← #13168691
Subgroups — #13168691
Order 1728.
1462 conjugacy classes of subgroups.
The subgroup lattice has 526 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C3×#3798 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11723689 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D3×C4⋊(C3⋊Dic3) | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11723404 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#63841 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | Dic3×#627 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11722928 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11722925 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10594992 | — | 3 | 2 | no | maximal |
| 10 | #10594511 | — | 3 | 1 | no | maximal |
| 11 | C2×C3×C4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C32×C4×D3 | C22 | 1 | 2 | yes | — |
| 13 | C2×#6294 | C22 | 1 | 2 | yes | — |
| 14 | C2×D3×C3⋊Dic3 | C22 | 1 | 4 | yes | — |
| 15 | C2×C3×#627 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C3×#626 | C22 | 1 | 2 | yes | — |
| 17 | C2×C3×#625 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#3798 | C4 | 1 | 8 | yes | complemented |
| 19 | C4⋊(C3⋊(C3⋊Dic3)) | C22 | 1 | 1 | yes | characteristic |
| 20 | C3×C4⋊(C3⋊Dic3) | C22 | 1 | 2 | yes | — |
| 21 | C32×C4⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 22 | #88815 | C22 | 1 | 2 | yes | — |
| 23 | Dic3⋊(C3⋊Dic3) | C22 | 1 | 4 | yes | — |
| 24 | #88803 | C22 | 1 | 2 | yes | — |
| 25 | Dic3×C3⋊Dic3 | C22 | 1 | 2 | yes | — |
| 26 | C3×(C2×D3)⋊Dic3 | C22 | 1 | 4 | yes | — |
| 27 | C3×Dic32 | C22 | 1 | 4 | yes | — |
| 28 | C2×C3×#235 | — | 3 | 2 | no | — |
| 29 | C2×#3798 | D3 | 1 | 1 | yes | characteristic |
| 30 | C2×C4⋊(C3⋊Dic3) | — | 3 | 2 | no | — |
| 31 | #64101 | — | 3 | 1 | no | — |
| 32 | C3×#926 | — | 3 | 2 | no | — |
| 33 | C3×#892 | — | 3 | 2 | no | — |
| 34 | #67⋊Dic3 | — | 3 | 4 | no | — |
| 35 | #67⋊Dic3 | — | 3 | 4 | no | — |
| 36 | C4×#627 | — | 3 | 2 | no | — |
| 37 | #63902 | — | 3 | 2 | no | — |
| 38 | #63900 | — | 3 | 1 | no | — |
| 39 | Dic3×D12 | — | 3 | 4 | no | — |
| 40 | D3×C4⋊Dic3 | — | 3 | 2 | no | — |
| 41 | D3×C4⋊Dic3 | — | 3 | 2 | no | — |
| 42 | D3×C4⋊Dic3 | — | 3 | 2 | no | — |
| 43 | D3×C4⋊Dic3 | — | 6 | 2 | no | — |
| 44 | #63880 | — | 3 | 4 | no | — |
| 45 | Dic3×Dic6 | — | 3 | 4 | no | — |
| 46 | #63841 | — | 3 | 2 | no | — |
| 47 | #63841 | — | 6 | 1 | no | — |
| 48 | #63841 | D3 | 1 | 2 | yes | complemented |
| 49 | C22×C3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 50 | C22×C32×D3 | C23 | 1 | 2 | yes | — |
| 51 | C2×C33×C4 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×C3⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 53 | C2×C3×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 54 | C2×C3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 55 | C3×C4×C3⋊D3 | C2×C4 | 1 | 4 | yes | complemented |
| 56 | C2×C32×Dic3 | C23 | 1 | 2 | yes | — |
| 57 | C2×C32×Dic3 | C23 | 1 | 2 | yes | — |
| 58 | C32×C4×D3 | C2×C4 | 1 | 8 | yes | complemented |
| 59 | #6294 | — | 4 | 2 | no | — |
| 60 | D3×C3⋊Dic3 | — | 4 | 4 | no | — |
| 61 | C3×#627 | C2×C4 | 1 | 4 | yes | complemented |
| 62 | C3×#626 | C2×C4 | 1 | 8 | yes | complemented |
| 63 | C3×#625 | C2×C4 | 1 | 4 | yes | complemented |
| 64 | #5827 | — | 9 | 1 | no | — |
| 65 | #5523 | — | 9 | 2 | no | — |
| 66 | C22×C32×C4 | — | 3 | 2 | no | — |
| 67 | C22×C3⋊Dic3 | — | 3 | 4 | no | — |
| 68 | C2×C4×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 69 | C2×C3×#67 | — | 3 | 2 | no | — |
| 70 | C2×C3×#67 | — | 3 | 2 | no | — |
| 71 | C3×#235 | — | 3 | 16 | no | — |
| 72 | C2×C3×D12 | — | 3 | 2 | no | — |
| 73 | C2×C3×C4×D3 | — | 2 | 2 | no | — |
| 74 | C2×C3×C4×D3 | — | 3 | 2 | no | — |
| 75 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 76 | C2×C3×C4×D3 | C2×D3 | 1 | 2 | yes | — |
| 77 | C2×C3×C4×D3 | C2×D3 | 1 | 2 | yes | — |
| 78 | C2×C3×Dic6 | — | 3 | 2 | no | — |
| 79 | C2×#627 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | C2×#626 | C2×D3 | 1 | 2 | yes | — |
| 81 | C2×#625 | C2×D3 | 1 | 1 | yes | characteristic |
| 82 | C2×#624 | — | 3 | 2 | no | — |
| 83 | C2×D3×Dic3 | — | 3 | 4 | no | — |
| 84 | C2×D3×Dic3 | — | 3 | 4 | no | — |
| 85 | C2×D3×Dic3 | — | 3 | 4 | no | — |
| 86 | C2×D3×Dic3 | — | 6 | 4 | no | — |
| 87 | #3798 | Dic3 | 1 | 8 | yes | complemented |
| 88 | C32×C4⋊C4 | — | 3 | 1 | no | — |
| 89 | #3752 | — | 3 | 2 | no | — |
| 90 | C4⋊(C3⋊Dic3) | — | 3 | 2 | no | — |
| 91 | C4⋊(C3⋊Dic3) | — | 3 | 1 | no | — |
| 92 | C4⋊(C3⋊Dic3) | — | 3 | 4 | no | — |
| 93 | C4⋊(C3⋊Dic3) | — | 6 | 1 | no | — |
| 94 | C4⋊(C3⋊Dic3) | — | 6 | 2 | no | — |
| 95 | C4⋊(C3⋊Dic3) | — | 12 | 1 | no | — |
| 96 | C4⋊(C3⋊Dic3) | C2×D3 | 1 | 2 | yes | — |
| 97 | C4×C3⋊Dic3 | — | 3 | 2 | no | — |
| 98 | C3×#217 | — | 3 | 4 | no | — |
| 99 | C3×(C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 100 | C3×C4⋊Dic3 | — | 2 | 1 | no | — |
| 101 | C3×C4⋊Dic3 | — | 3 | 2 | no | — |
| 102 | C3×C4⋊Dic3 | — | 3 | 2 | no | — |
| 103 | C3×C4⋊Dic3 | — | 6 | 2 | no | — |
| 104 | C3×C4⋊Dic3 | C2×D3 | 1 | 2 | yes | — |
| 105 | C3×C4×Dic3 | — | 3 | 4 | no | — |
| 106 | C3×C4×Dic3 | — | 3 | 4 | no | — |
| 107 | #3724 | — | 3 | 2 | no | — |
| 108 | Dic3⋊Dic3 | — | 3 | 4 | no | — |
| 109 | Dic3⋊Dic3 | — | 3 | 4 | no | — |
| 110 | Dic3⋊Dic3 | — | 3 | 4 | no | — |
| 111 | Dic3⋊Dic3 | — | 6 | 4 | no | — |
| 112 | (C2×D3)⋊Dic3 | — | 3 | 4 | no | — |
| 113 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 114 | (C2×D3)⋊Dic3 | C2×D3 | 1 | 4 | yes | — |
| 115 | Dic32 | — | 3 | 4 | no | — |
| 116 | Dic32 | — | 6 | 2 | no | — |
| 117 | Dic32 | C2×D3 | 1 | 4 | yes | — |
| 118 | C22×C33 | C24 | 1 | 1 | yes | characteristic |
| 119 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 120 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 121 | C2×C3×C3⋊D3 | C22×C4 | 1 | 2 | yes | — |
| 122 | C2×C32×D3 | — | 2 | 2 | no | — |
| 123 | C2×C32×D3 | — | 2 | 2 | no | — |
| 124 | C2×C32×D3 | C22×C4 | 1 | 4 | yes | — |
| 125 | C33×C4 | C22×C4 | 1 | 2 | yes | — |
| 126 | C3⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 127 | C3×C3⋊Dic3 | — | 2 | 4 | no | — |
| 128 | C3×C3⋊Dic3 | C22×C4 | 1 | 2 | yes | — |
| 129 | C32×Dic3 | — | 2 | 2 | no | — |
| 130 | C32×Dic3 | C22×C4 | 1 | 4 | yes | — |
| 131 | C2×C3×#41 | — | 9 | 1 | no | — |
| 132 | C2×#235 | — | 3 | 2 | no | — |
| 133 | C3×#117 | — | 9 | 2 | no | — |
| 134 | Q8×Dic3 | — | 9 | 2 | no | — |
| 135 | D4×Dic3 | — | 9 | 4 | no | — |
| 136 | D4×Dic3 | — | 9 | 2 | no | — |
| 137 | #926 | — | 3 | 2 | no | — |
| 138 | #926 | — | 9 | 1 | no | — |
| 139 | C2×C4⋊Dic3 | — | 9 | 1 | no | — |
| 140 | C2×C4⋊Dic3 | — | 9 | 2 | no | — |
| 141 | C2×C4⋊Dic3 | — | 9 | 2 | no | — |
| 142 | C2×C4⋊Dic3 | — | 18 | 2 | no | — |
| 143 | #892 | — | 3 | 2 | no | — |
| 144 | #892 | — | 9 | 2 | no | — |
| 145 | #892 | — | 18 | 1 | no | — |
| 146 | D3×C4⋊C4 | — | 9 | 2 | no | — |
| 147 | D3×C4⋊C4 | — | 9 | 2 | no | — |
| 148 | #67⋊C4 | — | 9 | 4 | no | — |
| 149 | #67⋊C4 | — | 9 | 4 | no | — |
| 150 | C4×D12 | — | 9 | 4 | no | — |
| 151 | C4×Dic6 | — | 9 | 4 | no | — |
| 152 | C23×C32 | — | 3 | 2 | no | — |
| 153 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 154 | C22×C3×D3 | — | 2 | 2 | no | — |
| 155 | C22×C3×D3 | — | 3 | 2 | no | — |
| 156 | C22×C3×D3 | — | 6 | 1 | no | — |
| 157 | C22×C3×D3 | C22×D3 | 1 | 2 | yes | — |
| 158 | C22×C3×D3 | C22×D3 | 1 | 2 | yes | — |
| 159 | C2×C32×C4 | — | 2 | 1 | no | — |
| 160 | C2×C32×C4 | — | 2 | 2 | no | — |
| 161 | C2×C32×C4 | — | 3 | 2 | no | — |
| 162 | C2×C32×C4 | — | 3 | 8 | no | — |
| 163 | C2×C32×C4 | — | 3 | 2 | no | — |
| 164 | C2×C32×C4 | — | 4 | 1 | no | — |
| 165 | C2×C32×C4 | C22×D3 | 1 | 2 | yes | — |
| 166 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 167 | C2×C3⋊Dic3 | — | 3 | 4 | no | — |
| 168 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 169 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 170 | C2×C3⋊Dic3 | — | 6 | 4 | no | — |
| 171 | C2×C3⋊Dic3 | — | 12 | 2 | no | — |
| 172 | C2×C3⋊Dic3 | — | 12 | 4 | no | — |
| 173 | C2×C3⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 174 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 175 | C4×C3⋊D3 | C2×Dic3 | 1 | 4 | yes | complemented |
| 176 | C3×#67 | — | 3 | 8 | no | — |
| 177 | C3×#67 | — | 3 | 8 | no | — |
| 178 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 179 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 180 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 181 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 182 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 183 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 184 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 185 | C2×C3×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 186 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 187 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 188 | C3×D12 | — | 3 | 8 | no | — |
| 189 | C3×C4×D3 | — | 2 | 8 | no | — |
| 190 | C3×C4×D3 | — | 3 | 8 | no | — |
| 191 | C3×C4×D3 | — | 6 | 4 | no | — |
| 192 | C3×C4×D3 | C4×D3 | 1 | 8 | yes | complemented |
| 193 | C3×C4×D3 | C2×Dic3 | 1 | 8 | yes | complemented |
| 194 | C3×Dic6 | — | 3 | 8 | no | — |
| 195 | #627 | C2×Dic3 | 1 | 4 | yes | complemented |
| 196 | #626 | C2×Dic3 | 1 | 8 | yes | complemented |
| 197 | #625 | C2×Dic3 | 1 | 4 | yes | complemented |
| 198 | #624 | — | 12 | 2 | no | — |
| 199 | D3×Dic3 | — | 12 | 4 | no | — |
| 200 | D3×Dic3 | — | 12 | 4 | no | — |
| 201 | D3×Dic3 | — | 12 | 4 | no | — |
| 202 | D3×Dic3 | — | 12 | 8 | no | — |
| 203 | #520 | — | 27 | 1 | no | Sylow |
| 204 | C2×C33 | C23×C4 | 1 | 1 | yes | characteristic |
| 205 | C2×C33 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 206 | C2×C33 | 2−1+4 | 1 | 1 | yes | characteristic |
| 207 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 208 | C32×D3 | — | 2 | 4 | no | — |
| 209 | C3×#41 | — | 9 | 8 | no | — |
| 210 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 211 | C2×C3×D4 | — | 9 | 2 | no | — |
| 212 | C2×C3×D4 | — | 9 | 1 | no | — |
| 213 | C22×C3×C4 | — | 3 | 2 | no | — |
| 214 | C22×C3×C4 | — | 3 | 2 | no | — |
| 215 | C22×C3×C4 | — | 6 | 2 | no | — |
| 216 | C22×C3×C4 | — | 9 | 1 | no | — |
| 217 | C2×#67 | — | 3 | 2 | no | — |
| 218 | C2×#67 | — | 3 | 2 | no | — |
| 219 | C22×Dic3 | — | 9 | 2 | no | — |
| 220 | C22×Dic3 | — | 9 | 4 | no | — |
| 221 | C22×Dic3 | — | 9 | 4 | no | — |
| 222 | C22×Dic3 | — | 18 | 4 | no | — |
| 223 | #235 | — | 3 | 16 | no | — |
| 224 | C2×D12 | — | 3 | 2 | no | — |
| 225 | C2×C4×D3 | — | 3 | 2 | no | — |
| 226 | C2×C4×D3 | — | 6 | 1 | no | — |
| 227 | C2×C4×D3 | — | 9 | 4 | no | — |
| 228 | C2×C4×D3 | — | 9 | 4 | no | — |
| 229 | C2×C4×D3 | D32 | 1 | 2 | yes | — |
| 230 | C2×Dic6 | — | 3 | 2 | no | — |
| 231 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 232 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 233 | C3×C4⋊C4 | — | 9 | 2 | no | — |
| 234 | C3×C22⋊C4 | — | 9 | 4 | no | — |
| 235 | C3×C42 | — | 9 | 4 | no | — |
| 236 | #217 | — | 3 | 4 | no | — |
| 237 | #217 | — | 9 | 2 | no | — |
| 238 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 239 | (C2×D3)⋊C4 | — | 9 | 4 | no | — |
| 240 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 241 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 242 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 243 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 244 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 245 | C4⋊Dic3 | — | 9 | 4 | no | — |
| 246 | C4⋊Dic3 | — | 9 | 4 | no | — |
| 247 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 248 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 249 | C4⋊Dic3 | — | 18 | 4 | no | — |
| 250 | C4⋊Dic3 | — | 18 | 1 | no | — |
| 251 | C4⋊Dic3 | — | 18 | 2 | no | — |
| 252 | C4⋊Dic3 | — | 36 | 1 | no | — |
| 253 | C4⋊Dic3 | D32 | 1 | 1 | yes | characteristic |
| 254 | Dic3⋊C4 | — | 9 | 4 | no | — |
| 255 | Dic3⋊C4 | — | 9 | 4 | no | — |
| 256 | C4×Dic3 | — | 3 | 4 | no | — |
| 257 | C4×Dic3 | — | 3 | 4 | no | — |
| 258 | C4×Dic3 | — | 9 | 4 | no | — |
| 259 | C4×Dic3 | — | 9 | 2 | no | — |
| 260 | C4×Dic3 | — | 18 | 2 | no | — |
| 261 | C22×C32 | — | 2 | 1 | no | — |
| 262 | C22×C32 | — | 2 | 2 | no | — |
| 263 | C22×C32 | — | 3 | 4 | no | — |
| 264 | C22×C32 | — | 4 | 1 | no | — |
| 265 | C22×C32 | — | 6 | 2 | no | — |
| 266 | C22×C32 | — | 6 | 2 | no | — |
| 267 | C22×C32 | C23×D3 | 1 | 2 | yes | — |
| 268 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 269 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 270 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 271 | C2×C3⋊D3 | C22×Dic3 | 1 | 2 | yes | — |
| 272 | C2×C3×D3 | — | 2 | 4 | no | — |
| 273 | C2×C3×D3 | — | 2 | 4 | no | — |
| 274 | C2×C3×D3 | — | 2 | 2 | no | — |
| 275 | C2×C3×D3 | — | 2 | 2 | no | — |
| 276 | C2×C3×D3 | — | 2 | 2 | no | — |
| 277 | C2×C3×D3 | — | 2 | 2 | no | — |
| 278 | C2×C3×D3 | — | 2 | 4 | no | — |
| 279 | C2×C3×D3 | — | 3 | 4 | no | — |
| 280 | C2×C3×D3 | — | 6 | 2 | no | — |
| 281 | C2×C3×D3 | — | 6 | 2 | no | — |
| 282 | C2×C3×D3 | — | 6 | 2 | no | — |
| 283 | C2×C3×D3 | — | 12 | 1 | no | — |
| 284 | C2×C3×D3 | — | 12 | 1 | no | — |
| 285 | C2×C3×D3 | C2×C4×D3 | 1 | 4 | yes | — |
| 286 | C2×C3×D3 | C22×Dic3 | 1 | 4 | yes | — |
| 287 | C32×C4 | — | 2 | 2 | no | — |
| 288 | C32×C4 | — | 2 | 4 | no | — |
| 289 | C32×C4 | — | 3 | 4 | no | — |
| 290 | C32×C4 | — | 4 | 2 | no | — |
| 291 | C32×C4 | — | 6 | 2 | no | — |
| 292 | C32×C4 | C2×C4×D3 | 1 | 4 | yes | — |
| 293 | C32×C4 | C22×Dic3 | 1 | 2 | yes | — |
| 294 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 295 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 296 | C3⋊Dic3 | — | 6 | 4 | no | — |
| 297 | C3⋊Dic3 | — | 12 | 4 | no | — |
| 298 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 299 | C3⋊Dic3 | — | 24 | 2 | no | — |
| 300 | C3⋊Dic3 | C22×Dic3 | 1 | 2 | yes | — |
| 301 | C3×Dic3 | — | 2 | 4 | no | — |
| 302 | C3×Dic3 | — | 2 | 4 | no | — |
| 303 | C3×Dic3 | — | 3 | 4 | no | — |
| 304 | C3×Dic3 | — | 4 | 2 | no | — |
| 305 | C3×Dic3 | — | 6 | 2 | no | — |
| 306 | C3×Dic3 | — | 6 | 4 | no | — |
| 307 | C3×Dic3 | — | 6 | 4 | no | — |
| 308 | C3×Dic3 | — | 12 | 4 | no | — |
| 309 | C3×Dic3 | C2×C4×D3 | 1 | 4 | yes | — |
| 310 | C3×Dic3 | C22×Dic3 | 1 | 4 | yes | — |
| 311 | C2×#41 | — | 9 | 1 | no | — |
| 312 | C4×Q8 | — | 27 | 2 | no | — |
| 313 | C4×D4 | — | 27 | 4 | no | — |
| 314 | C4×D4 | — | 27 | 2 | no | — |
| 315 | #117 | — | 9 | 2 | no | — |
| 316 | #117 | — | 27 | 1 | no | — |
| 317 | C2×C4⋊C4 | — | 27 | 1 | no | — |
| 318 | C2×C4⋊C4 | — | 27 | 2 | no | — |
| 319 | C33 | #520 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 320 | C23×C3 | — | 3 | 2 | no | — |
| 321 | C23×C3 | — | 3 | 2 | no | — |
| 322 | C23×C3 | — | 6 | 2 | no | — |
| 323 | C23×C3 | — | 9 | 1 | no | — |
| 324 | C22×D3 | — | 3 | 2 | no | — |
| 325 | C22×D3 | — | 6 | 1 | no | — |
| 326 | C22×D3 | C2×D32 | 1 | 2 | yes | — |
| 327 | C3×Q8 | — | 9 | 4 | no | — |
| 328 | C3×D4 | — | 9 | 8 | no | — |
| 329 | C3×D4 | — | 9 | 4 | no | — |
| 330 | C2×C3×C4 | — | 2 | 2 | no | — |
| 331 | C2×C3×C4 | — | 2 | 1 | no | — |
| 332 | C2×C3×C4 | — | 3 | 2 | no | — |
| 333 | C2×C3×C4 | — | 3 | 2 | no | — |
| 334 | C2×C3×C4 | — | 3 | 8 | no | — |
| 335 | C2×C3×C4 | — | 3 | 8 | no | — |
| 336 | C2×C3×C4 | — | 3 | 4 | no | — |
| 337 | C2×C3×C4 | — | 4 | 1 | no | — |
| 338 | C2×C3×C4 | — | 6 | 8 | no | — |
| 339 | C2×C3×C4 | — | 6 | 2 | no | — |
| 340 | C2×C3×C4 | — | 6 | 2 | no | — |
| 341 | C2×C3×C4 | — | 9 | 1 | no | — |
| 342 | C2×C3×C4 | — | 9 | 4 | no | — |
| 343 | C2×C3×C4 | — | 9 | 4 | no | — |
| 344 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 345 | C2×C3×C4 | C2×D32 | 1 | 2 | yes | — |
| 346 | #67 | — | 3 | 8 | no | — |
| 347 | #67 | — | 3 | 8 | no | — |
| 348 | C2×Dic3 | — | 3 | 2 | no | — |
| 349 | C2×Dic3 | — | 3 | 4 | no | — |
| 350 | C2×Dic3 | — | 3 | 4 | no | — |
| 351 | C2×Dic3 | — | 6 | 1 | no | — |
| 352 | C2×Dic3 | — | 6 | 4 | no | — |
| 353 | C2×Dic3 | — | 9 | 4 | no | — |
| 354 | C2×Dic3 | — | 9 | 2 | no | — |
| 355 | C2×Dic3 | — | 18 | 2 | no | — |
| 356 | C2×Dic3 | — | 18 | 4 | no | — |
| 357 | C2×Dic3 | — | 36 | 2 | no | — |
| 358 | C2×Dic3 | — | 36 | 2 | no | — |
| 359 | C2×Dic3 | — | 36 | 4 | no | — |
| 360 | C2×Dic3 | — | 36 | 4 | no | — |
| 361 | C2×Dic3 | — | 36 | 8 | no | — |
| 362 | C2×Dic3 | C2×D32 | 1 | 2 | yes | — |
| 363 | C2×Dic3 | C2×D32 | 1 | 2 | yes | — |
| 364 | D12 | — | 3 | 8 | no | — |
| 365 | C4×D3 | — | 3 | 8 | no | — |
| 366 | C4×D3 | — | 6 | 4 | no | — |
| 367 | C4×D3 | — | 36 | 4 | no | — |
| 368 | C4×D3 | — | 36 | 4 | no | — |
| 369 | C4×D3 | D3×Dic3 | 1 | 8 | yes | complemented |
| 370 | Dic6 | — | 3 | 8 | no | — |
| 371 | C2×C32 | — | 2 | 2 | no | — |
| 372 | C2×C32 | — | 2 | 1 | no | — |
| 373 | C2×C32 | — | 2 | 2 | no | — |
| 374 | C2×C32 | — | 2 | 1 | no | — |
| 375 | C2×C32 | — | 2 | 1 | no | — |
| 376 | C2×C32 | — | 2 | 2 | no | — |
| 377 | C2×C32 | — | 4 | 1 | no | — |
| 378 | C2×C32 | — | 4 | 1 | no | — |
| 379 | C2×C32 | — | 4 | 1 | no | — |
| 380 | C2×C32 | — | 6 | 4 | no | — |
| 381 | C2×C32 | C22×C4×D3 | 1 | 2 | yes | — |
| 382 | C2×C32 | #1009 | 1 | 1 | yes | characteristic |
| 383 | C2×C32 | #1009 | 1 | 2 | yes | — |
| 384 | C2×C32 | #1010 | 1 | 1 | yes | characteristic |
| 385 | C2×C32 | #1010 | 1 | 2 | yes | — |
| 386 | C2×C32 | C23×Dic3 | 1 | 1 | yes | characteristic |
| 387 | C3⋊D3 | — | 2 | 2 | no | — |
| 388 | C3×D3 | — | 2 | 8 | no | — |
| 389 | C3×D3 | — | 2 | 4 | no | — |
| 390 | C3×D3 | — | 2 | 4 | no | — |
| 391 | C3×D3 | — | 6 | 4 | no | — |
| 392 | C3×D3 | — | 12 | 2 | no | — |
| 393 | #41 | — | 9 | 8 | no | — |
| 394 | C2×Q8 | — | 9 | 1 | no | — |
| 395 | C2×D4 | — | 9 | 2 | no | — |
| 396 | C2×D4 | — | 9 | 1 | no | — |
| 397 | C22×C4 | — | 3 | 2 | no | — |
| 398 | C22×C4 | — | 9 | 1 | no | — |
| 399 | C22×C4 | — | 27 | 2 | no | — |
| 400 | C22×C4 | — | 27 | 4 | no | — |
| 401 | C4⋊C4 | — | 3 | 1 | no | — |
| 402 | C4⋊C4 | — | 9 | 2 | no | — |
| 403 | C4⋊C4 | — | 27 | 4 | no | — |
| 404 | C4⋊C4 | — | 27 | 2 | no | — |
| 405 | C4⋊C4 | — | 27 | 1 | no | — |
| 406 | C22⋊C4 | — | 9 | 4 | no | — |
| 407 | C22⋊C4 | — | 27 | 2 | no | — |
| 408 | C42 | — | 9 | 4 | no | — |
| 409 | C42 | — | 27 | 2 | no | — |
| 410 | C22×C3 | — | 2 | 2 | no | — |
| 411 | C22×C3 | — | 2 | 1 | no | — |
| 412 | C22×C3 | — | 3 | 4 | no | — |
| 413 | C22×C3 | — | 3 | 4 | no | — |
| 414 | C22×C3 | — | 4 | 1 | no | — |
| 415 | C22×C3 | — | 6 | 4 | no | — |
| 416 | C22×C3 | — | 6 | 4 | no | — |
| 417 | C22×C3 | — | 6 | 4 | no | — |
| 418 | C22×C3 | — | 6 | 2 | no | — |
| 419 | C22×C3 | — | 6 | 2 | no | — |
| 420 | C22×C3 | — | 6 | 2 | no | — |
| 421 | C22×C3 | — | 6 | 2 | no | — |
| 422 | C22×C3 | — | 9 | 2 | no | — |
| 423 | C22×C3 | — | 18 | 1 | no | — |
| 424 | C22×C3 | — | 18 | 1 | no | — |
| 425 | C22×C3 | C22×D32 | 1 | 2 | yes | — |
| 426 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 427 | C2×D3 | — | 2 | 2 | no | — |
| 428 | C2×D3 | — | 2 | 2 | no | — |
| 429 | C2×D3 | — | 3 | 4 | no | — |
| 430 | C2×D3 | — | 6 | 2 | no | — |
| 431 | C2×D3 | — | 6 | 2 | no | — |
| 432 | C2×D3 | — | 6 | 2 | no | — |
| 433 | C2×D3 | — | 12 | 1 | no | — |
| 434 | C2×D3 | — | 12 | 1 | no | — |
| 435 | C2×D3 | C2×D3×Dic3 | 1 | 4 | yes | — |
| 436 | C3×C4 | — | 2 | 2 | no | — |
| 437 | C3×C4 | — | 2 | 4 | no | — |
| 438 | C3×C4 | — | 3 | 4 | no | — |
| 439 | C3×C4 | — | 3 | 4 | no | — |
| 440 | C3×C4 | — | 4 | 2 | no | — |
| 441 | C3×C4 | — | 6 | 4 | no | — |
| 442 | C3×C4 | — | 6 | 4 | no | — |
| 443 | C3×C4 | — | 9 | 2 | no | — |
| 444 | C3×C4 | — | 12 | 2 | no | — |
| 445 | C3×C4 | — | 18 | 4 | no | — |
| 446 | C3×C4 | C4×D32 | 1 | 2 | yes | — |
| 447 | C3×C4 | C2×D3×Dic3 | 1 | 4 | yes | — |
| 448 | Dic3 | — | 2 | 2 | no | — |
| 449 | Dic3 | — | 3 | 4 | no | — |
| 450 | Dic3 | — | 6 | 2 | no | — |
| 451 | Dic3 | — | 6 | 4 | no | — |
| 452 | Dic3 | — | 6 | 4 | no | — |
| 453 | Dic3 | — | 12 | 4 | no | — |
| 454 | Dic3 | — | 18 | 4 | no | — |
| 455 | Dic3 | — | 18 | 2 | no | — |
| 456 | Dic3 | — | 36 | 4 | no | — |
| 457 | Dic3 | — | 36 | 2 | no | — |
| 458 | Dic3 | — | 72 | 2 | no | — |
| 459 | Dic3 | C2×D3×Dic3 | 1 | 4 | yes | — |
| 460 | C32 | — | 2 | 2 | no | — |
| 461 | C32 | — | 2 | 1 | no | — |
| 462 | C32 | — | 4 | 1 | no | — |
| 463 | C32 | #5523 | 1 | 2 | yes | complemented |
| 464 | C32 | #5827 | 1 | 1 | yes | characteristic, complemented |
| 465 | C23 | — | 3 | 2 | no | — |
| 466 | C23 | — | 9 | 1 | no | — |
| 467 | Q8 | — | 9 | 4 | no | — |
| 468 | D4 | — | 9 | 8 | no | — |
| 469 | D4 | — | 9 | 4 | no | — |
| 470 | C2×C4 | — | 3 | 2 | no | — |
| 471 | C2×C4 | — | 3 | 8 | no | — |
| 472 | C2×C4 | — | 3 | 2 | no | — |
| 473 | C2×C4 | — | 9 | 1 | no | — |
| 474 | C2×C4 | — | 9 | 4 | no | — |
| 475 | C2×C4 | — | 9 | 4 | no | — |
| 476 | C2×C4 | — | 27 | 2 | no | — |
| 477 | C2×C4 | — | 108 | 2 | no | — |
| 478 | C2×C4 | — | 108 | 4 | no | — |
| 479 | C2×C4 | D33 | 1 | 1 | yes | characteristic |
| 480 | C2×C3 | — | 2 | 2 | no | — |
| 481 | C2×C3 | — | 2 | 1 | no | — |
| 482 | C2×C3 | — | 2 | 1 | no | — |
| 483 | C2×C3 | — | 2 | 2 | no | — |
| 484 | C2×C3 | — | 2 | 1 | no | — |
| 485 | C2×C3 | — | 2 | 2 | no | — |
| 486 | C2×C3 | — | 4 | 1 | no | — |
| 487 | C2×C3 | — | 4 | 1 | no | — |
| 488 | C2×C3 | — | 4 | 1 | no | — |
| 489 | C2×C3 | — | 6 | 8 | no | — |
| 490 | C2×C3 | — | 6 | 4 | no | — |
| 491 | C2×C3 | — | 6 | 4 | no | — |
| 492 | C2×C3 | — | 18 | 2 | no | — |
| 493 | C2×C3 | #64298 | 1 | 2 | yes | — |
| 494 | C2×C3 | C2×C4×D32 | 1 | 1 | yes | characteristic |
| 495 | C2×C3 | #64308 | 1 | 2 | yes | — |
| 496 | C2×C3 | #64309 | 1 | 1 | yes | characteristic |
| 497 | C2×C3 | #64320 | 1 | 1 | yes | characteristic |
| 498 | C2×C3 | C22×D3×Dic3 | 1 | 2 | yes | — |
| 499 | D3 | — | 2 | 4 | no | — |
| 500 | D3 | — | 6 | 4 | no | — |
| 501 | D3 | — | 12 | 2 | no | — |
| 502 | C22 | — | 3 | 4 | no | — |
| 503 | C22 | — | 6 | 2 | no | — |
| 504 | C22 | — | 6 | 2 | no | — |
| 505 | C22 | — | 9 | 2 | no | — |
| 506 | C22 | — | 18 | 1 | no | — |
| 507 | C22 | — | 18 | 1 | no | — |
| 508 | C22 | C2×D33 | 1 | 1 | yes | characteristic |
| 509 | C4 | — | 3 | 4 | no | — |
| 510 | C4 | — | 6 | 2 | no | — |
| 511 | C4 | — | 9 | 2 | no | — |
| 512 | C4 | — | 18 | 4 | no | — |
| 513 | C4 | — | 54 | 2 | no | — |
| 514 | C4 | D32×Dic3 | 1 | 2 | yes | — |
| 515 | C3 | — | 2 | 1 | no | — |
| 516 | C3 | — | 2 | 2 | no | — |
| 517 | C3 | — | 4 | 1 | no | — |
| 518 | C3 | #10594511 | 1 | 1 | yes | characteristic, complemented |
| 519 | C3 | #10594992 | 1 | 2 | yes | complemented |
| 520 | C2 | — | 6 | 4 | no | — |
| 521 | C2 | — | 18 | 2 | no | — |
| 522 | C2 | #11724390 | 1 | 1 | yes | characteristic |
| 523 | C2 | #11724392 | 1 | 1 | yes | characteristic |
| 524 | C2 | C2×D32×Dic3 | 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