← #11662506
Subgroups — #11662506
Order 768.
2824 conjugacy classes of subgroups.
The subgroup lattice has 532 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×C3×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87275 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#5752 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83802 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #83801 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #83799 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #83797 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #83785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #83772 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #83742 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×#5115 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #60458 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C22×C3×#41 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#1009 | C22 | 1 | 2 | yes | — |
| 15 | C2×C3×#131 | — | 2 | 8 | no | — |
| 16 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C3×#131 | C22 | 1 | 3 | yes | complemented |
| 19 | C2×C3×#131 | C22 | 1 | 3 | yes | complemented |
| 20 | C22×C3×M16 | C22 | 1 | 3 | yes | complemented |
| 21 | C23×C3×C8 | C22 | 1 | 3 | yes | complemented |
| 22 | #5834 | — | 2 | 2 | no | — |
| 23 | #5833 | C22 | 1 | 6 | yes | complemented |
| 24 | #5830 | C22 | 1 | 6 | yes | complemented |
| 25 | #5829 | — | 2 | 6 | no | — |
| 26 | #5827 | C22 | 1 | 2 | yes | — |
| 27 | #5817 | — | 2 | 2 | no | — |
| 28 | D4×#67 | — | 2 | 6 | no | — |
| 29 | #5791 | C22 | 1 | 6 | yes | complemented |
| 30 | C2×#930 | C22 | 1 | 6 | yes | complemented |
| 31 | #5752 | — | 2 | 8 | no | — |
| 32 | C2×#908 | C22 | 1 | 6 | yes | complemented |
| 33 | C2×#904 | C22 | 1 | 3 | yes | complemented |
| 34 | C22×D24 | C22 | 1 | 3 | yes | complemented |
| 35 | #5135 | C22 | 1 | 12 | yes | complemented |
| 36 | #5134 | C22 | 1 | 12 | yes | complemented |
| 37 | #5133 | C22 | 1 | 6 | yes | complemented |
| 38 | #5131 | C22 | 1 | 6 | yes | complemented |
| 39 | #5121 | C22 | 1 | 6 | yes | complemented |
| 40 | #5116 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #5116 | C22 | 1 | 3 | yes | complemented |
| 42 | #5115 | C22 | 1 | 3 | yes | complemented |
| 43 | #5115 | C22 | 1 | 6 | yes | complemented |
| 44 | #5115 | C22 | 1 | 6 | yes | complemented |
| 45 | #5115 | C22 | 1 | 6 | yes | complemented |
| 46 | #5115 | C22 | 1 | 3 | yes | complemented |
| 47 | #5114 | C22 | 1 | 6 | yes | complemented |
| 48 | #5114 | C22 | 1 | 6 | yes | complemented |
| 49 | #5113 | C22 | 1 | 6 | yes | complemented |
| 50 | C2×#821 | C22 | 1 | 6 | yes | complemented |
| 51 | #5106 | C22 | 1 | 3 | yes | complemented |
| 52 | C2×#818 | C22 | 1 | 3 | yes | complemented |
| 53 | C2×#576 | — | 3 | 1 | no | — |
| 54 | C22×#131 | D3 | 1 | 1 | yes | characteristic, complemented |
| 55 | #3488 | — | 3 | 2 | no | — |
| 56 | #3062 | — | 3 | 6 | no | — |
| 57 | #3061 | — | 3 | 3 | no | — |
| 58 | #3058 | — | 3 | 3 | no | — |
| 59 | #3055 | — | 3 | 6 | no | — |
| 60 | #3050 | — | 3 | 3 | no | — |
| 61 | C2×#466 | — | 3 | 3 | no | — |
| 62 | #2913 | — | 3 | 1 | no | — |
| 63 | #2897 | — | 3 | 2 | no | — |
| 64 | C2×C3×#41 | — | 2 | 4 | no | — |
| 65 | C2×C3×#41 | — | 2 | 4 | no | — |
| 66 | C2×C3×#41 | D4 | 1 | 3 | yes | — |
| 67 | C2×C3×#41 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 69 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 71 | C22×C3×D4 | D4 | 1 | 3 | yes | — |
| 72 | C23×C3×C4 | C23 | 1 | 3 | yes | — |
| 73 | C22×#67 | — | 2 | 6 | no | — |
| 74 | #1009 | — | 2 | 8 | no | — |
| 75 | #1009 | — | 2 | 8 | no | — |
| 76 | C2×#239 | — | 2 | 2 | no | — |
| 77 | C2×D3×D4 | — | 2 | 6 | no | — |
| 78 | C2×#235 | C23 | 1 | 6 | yes | — |
| 79 | C22×D12 | C23 | 1 | 6 | yes | — |
| 80 | C3×#131 | — | 2 | 4 | no | — |
| 81 | C3×#131 | — | 2 | 12 | no | — |
| 82 | C3×#131 | — | 2 | 12 | no | — |
| 83 | C3×#131 | D4 | 1 | 8 | yes | complemented |
| 84 | C2×C3×M16 | — | 2 | 12 | no | — |
| 85 | C2×C3×M16 | C23 | 1 | 3 | yes | — |
| 86 | C2×C3×M16 | C23 | 1 | 6 | yes | — |
| 87 | C2×C3×M16 | C23 | 1 | 3 | yes | — |
| 88 | C22×C3×C8 | — | 2 | 12 | no | — |
| 89 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 91 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 92 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 93 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 94 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 95 | #953 | — | 2 | 6 | no | — |
| 96 | #947 | — | 2 | 6 | no | — |
| 97 | #946 | — | 2 | 6 | no | — |
| 98 | Q8×Dic3 | — | 2 | 2 | no | — |
| 99 | #940 | — | 2 | 6 | no | — |
| 100 | #939 | — | 2 | 12 | no | — |
| 101 | #938 | — | 2 | 6 | no | — |
| 102 | #937 | — | 2 | 12 | no | — |
| 103 | D4×Dic3 | — | 2 | 6 | no | — |
| 104 | #930 | — | 2 | 6 | no | — |
| 105 | #930 | — | 2 | 6 | no | — |
| 106 | #930 | C23 | 1 | 12 | yes | — |
| 107 | #930 | C23 | 1 | 6 | yes | — |
| 108 | #930 | C23 | 1 | 6 | yes | — |
| 109 | #929 | — | 2 | 6 | no | — |
| 110 | C4×#67 | — | 2 | 6 | no | — |
| 111 | C4×#67 | — | 2 | 6 | no | — |
| 112 | C2×(C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 113 | #926 | C23 | 1 | 6 | yes | — |
| 114 | C2×C4⋊Dic3 | C23 | 1 | 6 | yes | — |
| 115 | #924 | C23 | 1 | 6 | yes | — |
| 116 | #924 | C23 | 1 | 2 | yes | — |
| 117 | #908 | — | 2 | 24 | no | — |
| 118 | C2×Dic12 | C23 | 1 | 1 | yes | characteristic |
| 119 | #904 | — | 2 | 12 | no | — |
| 120 | C2×D24 | — | 2 | 12 | no | — |
| 121 | C2×D24 | C23 | 1 | 6 | yes | — |
| 122 | C2×D24 | C23 | 1 | 3 | yes | — |
| 123 | C2×#204 | C23 | 1 | 6 | yes | — |
| 124 | #821 | C23 | 1 | 6 | yes | — |
| 125 | #821 | C23 | 1 | 12 | yes | — |
| 126 | #821 | C23 | 1 | 6 | yes | — |
| 127 | #818 | C23 | 1 | 6 | yes | — |
| 128 | #818 | C23 | 1 | 3 | yes | — |
| 129 | #818 | C23 | 1 | 1 | yes | characteristic |
| 130 | #817 | C23 | 1 | 6 | yes | — |
| 131 | #816 | C23 | 1 | 6 | yes | — |
| 132 | #816 | C23 | 1 | 2 | yes | — |
| 133 | C2×H(5,𝔽2) | — | 3 | 2 | no | — |
| 134 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 135 | #576 | — | 6 | 8 | no | — |
| 136 | C2×AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 137 | C2×#135 | — | 3 | 3 | no | — |
| 138 | C22×D8 | — | 3 | 3 | no | — |
| 139 | C2×#131 | — | 2 | 8 | no | — |
| 140 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 141 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 142 | C2×#131 | C2×D3 | 1 | 3 | yes | complemented |
| 143 | C2×#131 | C2×D3 | 1 | 3 | yes | complemented |
| 144 | C22×M16 | C2×D3 | 1 | 3 | yes | complemented |
| 145 | C23×C8 | C2×D3 | 1 | 3 | yes | complemented |
| 146 | #550 | — | 6 | 2 | no | — |
| 147 | #548 | — | 6 | 2 | no | — |
| 148 | #546 | — | 6 | 6 | no | — |
| 149 | D42 | — | 6 | 6 | no | — |
| 150 | #537 | — | 3 | 6 | no | — |
| 151 | #535 | — | 3 | 6 | no | — |
| 152 | #525 | — | 3 | 6 | no | — |
| 153 | C2×#121 | — | 3 | 6 | no | — |
| 154 | #520 | — | 3 | 2 | no | — |
| 155 | #469 | — | 3 | 12 | no | — |
| 156 | #468 | — | 3 | 12 | no | — |
| 157 | #467 | — | 3 | 1 | no | — |
| 158 | #467 | — | 3 | 3 | no | — |
| 159 | #466 | — | 3 | 3 | no | — |
| 160 | #466 | — | 3 | 6 | no | — |
| 161 | #466 | — | 3 | 6 | no | — |
| 162 | #466 | — | 3 | 6 | no | — |
| 163 | #466 | — | 3 | 3 | no | — |
| 164 | #465 | — | 3 | 6 | no | — |
| 165 | #465 | — | 3 | 6 | no | — |
| 166 | #428 | — | 3 | 6 | no | — |
| 167 | #427 | — | 3 | 3 | no | — |
| 168 | C2×#107 | — | 3 | 3 | no | — |
| 169 | #418 | — | 3 | 6 | no | — |
| 170 | #417 | — | 3 | 6 | no | — |
| 171 | #416 | — | 3 | 6 | no | — |
| 172 | C2×#102 | — | 3 | 6 | no | — |
| 173 | C24×C3 | C2×D4 | 1 | 3 | yes | — |
| 174 | C23×D3 | — | 2 | 6 | no | — |
| 175 | C3×#41 | — | 2 | 4 | no | — |
| 176 | C3×#41 | — | 2 | 12 | no | — |
| 177 | C3×#41 | — | 2 | 6 | no | — |
| 178 | C3×#41 | — | 2 | 6 | no | — |
| 179 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 180 | C3×#41 | #41 | 1 | 4 | yes | — |
| 181 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 182 | C2×C3×Q8 | C2×D4 | 1 | 3 | yes | — |
| 183 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C3×D4 | — | 2 | 12 | no | — |
| 185 | C2×C3×D4 | C2×D4 | 1 | 6 | yes | — |
| 186 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 187 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 188 | C22×C3×C4 | — | 2 | 6 | no | — |
| 189 | C22×C3×C4 | — | 2 | 6 | no | — |
| 190 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 191 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 192 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 193 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 194 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 195 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 196 | C2×#67 | — | 2 | 6 | no | — |
| 197 | C2×#67 | — | 2 | 6 | no | — |
| 198 | C2×#67 | — | 2 | 6 | no | — |
| 199 | C2×#67 | — | 2 | 12 | no | — |
| 200 | C2×#67 | — | 8 | 12 | no | — |
| 201 | C22×Dic3 | — | 2 | 6 | no | — |
| 202 | #239 | — | 4 | 8 | no | — |
| 203 | D3×D4 | — | 4 | 24 | no | — |
| 204 | #235 | — | 2 | 12 | no | — |
| 205 | #235 | — | 2 | 12 | no | — |
| 206 | C2×D12 | — | 2 | 12 | no | — |
| 207 | C2×D12 | — | 2 | 12 | no | — |
| 208 | C2×D12 | — | 2 | 6 | no | — |
| 209 | C2×D12 | C24 | 1 | 6 | yes | — |
| 210 | C2×C4×D3 | — | 2 | 6 | no | — |
| 211 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 212 | C3×M16 | — | 2 | 6 | no | — |
| 213 | C3×M16 | — | 2 | 12 | no | — |
| 214 | C3×M16 | C2×D4 | 1 | 12 | yes | complemented |
| 215 | C2×C3×C8 | — | 2 | 6 | no | — |
| 216 | C2×C3×C8 | — | 2 | 2 | no | — |
| 217 | C2×C3×C8 | — | 2 | 6 | no | — |
| 218 | C2×C3×C8 | — | 2 | 6 | no | — |
| 219 | C2×C3×C8 | — | 2 | 6 | no | — |
| 220 | C2×C3×C8 | C2×D4 | 1 | 12 | yes | complemented |
| 221 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 222 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 223 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 224 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 225 | #217 | — | 2 | 2 | no | — |
| 226 | #217 | — | 2 | 6 | no | — |
| 227 | #217 | — | 2 | 6 | no | — |
| 228 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 229 | (C2×D3)⋊C4 | — | 2 | 12 | no | — |
| 230 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 231 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 232 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 233 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 234 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 235 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 236 | C4×Dic3 | — | 2 | 6 | no | — |
| 237 | Dic12 | — | 2 | 2 | no | — |
| 238 | D24 | — | 2 | 6 | no | — |
| 239 | D24 | — | 2 | 12 | no | — |
| 240 | #204 | — | 2 | 12 | no | — |
| 241 | H(5,𝔽2) | — | 6 | 8 | no | — |
| 242 | H(5,𝔽2) | — | 6 | 8 | no | — |
| 243 | C2×#41 | — | 2 | 4 | no | — |
| 244 | C2×#41 | — | 2 | 4 | no | — |
| 245 | C2×#41 | — | 3 | 6 | no | — |
| 246 | C2×#41 | — | 6 | 2 | no | — |
| 247 | C2×#41 | D12 | 1 | 3 | yes | — |
| 248 | C2×#41 | D12 | 1 | 1 | yes | characteristic |
| 249 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 250 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 251 | C22×Q8 | D12 | 1 | 1 | yes | characteristic |
| 252 | C22×D4 | — | 3 | 6 | no | — |
| 253 | C22×D4 | — | 6 | 6 | no | — |
| 254 | C22×D4 | — | 6 | 6 | no | — |
| 255 | C22×D4 | D12 | 1 | 3 | yes | — |
| 256 | C23×C4 | C22×D3 | 1 | 3 | yes | — |
| 257 | AGL(1,ℤ/8) | — | 6 | 24 | no | — |
| 258 | #135 | — | 6 | 12 | no | — |
| 259 | C2×Q16 | — | 3 | 1 | no | — |
| 260 | C2×SD16 | — | 3 | 6 | no | — |
| 261 | C2×D8 | — | 3 | 3 | no | — |
| 262 | C2×D8 | — | 3 | 6 | no | — |
| 263 | C2×D8 | — | 6 | 12 | no | — |
| 264 | #131 | — | 2 | 4 | no | — |
| 265 | #131 | — | 2 | 12 | no | — |
| 266 | #131 | — | 2 | 12 | no | — |
| 267 | #131 | #67 | 1 | 8 | yes | complemented |
| 268 | C2×M16 | — | 2 | 12 | no | — |
| 269 | C2×M16 | C22×D3 | 1 | 3 | yes | — |
| 270 | C2×M16 | C22×D3 | 1 | 6 | yes | — |
| 271 | C2×M16 | C22×D3 | 1 | 3 | yes | — |
| 272 | C22×C8 | — | 2 | 12 | no | — |
| 273 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 274 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 275 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 276 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 277 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 278 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 279 | #127 | — | 6 | 6 | no | — |
| 280 | #124 | — | 6 | 6 | no | — |
| 281 | #123 | — | 6 | 6 | no | — |
| 282 | C22⋊Q8 | — | 3 | 2 | no | — |
| 283 | C22⋊Q8 | — | 3 | 6 | no | — |
| 284 | C22⋊Q8 | — | 6 | 6 | no | — |
| 285 | #121 | — | 3 | 6 | no | — |
| 286 | #121 | — | 3 | 12 | no | — |
| 287 | #121 | — | 3 | 6 | no | — |
| 288 | #121 | — | 6 | 12 | no | — |
| 289 | #121 | — | 6 | 6 | no | — |
| 290 | #121 | — | 6 | 6 | no | — |
| 291 | #121 | — | 6 | 6 | no | — |
| 292 | #120 | — | 6 | 6 | no | — |
| 293 | #120 | — | 6 | 12 | no | — |
| 294 | C4×Q8 | — | 6 | 2 | no | — |
| 295 | C4×D4 | — | 6 | 6 | no | — |
| 296 | C4×D4 | — | 6 | 6 | no | — |
| 297 | C4×D4 | — | 6 | 6 | no | — |
| 298 | #117 | — | 3 | 6 | no | — |
| 299 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 300 | C2×C22⋊C4 | — | 6 | 6 | no | — |
| 301 | #107 | — | 3 | 3 | no | — |
| 302 | #107 | — | 3 | 6 | no | — |
| 303 | #107 | — | 3 | 1 | no | — |
| 304 | #106 | — | 3 | 6 | no | — |
| 305 | #103 | — | 3 | 2 | no | — |
| 306 | #103 | — | 3 | 6 | no | — |
| 307 | #102 | — | 3 | 6 | no | — |
| 308 | #102 | — | 3 | 12 | no | — |
| 309 | #102 | — | 3 | 6 | no | — |
| 310 | C23×C3 | — | 2 | 6 | no | — |
| 311 | C23×C3 | — | 2 | 6 | no | — |
| 312 | C23×C3 | — | 4 | 3 | no | — |
| 313 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 314 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 315 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 316 | C22×D3 | — | 2 | 6 | no | — |
| 317 | C22×D3 | — | 4 | 12 | no | — |
| 318 | C22×D3 | — | 8 | 6 | no | — |
| 319 | C22×D3 | — | 8 | 6 | no | — |
| 320 | C3×Q8 | — | 2 | 6 | no | — |
| 321 | C3×Q8 | #121 | 1 | 4 | yes | — |
| 322 | C3×D4 | — | 2 | 12 | no | — |
| 323 | C3×D4 | — | 2 | 6 | no | — |
| 324 | C3×D4 | #121 | 1 | 12 | yes | — |
| 325 | C2×C3×C4 | — | 2 | 6 | no | — |
| 326 | C2×C3×C4 | — | 2 | 6 | no | — |
| 327 | C2×C3×C4 | — | 2 | 6 | no | — |
| 328 | C2×C3×C4 | — | 2 | 1 | no | — |
| 329 | C2×C3×C4 | — | 2 | 3 | no | — |
| 330 | C2×C3×C4 | — | 2 | 1 | no | — |
| 331 | C2×C3×C4 | — | 2 | 3 | no | — |
| 332 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 333 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 334 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 335 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 336 | C2×C3×C4 | C2×#41 | 1 | 6 | yes | — |
| 337 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 338 | #67 | — | 4 | 12 | no | — |
| 339 | #67 | — | 4 | 12 | no | — |
| 340 | #67 | — | 8 | 6 | no | — |
| 341 | #67 | — | 8 | 12 | no | — |
| 342 | C2×Dic3 | — | 2 | 2 | no | — |
| 343 | C2×Dic3 | — | 2 | 6 | no | — |
| 344 | C2×Dic3 | — | 2 | 2 | no | — |
| 345 | C2×Dic3 | — | 8 | 6 | no | — |
| 346 | D12 | — | 2 | 6 | no | — |
| 347 | D12 | — | 2 | 6 | no | — |
| 348 | D12 | — | 4 | 12 | no | — |
| 349 | C4×D3 | — | 4 | 12 | no | — |
| 350 | Dic6 | — | 2 | 2 | no | — |
| 351 | Dic6 | — | 2 | 2 | no | — |
| 352 | C3×C8 | — | 2 | 1 | no | — |
| 353 | C3×C8 | — | 2 | 3 | no | — |
| 354 | C3×C8 | C22×D4 | 1 | 6 | yes | — |
| 355 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 356 | C24 | — | 6 | 6 | no | — |
| 357 | C24 | C2×D12 | 1 | 3 | yes | — |
| 358 | #41 | — | 2 | 4 | no | — |
| 359 | #41 | — | 2 | 12 | no | — |
| 360 | #41 | — | 2 | 6 | no | — |
| 361 | #41 | — | 2 | 6 | no | — |
| 362 | #41 | — | 6 | 12 | no | — |
| 363 | #41 | — | 6 | 12 | no | — |
| 364 | #41 | — | 12 | 8 | no | — |
| 365 | #41 | #235 | 1 | 4 | yes | — |
| 366 | #41 | C2×#67 | 1 | 4 | yes | — |
| 367 | C2×Q8 | — | 2 | 4 | no | — |
| 368 | C2×Q8 | — | 3 | 2 | no | — |
| 369 | C2×Q8 | C2×D12 | 1 | 3 | yes | — |
| 370 | C2×Q8 | C2×D12 | 1 | 1 | yes | characteristic |
| 371 | C2×D4 | — | 2 | 12 | no | — |
| 372 | C2×D4 | — | 3 | 6 | no | — |
| 373 | C2×D4 | — | 6 | 6 | no | — |
| 374 | C2×D4 | — | 6 | 6 | no | — |
| 375 | C2×D4 | — | 6 | 6 | no | — |
| 376 | C2×D4 | — | 6 | 12 | no | — |
| 377 | C2×D4 | — | 6 | 6 | no | — |
| 378 | C2×D4 | — | 6 | 12 | no | — |
| 379 | C2×D4 | — | 6 | 12 | no | — |
| 380 | C2×D4 | — | 12 | 24 | no | — |
| 381 | C2×D4 | — | 24 | 12 | no | — |
| 382 | C2×D4 | C2×D12 | 1 | 6 | yes | — |
| 383 | C2×D4 | C2×D12 | 1 | 3 | yes | — |
| 384 | C2×D4 | C2×D12 | 1 | 3 | yes | — |
| 385 | C22×C4 | — | 2 | 6 | no | — |
| 386 | C22×C4 | — | 2 | 6 | no | — |
| 387 | C22×C4 | — | 6 | 6 | no | — |
| 388 | C22×C4 | — | 6 | 6 | no | — |
| 389 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 390 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 391 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 392 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 393 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 394 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 395 | Q16 | — | 6 | 2 | no | — |
| 396 | SD16 | — | 6 | 12 | no | — |
| 397 | D8 | — | 6 | 6 | no | — |
| 398 | D8 | — | 6 | 12 | no | — |
| 399 | M16 | — | 2 | 6 | no | — |
| 400 | M16 | — | 2 | 12 | no | — |
| 401 | M16 | C2×#67 | 1 | 12 | yes | complemented |
| 402 | C2×C8 | — | 2 | 6 | no | — |
| 403 | C2×C8 | — | 2 | 2 | no | — |
| 404 | C2×C8 | — | 2 | 6 | no | — |
| 405 | C2×C8 | — | 2 | 6 | no | — |
| 406 | C2×C8 | — | 2 | 6 | no | — |
| 407 | C2×C8 | C2×#67 | 1 | 12 | yes | complemented |
| 408 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 409 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 410 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 411 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 412 | C4⋊C4 | — | 3 | 2 | no | — |
| 413 | C4⋊C4 | — | 3 | 6 | no | — |
| 414 | C4⋊C4 | — | 6 | 6 | no | — |
| 415 | C4⋊C4 | — | 6 | 2 | no | — |
| 416 | C4⋊C4 | — | 6 | 6 | no | — |
| 417 | C22⋊C4 | — | 6 | 6 | no | — |
| 418 | C22⋊C4 | — | 6 | 2 | no | — |
| 419 | C22⋊C4 | — | 6 | 6 | no | — |
| 420 | C22⋊C4 | — | 6 | 6 | no | — |
| 421 | C22⋊C4 | — | 6 | 12 | no | — |
| 422 | C22⋊C4 | — | 6 | 6 | no | — |
| 423 | C42 | — | 6 | 6 | no | — |
| 424 | C22×C3 | — | 2 | 3 | no | — |
| 425 | C22×C3 | — | 2 | 1 | no | — |
| 426 | C22×C3 | — | 2 | 1 | no | — |
| 427 | C22×C3 | — | 2 | 3 | no | — |
| 428 | C22×C3 | — | 2 | 3 | no | — |
| 429 | C22×C3 | — | 2 | 3 | no | — |
| 430 | C22×C3 | — | 2 | 3 | no | — |
| 431 | C22×C3 | — | 4 | 12 | no | — |
| 432 | C22×C3 | C2×#121 | 1 | 6 | yes | — |
| 433 | C22×C3 | #576 | 1 | 2 | yes | complemented |
| 434 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 435 | C2×D3 | — | 4 | 6 | no | — |
| 436 | C2×D3 | — | 4 | 6 | no | — |
| 437 | C2×D3 | — | 4 | 6 | no | — |
| 438 | C2×D3 | — | 16 | 12 | no | — |
| 439 | C3×C4 | — | 2 | 1 | no | — |
| 440 | C3×C4 | — | 2 | 3 | no | — |
| 441 | C3×C4 | C2×#121 | 1 | 6 | yes | — |
| 442 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 443 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 444 | Dic3 | — | 4 | 2 | no | — |
| 445 | Dic3 | — | 4 | 2 | no | — |
| 446 | Dic3 | — | 4 | 6 | no | — |
| 447 | C23 | — | 2 | 6 | no | — |
| 448 | C23 | — | 2 | 6 | no | — |
| 449 | C23 | — | 4 | 3 | no | — |
| 450 | C23 | — | 6 | 6 | no | — |
| 451 | C23 | — | 12 | 12 | no | — |
| 452 | C23 | — | 24 | 6 | no | — |
| 453 | C23 | — | 24 | 6 | no | — |
| 454 | C23 | C22×D12 | 1 | 3 | yes | — |
| 455 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 456 | C23 | C22×D12 | 1 | 3 | yes | — |
| 457 | Q8 | — | 2 | 6 | no | — |
| 458 | Q8 | — | 6 | 2 | no | — |
| 459 | Q8 | — | 6 | 2 | no | — |
| 460 | Q8 | #930 | 1 | 4 | yes | — |
| 461 | D4 | — | 2 | 12 | no | — |
| 462 | D4 | — | 2 | 6 | no | — |
| 463 | D4 | — | 6 | 6 | no | — |
| 464 | D4 | — | 6 | 6 | no | — |
| 465 | D4 | — | 12 | 12 | no | — |
| 466 | D4 | — | 12 | 12 | no | — |
| 467 | D4 | — | 12 | 12 | no | — |
| 468 | D4 | — | 24 | 12 | no | — |
| 469 | D4 | — | 24 | 6 | no | — |
| 470 | D4 | #930 | 1 | 12 | yes | — |
| 471 | C2×C4 | — | 2 | 6 | no | — |
| 472 | C2×C4 | — | 2 | 1 | no | — |
| 473 | C2×C4 | — | 2 | 3 | no | — |
| 474 | C2×C4 | — | 2 | 1 | no | — |
| 475 | C2×C4 | — | 2 | 3 | no | — |
| 476 | C2×C4 | — | 2 | 6 | no | — |
| 477 | C2×C4 | — | 2 | 6 | no | — |
| 478 | C2×C4 | — | 6 | 2 | no | — |
| 479 | C2×C4 | — | 6 | 6 | no | — |
| 480 | C2×C4 | — | 6 | 2 | no | — |
| 481 | C2×C4 | — | 12 | 12 | no | — |
| 482 | C2×C4 | — | 24 | 6 | no | — |
| 483 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 484 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 485 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 486 | C2×C4 | C2×#235 | 1 | 6 | yes | — |
| 487 | C2×C4 | C22×#67 | 1 | 6 | yes | — |
| 488 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 489 | C8 | — | 2 | 1 | no | — |
| 490 | C8 | — | 2 | 3 | no | — |
| 491 | C8 | C22×#67 | 1 | 2 | yes | — |
| 492 | C8 | C22×#67 | 1 | 6 | yes | — |
| 493 | C2×C3 | — | 2 | 6 | no | — |
| 494 | C2×C3 | — | 2 | 2 | no | — |
| 495 | C2×C3 | — | 4 | 3 | no | — |
| 496 | C2×C3 | C22×#121 | 1 | 1 | yes | characteristic |
| 497 | C2×C3 | C2×#576 | 1 | 1 | yes | characteristic |
| 498 | C2×C3 | #3584 | 1 | 1 | yes | characteristic |
| 499 | D3 | — | 8 | 6 | no | — |
| 500 | C22 | — | 2 | 3 | no | — |
| 501 | C22 | — | 2 | 1 | no | — |
| 502 | C22 | — | 2 | 3 | no | — |
| 503 | C22 | — | 2 | 1 | no | — |
| 504 | C22 | — | 2 | 3 | no | — |
| 505 | C22 | — | 2 | 3 | no | — |
| 506 | C22 | — | 2 | 3 | no | — |
| 507 | C22 | — | 4 | 12 | no | — |
| 508 | C22 | — | 12 | 6 | no | — |
| 509 | C22 | — | 12 | 6 | no | — |
| 510 | C22 | — | 12 | 6 | no | — |
| 511 | C22 | — | 48 | 12 | no | — |
| 512 | C22 | #5752 | 1 | 2 | yes | complemented |
| 513 | C22 | C2×#930 | 1 | 6 | yes | — |
| 514 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 515 | C4 | — | 2 | 1 | no | — |
| 516 | C4 | — | 2 | 3 | no | — |
| 517 | C4 | — | 12 | 6 | no | — |
| 518 | C4 | — | 12 | 2 | no | — |
| 519 | C4 | — | 12 | 2 | no | — |
| 520 | C4 | C2×#930 | 1 | 6 | yes | — |
| 521 | C4 | C22×#235 | 1 | 1 | yes | characteristic |
| 522 | C4 | C23×#67 | 1 | 1 | yes | characteristic |
| 523 | C3 | #60458 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 524 | C2 | — | 2 | 2 | no | — |
| 525 | C2 | — | 2 | 6 | no | — |
| 526 | C2 | — | 4 | 3 | no | — |
| 527 | C2 | — | 24 | 6 | no | — |
| 528 | C2 | C2×#5752 | 1 | 1 | yes | characteristic |
| 529 | C2 | #87163 | 1 | 1 | yes | characteristic |
| 530 | C2 | C22×#930 | 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