | C32 | — | 9 | 1 | no | — |
| 284 | C32 | — | 9 | 1 | no | — |
| 285 | C32 | — | 9 | 1 | no | — |
| 286 | C32 | — | 9 | 1 | no | — |
| 287 | C32 | — | 9 | 1 | no | — |
| 288 | C32 | — | 9 | 1 | no | — |
| 289 | C32 | — | 9 | 1 | no | — |
| 290 | C32 | — | 9 | 1 | no | — |
| 291 | C32 | — | 9 | 1 | no | — |
| 292 | C32 | — | 9 | 1 | no | — |
| 293 | C32 | — | 9 | 1 | no | — |
| 294 | C32 | — | 9 | 1 | no | — |
| 295 | C32 | — | 9 | 1 | no | — |
| 296 | C32 | C9⋊H(3,𝔽3) | 1 | 9 | yes | — |
| 297 | C32 | C32×H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 298 | C32 | C32×3−1+2 | 1 | 1 | yes | characteristic |
| 299 | C32 | C32×3−1+2 | 1 | 1 | yes | characteristic |
| 300 | C32 | C3×#737 | 1 | 1 | yes | characteristic |
| 301 | C32 | C3×#737 | 1 | 1 | yes | characteristic |
| 302 | C32 | C3×#737 | 1 | 1 | yes | characteristic |
| 303 | C32 | C3×#737 | 1 | 1 | yes | characteristic |
| 304 | C32 | 3−1+4 | 1 | 1 | yes | characteristic |
| 305 | C32 | 3−1+4 | 1 | 1 | yes | characteristic |
| 306 | C32 | 3−1+4 | 1 | 1 | yes | characteristic |
| 307 | C32 | 3−1+4 | 1 | 1 | yes | characteristic |
| 308 | C32 | 3−1+4 | 1 | 1 | yes | characteristic |
| 309 | C32 | 3−1+4 | 1 | 1 | yes | characteristic |
| 310 | C9 | — | 3 | 9 | no | — |
| 311 | C9 | — | 3 | 9 | no | — |
| 312 | C9 | — | 3 | 3 | no | — |
| 313 | C9 | — | 3 | 6 | no | — |
| 314 | C9 | — | 9 | 6 | no | — |
| 315 | C9 | — | 9 | 6 | no | — |
| 316 | C9 | — | 9 | 2 | no | — |
| 317 | C9 | — | 9 | 2 | no | — |
| 318 | C9 | — | 9 | 2 | no | — |
| 319 | C9 | — | 9 | 3 | no | — |
| 320 | C9 | — | 9 | 6 | no | — |
| 321 | C3 | — | 3 | 9 | no | — |
| 322 | C3 | — | 9 | 3 | no | — |
| 323 | C3 | — | 9 | 3 | no | — |
| 324 | C3 | — | 9 | 3 | no | — |
| 325 | C3 | C3×C9⋊H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 326 | C3 | #10624872 | 1 | 1 | yes | characteristic |
| 327 | C3 | #10624889 | 1 | 1 | yes | characteristic |
| 328 | C3 | #10624890 | 1 | 1 | yes | characteristic |
| 329 | C3 | #10624894 | 1 | 1 | yes | characteristic |
| 330 | C3 | H(3,𝔽3)×3−1+2 | 1 | 1 | yes | characteristic |
| 331 | C3 | #10624896 | 1 | 1 | yes | characteristic |
| 332 | C3 | 3−1+22 | 1 | 1 | yes | characteristic |
| 333 | C3 | #10624899 | 1 | 1 | yes | characteristic |
| 334 | C3 | #10624899 | 1 | 1 | yes | characteristic |
| 335 | C3 | #10624899 | 1 | 1 | yes | characteristic |
| 336 | C3 | #10624903 | 1 | 1 | yes | characteristic |
| 337 | C3 | #10624906 | 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