← #13148764
Subgroups — #13148764
Order 1728.
670 conjugacy classes of subgroups.
The subgroup lattice has 596 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11721743 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C9×#889 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×#63451 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11720971 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C4×#6189 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11720928 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #11720928 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11720917 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #11720916 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #11720905 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #11720905 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #11720902 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #11720902 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #11720901 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #11720900 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #10594597 | — | 3 | 1 | no | maximal |
| 17 | #10589787 | — | 3 | 1 | no | maximal |
| 18 | C2×#6226 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#6189 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#6189 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#6189 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×C9×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 23 | #88534 | C22 | 1 | 1 | yes | characteristic |
| 24 | #88534 | C22 | 1 | 1 | yes | characteristic |
| 25 | C4×C3⋊Dic9 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4×C3⋊Dic9 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×C3⋊Dic9 | C22 | 1 | 1 | yes | characteristic |
| 28 | C9×C4⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 29 | C9×Dic3⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 30 | C9×Dic3⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 31 | C9×Dic3⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 32 | C9×Dic3⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×C9×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 34 | C3×C4⋊Dic9 | C22 | 1 | 1 | yes | characteristic |
| 35 | C3×Dic9⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×Dic9⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 37 | C3×Dic9⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 38 | C3×Dic9⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 39 | C3×C4×Dic9 | C22 | 1 | 1 | yes | characteristic |
| 40 | Dic3⋊Dic9 | C22 | 1 | 1 | yes | characteristic |
| 41 | Dic3⋊Dic9 | C22 | 1 | 1 | yes | characteristic |
| 42 | Dic3⋊Dic9 | C22 | 1 | 1 | yes | characteristic |
| 43 | #88442 | C22 | 1 | 1 | yes | characteristic |
| 44 | #88442 | C22 | 1 | 1 | yes | characteristic |
| 45 | #88442 | C22 | 1 | 1 | yes | characteristic |
| 46 | Dic9⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 47 | Dic9⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 48 | Dic9⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 49 | Dic3×Dic9 | C22 | 1 | 1 | yes | characteristic |
| 50 | Dic3×Dic9 | C22 | 1 | 1 | yes | characteristic |
| 51 | Dic3×Dic9 | C22 | 1 | 1 | yes | characteristic |
| 52 | Dic3×Dic9 | C22 | 1 | 1 | yes | characteristic |
| 53 | #64096 | — | 3 | 1 | no | — |
| 54 | C3×#889 | — | 3 | 1 | no | — |
| 55 | C3×#889 | D3 | 1 | 1 | yes | characteristic |
| 56 | #63919 | — | 3 | 1 | no | — |
| 57 | C4×#627 | — | 3 | 1 | no | — |
| 58 | #63870 | — | 3 | 1 | no | — |
| 59 | #63870 | — | 3 | 1 | no | — |
| 60 | #63846 | — | 3 | 1 | no | — |
| 61 | #63846 | — | 3 | 1 | no | — |
| 62 | #63840 | — | 3 | 1 | no | — |
| 63 | #63840 | — | 3 | 1 | no | — |
| 64 | #63838 | — | 3 | 1 | no | — |
| 65 | #63838 | — | 3 | 1 | no | — |
| 66 | #63837 | — | 3 | 1 | no | — |
| 67 | #63837 | — | 3 | 1 | no | — |
| 68 | C9×#125 | — | 3 | 1 | no | — |
| 69 | #63452 | — | 3 | 1 | no | — |
| 70 | #63451 | — | 3 | 1 | no | — |
| 71 | #63451 | — | 3 | 1 | no | — |
| 72 | #63451 | — | 3 | 1 | no | — |
| 73 | #63451 | D3 | 1 | 1 | yes | characteristic |
| 74 | #63450 | — | 3 | 1 | no | — |
| 75 | #63450 | — | 3 | 1 | no | — |
| 76 | #63450 | — | 3 | 1 | no | — |
| 77 | #63449 | — | 3 | 1 | no | — |
| 78 | #63449 | — | 3 | 1 | no | — |
| 79 | #63449 | — | 3 | 1 | no | — |
| 80 | #63449 | — | 3 | 1 | no | — |
| 81 | #63449 | — | 6 | 1 | no | — |
| 82 | C4×Dic18 | — | 3 | 1 | no | — |
| 83 | C4×Dic18 | — | 3 | 1 | no | — |
| 84 | C2×C3×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×C3×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×C3×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C3⋊Dic9 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×C3⋊Dic9 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×C3⋊Dic9 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×C3⋊Dic9 | C23 | 1 | 1 | yes | characteristic |
| 91 | #6226 | — | 2 | 2 | no | — |
| 92 | C2×C9×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C9×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C9×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C9×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×C3×Dic9 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×C3×Dic9 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×C3×Dic9 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×C3×Dic9 | C23 | 1 | 1 | yes | characteristic |
| 100 | #6189 | — | 2 | 2 | no | — |
| 101 | #6189 | — | 2 | 2 | no | — |
| 102 | #6189 | Q8 | 1 | 4 | yes | complemented |
| 103 | #5685 | — | 9 | 1 | no | — |
| 104 | #5685 | — | 9 | 1 | no | — |
| 105 | C2×#634 | — | 3 | 1 | no | — |
| 106 | C2×#627 | — | 3 | 1 | no | — |
| 107 | C2×#627 | — | 3 | 1 | no | — |
| 108 | C2×#627 | — | 3 | 1 | no | — |
| 109 | C32×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 110 | #3750 | — | 3 | 1 | no | — |
| 111 | #3750 | — | 3 | 1 | no | — |
| 112 | C4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 113 | C4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 114 | C4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 115 | C3×C4⋊Dic3 | — | 3 | 1 | no | — |
| 116 | C3×C4⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 117 | C3×Dic3⋊C4 | — | 3 | 1 | no | — |
| 118 | C3×Dic3⋊C4 | — | 3 | 1 | no | — |
| 119 | C3×Dic3⋊C4 | — | 3 | 1 | no | — |
| 120 | C3×Dic3⋊C4 | — | 3 | 1 | no | — |
| 121 | C3×Dic3⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 122 | C3×Dic3⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 123 | C3×Dic3⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 124 | C3×Dic3⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 125 | C3×C4×Dic3 | — | 3 | 1 | no | — |
| 126 | C3×C4×Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 127 | #3724 | — | 3 | 1 | no | — |
| 128 | #3724 | — | 3 | 1 | no | — |
| 129 | #3724 | — | 3 | 1 | no | — |
| 130 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 131 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 132 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 133 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 134 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 135 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 136 | Dic32 | — | 3 | 1 | no | — |
| 137 | Dic32 | — | 3 | 1 | no | — |
| 138 | Dic32 | — | 3 | 1 | no | — |
| 139 | Dic32 | — | 3 | 1 | no | — |
| 140 | C2×Dic18 | — | 3 | 1 | no | — |
| 141 | C2×Dic18 | — | 3 | 1 | no | — |
| 142 | C2×Dic18 | — | 3 | 1 | no | — |
| 143 | C2×Dic18 | — | 3 | 1 | no | — |
| 144 | C2×Dic18 | — | 6 | 1 | no | — |
| 145 | C9×C4⋊C4 | — | 2 | 1 | no | — |
| 146 | C9×C4⋊C4 | — | 3 | 1 | no | — |
| 147 | C9×C4⋊C4 | — | 3 | 1 | no | — |
| 148 | C9×C4⋊C4 | — | 3 | 1 | no | — |
| 149 | C9×C4⋊C4 | — | 3 | 1 | no | — |
| 150 | C9×C4⋊C4 | — | 3 | 1 | no | — |
| 151 | C9×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 152 | C42×C9 | — | 3 | 1 | no | — |
| 153 | C4⋊Dic9 | — | 3 | 1 | no | — |
| 154 | C4⋊Dic9 | — | 3 | 1 | no | — |
| 155 | C4⋊Dic9 | — | 3 | 1 | no | — |
| 156 | C4⋊Dic9 | C2×D3 | 1 | 1 | yes | characteristic |
| 157 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 158 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 159 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 160 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 161 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 162 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 163 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 164 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 165 | Dic9⋊C4 | — | 6 | 1 | no | — |
| 166 | Dic9⋊C4 | — | 6 | 1 | no | — |
| 167 | Dic9⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 168 | Dic9⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 169 | Dic9⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 170 | Dic9⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 171 | C4×Dic9 | — | 3 | 1 | no | — |
| 172 | C4×Dic9 | — | 3 | 1 | no | — |
| 173 | C4×Dic9 | — | 3 | 1 | no | — |
| 174 | C4×Dic9 | — | 3 | 1 | no | — |
| 175 | C4×Dic9 | — | 3 | 1 | no | — |
| 176 | C4×Dic9 | — | 3 | 1 | no | — |
| 177 | C4×Dic9 | — | 3 | 1 | no | — |
| 178 | C4×Dic9 | — | 6 | 1 | no | — |
| 179 | C4×Dic9 | — | 6 | 1 | no | — |
| 180 | C4×Dic9 | — | 6 | 1 | no | — |
| 181 | C4×Dic9 | C2×D3 | 1 | 1 | yes | characteristic |
| 182 | C22×C3×C9 | C24 | 1 | 1 | yes | characteristic |
| 183 | C3×C4×C9 | — | 2 | 1 | no | — |
| 184 | C3×C4×C9 | — | 2 | 1 | no | — |
| 185 | C3×C4×C9 | — | 2 | 1 | no | — |
| 186 | C3⋊Dic9 | — | 2 | 1 | no | — |
| 187 | C3⋊Dic9 | — | 2 | 1 | no | — |
| 188 | C3⋊Dic9 | C2×Q8 | 1 | 2 | yes | — |
| 189 | C3⋊Dic9 | #41 | 1 | 2 | yes | — |
| 190 | C9×Dic3 | — | 2 | 1 | no | — |
| 191 | C9×Dic3 | — | 2 | 1 | no | — |
| 192 | C9×Dic3 | — | 2 | 1 | no | — |
| 193 | C9×Dic3 | C2×Q8 | 1 | 2 | yes | — |
| 194 | C3×Dic9 | — | 2 | 1 | no | — |
| 195 | C3×Dic9 | — | 2 | 1 | no | — |
| 196 | C3×Dic9 | — | 2 | 1 | no | — |
| 197 | C3×Dic9 | C2×Q8 | 1 | 2 | yes | — |
| 198 | C3×#125 | — | 3 | 1 | no | — |
| 199 | C3×#125 | — | 9 | 1 | no | — |
| 200 | #890 | — | 9 | 1 | no | — |
| 201 | #890 | — | 9 | 1 | no | — |
| 202 | #889 | — | 3 | 1 | no | — |
| 203 | #889 | — | 9 | 1 | no | — |
| 204 | #889 | — | 9 | 1 | no | — |
| 205 | #889 | — | 9 | 1 | no | — |
| 206 | #889 | — | 9 | 1 | no | — |
| 207 | #889 | — | 9 | 1 | no | — |
| 208 | #889 | — | 9 | 1 | no | — |
| 209 | #889 | D9 | 1 | 1 | yes | characteristic |
| 210 | #888 | — | 9 | 1 | no | — |
| 211 | #888 | — | 9 | 1 | no | — |
| 212 | #888 | — | 9 | 1 | no | — |
| 213 | #888 | — | 9 | 1 | no | — |
| 214 | #888 | — | 9 | 1 | no | — |
| 215 | #888 | — | 9 | 1 | no | — |
| 216 | #887 | — | 9 | 1 | no | — |
| 217 | #887 | — | 9 | 1 | no | — |
| 218 | #887 | — | 9 | 1 | no | — |
| 219 | #887 | — | 9 | 1 | no | — |
| 220 | #887 | — | 9 | 1 | no | — |
| 221 | #887 | — | 9 | 1 | no | — |
| 222 | #887 | — | 9 | 1 | no | — |
| 223 | #887 | — | 9 | 1 | no | — |
| 224 | #887 | — | 18 | 1 | no | — |
| 225 | C4×Dic6 | — | 9 | 1 | no | — |
| 226 | C4×Dic6 | — | 9 | 1 | no | — |
| 227 | C4×Dic6 | — | 9 | 1 | no | — |
| 228 | C4×Dic6 | — | 9 | 1 | no | — |
| 229 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 230 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 231 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 232 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 233 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 234 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 235 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 236 | #634 | — | 6 | 2 | no | — |
| 237 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 238 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 239 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 240 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 241 | C2×C3×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 242 | C2×C3×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 243 | C2×C3×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 244 | C2×C3×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 245 | #627 | — | 3 | 4 | no | — |
| 246 | #627 | — | 6 | 2 | no | — |
| 247 | #627 | — | 6 | 2 | no | — |
| 248 | C2×C4×C9 | — | 2 | 1 | no | — |
| 249 | C2×C4×C9 | — | 2 | 1 | no | — |
| 250 | C2×C4×C9 | — | 2 | 1 | no | — |
| 251 | C2×C4×C9 | — | 3 | 1 | no | — |
| 252 | C2×C4×C9 | — | 3 | 1 | no | — |
| 253 | C2×C4×C9 | — | 3 | 1 | no | — |
| 254 | C2×C4×C9 | — | 3 | 1 | no | — |
| 255 | C2×C4×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 258 | C2×Dic9 | — | 3 | 1 | no | — |
| 259 | C2×Dic9 | — | 3 | 1 | no | — |
| 260 | C2×Dic9 | — | 3 | 1 | no | — |
| 261 | C2×Dic9 | — | 3 | 1 | no | — |
| 262 | C2×Dic9 | — | 6 | 1 | no | — |
| 263 | C2×Dic9 | — | 6 | 1 | no | — |
| 264 | C2×Dic9 | — | 6 | 1 | no | — |
| 265 | C2×Dic9 | — | 6 | 1 | no | — |
| 266 | C2×Dic9 | C22×D3 | 1 | 1 | yes | characteristic |
| 267 | C2×Dic9 | C22×D3 | 1 | 1 | yes | characteristic |
| 268 | C2×Dic9 | C22×D3 | 1 | 1 | yes | characteristic |
| 269 | C2×Dic9 | C22×D3 | 1 | 1 | yes | characteristic |
| 270 | Dic18 | — | 3 | 4 | no | — |
| 271 | Dic18 | — | 6 | 2 | no | — |
| 272 | Dic18 | — | 6 | 2 | no | — |
| 273 | Dic18 | — | 6 | 2 | no | — |
| 274 | Dic18 | — | 6 | 4 | no | — |
| 275 | #557 | — | 27 | 1 | no | Sylow |
| 276 | C2×C3×C9 | C22×Q8 | 1 | 1 | yes | characteristic |
| 277 | C2×C3×C9 | C2×#41 | 1 | 1 | yes | characteristic |
| 278 | C2×C3×C9 | 2−1+4 | 1 | 1 | yes | characteristic |
| 279 | C2×Dic6 | — | 9 | 1 | no | — |
| 280 | C2×Dic6 | — | 9 | 1 | no | — |
| 281 | C2×Dic6 | — | 9 | 1 | no | — |
| 282 | C2×Dic6 | — | 9 | 1 | no | — |
| 283 | C2×Dic6 | — | 9 | 1 | no | — |
| 284 | C2×Dic6 | — | 9 | 1 | no | — |
| 285 | C2×Dic6 | — | 9 | 1 | no | — |
| 286 | C2×Dic6 | — | 9 | 1 | no | — |
| 287 | C2×Dic6 | — | 18 | 1 | no | — |
| 288 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 289 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 290 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 291 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 292 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 293 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 294 | C3×C4⋊C4 | — | 9 | 1 | no | — |
| 295 | C3×C4⋊C4 | — | 9 | 1 | no | — |
| 296 | C3×C4⋊C4 | — | 9 | 1 | no | — |
| 297 | C3×C4⋊C4 | — | 9 | 1 | no | — |
| 298 | C3×C4⋊C4 | — | 9 | 1 | no | — |
| 299 | C3×C4⋊C4 | C2×D9 | 1 | 1 | yes | characteristic |
| 300 | C3×C4⋊C4 | D32 | 1 | 1 | yes | characteristic |
| 301 | C3×C42 | — | 3 | 1 | no | — |
| 302 | C3×C42 | — | 9 | 1 | no | — |
| 303 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 304 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 305 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 306 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 307 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 308 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 309 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 310 | C4⋊Dic3 | C2×D9 | 1 | 1 | yes | characteristic |
| 311 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 312 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 313 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 314 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 315 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 316 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 317 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 318 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 319 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 320 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 321 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 322 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 323 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 324 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 325 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 326 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 327 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 328 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 329 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 330 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 331 | Dic3⋊C4 | — | 18 | 1 | no | — |
| 332 | Dic3⋊C4 | — | 18 | 1 | no | — |
| 333 | Dic3⋊C4 | C2×D9 | 1 | 1 | yes | characteristic |
| 334 | Dic3⋊C4 | C2×D9 | 1 | 1 | yes | characteristic |
| 335 | Dic3⋊C4 | C2×D9 | 1 | 1 | yes | characteristic |
| 336 | Dic3⋊C4 | C2×D9 | 1 | 1 | yes | characteristic |
| 337 | C4×Dic3 | — | 3 | 1 | no | — |
| 338 | C4×Dic3 | — | 9 | 1 | no | — |
| 339 | C4×Dic3 | — | 9 | 1 | no | — |
| 340 | C4×Dic3 | — | 9 | 1 | no | — |
| 341 | C4×Dic3 | — | 9 | 1 | no | — |
| 342 | C4×Dic3 | — | 9 | 1 | no | — |
| 343 | C4×Dic3 | — | 9 | 1 | no | — |
| 344 | C4×Dic3 | — | 9 | 1 | no | — |
| 345 | C4×Dic3 | — | 9 | 1 | no | — |
| 346 | C4×Dic3 | — | 9 | 1 | no | — |
| 347 | C4×Dic3 | — | 9 | 1 | no | — |
| 348 | C4×Dic3 | — | 9 | 1 | no | — |
| 349 | C4×Dic3 | — | 9 | 1 | no | — |
| 350 | C4×Dic3 | — | 9 | 1 | no | — |
| 351 | C4×Dic3 | — | 9 | 1 | no | — |
| 352 | C4×Dic3 | — | 18 | 1 | no | — |
| 353 | C4×Dic3 | — | 18 | 1 | no | — |
| 354 | C4×Dic3 | — | 18 | 1 | no | — |
| 355 | C4×Dic3 | C2×D9 | 1 | 1 | yes | characteristic |
| 356 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 357 | C32×C4 | — | 2 | 1 | no | — |
| 358 | C32×C4 | — | 2 | 1 | no | — |
| 359 | C32×C4 | — | 2 | 1 | no | — |
| 360 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 361 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 362 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 363 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 364 | C3×Dic3 | — | 2 | 1 | no | — |
| 365 | C3×Dic3 | — | 2 | 1 | no | — |
| 366 | C3×Dic3 | — | 2 | 1 | no | — |
| 367 | C3×Dic3 | — | 3 | 2 | no | — |
| 368 | C3×Dic3 | — | 6 | 1 | no | — |
| 369 | C3×Dic3 | — | 6 | 1 | no | — |
| 370 | C3×Dic3 | — | 6 | 1 | no | — |
| 371 | C3×Dic3 | D3×Q8 | 1 | 2 | yes | — |
| 372 | C22×C9 | — | 2 | 1 | no | — |
| 373 | C22×C9 | C23×D3 | 1 | 1 | yes | characteristic |
| 374 | C4×C9 | — | 2 | 2 | no | — |
| 375 | C4×C9 | — | 2 | 1 | no | — |
| 376 | C4×C9 | — | 2 | 1 | no | — |
| 377 | C4×C9 | — | 2 | 1 | no | — |
| 378 | C4×C9 | — | 3 | 2 | no | — |
| 379 | C4×C9 | — | 4 | 1 | no | — |
| 380 | C4×C9 | — | 4 | 1 | no | — |
| 381 | C4×C9 | — | 6 | 1 | no | — |
| 382 | C4×C9 | — | 6 | 1 | no | — |
| 383 | C4×C9 | — | 6 | 1 | no | — |
| 384 | Dic9 | — | 2 | 1 | no | — |
| 385 | Dic9 | — | 2 | 1 | no | — |
| 386 | Dic9 | — | 2 | 1 | no | — |
| 387 | Dic9 | — | 3 | 2 | no | — |
| 388 | Dic9 | — | 3 | 2 | no | — |
| 389 | Dic9 | — | 6 | 2 | no | — |
| 390 | Dic9 | — | 6 | 2 | no | — |
| 391 | Dic9 | — | 6 | 2 | no | — |
| 392 | Dic9 | — | 6 | 1 | no | — |
| 393 | Dic9 | — | 6 | 1 | no | — |
| 394 | Dic9 | — | 12 | 1 | no | — |
| 395 | Dic9 | D3×Q8 | 1 | 2 | yes | — |
| 396 | C4⋊Q8 | — | 27 | 1 | no | — |
| 397 | C4⋊Q8 | — | 27 | 1 | no | — |
| 398 | C4⋊Q8 | — | 27 | 1 | no | — |
| 399 | #125 | — | 3 | 1 | no | — |
| 400 | #125 | — | 9 | 1 | no | — |
| 401 | #125 | — | 27 | 1 | no | — |
| 402 | #125 | — | 27 | 1 | no | — |
| 403 | #125 | — | 27 | 1 | no | — |
| 404 | #125 | — | 27 | 1 | no | — |
| 405 | C4×Q8 | — | 27 | 1 | no | — |
| 406 | C4×Q8 | — | 27 | 1 | no | — |
| 407 | C4×Q8 | — | 27 | 1 | no | — |
| 408 | C4×Q8 | — | 27 | 1 | no | — |
| 409 | C4×Q8 | — | 27 | 1 | no | — |
| 410 | C4×Q8 | — | 27 | 1 | no | — |
| 411 | C3×C9 | #557 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 412 | C2×C3×C4 | — | 2 | 1 | no | — |
| 413 | C2×C3×C4 | — | 2 | 1 | no | — |
| 414 | C2×C3×C4 | — | 2 | 1 | no | — |
| 415 | C2×C3×C4 | — | 3 | 1 | no | — |
| 416 | C2×C3×C4 | — | 3 | 1 | no | — |
| 417 | C2×C3×C4 | — | 3 | 1 | no | — |
| 418 | C2×C3×C4 | — | 3 | 1 | no | — |
| 419 | C2×C3×C4 | — | 9 | 1 | no | — |
| 420 | C2×C3×C4 | — | 9 | 1 | no | — |
| 421 | C2×C3×C4 | — | 9 | 1 | no | — |
| 422 | C2×C3×C4 | — | 9 | 1 | no | — |
| 423 | C2×C3×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 424 | C2×C3×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 425 | C2×C3×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 426 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 427 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 428 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 429 | C2×Dic3 | — | 3 | 1 | no | — |
| 430 | C2×Dic3 | — | 3 | 1 | no | — |
| 431 | C2×Dic3 | — | 3 | 1 | no | — |
| 432 | C2×Dic3 | — | 3 | 1 | no | — |
| 433 | C2×Dic3 | — | 9 | 1 | no | — |
| 434 | C2×Dic3 | — | 9 | 1 | no | — |
| 435 | C2×Dic3 | — | 9 | 1 | no | — |
| 436 | C2×Dic3 | — | 9 | 1 | no | — |
| 437 | C2×Dic3 | — | 9 | 1 | no | — |
| 438 | C2×Dic3 | — | 9 | 1 | no | — |
| 439 | C2×Dic3 | — | 9 | 1 | no | — |
| 440 | C2×Dic3 | — | 9 | 1 | no | — |
| 441 | C2×Dic3 | — | 18 | 1 | no | — |
| 442 | C2×Dic3 | — | 18 | 1 | no | — |
| 443 | C2×Dic3 | — | 18 | 1 | no | — |
| 444 | C2×Dic3 | — | 18 | 1 | no | — |
| 445 | C2×Dic3 | C22×D9 | 1 | 1 | yes | characteristic |
| 446 | C2×Dic3 | C22×D9 | 1 | 1 | yes | characteristic |
| 447 | C2×Dic3 | C22×D9 | 1 | 1 | yes | characteristic |
| 448 | C2×Dic3 | C22×D9 | 1 | 1 | yes | characteristic |
| 449 | Dic6 | — | 9 | 4 | no | — |
| 450 | Dic6 | — | 9 | 4 | no | — |
| 451 | Dic6 | — | 18 | 2 | no | — |
| 452 | Dic6 | — | 18 | 2 | no | — |
| 453 | Dic6 | — | 18 | 2 | no | — |
| 454 | Dic6 | — | 18 | 2 | no | — |
| 455 | Dic6 | — | 18 | 2 | no | — |
| 456 | Dic6 | — | 18 | 2 | no | — |
| 457 | Dic6 | — | 18 | 4 | no | — |
| 458 | C2×C32 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 459 | C2×C32 | D3×#41 | 1 | 1 | yes | characteristic |
| 460 | C2×C32 | #1010 | 1 | 1 | yes | characteristic |
| 461 | C2×C9 | — | 2 | 1 | no | — |
| 462 | C2×C9 | — | 2 | 1 | no | — |
| 463 | C2×C9 | — | 2 | 1 | no | — |
| 464 | C2×C9 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 465 | C2×C9 | D3×#41 | 1 | 1 | yes | characteristic |
| 466 | C2×C9 | #1010 | 1 | 1 | yes | characteristic |
| 467 | C2×Q8 | — | 27 | 1 | no | — |
| 468 | C2×Q8 | — | 27 | 1 | no | — |
| 469 | C2×Q8 | — | 27 | 1 | no | — |
| 470 | C2×Q8 | — | 27 | 1 | no | — |
| 471 | C4⋊C4 | — | 3 | 1 | no | — |
| 472 | C4⋊C4 | — | 3 | 1 | no | — |
| 473 | C4⋊C4 | — | 3 | 1 | no | — |
| 474 | C4⋊C4 | — | 3 | 1 | no | — |
| 475 | C4⋊C4 | — | 3 | 1 | no | — |
| 476 | C4⋊C4 | — | 9 | 1 | no | — |
| 477 | C4⋊C4 | — | 9 | 1 | no | — |
| 478 | C4⋊C4 | — | 9 | 1 | no | — |
| 479 | C4⋊C4 | — | 9 | 1 | no | — |
| 480 | C4⋊C4 | — | 9 | 1 | no | — |
| 481 | C4⋊C4 | — | 27 | 1 | no | — |
| 482 | C4⋊C4 | — | 27 | 1 | no | — |
| 483 | C4⋊C4 | — | 27 | 1 | no | — |
| 484 | C4⋊C4 | — | 27 | 1 | no | — |
| 485 | C4⋊C4 | — | 27 | 1 | no | — |
| 486 | C4⋊C4 | — | 27 | 1 | no | — |
| 487 | C4⋊C4 | — | 27 | 1 | no | — |
| 488 | C4⋊C4 | — | 27 | 1 | no | — |
| 489 | C4⋊C4 | — | 27 | 1 | no | — |
| 490 | C4⋊C4 | — | 27 | 1 | no | — |
| 491 | C4⋊C4 | — | 27 | 1 | no | — |
| 492 | C4⋊C4 | D3×D9 | 1 | 1 | yes | characteristic |
| 493 | C42 | — | 3 | 1 | no | — |
| 494 | C42 | — | 9 | 1 | no | — |
| 495 | C42 | — | 27 | 1 | no | — |
| 496 | C42 | — | 27 | 1 | no | — |
| 497 | C42 | — | 27 | 1 | no | — |
| 498 | C42 | — | 27 | 1 | no | — |
| 499 | C42 | — | 27 | 1 | no | — |
| 500 | C42 | — | 27 | 1 | no | — |
| 501 | C42 | — | 27 | 1 | no | — |
| 502 | C22×C3 | — | 2 | 1 | no | — |
| 503 | C22×C3 | C23×D9 | 1 | 1 | yes | characteristic |
| 504 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 505 | C3×C4 | — | 2 | 2 | no | — |
| 506 | C3×C4 | — | 2 | 1 | no | — |
| 507 | C3×C4 | — | 2 | 1 | no | — |
| 508 | C3×C4 | — | 2 | 1 | no | — |
| 509 | C3×C4 | — | 2 | 1 | no | — |
| 510 | C3×C4 | — | 2 | 1 | no | — |
| 511 | C3×C4 | — | 2 | 1 | no | — |
| 512 | C3×C4 | — | 3 | 2 | no | — |
| 513 | C3×C4 | — | 4 | 1 | no | — |
| 514 | C3×C4 | — | 4 | 1 | no | — |
| 515 | C3×C4 | — | 6 | 1 | no | — |
| 516 | C3×C4 | — | 6 | 1 | no | — |
| 517 | C3×C4 | — | 6 | 1 | no | — |
| 518 | C3×C4 | — | 9 | 2 | no | — |
| 519 | C3×C4 | — | 18 | 1 | no | — |
| 520 | C3×C4 | — | 18 | 1 | no | — |
| 521 | C3×C4 | — | 18 | 1 | no | — |
| 522 | Dic3 | — | 2 | 1 | no | — |
| 523 | Dic3 | — | 2 | 1 | no | — |
| 524 | Dic3 | — | 2 | 1 | no | — |
| 525 | Dic3 | — | 3 | 2 | no | — |
| 526 | Dic3 | — | 6 | 1 | no | — |
| 527 | Dic3 | — | 6 | 1 | no | — |
| 528 | Dic3 | — | 6 | 1 | no | — |
| 529 | Dic3 | — | 9 | 2 | no | — |
| 530 | Dic3 | — | 9 | 2 | no | — |
| 531 | Dic3 | — | 9 | 2 | no | — |
| 532 | Dic3 | — | 9 | 2 | no | — |
| 533 | Dic3 | — | 18 | 2 | no | — |
| 534 | Dic3 | — | 18 | 2 | no | — |
| 535 | Dic3 | — | 18 | 2 | no | — |
| 536 | Dic3 | — | 18 | 1 | no | — |
| 537 | Dic3 | — | 18 | 1 | no | — |
| 538 | Dic3 | — | 18 | 1 | no | — |
| 539 | Dic3 | — | 18 | 1 | no | — |
| 540 | Dic3 | — | 36 | 1 | no | — |
| 541 | Dic3 | Q8×D9 | 1 | 2 | yes | — |
| 542 | C32 | #5685 | 1 | 1 | yes | characteristic |
| 543 | C9 | — | 2 | 1 | no | — |
| 544 | C9 | #5685 | 1 | 1 | yes | characteristic, complemented |
| 545 | Q8 | — | 27 | 4 | no | — |
| 546 | Q8 | — | 54 | 2 | no | — |
| 547 | Q8 | — | 54 | 2 | no | — |
| 548 | Q8 | — | 54 | 2 | no | — |
| 549 | C2×C4 | — | 3 | 1 | no | — |
| 550 | C2×C4 | — | 3 | 1 | no | — |
| 551 | C2×C4 | — | 3 | 1 | no | — |
| 552 | C2×C4 | — | 3 | 1 | no | — |
| 553 | C2×C4 | — | 9 | 1 | no | — |
| 554 | C2×C4 | — | 9 | 1 | no | — |
| 555 | C2×C4 | — | 9 | 1 | no | — |
| 556 | C2×C4 | — | 9 | 1 | no | — |
| 557 | C2×C4 | — | 27 | 1 | no | — |
| 558 | C2×C4 | — | 27 | 1 | no | — |
| 559 | C2×C4 | — | 27 | 1 | no | — |
| 560 | C2×C4 | — | 27 | 1 | no | — |
| 561 | C2×C4 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 562 | C2×C4 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 563 | C2×C4 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 564 | C2×C3 | — | 2 | 1 | no | — |
| 565 | C2×C3 | — | 2 | 1 | no | — |
| 566 | C2×C3 | — | 2 | 1 | no | — |
| 567 | C2×C3 | C2×Q8×D9 | 1 | 1 | yes | characteristic |
| 568 | C2×C3 | #41×D9 | 1 | 1 | yes | characteristic |
| 569 | C2×C3 | #63716 | 1 | 1 | yes | characteristic |
| 570 | C2×C3 | #64306 | 1 | 1 | yes | characteristic |
| 571 | C2×C3 | #64309 | 1 | 1 | yes | characteristic |
| 572 | C2×C3 | D32×Q8 | 1 | 1 | yes | characteristic |
| 573 | C22 | C22×D3×D9 | 1 | 1 | yes | characteristic |
| 574 | C4 | — | 2 | 1 | no | — |
| 575 | C4 | — | 2 | 1 | no | — |
| 576 | C4 | — | 2 | 1 | no | — |
| 577 | C4 | — | 3 | 2 | no | — |
| 578 | C4 | — | 6 | 1 | no | — |
| 579 | C4 | — | 6 | 1 | no | — |
| 580 | C4 | — | 6 | 1 | no | — |
| 581 | C4 | — | 9 | 2 | no | — |
| 582 | C4 | — | 18 | 1 | no | — |
| 583 | C4 | — | 18 | 1 | no | — |
| 584 | C4 | — | 18 | 1 | no | — |
| 585 | C4 | — | 27 | 2 | no | — |
| 586 | C4 | — | 27 | 2 | no | — |
| 587 | C4 | — | 54 | 1 | no | — |
| 588 | C4 | — | 54 | 1 | no | — |
| 589 | C3 | — | 2 | 1 | no | — |
| 590 | C3 | #10589787 | 1 | 1 | yes | characteristic, complemented |
| 591 | C3 | #10594597 | 1 | 1 | yes | characteristic |
| 592 | C2 | #11722475 | 1 | 1 | yes | characteristic |
| 593 | C2 | #11722494 | 1 | 1 | yes | characteristic |
| 594 | C2 | D3×Q8×D9 | 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