← #72222739
Subgroups — #72222739
Order 2304.
1516 conjugacy classes of subgroups.
The subgroup lattice has 681 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11899422 | C2 | 1 | 2 | yes | maximal |
| 2 | #11857303 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11795943 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11795942 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11795925 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | D3×#4466 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C3×D3×#347 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C3⋊D3×#347 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10947846 | — | 3 | 2 | no | maximal |
| 10 | C2×#63803 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×#63803 | C22 | 1 | 1 | yes | characteristic |
| 12 | C4×#3798 | C4 | 1 | 1 | yes | characteristic |
| 13 | C3⋊D3×M32 | C22 | 1 | 2 | yes | — |
| 14 | C3⋊D3×#97 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×D3×M32 | C22 | 1 | 4 | yes | — |
| 16 | C3×D3×#97 | C22 | 1 | 2 | yes | — |
| 17 | #10590703 | C4 | 1 | 1 | yes | characteristic |
| 18 | #10590703 | C22 | 1 | 1 | yes | characteristic |
| 19 | #10590693 | C4 | 1 | 2 | yes | — |
| 20 | #10590693 | C22 | 1 | 2 | yes | — |
| 21 | #10590625 | C22 | 1 | 2 | yes | — |
| 22 | D3×#812 | C22 | 1 | 4 | yes | — |
| 23 | #10590334 | C4 | 1 | 2 | yes | — |
| 24 | #10590247 | C4 | 1 | 1 | yes | characteristic |
| 25 | #10590229 | C4 | 1 | 4 | yes | complemented |
| 26 | #10590228 | C4 | 1 | 8 | yes | complemented |
| 27 | #10590227 | C4 | 1 | 4 | yes | complemented |
| 28 | C32×#347 | C22 | 1 | 1 | yes | characteristic |
| 29 | #10589378 | C22 | 1 | 2 | yes | — |
| 30 | #10589332 | C22 | 1 | 1 | yes | characteristic |
| 31 | C3×#4512 | C22 | 1 | 4 | yes | — |
| 32 | C3×#4466 | C22 | 1 | 2 | yes | — |
| 33 | #10589106 | C22 | 1 | 2 | yes | — |
| 34 | #10589105 | C22 | 1 | 4 | yes | — |
| 35 | #82007 | — | 3 | 4 | no | — |
| 36 | #78486 | — | 3 | 2 | no | — |
| 37 | C2×C3×#347 | — | 3 | 2 | no | — |
| 38 | #71425 | — | 3 | 4 | no | — |
| 39 | C2×#4466 | — | 3 | 2 | no | — |
| 40 | #69087 | — | 3 | 4 | no | — |
| 41 | #69087 | — | 3 | 4 | no | — |
| 42 | D3×#347 | — | 3 | 2 | no | — |
| 43 | D3×#347 | — | 3 | 2 | no | — |
| 44 | D3×#347 | — | 3 | 2 | no | — |
| 45 | D3×#347 | — | 6 | 1 | no | — |
| 46 | D3×#347 | D3 | 1 | 2 | yes | complemented |
| 47 | C2×#3798 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C2×C8×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×C8×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 50 | C42×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×C3×D3×C8 | C2×C4 | 1 | 2 | yes | — |
| 52 | C2×C3×D3×C8 | C23 | 1 | 2 | yes | — |
| 53 | C3×C42×D3 | C2×C4 | 1 | 2 | yes | — |
| 54 | C4×#627 | — | 2 | 1 | no | — |
| 55 | C4×#626 | — | 2 | 2 | no | — |
| 56 | C4×#625 | — | 2 | 1 | no | — |
| 57 | #63874 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | #63855 | C2×C4 | 1 | 2 | yes | — |
| 59 | C2×#3712 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C2×#3712 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C2×#3711 | C2×C4 | 1 | 2 | yes | — |
| 62 | C2×#3711 | C2×C4 | 1 | 2 | yes | — |
| 63 | #63803 | — | 2 | 2 | no | — |
| 64 | #63803 | — | 2 | 1 | no | — |
| 65 | #63803 | — | 2 | 1 | no | — |
| 66 | #63803 | C2×C4 | 1 | 2 | yes | — |
| 67 | #63803 | C2×C4 | 1 | 4 | yes | — |
| 68 | #63803 | C2×C4 | 1 | 2 | yes | — |
| 69 | C32×M32 | C23 | 1 | 2 | yes | — |
| 70 | C32×#97 | C23 | 1 | 1 | yes | characteristic |
| 71 | #63642 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | #63642 | C23 | 1 | 1 | yes | characteristic |
| 73 | #63639 | C23 | 1 | 2 | yes | — |
| 74 | #63630 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | #63625 | C2×C4 | 1 | 4 | yes | complemented |
| 76 | C16×C3⋊D3 | C2×C4 | 1 | 4 | yes | complemented |
| 77 | C3×#815 | C2×C4 | 1 | 2 | yes | — |
| 78 | C3×#815 | C23 | 1 | 2 | yes | — |
| 79 | C3×#812 | C23 | 1 | 4 | yes | — |
| 80 | C3×#803 | C2×C4 | 1 | 2 | yes | — |
| 81 | C3×#798 | C2×C4 | 1 | 8 | yes | complemented |
| 82 | C3×D3×C16 | C2×C4 | 1 | 8 | yes | complemented |
| 83 | #63553 | C2×C4 | 1 | 2 | yes | — |
| 84 | Dic3×C3⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 85 | Dic3×C3⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 86 | #63544 | C2×C4 | 1 | 4 | yes | complemented |
| 87 | #63543 | C2×C4 | 1 | 8 | yes | complemented |
| 88 | #63542 | C2×C4 | 1 | 4 | yes | complemented |
| 89 | D3×C3⋊C16 | C2×C4 | 1 | 8 | yes | complemented |
| 90 | #33329 | — | 9 | 1 | no | Sylow |
| 91 | C2×#901 | — | 3 | 2 | no | — |
| 92 | C2×#901 | — | 3 | 2 | no | — |
| 93 | C4×#235 | — | 3 | 2 | no | — |
| 94 | C2×C3×M32 | — | 3 | 4 | no | — |
| 95 | C2×C3×#97 | — | 3 | 2 | no | — |
| 96 | #5101 | — | 3 | 2 | no | — |
| 97 | #5101 | — | 3 | 2 | no | — |
| 98 | C2×#812 | — | 3 | 4 | no | — |
| 99 | C4×#208 | — | 3 | 2 | no | — |
| 100 | #4907 | — | 3 | 8 | no | — |
| 101 | #4907 | — | 3 | 8 | no | — |
| 102 | D3×M32 | — | 3 | 4 | no | — |
| 103 | D3×M32 | — | 3 | 4 | no | — |
| 104 | D3×M32 | — | 3 | 4 | no | — |
| 105 | D3×M32 | — | 6 | 2 | no | — |
| 106 | D3×M32 | C2×D3 | 1 | 4 | yes | — |
| 107 | #4901 | — | 3 | 8 | no | — |
| 108 | #4901 | — | 3 | 8 | no | — |
| 109 | #4708 | — | 3 | 2 | no | — |
| 110 | #4708 | — | 3 | 2 | no | — |
| 111 | #4708 | — | 3 | 2 | no | — |
| 112 | #4708 | — | 3 | 2 | no | — |
| 113 | #4707 | — | 3 | 2 | no | — |
| 114 | #4707 | — | 3 | 2 | no | — |
| 115 | D3×#97 | — | 3 | 2 | no | — |
| 116 | D3×#97 | — | 6 | 1 | no | — |
| 117 | D3×#97 | C2×D3 | 1 | 2 | yes | — |
| 118 | C3×#347 | — | 2 | 1 | no | — |
| 119 | C3×#347 | — | 3 | 4 | no | — |
| 120 | C3×#347 | — | 3 | 2 | no | — |
| 121 | C3×#347 | C2×D3 | 1 | 2 | yes | — |
| 122 | #4512 | — | 3 | 4 | no | — |
| 123 | #4512 | — | 3 | 4 | no | — |
| 124 | #4512 | — | 3 | 4 | no | — |
| 125 | #4512 | — | 6 | 2 | no | — |
| 126 | #4512 | C2×D3 | 1 | 4 | yes | — |
| 127 | #4466 | — | 3 | 2 | no | — |
| 128 | #4466 | — | 3 | 4 | no | — |
| 129 | #4466 | — | 6 | 1 | no | — |
| 130 | #4466 | C2×D3 | 1 | 2 | yes | — |
| 131 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 132 | C2×C4×C3⋊D3 | C22×C4 | 1 | 1 | yes | characteristic |
| 133 | C2×C3×C4×D3 | — | 2 | 2 | no | — |
| 134 | C2×C3×C4×D3 | C22×C4 | 1 | 2 | yes | — |
| 135 | C2×#627 | M16 | 1 | 1 | yes | characteristic |
| 136 | C2×#626 | M16 | 1 | 2 | yes | — |
| 137 | C2×#625 | M16 | 1 | 1 | yes | characteristic |
| 138 | #3798 | C42 | 1 | 1 | yes | characteristic |
| 139 | #3798 | C42 | 1 | 2 | yes | — |
| 140 | #3798 | C42 | 1 | 1 | yes | characteristic |
| 141 | #3798 | M16 | 1 | 1 | yes | characteristic |
| 142 | #3798 | M16 | 1 | 2 | yes | — |
| 143 | #3798 | M16 | 1 | 1 | yes | characteristic |
| 144 | C2×C32×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 145 | C2×C32×C8 | C24 | 1 | 1 | yes | characteristic |
| 146 | C32×C42 | C22×C4 | 1 | 1 | yes | characteristic |
| 147 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 148 | C4×C3⋊Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 149 | C2×C3⋊(C3⋊C8) | C22×C4 | 1 | 1 | yes | characteristic |
| 150 | C2×C3⋊(C3⋊C8) | C22×C4 | 1 | 1 | yes | characteristic |
| 151 | C8×C3⋊D3 | — | 2 | 1 | no | — |
| 152 | C8×C3⋊D3 | — | 2 | 1 | no | — |
| 153 | C8×C3⋊D3 | C22×C4 | 1 | 2 | yes | — |
| 154 | C8×C3⋊D3 | C22×C4 | 1 | 2 | yes | — |
| 155 | C3×C4×Dic3 | — | 2 | 2 | no | — |
| 156 | C3×C4×Dic3 | C22×C4 | 1 | 2 | yes | — |
| 157 | C2×C3×C3⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 158 | C2×C3×C3⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 159 | C3×D3×C8 | — | 2 | 2 | no | — |
| 160 | C3×D3×C8 | — | 2 | 2 | no | — |
| 161 | C3×D3×C8 | C22×C4 | 1 | 4 | yes | — |
| 162 | C3×D3×C8 | C22×C4 | 1 | 4 | yes | — |
| 163 | #3724 | — | 2 | 1 | no | — |
| 164 | Dic3⋊Dic3 | — | 2 | 2 | no | — |
| 165 | #3722 | — | 2 | 1 | no | — |
| 166 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 167 | #3712 | — | 2 | 1 | no | — |
| 168 | #3712 | — | 2 | 1 | no | — |
| 169 | #3712 | C42 | 1 | 2 | yes | — |
| 170 | #3712 | C42 | 1 | 2 | yes | — |
| 171 | #3711 | — | 2 | 2 | no | — |
| 172 | #3711 | — | 2 | 2 | no | — |
| 173 | #3711 | C42 | 1 | 4 | yes | — |
| 174 | #3711 | C42 | 1 | 4 | yes | — |
| 175 | C32×C16 | C22×C4 | 1 | 4 | yes | — |
| 176 | C3⋊(C3⋊C16) | C22×C4 | 1 | 4 | yes | — |
| 177 | C3×C3⋊C16 | C22×C4 | 1 | 8 | yes | — |
| 178 | #3407 | — | 9 | 2 | no | — |
| 179 | #2875 | — | 9 | 1 | no | — |
| 180 | #2110 | — | 9 | 2 | no | — |
| 181 | #2110 | — | 9 | 4 | no | — |
| 182 | C2×#347 | — | 3 | 2 | no | — |
| 183 | C2×#347 | — | 9 | 1 | no | — |
| 184 | C2×#347 | — | 9 | 2 | no | — |
| 185 | C2×#347 | — | 9 | 1 | no | — |
| 186 | C2×#235 | — | 3 | 2 | no | — |
| 187 | C22×C3×C8 | — | 3 | 2 | no | — |
| 188 | C22×C3×C8 | — | 3 | 2 | no | — |
| 189 | C2×C3×C42 | — | 3 | 2 | no | — |
| 190 | C4×#67 | — | 6 | 2 | no | — |
| 191 | C4×#67 | — | 6 | 2 | no | — |
| 192 | #926 | — | 3 | 2 | no | — |
| 193 | C2×#208 | — | 3 | 2 | no | — |
| 194 | C2×#208 | — | 3 | 2 | no | — |
| 195 | #901 | — | 3 | 4 | no | — |
| 196 | #901 | — | 3 | 4 | no | — |
| 197 | #901 | — | 3 | 4 | no | — |
| 198 | #901 | — | 3 | 4 | no | — |
| 199 | #901 | — | 6 | 2 | no | — |
| 200 | #901 | — | 6 | 2 | no | — |
| 201 | #901 | — | 6 | 2 | no | — |
| 202 | #901 | — | 6 | 2 | no | — |
| 203 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 204 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 205 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 206 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 207 | C2×D3×C8 | — | 3 | 2 | no | — |
| 208 | C2×D3×C8 | — | 3 | 2 | no | — |
| 209 | C2×D3×C8 | — | 6 | 1 | no | — |
| 210 | C2×D3×C8 | — | 6 | 1 | no | — |
| 211 | C2×D3×C8 | C4×D3 | 1 | 2 | yes | — |
| 212 | C2×D3×C8 | C22×D3 | 1 | 2 | yes | — |
| 213 | C4×D12 | — | 6 | 2 | no | — |
| 214 | #872 | — | 3 | 2 | no | — |
| 215 | #872 | — | 3 | 2 | no | — |
| 216 | C42×D3 | — | 3 | 2 | no | — |
| 217 | C42×D3 | — | 6 | 1 | no | — |
| 218 | C42×D3 | C4×D3 | 1 | 2 | yes | — |
| 219 | C4×Dic6 | — | 6 | 2 | no | — |
| 220 | C3×M32 | — | 2 | 2 | no | — |
| 221 | C3×M32 | — | 3 | 4 | no | — |
| 222 | C3×M32 | — | 3 | 8 | no | — |
| 223 | C3×M32 | C22×D3 | 1 | 4 | yes | — |
| 224 | C2×C3×C16 | — | 3 | 8 | no | — |
| 225 | C3×#97 | — | 2 | 1 | no | — |
| 226 | C3×#97 | — | 3 | 2 | no | — |
| 227 | C3×#97 | — | 3 | 2 | no | — |
| 228 | C3×#97 | — | 3 | 2 | no | — |
| 229 | C3×#97 | C22×D3 | 1 | 2 | yes | — |
| 230 | #815 | — | 3 | 2 | no | — |
| 231 | #815 | — | 3 | 2 | no | — |
| 232 | #815 | — | 6 | 1 | no | — |
| 233 | #815 | — | 6 | 1 | no | — |
| 234 | #815 | C4×D3 | 1 | 2 | yes | — |
| 235 | #815 | C22×D3 | 1 | 2 | yes | — |
| 236 | C8×Dic3 | — | 3 | 2 | no | — |
| 237 | C8×Dic3 | — | 3 | 2 | no | — |
| 238 | C8×Dic3 | — | 3 | 2 | no | — |
| 239 | C8×Dic3 | — | 3 | 2 | no | — |
| 240 | #812 | — | 3 | 4 | no | — |
| 241 | #812 | — | 3 | 8 | no | — |
| 242 | #812 | — | 6 | 2 | no | — |
| 243 | #812 | C22×D3 | 1 | 4 | yes | — |
| 244 | C2×C3⋊C16 | — | 3 | 8 | no | — |
| 245 | #803 | — | 3 | 2 | no | — |
| 246 | #803 | — | 6 | 1 | no | — |
| 247 | #803 | C4×D3 | 1 | 2 | yes | — |
| 248 | C4×C3⋊C8 | — | 3 | 2 | no | — |
| 249 | C4×C3⋊C8 | — | 3 | 2 | no | — |
| 250 | #798 | — | 3 | 8 | no | — |
| 251 | #798 | — | 3 | 8 | no | — |
| 252 | #798 | — | 3 | 8 | no | — |
| 253 | #798 | — | 6 | 4 | no | — |
| 254 | #798 | C4×D3 | 1 | 8 | yes | complemented |
| 255 | D3×C16 | — | 3 | 8 | no | — |
| 256 | D3×C16 | — | 3 | 8 | no | — |
| 257 | D3×C16 | — | 3 | 8 | no | — |
| 258 | D3×C16 | — | 6 | 4 | no | — |
| 259 | D3×C16 | C4×D3 | 1 | 8 | yes | complemented |
| 260 | C22×C3⋊D3 | C2×M16 | 1 | 1 | yes | characteristic |
| 261 | C22×C3×D3 | C2×M16 | 1 | 2 | yes | — |
| 262 | C2×C32×C4 | — | 2 | 1 | no | — |
| 263 | C2×C32×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 264 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 265 | C2×C3⋊Dic3 | C2×M16 | 1 | 1 | yes | characteristic |
| 266 | C4×C3⋊D3 | — | 8 | 1 | no | — |
| 267 | C4×C3⋊D3 | C2×C42 | 1 | 1 | yes | characteristic |
| 268 | C4×C3⋊D3 | C2×C42 | 1 | 1 | yes | characteristic |
| 269 | C4×C3⋊D3 | C2×M16 | 1 | 1 | yes | characteristic |
| 270 | C4×C3⋊D3 | C2×M16 | 1 | 1 | yes | characteristic |
| 271 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 272 | C2×C3×Dic3 | C2×M16 | 1 | 2 | yes | — |
| 273 | C3×C4×D3 | — | 8 | 2 | no | — |
| 274 | C3×C4×D3 | C2×C42 | 1 | 2 | yes | — |
| 275 | C3×C4×D3 | C2×C42 | 1 | 2 | yes | — |
| 276 | C3×C4×D3 | C2×M16 | 1 | 2 | yes | — |
| 277 | C3×C4×D3 | C2×M16 | 1 | 2 | yes | — |
| 278 | #627 | #97 | 1 | 1 | yes | characteristic |
| 279 | #627 | #97 | 1 | 2 | yes | — |
| 280 | #627 | #97 | 1 | 1 | yes | characteristic |
| 281 | #626 | #97 | 1 | 2 | yes | — |
| 282 | #626 | #97 | 1 | 2 | yes | — |
| 283 | #626 | #97 | 1 | 2 | yes | — |
| 284 | #626 | #97 | 1 | 2 | yes | — |
| 285 | #625 | #97 | 1 | 1 | yes | characteristic |
| 286 | #625 | #97 | 1 | 2 | yes | — |
| 287 | #625 | #97 | 1 | 1 | yes | characteristic |
| 288 | C32×C8 | — | 2 | 1 | no | — |
| 289 | C32×C8 | C23×C4 | 1 | 2 | yes | — |
| 290 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 291 | C3⋊(C3⋊C8) | C2×C42 | 1 | 2 | yes | — |
| 292 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 293 | C3×C3⋊C8 | C2×C42 | 1 | 4 | yes | — |
| 294 | C2×#131 | — | 9 | 1 | no | — |
| 295 | C2×#131 | — | 9 | 1 | no | — |
| 296 | C4×#41 | — | 9 | 1 | no | — |
| 297 | #504 | — | 9 | 4 | no | — |
| 298 | #504 | — | 9 | 8 | no | — |
| 299 | #504 | — | 9 | 4 | no | — |
| 300 | C2×M32 | — | 3 | 4 | no | — |
| 301 | C2×M32 | — | 9 | 2 | no | — |
| 302 | C2×M32 | — | 9 | 4 | no | — |
| 303 | C2×M32 | — | 9 | 2 | no | — |
| 304 | #405 | — | 9 | 1 | no | — |
| 305 | #405 | — | 9 | 1 | no | — |
| 306 | #405 | — | 9 | 2 | no | — |
| 307 | #405 | — | 9 | 2 | no | — |
| 308 | C4×M16 | — | 9 | 1 | no | — |
| 309 | C4×M16 | — | 9 | 2 | no | — |
| 310 | C2×#97 | — | 3 | 2 | no | — |
| 311 | C2×#97 | — | 9 | 1 | no | — |
| 312 | #347 | — | 3 | 4 | no | — |
| 313 | #347 | — | 3 | 2 | no | — |
| 314 | #347 | — | 9 | 4 | no | — |
| 315 | #347 | — | 9 | 2 | no | — |
| 316 | #347 | — | 9 | 2 | no | — |
| 317 | #347 | — | 9 | 1 | no | — |
| 318 | #347 | D32 | 1 | 1 | yes | characteristic |
| 319 | C22×C3×C4 | — | 3 | 2 | no | — |
| 320 | C22×C3×C4 | — | 6 | 2 | no | — |
| 321 | C2×#67 | — | 3 | 2 | no | — |
| 322 | C2×#67 | — | 3 | 2 | no | — |
| 323 | #235 | — | 3 | 2 | no | — |
| 324 | #235 | — | 3 | 2 | no | — |
| 325 | #235 | — | 3 | 2 | no | — |
| 326 | #235 | — | 3 | 2 | no | — |
| 327 | #235 | — | 3 | 2 | no | — |
| 328 | #235 | — | 3 | 2 | no | — |
| 329 | #235 | — | 3 | 2 | no | — |
| 330 | #235 | — | 3 | 2 | no | — |
| 331 | C2×D12 | — | 3 | 2 | no | — |
| 332 | C2×C4×D3 | — | 2 | 2 | no | — |
| 333 | C2×C4×D3 | — | 3 | 2 | no | — |
| 334 | C2×C4×D3 | — | 6 | 1 | no | — |
| 335 | C2×C4×D3 | — | 6 | 2 | no | — |
| 336 | C2×C4×D3 | — | 12 | 1 | no | — |
| 337 | C2×C4×D3 | C2×C4×D3 | 1 | 2 | yes | — |
| 338 | C2×Dic6 | — | 3 | 2 | no | — |
| 339 | C2×C3×C8 | — | 2 | 1 | no | — |
| 340 | C2×C3×C8 | — | 2 | 1 | no | — |
| 341 | C2×C3×C8 | — | 3 | 2 | no | — |
| 342 | C2×C3×C8 | — | 3 | 4 | no | — |
| 343 | C2×C3×C8 | — | 3 | 4 | no | — |
| 344 | C2×C3×C8 | — | 3 | 2 | no | — |
| 345 | C2×C3×C8 | — | 6 | 2 | no | — |
| 346 | C2×C3×C8 | — | 6 | 2 | no | — |
| 347 | C2×C3×C8 | C2×C4×D3 | 1 | 2 | yes | — |
| 348 | C2×C3×C8 | C23×D3 | 1 | 2 | yes | — |
| 349 | C3×C42 | — | 2 | 1 | no | — |
| 350 | C3×C42 | — | 3 | 2 | no | — |
| 351 | C3×C42 | — | 6 | 2 | no | — |
| 352 | C3×C42 | C2×C4×D3 | 1 | 2 | yes | — |
| 353 | #217 | — | 6 | 2 | no | — |
| 354 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 355 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 356 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 357 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 358 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 359 | C4×Dic3 | — | 2 | 2 | no | — |
| 360 | C4×Dic3 | — | 3 | 2 | no | — |
| 361 | C4×Dic3 | — | 6 | 1 | no | — |
| 362 | C4×Dic3 | — | 6 | 2 | no | — |
| 363 | C4×Dic3 | — | 12 | 1 | no | — |
| 364 | C4×Dic3 | C2×C4×D3 | 1 | 2 | yes | — |
| 365 | #208 | — | 3 | 4 | no | — |
| 366 | #208 | — | 3 | 4 | no | — |
| 367 | #208 | — | 6 | 2 | no | — |
| 368 | #208 | — | 6 | 2 | no | — |
| 369 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 370 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 371 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 372 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 373 | C2×C3⋊C8 | C2×C4×D3 | 1 | 2 | yes | — |
| 374 | C2×C3⋊C8 | C2×C4×D3 | 1 | 2 | yes | — |
| 375 | ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 376 | ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 377 | ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 378 | ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 379 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 380 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 381 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 382 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 383 | D3×C8 | — | 2 | 2 | no | — |
| 384 | D3×C8 | — | 2 | 2 | no | — |
| 385 | D3×C8 | — | 3 | 4 | no | — |
| 386 | D3×C8 | — | 3 | 4 | no | — |
| 387 | D3×C8 | — | 6 | 2 | no | — |
| 388 | D3×C8 | — | 6 | 2 | no | — |
| 389 | D3×C8 | — | 6 | 2 | no | — |
| 390 | D3×C8 | — | 6 | 2 | no | — |
| 391 | D3×C8 | — | 12 | 1 | no | — |
| 392 | D3×C8 | — | 12 | 1 | no | — |
| 393 | D3×C8 | C2×C4×D3 | 1 | 4 | yes | — |
| 394 | D3×C8 | C2×C4×D3 | 1 | 4 | yes | — |
| 395 | C3×C16 | — | 2 | 4 | no | — |
| 396 | C3×C16 | — | 3 | 8 | no | — |
| 397 | C3×C16 | C2×C4×D3 | 1 | 8 | yes | — |
| 398 | C3⋊C16 | — | 3 | 8 | no | — |
| 399 | C3⋊C16 | — | 6 | 4 | no | — |
| 400 | C3⋊C16 | C2×C4×D3 | 1 | 8 | yes | — |
| 401 | C22×C32 | C22×M16 | 1 | 1 | yes | characteristic |
| 402 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 403 | C2×C3⋊D3 | C2×#97 | 1 | 1 | yes | characteristic |
| 404 | C2×C3⋊D3 | C2×#97 | 1 | 1 | yes | characteristic |
| 405 | C2×C3×D3 | — | 4 | 2 | no | — |
| 406 | C2×C3×D3 | C2×#97 | 1 | 2 | yes | — |
| 407 | C2×C3×D3 | C2×#97 | 1 | 2 | yes | — |
| 408 | C32×C4 | — | 4 | 1 | no | — |
| 409 | C32×C4 | C22×C42 | 1 | 1 | yes | characteristic |
| 410 | C32×C4 | C22×M16 | 1 | 1 | yes | characteristic |
| 411 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 412 | C3⋊Dic3 | C2×#97 | 1 | 1 | yes | characteristic |
| 413 | C3⋊Dic3 | C2×#97 | 1 | 1 | yes | characteristic |
| 414 | C3×Dic3 | — | 4 | 2 | no | — |
| 415 | C3×Dic3 | C2×#97 | 1 | 2 | yes | — |
| 416 | C3×Dic3 | C2×#97 | 1 | 2 | yes | — |
| 417 | C2×#41 | — | 9 | 1 | no | — |
| 418 | #131 | — | 9 | 2 | no | — |
| 419 | #131 | — | 9 | 4 | no | — |
| 420 | #131 | — | 9 | 2 | no | — |
| 421 | #131 | — | 18 | 2 | no | — |
| 422 | #131 | — | 18 | 1 | no | — |
| 423 | #131 | — | 18 | 1 | no | — |
| 424 | C2×M16 | — | 9 | 1 | no | — |
| 425 | C2×M16 | — | 9 | 1 | no | — |
| 426 | C2×M16 | — | 9 | 2 | no | — |
| 427 | C2×M16 | — | 9 | 2 | no | — |
| 428 | C22×C8 | — | 3 | 2 | no | — |
| 429 | C22×C8 | — | 3 | 2 | no | — |
| 430 | C22×C8 | — | 9 | 1 | no | — |
| 431 | C22×C8 | — | 9 | 1 | no | — |
| 432 | C4×Q8 | — | 18 | 1 | no | — |
| 433 | C4×D4 | — | 18 | 2 | no | — |
| 434 | C4×D4 | — | 18 | 1 | no | — |
| 435 | #117 | — | 9 | 1 | no | — |
| 436 | #117 | — | 9 | 2 | no | — |
| 437 | C2×C42 | — | 3 | 2 | no | — |
| 438 | C2×C42 | — | 9 | 1 | no | — |
| 439 | M32 | — | 3 | 4 | no | — |
| 440 | M32 | — | 3 | 8 | no | — |
| 441 | M32 | — | 9 | 4 | no | — |
| 442 | M32 | — | 9 | 8 | no | — |
| 443 | M32 | — | 9 | 2 | no | — |
| 444 | M32 | — | 9 | 4 | no | — |
| 445 | M32 | C2×D32 | 1 | 2 | yes | — |
| 446 | C2×C16 | — | 3 | 8 | no | — |
| 447 | C2×C16 | — | 9 | 4 | no | — |
| 448 | C2×C16 | — | 9 | 8 | no | — |
| 449 | C2×C16 | — | 9 | 4 | no | — |
| 450 | #97 | — | 3 | 2 | no | — |
| 451 | #97 | — | 3 | 2 | no | — |
| 452 | #97 | — | 3 | 2 | no | — |
| 453 | #97 | — | 9 | 1 | no | — |
| 454 | #97 | — | 9 | 1 | no | — |
| 455 | #97 | — | 9 | 1 | no | — |
| 456 | #97 | C2×D32 | 1 | 1 | yes | characteristic |
| 457 | C4×C8 | — | 9 | 2 | no | — |
| 458 | C4×C8 | — | 9 | 2 | no | — |
| 459 | C4×C8 | — | 9 | 2 | no | — |
| 460 | C23×C3 | — | 3 | 2 | no | — |
| 461 | C22×D3 | — | 3 | 2 | no | — |
| 462 | C22×D3 | — | 6 | 1 | no | — |
| 463 | C22×D3 | D3×M16 | 1 | 2 | yes | — |
| 464 | C2×C3×C4 | — | 2 | 2 | no | — |
| 465 | C2×C3×C4 | — | 2 | 1 | no | — |
| 466 | C2×C3×C4 | — | 3 | 2 | no | — |
| 467 | C2×C3×C4 | — | 3 | 2 | no | — |
| 468 | C2×C3×C4 | — | 3 | 2 | no | — |
| 469 | C2×C3×C4 | — | 3 | 2 | no | — |
| 470 | C2×C3×C4 | — | 3 | 2 | no | — |
| 471 | C2×C3×C4 | — | 4 | 1 | no | — |
| 472 | C2×C3×C4 | — | 6 | 2 | no | — |
| 473 | C2×C3×C4 | — | 24 | 2 | no | — |
| 474 | C2×C3×C4 | C22×C4×D3 | 1 | 2 | yes | — |
| 475 | #67 | — | 3 | 2 | no | — |
| 476 | #67 | — | 3 | 2 | no | — |
| 477 | #67 | — | 3 | 2 | no | — |
| 478 | #67 | — | 3 | 2 | no | — |
| 479 | #67 | — | 3 | 2 | no | — |
| 480 | #67 | — | 3 | 2 | no | — |
| 481 | #67 | — | 3 | 2 | no | — |
| 482 | #67 | — | 3 | 2 | no | — |
| 483 | C2×Dic3 | — | 2 | 2 | no | — |
| 484 | C2×Dic3 | — | 3 | 2 | no | — |
| 485 | C2×Dic3 | — | 6 | 1 | no | — |
| 486 | C2×Dic3 | — | 6 | 2 | no | — |
| 487 | C2×Dic3 | — | 12 | 1 | no | — |
| 488 | C2×Dic3 | D3×M16 | 1 | 2 | yes | — |
| 489 | D12 | — | 3 | 2 | no | — |
| 490 | D12 | — | 3 | 2 | no | — |
| 491 | D12 | — | 3 | 2 | no | — |
| 492 | D12 | — | 3 | 2 | no | — |
| 493 | C4×D3 | — | 3 | 2 | no | — |
| 494 | C4×D3 | — | 3 | 2 | no | — |
| 495 | C4×D3 | — | 3 | 2 | no | — |
| 496 | C4×D3 | — | 3 | 2 | no | — |
| 497 | C4×D3 | — | 6 | 1 | no | — |
| 498 | C4×D3 | — | 6 | 1 | no | — |
| 499 | C4×D3 | — | 6 | 1 | no | — |
| 500 | C4×D3 | — | 6 | 1 | no | — |
| 501 | C4×D3 | — | 8 | 2 | no | — |
| 502 | C4×D3 | — | 24 | 2 | no | — |
| 503 | C4×D3 | — | 24 | 2 | no | — |
| 504 | C4×D3 | C42×D3 | 1 | 2 | yes | — |
| 505 | C4×D3 | C42×D3 | 1 | 2 | yes | — |
| 506 | C4×D3 | D3×M16 | 1 | 2 | yes | — |
| 507 | C4×D3 | D3×M16 | 1 | 2 | yes | — |
| 508 | Dic6 | — | 3 | 2 | no | — |
| 509 | Dic6 | — | 3 | 2 | no | — |
| 510 | Dic6 | — | 3 | 2 | no | — |
| 511 | Dic6 | — | 3 | 2 | no | — |
| 512 | C3×C8 | — | 2 | 2 | no | — |
| 513 | C3×C8 | — | 2 | 2 | no | — |
| 514 | C3×C8 | — | 3 | 4 | no | — |
| 515 | C3×C8 | — | 4 | 1 | no | — |
| 516 | C3×C8 | — | 6 | 2 | no | — |
| 517 | C3×C8 | C22×C4×D3 | 1 | 4 | yes | — |
| 518 | C3⋊C8 | — | 2 | 2 | no | — |
| 519 | C3⋊C8 | — | 3 | 4 | no | — |
| 520 | C3⋊C8 | — | 6 | 2 | no | — |
| 521 | C3⋊C8 | — | 6 | 2 | no | — |
| 522 | C3⋊C8 | — | 12 | 1 | no | — |
| 523 | C3⋊C8 | C42×D3 | 1 | 4 | yes | — |
| 524 | C2×C32 | — | 2 | 1 | no | — |
| 525 | C2×C32 | C22×#97 | 1 | 1 | yes | characteristic |
| 526 | C3⋊D3 | — | 2 | 1 | no | — |
| 527 | C3⋊D3 | — | 2 | 1 | no | — |
| 528 | C3×D3 | — | 2 | 2 | no | — |
| 529 | C3×D3 | — | 2 | 2 | no | — |
| 530 | #41 | — | 9 | 1 | no | — |
| 531 | #41 | — | 9 | 2 | no | — |
| 532 | #41 | — | 9 | 1 | no | — |
| 533 | #41 | — | 9 | 2 | no | — |
| 534 | #41 | — | 9 | 1 | no | — |
| 535 | #41 | — | 9 | 1 | no | — |
| 536 | C2×Q8 | — | 9 | 1 | no | — |
| 537 | C2×D4 | — | 9 | 2 | no | — |
| 538 | C2×D4 | — | 9 | 1 | no | — |
| 539 | C22×C4 | — | 3 | 2 | no | — |
| 540 | C22×C4 | — | 6 | 2 | no | — |
| 541 | C22×C4 | — | 9 | 1 | no | — |
| 542 | C22×C4 | — | 18 | 1 | no | — |
| 543 | M16 | — | 9 | 2 | no | — |
| 544 | M16 | — | 9 | 2 | no | — |
| 545 | M16 | — | 9 | 4 | no | — |
| 546 | M16 | — | 9 | 4 | no | — |
| 547 | M16 | — | 18 | 1 | no | — |
| 548 | M16 | — | 18 | 1 | no | — |
| 549 | M16 | — | 18 | 2 | no | — |
| 550 | M16 | — | 18 | 2 | no | — |
| 551 | C2×C8 | — | 3 | 2 | no | — |
| 552 | C2×C8 | — | 3 | 4 | no | — |
| 553 | C2×C8 | — | 3 | 4 | no | — |
| 554 | C2×C8 | — | 3 | 2 | no | — |
| 555 | C2×C8 | — | 6 | 2 | no | — |
| 556 | C2×C8 | — | 6 | 2 | no | — |
| 557 | C2×C8 | — | 9 | 1 | no | — |
| 558 | C2×C8 | — | 9 | 2 | no | — |
| 559 | C2×C8 | — | 9 | 2 | no | — |
| 560 | C2×C8 | — | 9 | 1 | no | — |
| 561 | C2×C8 | — | 18 | 1 | no | — |
| 562 | C2×C8 | — | 18 | 1 | no | — |
| 563 | C2×C8 | C4×D32 | 1 | 1 | yes | characteristic |
| 564 | C2×C8 | C22×D32 | 1 | 1 | yes | characteristic |
| 565 | C4⋊C4 | — | 18 | 2 | no | — |
| 566 | C4⋊C4 | — | 18 | 1 | no | — |
| 567 | C22⋊C4 | — | 18 | 1 | no | — |
| 568 | C22⋊C4 | — | 18 | 2 | no | — |
| 569 | C42 | — | 3 | 2 | no | — |
| 570 | C42 | — | 6 | 2 | no | — |
| 571 | C42 | — | 9 | 1 | no | — |
| 572 | C42 | — | 18 | 1 | no | — |
| 573 | C42 | C4×D32 | 1 | 1 | yes | characteristic |
| 574 | C16 | — | 3 | 8 | no | — |
| 575 | C16 | — | 9 | 4 | no | — |
| 576 | C16 | C4×D32 | 1 | 4 | yes | — |
| 577 | C22×C3 | — | 2 | 1 | no | — |
| 578 | C22×C3 | — | 3 | 2 | no | — |
| 579 | C22×C3 | — | 3 | 2 | no | — |
| 580 | C22×C3 | — | 12 | 2 | no | — |
| 581 | C22×C3 | C2×D3×M16 | 1 | 2 | yes | — |
| 582 | C2×D3 | — | 3 | 2 | no | — |
| 583 | C2×D3 | — | 3 | 2 | no | — |
| 584 | C2×D3 | — | 4 | 2 | no | — |
| 585 | C2×D3 | — | 6 | 1 | no | — |
| 586 | C2×D3 | — | 6 | 1 | no | — |
| 587 | C2×D3 | — | 12 | 2 | no | — |
| 588 | C2×D3 | — | 12 | 2 | no | — |
| 589 | C2×D3 | D3×#97 | 1 | 2 | yes | — |
| 590 | C2×D3 | D3×#97 | 1 | 2 | yes | — |
| 591 | C3×C4 | — | 2 | 1 | no | — |
| 592 | C3×C4 | — | 2 | 1 | no | — |
| 593 | C3×C4 | — | 3 | 2 | no | — |
| 594 | C3×C4 | — | 3 | 2 | no | — |
| 595 | C3×C4 | — | 4 | 2 | no | — |
| 596 | C3×C4 | — | 8 | 1 | no | — |
| 597 | C3×C4 | — | 12 | 2 | no | — |
| 598 | C3×C4 | C2×C42×D3 | 1 | 2 | yes | — |
| 599 | C3×C4 | C2×D3×M16 | 1 | 2 | yes | — |
| 600 | Dic3 | — | 3 | 2 | no | — |
| 601 | Dic3 | — | 3 | 2 | no | — |
| 602 | Dic3 | — | 4 | 2 | no | — |
| 603 | Dic3 | — | 6 | 1 | no | — |
| 604 | Dic3 | — | 6 | 1 | no | — |
| 605 | Dic3 | — | 12 | 2 | no | — |
| 606 | Dic3 | — | 24 | 1 | no | — |
| 607 | Dic3 | D3×#97 | 1 | 2 | yes | — |
| 608 | Dic3 | D3×#97 | 1 | 2 | yes | — |
| 609 | C32 | #33329 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 610 | C23 | — | 3 | 2 | no | — |
| 611 | C23 | — | 9 | 1 | no | — |
| 612 | Q8 | — | 9 | 1 | no | — |
| 613 | Q8 | — | 9 | 2 | no | — |
| 614 | Q8 | — | 9 | 1 | no | — |
| 615 | D4 | — | 9 | 2 | no | — |
| 616 | D4 | — | 9 | 2 | no | — |
| 617 | D4 | — | 9 | 2 | no | — |
| 618 | D4 | — | 9 | 2 | no | — |
| 619 | D4 | — | 9 | 1 | no | — |
| 620 | D4 | — | 9 | 2 | no | — |
| 621 | D4 | — | 9 | 1 | no | — |
| 622 | C2×C4 | — | 2 | 1 | no | — |
| 623 | C2×C4 | — | 3 | 2 | no | — |
| 624 | C2×C4 | — | 3 | 2 | no | — |
| 625 | C2×C4 | — | 3 | 2 | no | — |
| 626 | C2×C4 | — | 3 | 2 | no | — |
| 627 | C2×C4 | — | 3 | 2 | no | — |
| 628 | C2×C4 | — | 6 | 2 | no | — |
| 629 | C2×C4 | — | 9 | 1 | no | — |
| 630 | C2×C4 | — | 9 | 1 | no | — |
| 631 | C2×C4 | — | 9 | 1 | no | — |
| 632 | C2×C4 | — | 9 | 1 | no | — |
| 633 | C2×C4 | — | 9 | 1 | no | — |
| 634 | C2×C4 | — | 18 | 1 | no | — |
| 635 | C2×C4 | — | 24 | 2 | no | — |
| 636 | C2×C4 | — | 72 | 1 | no | — |
| 637 | C2×C4 | C2×C4×D32 | 1 | 1 | yes | characteristic |
| 638 | C8 | — | 2 | 1 | no | — |
| 639 | C8 | — | 3 | 4 | no | — |
| 640 | C8 | — | 6 | 2 | no | — |
| 641 | C8 | — | 9 | 2 | no | — |
| 642 | C8 | — | 18 | 1 | no | — |
| 643 | C8 | C2×C4×D32 | 1 | 2 | yes | — |
| 644 | C2×C3 | — | 2 | 2 | no | — |
| 645 | C2×C3 | — | 2 | 1 | no | — |
| 646 | C2×C3 | — | 4 | 1 | no | — |
| 647 | C2×C3 | — | 6 | 2 | no | — |
| 648 | C2×C3 | — | 6 | 2 | no | — |
| 649 | C2×C3 | C2×D3×#97 | 1 | 2 | yes | — |
| 650 | D3 | — | 2 | 2 | no | — |
| 651 | D3 | — | 2 | 2 | no | — |
| 652 | D3 | — | 6 | 2 | no | — |
| 653 | D3 | — | 6 | 2 | no | — |
| 654 | D3 | — | 6 | 2 | no | — |
| 655 | D3 | — | 12 | 1 | no | — |
| 656 | C22 | — | 3 | 2 | no | — |
| 657 | C22 | — | 3 | 2 | no | — |
| 658 | C22 | — | 9 | 1 | no | — |
| 659 | C22 | — | 9 | 1 | no | — |
| 660 | C22 | — | 12 | 2 | no | — |
| 661 | C22 | — | 36 | 1 | no | — |
| 662 | C22 | D32×M16 | 1 | 1 | yes | characteristic |
| 663 | C4 | — | 3 | 2 | no | — |
| 664 | C4 | — | 3 | 2 | no | — |
| 665 | C4 | — | 4 | 1 | no | — |
| 666 | C4 | — | 9 | 1 | no | — |
| 667 | C4 | — | 9 | 1 | no | — |
| 668 | C4 | — | 12 | 2 | no | — |
| 669 | C4 | — | 36 | 1 | no | — |
| 670 | C4 | C42×D32 | 1 | 1 | yes | characteristic |
| 671 | C4 | D32×M16 | 1 | 1 | yes | characteristic |
| 672 | C3 | — | 2 | 1 | no | — |
| 673 | C3 | #10947846 | 1 | 2 | yes | complemented |
| 674 | C2 | — | 2 | 1 | no | — |
| 675 | C2 | — | 6 | 2 | no | — |
| 676 | C2 | — | 6 | 2 | no | — |
| 677 | C2 | — | 18 | 1 | no | — |
| 678 | C2 | — | 18 | 1 | no | — |
| 679 | C2 | D32×#97 | 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