← #11919281
Subgroups — #11919281
Order 1152.
12389 conjugacy classes of subgroups.
The subgroup lattice has 519 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10596758 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×D3×H(5,𝔽2) | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10596696 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #10596695 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #10596692 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #10596679 | C2 | 1 | 9 | yes | maximal, complemented |
| 7 | C2×#64313 | C2 | 1 | 9 | yes | maximal, complemented |
| 8 | D3×#1004 | C2 | 1 | 18 | yes | maximal, complemented |
| 9 | #87568 | — | 3 | 2 | no | maximal |
| 10 | C32×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #64367 | C22 | 1 | 6 | yes | complemented |
| 12 | #41×C3⋊D3 | C22 | 1 | 6 | yes | complemented |
| 13 | #64361 | C22 | 1 | 9 | yes | complemented |
| 14 | C2×#3830 | C22 | 1 | 9 | yes | complemented |
| 15 | C3×#1009 | C22 | 1 | 12 | yes | complemented |
| 16 | C3×D3×#41 | C22 | 1 | 12 | yes | complemented |
| 17 | C3×#1004 | C22 | 1 | 18 | yes | complemented |
| 18 | C2×C3×D3×D4 | C22 | 1 | 18 | yes | complemented |
| 19 | #64330 | C22 | 1 | 36 | yes | complemented |
| 20 | C2×D3×#67 | C22 | 1 | 36 | yes | complemented |
| 21 | C22×#625 | C22 | 1 | 6 | yes | complemented |
| 22 | C2×#3805 | C22 | 1 | 18 | yes | complemented |
| 23 | #64320 | C22 | 1 | 6 | yes | complemented |
| 24 | #64319 | C22 | 1 | 12 | yes | complemented |
| 25 | #64316 | C22 | 1 | 2 | yes | complemented |
| 26 | #64315 | C22 | 1 | 12 | yes | complemented |
| 27 | #64314 | C22 | 1 | 36 | yes | complemented |
| 28 | #64313 | C22 | 1 | 72 | yes | complemented |
| 29 | #64313 | C22 | 1 | 18 | yes | complemented |
| 30 | #64313 | C22 | 1 | 36 | yes | complemented |
| 31 | D3×#237 | C22 | 1 | 72 | yes | complemented |
| 32 | D32×D4 | C22 | 1 | 36 | yes | complemented |
| 33 | #64309 | C22 | 1 | 18 | yes | complemented |
| 34 | #64307 | C22 | 1 | 36 | yes | complemented |
| 35 | #64306 | C22 | 1 | 18 | yes | complemented |
| 36 | D3×#235 | C22 | 1 | 36 | yes | complemented |
| 37 | C2×#3802 | C22 | 1 | 9 | yes | complemented |
| 38 | C2×#3798 | C22 | 1 | 9 | yes | complemented |
| 39 | #64298 | C22 | 1 | 18 | yes | complemented |
| 40 | C2×#3795 | C22 | 1 | 18 | yes | complemented |
| 41 | C2×C3×H(5,𝔽2) | — | 3 | 2 | no | — |
| 42 | #5966 | — | 3 | 2 | no | — |
| 43 | #5966 | — | 3 | 12 | no | — |
| 44 | #5966 | — | 3 | 18 | no | — |
| 45 | #5966 | — | 6 | 1 | no | — |
| 46 | D3×H(5,𝔽2) | — | 3 | 12 | no | — |
| 47 | D3×H(5,𝔽2) | — | 3 | 18 | no | — |
| 48 | D3×H(5,𝔽2) | D3 | 1 | 2 | yes | complemented |
| 49 | #5964 | — | 3 | 12 | no | — |
| 50 | #5964 | — | 3 | 12 | no | — |
| 51 | C2×#1004 | — | 3 | 18 | no | — |
| 52 | C2×#1004 | — | 3 | 18 | no | — |
| 53 | C23×C3×D3 | C23 | 1 | 12 | yes | complemented |
| 54 | C22×D32 | C23 | 1 | 18 | yes | complemented |
| 55 | C32×#41 | C23 | 1 | 6 | yes | complemented |
| 56 | C2×C32×D4 | C23 | 1 | 9 | yes | complemented |
| 57 | C2×#638 | C23 | 1 | 18 | yes | complemented |
| 58 | C22×C3⋊Dic3 | C23 | 1 | 6 | yes | complemented |
| 59 | #3832 | C23 | 1 | 2 | yes | complemented |
| 60 | Q8×C3⋊D3 | C23 | 1 | 6 | yes | complemented |
| 61 | #3830 | C23 | 1 | 18 | yes | complemented |
| 62 | #3830 | C23 | 1 | 36 | yes | complemented |
| 63 | D4×C3⋊D3 | C23 | 1 | 18 | yes | complemented |
| 64 | #3828 | C23 | 1 | 18 | yes | complemented |
| 65 | C2×C4×C3⋊D3 | C23 | 1 | 9 | yes | complemented |
| 66 | C2×#634 | C23 | 1 | 9 | yes | complemented |
| 67 | C2×C3×#67 | C23 | 1 | 36 | yes | complemented |
| 68 | C3×#239 | C23 | 1 | 12 | yes | complemented |
| 69 | C3×D3×Q8 | C23 | 1 | 4 | yes | complemented |
| 70 | C3×#237 | C23 | 1 | 36 | yes | complemented |
| 71 | C3×D3×D4 | C23 | 1 | 72 | yes | complemented |
| 72 | C3×D3×D4 | C23 | 1 | 36 | yes | complemented |
| 73 | C3×#235 | C23 | 1 | 36 | yes | complemented |
| 74 | C2×C3×D12 | C23 | 1 | 18 | yes | complemented |
| 75 | C2×C3×C4×D3 | C23 | 1 | 18 | yes | complemented |
| 76 | #3811 | C23 | 1 | 36 | yes | complemented |
| 77 | D3×#67 | C23 | 1 | 72 | yes | complemented |
| 78 | D3×#67 | C23 | 1 | 144 | yes | complemented |
| 79 | C2×#627 | C23 | 1 | 9 | yes | complemented |
| 80 | C2×#626 | C23 | 1 | 18 | yes | complemented |
| 81 | C2×#625 | C23 | 1 | 36 | yes | complemented |
| 82 | C2×#625 | C23 | 1 | 9 | yes | complemented |
| 83 | C2×#625 | C23 | 1 | 18 | yes | complemented |
| 84 | #3805 | C23 | 1 | 72 | yes | complemented |
| 85 | #3805 | C23 | 1 | 36 | yes | complemented |
| 86 | #3804 | C23 | 1 | 72 | yes | complemented |
| 87 | C2×D3×Dic3 | C23 | 1 | 36 | yes | complemented |
| 88 | #3802 | C23 | 1 | 18 | yes | complemented |
| 89 | #3802 | C23 | 1 | 36 | yes | complemented |
| 90 | D3×D12 | C23 | 1 | 36 | yes | complemented |
| 91 | C4×D32 | C23 | 1 | 36 | yes | complemented |
| 92 | #3799 | C23 | 1 | 12 | yes | complemented |
| 93 | #3798 | C23 | 1 | 6 | yes | complemented |
| 94 | #3798 | C23 | 1 | 36 | yes | complemented |
| 95 | #3798 | C23 | 1 | 18 | yes | complemented |
| 96 | #3797 | C23 | 1 | 6 | yes | complemented |
| 97 | #3796 | C23 | 1 | 36 | yes | complemented |
| 98 | #3795 | C23 | 1 | 36 | yes | complemented |
| 99 | #3795 | C23 | 1 | 72 | yes | complemented |
| 100 | D3×Dic6 | C23 | 1 | 36 | yes | complemented |
| 101 | H(7,𝔽2) | — | 9 | 1 | no | Sylow |
| 102 | C3×H(5,𝔽2) | — | 2 | 1 | no | — |
| 103 | C3×H(5,𝔽2) | — | 3 | 12 | no | — |
| 104 | C3×H(5,𝔽2) | — | 3 | 18 | no | — |
| 105 | C3×H(5,𝔽2) | C2×D3 | 1 | 2 | yes | complemented |
| 106 | C2×C3×#41 | — | 3 | 12 | no | — |
| 107 | C22×C3×D4 | — | 3 | 18 | no | — |
| 108 | C22×#67 | — | 3 | 12 | no | — |
| 109 | C22×#67 | — | 3 | 36 | no | — |
| 110 | #1010 | — | 3 | 12 | no | — |
| 111 | #1010 | — | 3 | 12 | no | — |
| 112 | #1010 | — | 3 | 36 | no | — |
| 113 | #1010 | — | 3 | 36 | no | — |
| 114 | #1010 | — | 6 | 6 | no | — |
| 115 | #1009 | — | 3 | 12 | no | — |
| 116 | #1009 | — | 3 | 36 | no | — |
| 117 | #1009 | — | 3 | 36 | no | — |
| 118 | #1009 | C2×D3 | 1 | 12 | yes | complemented |
| 119 | D3×#41 | — | 3 | 12 | no | — |
| 120 | D3×#41 | — | 3 | 24 | no | — |
| 121 | D3×#41 | — | 3 | 72 | no | — |
| 122 | D3×#41 | — | 3 | 36 | no | — |
| 123 | D3×#41 | — | 3 | 36 | no | — |
| 124 | D3×#41 | — | 6 | 6 | no | — |
| 125 | D3×#41 | C2×D3 | 1 | 12 | yes | complemented |
| 126 | #1007 | — | 3 | 12 | no | — |
| 127 | #1007 | — | 3 | 4 | no | — |
| 128 | #1004 | — | 3 | 18 | no | — |
| 129 | #1004 | — | 3 | 72 | no | — |
| 130 | #1004 | — | 3 | 36 | no | — |
| 131 | #1004 | — | 3 | 72 | no | — |
| 132 | #1004 | — | 3 | 36 | no | — |
| 133 | #1004 | — | 3 | 72 | no | — |
| 134 | #1004 | — | 3 | 72 | no | — |
| 135 | #1004 | — | 3 | 36 | no | — |
| 136 | #1004 | — | 6 | 9 | no | — |
| 137 | #1004 | C2×D3 | 1 | 18 | yes | complemented |
| 138 | C2×#237 | — | 3 | 18 | no | — |
| 139 | C2×#237 | — | 3 | 36 | no | — |
| 140 | C2×#237 | — | 3 | 72 | no | — |
| 141 | C2×#237 | — | 3 | 18 | no | — |
| 142 | C2×#237 | — | 6 | 9 | no | — |
| 143 | C2×D3×D4 | — | 3 | 36 | no | — |
| 144 | C2×D3×D4 | — | 3 | 72 | no | — |
| 145 | C2×D3×D4 | — | 3 | 18 | no | — |
| 146 | C2×D3×D4 | C2×D3 | 1 | 18 | yes | complemented |
| 147 | C2×#235 | — | 3 | 36 | no | — |
| 148 | C2×#235 | — | 3 | 18 | no | — |
| 149 | C2×#235 | — | 3 | 18 | no | — |
| 150 | C23×C32 | C24 | 1 | 6 | yes | — |
| 151 | C22×C3⋊D3 | C24 | 1 | 9 | yes | — |
| 152 | C22×C3×D3 | — | 8 | 12 | no | — |
| 153 | C22×C3×D3 | C24 | 1 | 36 | yes | — |
| 154 | C22×C3×D3 | C24 | 1 | 18 | yes | — |
| 155 | C2×D32 | — | 8 | 18 | no | — |
| 156 | C2×D32 | C24 | 1 | 36 | yes | — |
| 157 | C32×Q8 | C24 | 1 | 2 | yes | — |
| 158 | C32×D4 | C24 | 1 | 18 | yes | — |
| 159 | C2×C32×C4 | C24 | 1 | 9 | yes | — |
| 160 | #638 | C24 | 1 | 36 | yes | — |
| 161 | C2×C3⋊Dic3 | C24 | 1 | 18 | yes | — |
| 162 | C2×C3⋊Dic3 | C24 | 1 | 9 | yes | — |
| 163 | C4⋊(C3⋊D3) | C24 | 1 | 6 | yes | — |
| 164 | C4×C3⋊D3 | C24 | 1 | 18 | yes | — |
| 165 | C4×C3⋊D3 | C24 | 1 | 6 | yes | — |
| 166 | #634 | C24 | 1 | 18 | yes | — |
| 167 | C3×#67 | C24 | 1 | 72 | yes | — |
| 168 | C2×C3×Dic3 | C24 | 1 | 18 | yes | — |
| 169 | C3×D12 | C24 | 1 | 36 | yes | — |
| 170 | C3×C4×D3 | C24 | 1 | 36 | yes | — |
| 171 | C3×C4×D3 | C24 | 1 | 12 | yes | — |
| 172 | C3×Dic6 | C24 | 1 | 12 | yes | — |
| 173 | #627 | C24 | 1 | 18 | yes | — |
| 174 | #627 | C24 | 1 | 6 | yes | — |
| 175 | #626 | C24 | 1 | 36 | yes | — |
| 176 | #626 | C24 | 1 | 12 | yes | — |
| 177 | #625 | C24 | 1 | 18 | yes | — |
| 178 | #625 | C24 | 1 | 36 | yes | — |
| 179 | #625 | C24 | 1 | 1 | yes | characteristic |
| 180 | #625 | C24 | 1 | 9 | yes | — |
| 181 | #624 | C24 | 1 | 12 | yes | — |
| 182 | D3×Dic3 | C24 | 1 | 72 | yes | — |
| 183 | #585 | — | 9 | 6 | no | — |
| 184 | #585 | — | 9 | 12 | no | — |
| 185 | #585 | — | 9 | 9 | no | — |
| 186 | #585 | — | 9 | 1 | no | — |
| 187 | C2×H(5,𝔽2) | — | 3 | 2 | no | — |
| 188 | C2×H(5,𝔽2) | — | 9 | 9 | no | — |
| 189 | C2×H(5,𝔽2) | — | 9 | 18 | no | — |
| 190 | C2×H(5,𝔽2) | — | 9 | 6 | no | — |
| 191 | C24×C3 | — | 3 | 12 | no | — |
| 192 | C23×D3 | — | 3 | 36 | no | — |
| 193 | C23×D3 | C22×D3 | 1 | 12 | yes | complemented |
| 194 | C3×#41 | — | 2 | 6 | no | — |
| 195 | C3×#41 | — | 3 | 12 | no | — |
| 196 | C3×#41 | — | 3 | 36 | no | — |
| 197 | C3×#41 | — | 3 | 36 | no | — |
| 198 | C3×#41 | C22×D3 | 1 | 12 | yes | complemented |
| 199 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 200 | C2×C3×D4 | — | 2 | 9 | no | — |
| 201 | C2×C3×D4 | — | 3 | 36 | no | — |
| 202 | C2×C3×D4 | — | 3 | 72 | no | — |
| 203 | C2×C3×D4 | — | 3 | 36 | no | — |
| 204 | C2×C3×D4 | — | 3 | 18 | no | — |
| 205 | C2×C3×D4 | C22×D3 | 1 | 18 | yes | complemented |
| 206 | C22×C3×C4 | — | 3 | 18 | no | — |
| 207 | C2×#67 | — | 3 | 36 | no | — |
| 208 | C2×#67 | — | 3 | 36 | no | — |
| 209 | C2×#67 | — | 3 | 18 | no | — |
| 210 | C2×#67 | — | 3 | 36 | no | — |
| 211 | C2×#67 | — | 3 | 36 | no | — |
| 212 | C2×#67 | — | 3 | 72 | no | — |
| 213 | C2×#67 | — | 3 | 144 | no | — |
| 214 | C2×#67 | — | 3 | 18 | no | — |
| 215 | C2×#67 | — | 6 | 18 | no | — |
| 216 | C2×#67 | C22×D3 | 1 | 36 | yes | complemented |
| 217 | C22×Dic3 | — | 3 | 12 | no | — |
| 218 | C22×Dic3 | — | 3 | 36 | no | — |
| 219 | C22×Dic3 | — | 6 | 6 | no | — |
| 220 | #239 | — | 3 | 4 | no | — |
| 221 | #239 | — | 3 | 36 | no | — |
| 222 | #239 | — | 3 | 12 | no | — |
| 223 | #239 | — | 6 | 2 | no | — |
| 224 | #239 | C22×D3 | 1 | 12 | yes | complemented |
| 225 | D3×Q8 | — | 3 | 12 | no | — |
| 226 | D3×Q8 | — | 3 | 36 | no | — |
| 227 | D3×Q8 | — | 3 | 12 | no | — |
| 228 | D3×Q8 | — | 6 | 6 | no | — |
| 229 | D3×Q8 | C22×D3 | 1 | 4 | yes | complemented |
| 230 | #237 | — | 3 | 36 | no | — |
| 231 | #237 | — | 3 | 72 | no | — |
| 232 | #237 | — | 3 | 144 | no | — |
| 233 | #237 | — | 3 | 72 | no | — |
| 234 | #237 | — | 3 | 72 | no | — |
| 235 | #237 | — | 3 | 72 | no | — |
| 236 | #237 | — | 3 | 36 | no | — |
| 237 | #237 | — | 3 | 36 | no | — |
| 238 | #237 | — | 6 | 18 | no | — |
| 239 | #237 | — | 6 | 36 | no | — |
| 240 | #237 | C22×D3 | 1 | 36 | yes | complemented |
| 241 | D3×D4 | — | 3 | 144 | no | — |
| 242 | D3×D4 | — | 3 | 72 | no | — |
| 243 | D3×D4 | — | 3 | 36 | no | — |
| 244 | D3×D4 | — | 3 | 72 | no | — |
| 245 | D3×D4 | — | 3 | 36 | no | — |
| 246 | D3×D4 | — | 3 | 72 | no | — |
| 247 | D3×D4 | — | 3 | 36 | no | — |
| 248 | D3×D4 | — | 6 | 18 | no | — |
| 249 | D3×D4 | C22×D3 | 1 | 72 | yes | complemented |
| 250 | D3×D4 | C22×D3 | 1 | 36 | yes | complemented |
| 251 | #235 | — | 3 | 36 | no | — |
| 252 | #235 | — | 3 | 72 | no | — |
| 253 | #235 | — | 3 | 36 | no | — |
| 254 | #235 | — | 3 | 72 | no | — |
| 255 | #235 | — | 3 | 36 | no | — |
| 256 | #235 | — | 3 | 12 | no | — |
| 257 | #235 | — | 3 | 36 | no | — |
| 258 | #235 | — | 3 | 36 | no | — |
| 259 | #235 | — | 3 | 12 | no | — |
| 260 | #235 | — | 6 | 18 | no | — |
| 261 | #235 | C22×D3 | 1 | 36 | yes | complemented |
| 262 | C2×D12 | — | 3 | 18 | no | — |
| 263 | C2×D12 | — | 3 | 36 | no | — |
| 264 | C2×D12 | C22×D3 | 1 | 18 | yes | complemented |
| 265 | C2×C4×D3 | — | 3 | 36 | no | — |
| 266 | C2×C4×D3 | — | 3 | 18 | no | — |
| 267 | C2×C4×D3 | — | 3 | 72 | no | — |
| 268 | C2×C4×D3 | — | 6 | 9 | no | — |
| 269 | C2×C4×D3 | C22×D3 | 1 | 18 | yes | complemented |
| 270 | C2×Dic6 | — | 3 | 18 | no | — |
| 271 | C2×Dic6 | — | 3 | 18 | no | — |
| 272 | C2×Dic6 | — | 3 | 36 | no | — |
| 273 | C2×Dic6 | — | 6 | 9 | no | — |
| 274 | C22×C32 | — | 4 | 6 | no | — |
| 275 | C22×C32 | C25 | 1 | 9 | yes | — |
| 276 | C2×C3⋊D3 | — | 4 | 9 | no | — |
| 277 | C2×C3⋊D3 | C25 | 1 | 6 | yes | — |
| 278 | C2×C3×D3 | — | 4 | 36 | no | — |
| 279 | C2×C3×D3 | — | 4 | 18 | no | — |
| 280 | C2×C3×D3 | C25 | 1 | 18 | yes | — |
| 281 | C2×C3×D3 | C25 | 1 | 2 | yes | — |
| 282 | D32 | — | 4 | 36 | no | — |
| 283 | C32×C4 | C25 | 1 | 6 | yes | — |
| 284 | C3⋊Dic3 | C25 | 1 | 9 | yes | — |
| 285 | C3⋊Dic3 | C25 | 1 | 1 | yes | characteristic |
| 286 | C3×Dic3 | C25 | 1 | 12 | yes | — |
| 287 | 2−1+4 | — | 9 | 2 | no | — |
| 288 | 2−1+4 | — | 9 | 12 | no | — |
| 289 | 2−1+4 | — | 9 | 18 | no | — |
| 290 | 2−1+4 | — | 9 | 18 | no | — |
| 291 | 2−1+4 | — | 9 | 6 | no | — |
| 292 | H(5,𝔽2) | — | 3 | 12 | no | — |
| 293 | H(5,𝔽2) | — | 3 | 18 | no | — |
| 294 | H(5,𝔽2) | — | 9 | 36 | no | — |
| 295 | H(5,𝔽2) | — | 9 | 18 | no | — |
| 296 | H(5,𝔽2) | — | 9 | 72 | no | — |
| 297 | H(5,𝔽2) | — | 9 | 36 | no | — |
| 298 | H(5,𝔽2) | — | 9 | 36 | no | — |
| 299 | H(5,𝔽2) | — | 9 | 36 | no | — |
| 300 | H(5,𝔽2) | — | 9 | 6 | no | — |
| 301 | H(5,𝔽2) | — | 9 | 9 | no | — |
| 302 | H(5,𝔽2) | D32 | 1 | 1 | yes | characteristic, complemented |
| 303 | C2×#41 | — | 3 | 12 | no | — |
| 304 | C2×#41 | — | 9 | 9 | no | — |
| 305 | C2×#41 | — | 9 | 18 | no | — |
| 306 | C2×#41 | — | 9 | 36 | no | — |
| 307 | C2×#41 | — | 9 | 18 | no | — |
| 308 | C2×#41 | — | 9 | 72 | no | — |
| 309 | C2×#41 | — | 9 | 12 | no | — |
| 310 | C2×#41 | — | 9 | 18 | no | — |
| 311 | C2×#41 | — | 9 | 6 | no | — |
| 312 | C2×#41 | — | 9 | 9 | no | — |
| 313 | C22×D4 | — | 3 | 18 | no | — |
| 314 | C22×D4 | — | 9 | 36 | no | — |
| 315 | C22×D4 | — | 9 | 9 | no | — |
| 316 | C22×D4 | — | 9 | 36 | no | — |
| 317 | C22×D4 | — | 9 | 6 | no | — |
| 318 | C23×C3 | — | 2 | 6 | no | — |
| 319 | C23×C3 | — | 3 | 36 | no | — |
| 320 | C23×C3 | — | 3 | 18 | no | — |
| 321 | C23×C3 | — | 24 | 12 | no | — |
| 322 | C23×C3 | C23×D3 | 1 | 12 | yes | — |
| 323 | C22×D3 | — | 3 | 18 | no | — |
| 324 | C22×D3 | — | 3 | 72 | no | — |
| 325 | C22×D3 | — | 6 | 9 | no | — |
| 326 | C22×D3 | — | 8 | 12 | no | — |
| 327 | C22×D3 | — | 24 | 36 | no | — |
| 328 | C22×D3 | C23×D3 | 1 | 36 | yes | — |
| 329 | C22×D3 | C23×D3 | 1 | 18 | yes | — |
| 330 | C3×Q8 | — | 2 | 2 | no | — |
| 331 | C3×Q8 | — | 3 | 12 | no | — |
| 332 | C3×Q8 | C23×D3 | 1 | 4 | yes | — |
| 333 | C3×D4 | — | 2 | 18 | no | — |
| 334 | C3×D4 | — | 3 | 72 | no | — |
| 335 | C3×D4 | — | 3 | 36 | no | — |
| 336 | C3×D4 | C23×D3 | 1 | 36 | yes | — |
| 337 | C2×C3×C4 | — | 2 | 9 | no | — |
| 338 | C2×C3×C4 | — | 3 | 18 | no | — |
| 339 | C2×C3×C4 | — | 3 | 36 | no | — |
| 340 | C2×C3×C4 | — | 3 | 12 | no | — |
| 341 | C2×C3×C4 | C23×D3 | 1 | 18 | yes | — |
| 342 | #67 | — | 3 | 72 | no | — |
| 343 | #67 | — | 3 | 18 | no | — |
| 344 | #67 | — | 3 | 2 | no | — |
| 345 | #67 | — | 3 | 72 | no | — |
| 346 | #67 | — | 3 | 18 | no | — |
| 347 | #67 | — | 3 | 18 | no | — |
| 348 | #67 | — | 3 | 12 | no | — |
| 349 | #67 | — | 3 | 36 | no | — |
| 350 | #67 | — | 6 | 36 | no | — |
| 351 | #67 | C23×D3 | 1 | 72 | yes | — |
| 352 | C2×Dic3 | — | 3 | 36 | no | — |
| 353 | C2×Dic3 | — | 3 | 18 | no | — |
| 354 | C2×Dic3 | — | 3 | 72 | no | — |
| 355 | C2×Dic3 | — | 6 | 18 | no | — |
| 356 | C2×Dic3 | — | 6 | 9 | no | — |
| 357 | C2×Dic3 | C23×D3 | 1 | 18 | yes | — |
| 358 | D12 | — | 3 | 36 | no | — |
| 359 | D12 | — | 3 | 12 | no | — |
| 360 | D12 | — | 3 | 12 | no | — |
| 361 | D12 | — | 6 | 6 | no | — |
| 362 | D12 | C23×D3 | 1 | 36 | yes | — |
| 363 | C4×D3 | — | 3 | 72 | no | — |
| 364 | C4×D3 | — | 3 | 36 | no | — |
| 365 | C4×D3 | — | 3 | 12 | no | — |
| 366 | C4×D3 | — | 3 | 24 | no | — |
| 367 | C4×D3 | — | 6 | 6 | no | — |
| 368 | C4×D3 | — | 6 | 18 | no | — |
| 369 | C4×D3 | C23×D3 | 1 | 36 | yes | — |
| 370 | C4×D3 | C23×D3 | 1 | 12 | yes | — |
| 371 | Dic6 | — | 3 | 36 | no | — |
| 372 | Dic6 | — | 3 | 36 | no | — |
| 373 | Dic6 | — | 3 | 12 | no | — |
| 374 | Dic6 | — | 6 | 18 | no | — |
| 375 | Dic6 | C23×D3 | 1 | 12 | yes | — |
| 376 | C2×C32 | — | 2 | 9 | no | — |
| 377 | C2×C32 | C26 | 1 | 1 | yes | characteristic |
| 378 | C3⋊D3 | — | 2 | 6 | no | — |
| 379 | C3×D3 | — | 2 | 18 | no | — |
| 380 | C3×D3 | — | 2 | 2 | no | — |
| 381 | C24 | — | 3 | 12 | no | — |
| 382 | C24 | — | 9 | 18 | no | — |
| 383 | #41 | — | 3 | 12 | no | — |
| 384 | #41 | — | 3 | 36 | no | — |
| 385 | #41 | — | 3 | 36 | no | — |
| 386 | #41 | — | 9 | 6 | no | — |
| 387 | #41 | — | 9 | 36 | no | — |
| 388 | #41 | — | 9 | 18 | no | — |
| 389 | #41 | — | 9 | 72 | no | — |
| 390 | #41 | — | 9 | 36 | no | — |
| 391 | #41 | — | 9 | 72 | no | — |
| 392 | #41 | — | 9 | 12 | no | — |
| 393 | #41 | — | 9 | 36 | no | — |
| 394 | #41 | — | 9 | 72 | no | — |
| 395 | #41 | — | 9 | 36 | no | — |
| 396 | #41 | — | 9 | 2 | no | — |
| 397 | #41 | — | 9 | 36 | no | — |
| 398 | #41 | — | 9 | 18 | no | — |
| 399 | #41 | — | 9 | 18 | no | — |
| 400 | #41 | C2×D32 | 1 | 6 | yes | complemented |
| 401 | C2×Q8 | — | 3 | 4 | no | — |
| 402 | C2×Q8 | — | 9 | 9 | no | — |
| 403 | C2×Q8 | — | 9 | 36 | no | — |
| 404 | C2×Q8 | — | 9 | 6 | no | — |
| 405 | C2×Q8 | — | 9 | 6 | no | — |
| 406 | C2×Q8 | — | 9 | 9 | no | — |
| 407 | C2×D4 | — | 3 | 36 | no | — |
| 408 | C2×D4 | — | 3 | 36 | no | — |
| 409 | C2×D4 | — | 3 | 72 | no | — |
| 410 | C2×D4 | — | 3 | 18 | no | — |
| 411 | C2×D4 | — | 9 | 36 | no | — |
| 412 | C2×D4 | — | 9 | 18 | no | — |
| 413 | C2×D4 | — | 9 | 36 | no | — |
| 414 | C2×D4 | — | 9 | 18 | no | — |
| 415 | C2×D4 | — | 9 | 36 | no | — |
| 416 | C2×D4 | — | 9 | 72 | no | — |
| 417 | C2×D4 | — | 9 | 144 | no | — |
| 418 | C2×D4 | — | 9 | 9 | no | — |
| 419 | C2×D4 | — | 9 | 36 | no | — |
| 420 | C2×D4 | — | 9 | 18 | no | — |
| 421 | C2×D4 | — | 9 | 18 | no | — |
| 422 | C2×D4 | — | 9 | 18 | no | — |
| 423 | C2×D4 | C2×D32 | 1 | 9 | yes | complemented |
| 424 | C22×C4 | — | 3 | 18 | no | — |
| 425 | C22×C4 | — | 9 | 36 | no | — |
| 426 | C22×C4 | — | 9 | 36 | no | — |
| 427 | C22×C4 | — | 9 | 6 | no | — |
| 428 | C22×C4 | — | 9 | 9 | no | — |
| 429 | C22×C3 | — | 2 | 9 | no | — |
| 430 | C22×C3 | — | 3 | 18 | no | — |
| 431 | C22×C3 | — | 3 | 2 | no | — |
| 432 | C22×C3 | — | 4 | 12 | no | — |
| 433 | C22×C3 | — | 8 | 6 | no | — |
| 434 | C22×C3 | — | 12 | 36 | no | — |
| 435 | C22×C3 | — | 12 | 18 | no | — |
| 436 | C22×C3 | C24×D3 | 1 | 18 | yes | — |
| 437 | C2×D3 | — | 3 | 12 | no | — |
| 438 | C2×D3 | — | 4 | 18 | no | — |
| 439 | C2×D3 | — | 4 | 36 | no | — |
| 440 | C2×D3 | — | 6 | 6 | no | — |
| 441 | C2×D3 | — | 12 | 72 | no | — |
| 442 | C2×D3 | — | 12 | 18 | no | — |
| 443 | C2×D3 | — | 24 | 9 | no | — |
| 444 | C2×D3 | C24×D3 | 1 | 18 | yes | — |
| 445 | C2×D3 | C24×D3 | 1 | 2 | yes | — |
| 446 | C3×C4 | — | 2 | 6 | no | — |
| 447 | C3×C4 | — | 3 | 12 | no | — |
| 448 | C3×C4 | C24×D3 | 1 | 12 | yes | — |
| 449 | Dic3 | — | 3 | 18 | no | — |
| 450 | Dic3 | — | 3 | 2 | no | — |
| 451 | Dic3 | — | 6 | 9 | no | — |
| 452 | Dic3 | — | 6 | 1 | no | — |
| 453 | Dic3 | C24×D3 | 1 | 12 | yes | — |
| 454 | C32 | H(7,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 455 | C23 | — | 3 | 18 | no | — |
| 456 | C23 | — | 3 | 36 | no | — |
| 457 | C23 | — | 9 | 36 | no | — |
| 458 | C23 | — | 9 | 9 | no | — |
| 459 | C23 | — | 24 | 12 | no | — |
| 460 | C23 | — | 72 | 18 | no | — |
| 461 | C23 | C22×D32 | 1 | 6 | yes | — |
| 462 | Q8 | — | 3 | 12 | no | — |
| 463 | Q8 | — | 9 | 6 | no | — |
| 464 | Q8 | — | 9 | 18 | no | — |
| 465 | Q8 | — | 9 | 18 | no | — |
| 466 | Q8 | C22×D32 | 1 | 2 | yes | — |
| 467 | D4 | — | 3 | 72 | no | — |
| 468 | D4 | — | 3 | 36 | no | — |
| 469 | D4 | — | 9 | 12 | no | — |
| 470 | D4 | — | 9 | 36 | no | — |
| 471 | D4 | — | 9 | 1 | no | — |
| 472 | D4 | — | 9 | 18 | no | — |
| 473 | D4 | — | 9 | 9 | no | — |
| 474 | D4 | — | 9 | 36 | no | — |
| 475 | D4 | — | 9 | 36 | no | — |
| 476 | D4 | — | 9 | 6 | no | — |
| 477 | D4 | C22×D32 | 1 | 18 | yes | — |
| 478 | C2×C4 | — | 3 | 18 | no | — |
| 479 | C2×C4 | — | 3 | 12 | no | — |
| 480 | C2×C4 | — | 3 | 36 | no | — |
| 481 | C2×C4 | — | 9 | 12 | no | — |
| 482 | C2×C4 | — | 9 | 72 | no | — |
| 483 | C2×C4 | — | 9 | 18 | no | — |
| 484 | C2×C4 | — | 9 | 9 | no | — |
| 485 | C2×C4 | — | 9 | 18 | no | — |
| 486 | C2×C4 | — | 9 | 6 | no | — |
| 487 | C2×C4 | C22×D32 | 1 | 9 | yes | — |
| 488 | C2×C3 | — | 2 | 18 | no | — |
| 489 | C2×C3 | — | 2 | 1 | no | — |
| 490 | C2×C3 | — | 4 | 9 | no | — |
| 491 | C2×C3 | — | 6 | 18 | no | — |
| 492 | C2×C3 | — | 6 | 2 | no | — |
| 493 | C2×C3 | C25×D3 | 1 | 2 | yes | — |
| 494 | D3 | — | 2 | 2 | no | — |
| 495 | D3 | — | 2 | 18 | no | — |
| 496 | D3 | — | 6 | 12 | no | — |
| 497 | D3 | — | 12 | 6 | no | — |
| 498 | C22 | — | 3 | 2 | no | — |
| 499 | C22 | — | 3 | 18 | no | — |
| 500 | C22 | — | 4 | 6 | no | — |
| 501 | C22 | — | 9 | 6 | no | — |
| 502 | C22 | — | 12 | 18 | no | — |
| 503 | C22 | — | 12 | 36 | no | — |
| 504 | C22 | — | 36 | 9 | no | — |
| 505 | C22 | — | 36 | 36 | no | — |
| 506 | C22 | C23×D32 | 1 | 9 | yes | — |
| 507 | C4 | — | 3 | 12 | no | — |
| 508 | C4 | — | 9 | 9 | no | — |
| 509 | C4 | — | 9 | 1 | no | — |
| 510 | C4 | C23×D32 | 1 | 6 | yes | — |
| 511 | C3 | — | 2 | 1 | no | — |
| 512 | C3 | #87568 | 1 | 2 | yes | complemented |
| 513 | C2 | — | 2 | 9 | no | — |
| 514 | C2 | — | 6 | 2 | no | — |
| 515 | C2 | — | 6 | 18 | no | — |
| 516 | C2 | — | 18 | 6 | no | — |
| 517 | C2 | C24×D32 | 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