← #135×Dic9 #11859978
Subgroups — #135×Dic9 #11859978
Order 1152.
750 conjugacy classes of subgroups.
The subgroup lattice has 279 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C9×#135 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #41×Dic9 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10588917 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | Q16×Dic9 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | SD16×Dic9 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | D8×Dic9 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10588787 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C8×Dic9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | Dic3×#135 | — | 3 | 1 | no | maximal |
| 10 | C2×C9×#41 | C22 | 1 | 2 | yes | — |
| 11 | C9×#135 | C4 | 1 | 8 | yes | complemented |
| 12 | C2×C9×Q16 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C9×SD16 | C22 | 1 | 2 | yes | — |
| 14 | C2×C9×D8 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×C8×C9 | C22 | 1 | 1 | yes | characteristic |
| 16 | Q8×Dic9 | C22 | 1 | 4 | yes | — |
| 17 | D4×Dic9 | — | 2 | 4 | no | — |
| 18 | D4×Dic9 | C22 | 1 | 4 | yes | — |
| 19 | #63488 | — | 2 | 2 | no | — |
| 20 | #63488 | C22 | 1 | 2 | yes | — |
| 21 | C2×C4×Dic9 | — | 2 | 2 | no | — |
| 22 | C2×C4×Dic9 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×C9⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 24 | #63395 | C22 | 1 | 4 | yes | — |
| 25 | #63392 | C22 | 1 | 4 | yes | — |
| 26 | #63378 | C22 | 1 | 2 | yes | — |
| 27 | #63377 | C22 | 1 | 2 | yes | — |
| 28 | C8×Dic9 | C22 | 1 | 2 | yes | — |
| 29 | C8×Dic9 | C22 | 1 | 2 | yes | — |
| 30 | C2×C3×#135 | D3 | 1 | 1 | yes | characteristic |
| 31 | Dic3×#41 | — | 3 | 2 | no | — |
| 32 | #5233 | — | 3 | 2 | no | — |
| 33 | Dic3×Q16 | — | 3 | 2 | no | — |
| 34 | Dic3×SD16 | — | 3 | 4 | no | — |
| 35 | Dic3×D8 | — | 3 | 2 | no | — |
| 36 | #5106 | — | 3 | 1 | no | — |
| 37 | C2×C8×Dic3 | — | 3 | 1 | no | — |
| 38 | C9×#41 | — | 2 | 4 | no | — |
| 39 | C9×#41 | C2×C4 | 1 | 8 | yes | complemented |
| 40 | C2×Q8×C9 | C23 | 1 | 2 | yes | — |
| 41 | C2×D4×C9 | — | 2 | 2 | no | — |
| 42 | C2×D4×C9 | C23 | 1 | 2 | yes | — |
| 43 | C22×C4×C9 | — | 2 | 2 | no | — |
| 44 | C22×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 45 | C22×Dic9 | — | 2 | 4 | no | — |
| 46 | C22×Dic9 | D4 | 1 | 2 | yes | — |
| 47 | C9×Q16 | C2×C4 | 1 | 4 | yes | complemented |
| 48 | C9×SD16 | C2×C4 | 1 | 8 | yes | complemented |
| 49 | C9×D8 | C2×C4 | 1 | 4 | yes | complemented |
| 50 | C2×C8×C9 | C2×C4 | 1 | 4 | yes | complemented |
| 51 | C2×C8×C9 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×C8×C9 | C23 | 1 | 1 | yes | characteristic |
| 53 | #3676 | — | 2 | 2 | no | — |
| 54 | #3676 | — | 2 | 4 | no | — |
| 55 | C4⋊Dic9 | — | 2 | 4 | no | — |
| 56 | C4⋊Dic9 | C23 | 1 | 4 | yes | — |
| 57 | C4×Dic9 | — | 2 | 2 | no | — |
| 58 | C4×Dic9 | — | 2 | 4 | no | — |
| 59 | C4×Dic9 | D4 | 1 | 1 | yes | characteristic |
| 60 | C4×Dic9 | D4 | 1 | 1 | yes | characteristic |
| 61 | C4×Dic9 | C23 | 1 | 2 | yes | — |
| 62 | C2×C9⋊C8 | — | 2 | 2 | no | — |
| 63 | C2×C9⋊C8 | C23 | 1 | 2 | yes | — |
| 64 | C4×#135 | — | 9 | 1 | no | Sylow |
| 65 | C2×C3×#41 | C2×D3 | 1 | 2 | yes | — |
| 66 | C3×#135 | Dic3 | 1 | 8 | yes | — |
| 67 | C2×C3×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 68 | C2×C3×SD16 | C2×D3 | 1 | 2 | yes | — |
| 69 | C2×C3×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | C22×C3×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 71 | Q8×Dic3 | — | 3 | 4 | no | — |
| 72 | D4×Dic3 | — | 3 | 4 | no | — |
| 73 | D4×Dic3 | — | 6 | 4 | no | — |
| 74 | #926 | — | 3 | 2 | no | — |
| 75 | #926 | — | 6 | 2 | no | — |
| 76 | C2×C4×Dic3 | — | 3 | 1 | no | — |
| 77 | C2×C4×Dic3 | — | 6 | 2 | no | — |
| 78 | C22×C3⋊C8 | — | 3 | 1 | no | — |
| 79 | #835 | — | 3 | 4 | no | — |
| 80 | #832 | — | 3 | 4 | no | — |
| 81 | #818 | — | 3 | 2 | no | — |
| 82 | #817 | — | 3 | 2 | no | — |
| 83 | C8×Dic3 | — | 3 | 2 | no | — |
| 84 | C8×Dic3 | — | 3 | 2 | no | — |
| 85 | C23×C9 | — | 2 | 2 | no | — |
| 86 | C23×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | Q8×C9 | — | 2 | 2 | no | — |
| 88 | Q8×C9 | C22×C4 | 1 | 4 | yes | — |
| 89 | D4×C9 | — | 2 | 8 | no | — |
| 90 | D4×C9 | — | 2 | 2 | no | — |
| 91 | D4×C9 | C22×C4 | 1 | 4 | yes | — |
| 92 | C2×C4×C9 | — | 2 | 2 | no | — |
| 93 | C2×C4×C9 | — | 2 | 8 | no | — |
| 94 | C2×C4×C9 | C22×C4 | 1 | 2 | yes | — |
| 95 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C4×C9 | #41 | 1 | 2 | yes | — |
| 97 | C2×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 98 | C2×Dic9 | — | 2 | 4 | no | — |
| 99 | C2×Dic9 | — | 2 | 4 | no | — |
| 100 | C2×Dic9 | — | 4 | 8 | no | — |
| 101 | C2×Dic9 | C2×D4 | 1 | 2 | yes | — |
| 102 | C2×Dic9 | C2×D4 | 1 | 2 | yes | — |
| 103 | C8×C9 | C22×C4 | 1 | 2 | yes | — |
| 104 | C8×C9 | C22×C4 | 1 | 2 | yes | — |
| 105 | C9⋊C8 | — | 2 | 2 | no | — |
| 106 | C2×#135 | D9 | 1 | 1 | yes | characteristic |
| 107 | C4×#41 | — | 9 | 2 | no | — |
| 108 | C4×Q16 | — | 9 | 2 | no | — |
| 109 | C4×SD16 | — | 9 | 4 | no | — |
| 110 | C4×D8 | — | 9 | 2 | no | — |
| 111 | #427 | — | 9 | 1 | no | — |
| 112 | #416 | — | 9 | 2 | no | — |
| 113 | C2×C4×C8 | — | 9 | 1 | no | — |
| 114 | C3×#41 | — | 2 | 4 | no | — |
| 115 | C3×#41 | C2×Dic3 | 1 | 8 | yes | — |
| 116 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 117 | C2×C3×D4 | — | 2 | 2 | no | — |
| 118 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | — |
| 119 | C22×C3×C4 | — | 2 | 2 | no | — |
| 120 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 121 | C22×Dic3 | — | 3 | 2 | no | — |
| 122 | C22×Dic3 | — | 6 | 4 | no | — |
| 123 | C3×Q16 | C2×Dic3 | 1 | 4 | yes | — |
| 124 | C3×SD16 | C2×Dic3 | 1 | 8 | yes | — |
| 125 | C3×D8 | C2×Dic3 | 1 | 4 | yes | — |
| 126 | C2×C3×C8 | C2×Dic3 | 1 | 4 | yes | — |
| 127 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 128 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 129 | #217 | — | 6 | 4 | no | — |
| 130 | #217 | — | 6 | 2 | no | — |
| 131 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 132 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 133 | C4×Dic3 | — | 3 | 1 | no | — |
| 134 | C4×Dic3 | — | 3 | 1 | no | — |
| 135 | C4×Dic3 | — | 3 | 2 | no | — |
| 136 | C4×Dic3 | — | 6 | 4 | no | — |
| 137 | C4×Dic3 | — | 6 | 2 | no | — |
| 138 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 139 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 140 | C22×C9 | — | 2 | 2 | no | — |
| 141 | C22×C9 | — | 2 | 4 | no | — |
| 142 | C22×C9 | — | 4 | 4 | no | — |
| 143 | C22×C9 | C4×D4 | 1 | 2 | yes | — |
| 144 | C22×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 145 | C4×C9 | — | 2 | 4 | no | — |
| 146 | C4×C9 | C4×D4 | 1 | 2 | yes | — |
| 147 | C4×C9 | C23×C4 | 1 | 1 | yes | characteristic |
| 148 | C4×C9 | C2×#41 | 1 | 1 | yes | characteristic |
| 149 | Dic9 | — | 2 | 2 | no | — |
| 150 | Dic9 | — | 4 | 4 | no | — |
| 151 | Dic9 | #135 | 1 | 4 | yes | direct product factor |
| 152 | C2×#41 | C2×D9 | 1 | 2 | yes | — |
| 153 | #135 | Dic9 | 1 | 8 | yes | direct product factor |
| 154 | C2×Q16 | C2×D9 | 1 | 1 | yes | characteristic |
| 155 | C2×SD16 | C2×D9 | 1 | 2 | yes | — |
| 156 | C2×D8 | C2×D9 | 1 | 1 | yes | characteristic |
| 157 | C22×C8 | — | 9 | 1 | no | — |
| 158 | C22×C8 | C2×D9 | 1 | 1 | yes | characteristic |
| 159 | C4×Q8 | — | 9 | 4 | no | — |
| 160 | C4×D4 | — | 9 | 4 | no | — |
| 161 | C4×D4 | — | 18 | 4 | no | — |
| 162 | #117 | — | 9 | 2 | no | — |
| 163 | #117 | — | 18 | 2 | no | — |
| 164 | C2×C42 | — | 9 | 1 | no | — |
| 165 | C2×C42 | — | 18 | 2 | no | — |
| 166 | #107 | — | 9 | 2 | no | — |
| 167 | #106 | — | 9 | 2 | no | — |
| 168 | #103 | — | 9 | 4 | no | — |
| 169 | #102 | — | 9 | 4 | no | — |
| 170 | C4×C8 | — | 9 | 2 | no | — |
| 171 | C4×C8 | — | 9 | 2 | no | — |
| 172 | C23×C3 | — | 2 | 2 | no | — |
| 173 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 174 | C3×Q8 | — | 2 | 2 | no | — |
| 175 | C3×Q8 | C22×Dic3 | 1 | 4 | yes | — |
| 176 | C3×D4 | — | 2 | 8 | no | — |
| 177 | C3×D4 | — | 2 | 2 | no | — |
| 178 | C3×D4 | C22×Dic3 | 1 | 4 | yes | — |
| 179 | C2×C3×C4 | — | 2 | 2 | no | — |
| 180 | C2×C3×C4 | — | 2 | 8 | no | — |
| 181 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 182 | C2×C3×C4 | #237 | 1 | 2 | yes | — |
| 183 | C2×C3×C4 | C22×Dic3 | 1 | 2 | yes | — |
| 184 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 185 | C2×Dic3 | — | 3 | 2 | no | — |
| 186 | C2×Dic3 | — | 3 | 2 | no | — |
| 187 | C2×Dic3 | — | 6 | 4 | no | — |
| 188 | C2×Dic3 | — | 6 | 4 | no | — |
| 189 | C2×Dic3 | — | 12 | 8 | no | — |
| 190 | C3×C8 | C22×Dic3 | 1 | 2 | yes | — |
| 191 | C3×C8 | C22×Dic3 | 1 | 2 | yes | — |
| 192 | C3⋊C8 | — | 6 | 2 | no | — |
| 193 | C2×C9 | — | 2 | 2 | no | — |
| 194 | C2×C9 | — | 4 | 4 | no | — |
| 195 | C2×C9 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 196 | C2×C9 | C2×#135 | 1 | 2 | yes | — |
| 197 | #41 | — | 2 | 4 | no | — |
| 198 | #41 | C2×Dic9 | 1 | 8 | yes | complemented |
| 199 | C2×Q8 | C22×D9 | 1 | 2 | yes | — |
| 200 | C2×D4 | — | 2 | 2 | no | — |
| 201 | C2×D4 | C22×D9 | 1 | 2 | yes | — |
| 202 | C22×C4 | — | 2 | 2 | no | — |
| 203 | C22×C4 | — | 9 | 2 | no | — |
| 204 | C22×C4 | — | 18 | 4 | no | — |
| 205 | C22×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 206 | Q16 | C2×Dic9 | 1 | 4 | yes | complemented |
| 207 | SD16 | C2×Dic9 | 1 | 8 | yes | complemented |
| 208 | D8 | C2×Dic9 | 1 | 4 | yes | complemented |
| 209 | C2×C8 | — | 9 | 2 | no | — |
| 210 | C2×C8 | — | 18 | 2 | no | — |
| 211 | C2×C8 | C2×Dic9 | 1 | 4 | yes | complemented |
| 212 | C2×C8 | C22×D9 | 1 | 1 | yes | characteristic |
| 213 | C2×C8 | C22×D9 | 1 | 1 | yes | characteristic |
| 214 | C4⋊C4 | — | 9 | 4 | no | — |
| 215 | C4⋊C4 | — | 18 | 4 | no | — |
| 216 | C22⋊C4 | — | 18 | 4 | no | — |
| 217 | C22⋊C4 | — | 18 | 2 | no | — |
| 218 | C42 | — | 9 | 1 | no | — |
| 219 | C42 | — | 9 | 1 | no | — |
| 220 | C42 | — | 9 | 2 | no | — |
| 221 | C42 | — | 18 | 4 | no | — |
| 222 | C42 | — | 18 | 2 | no | — |
| 223 | C22×C3 | — | 2 | 2 | no | — |
| 224 | C22×C3 | — | 2 | 4 | no | — |
| 225 | C22×C3 | — | 4 | 4 | no | — |
| 226 | C22×C3 | D4×Dic3 | 1 | 2 | yes | — |
| 227 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 228 | C3×C4 | — | 2 | 4 | no | — |
| 229 | C3×C4 | D4×Dic3 | 1 | 2 | yes | — |
| 230 | C3×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 231 | C3×C4 | C23×Dic3 | 1 | 1 | yes | characteristic |
| 232 | Dic3 | — | 3 | 4 | no | — |
| 233 | Dic3 | — | 6 | 2 | no | — |
| 234 | Dic3 | — | 12 | 4 | no | — |
| 235 | C9 | C4×#135 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 236 | C23 | — | 2 | 2 | no | — |
| 237 | C23 | D4×D9 | 1 | 1 | yes | characteristic |
| 238 | Q8 | — | 2 | 2 | no | — |
| 239 | Q8 | C22×Dic9 | 1 | 4 | yes | — |
| 240 | D4 | — | 2 | 8 | no | — |
| 241 | D4 | — | 2 | 2 | no | — |
| 242 | D4 | C22×Dic9 | 1 | 4 | yes | — |
| 243 | C2×C4 | — | 2 | 2 | no | — |
| 244 | C2×C4 | — | 2 | 8 | no | — |
| 245 | C2×C4 | — | 9 | 2 | no | — |
| 246 | C2×C4 | — | 9 | 2 | no | — |
| 247 | C2×C4 | — | 18 | 4 | no | — |
| 248 | C2×C4 | — | 18 | 4 | no | — |
| 249 | C2×C4 | — | 36 | 8 | no | — |
| 250 | C2×C4 | D4×D9 | 1 | 1 | yes | characteristic |
| 251 | C2×C4 | #3699 | 1 | 2 | yes | — |
| 252 | C2×C4 | C22×Dic9 | 1 | 2 | yes | — |
| 253 | C2×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 254 | C8 | — | 18 | 2 | no | — |
| 255 | C8 | C22×Dic9 | 1 | 2 | yes | — |
| 256 | C8 | C22×Dic9 | 1 | 2 | yes | — |
| 257 | C2×C3 | — | 2 | 2 | no | — |
| 258 | C2×C3 | — | 4 | 4 | no | — |
| 259 | C2×C3 | D3×#135 | 1 | 2 | yes | — |
| 260 | C2×C3 | C2×D4×Dic3 | 1 | 1 | yes | characteristic |
| 261 | C22 | — | 2 | 2 | no | — |
| 262 | C22 | — | 2 | 4 | no | — |
| 263 | C22 | — | 4 | 4 | no | — |
| 264 | C22 | D4×Dic9 | 1 | 2 | yes | — |
| 265 | C22 | C2×D4×D9 | 1 | 1 | yes | characteristic |
| 266 | C4 | — | 2 | 4 | no | — |
| 267 | C4 | — | 9 | 4 | no | — |
| 268 | C4 | — | 18 | 2 | no | — |
| 269 | C4 | — | 36 | 4 | no | — |
| 270 | C4 | D4×Dic9 | 1 | 2 | yes | — |
| 271 | C4 | C2×#3699 | 1 | 1 | yes | characteristic |
| 272 | C4 | C23×Dic9 | 1 | 1 | yes | characteristic |
| 273 | C3 | Dic3×#135 | 1 | 1 | yes | characteristic |
| 274 | C2 | — | 2 | 2 | no | — |
| 275 | C2 | — | 4 | 4 | no | — |
| 276 | C2 | D9×#135 | 1 | 2 | yes | — |
| 277 | C2 | C2×D4×Dic9 | 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