Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3158 conjugacy classes of subgroups.
The subgroup lattice has 522 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#909 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#5748 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #85735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#5526 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2873 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #78576 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #78564 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #78538 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #78531 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #60645 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C22×#235 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×#235 | C22 | 1 | 2 | yes | — |
| 13 | C23×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C3×M16 | C22 | 1 | 2 | yes | — |
| 15 | C2×C3×#117 | C22 | 1 | 1 | yes | characteristic |
| 16 | #5748 | — | 2 | 16 | no | — |
| 17 | C2×#909 | — | 2 | 16 | no | — |
| 18 | C2×#909 | C22 | 1 | 4 | yes | complemented |
| 19 | C2×#909 | C22 | 1 | 4 | yes | complemented |
| 20 | C2×#909 | C22 | 1 | 8 | yes | complemented |
| 21 | C2×#909 | C22 | 1 | 8 | yes | complemented |
| 22 | C2×#908 | C22 | 1 | 4 | yes | complemented |
| 23 | C2×#908 | C22 | 1 | 4 | yes | complemented |
| 24 | C22×Dic12 | C22 | 1 | 4 | yes | complemented |
| 25 | C2×#904 | C22 | 1 | 8 | yes | — |
| 26 | C22×#204 | C22 | 1 | 4 | yes | complemented |
| 27 | #5526 | — | 2 | 4 | no | — |
| 28 | #5526 | C22 | 1 | 8 | yes | complemented |
| 29 | #5526 | C22 | 1 | 4 | yes | complemented |
| 30 | #5525 | C22 | 1 | 4 | yes | complemented |
| 31 | #5524 | — | 2 | 4 | no | — |
| 32 | #5510 | — | 2 | 2 | no | — |
| 33 | C2×#897 | — | 2 | 2 | no | — |
| 34 | #5493 | — | 2 | 2 | no | — |
| 35 | C2×#886 | — | 2 | 2 | no | — |
| 36 | #5477 | C22 | 1 | 4 | yes | — |
| 37 | C2×#875 | C22 | 1 | 2 | yes | complemented |
| 38 | C2×#869 | C22 | 1 | 2 | yes | complemented |
| 39 | C3×#405 | C22 | 1 | 8 | yes | complemented |
| 40 | C3×C4×M16 | C22 | 1 | 4 | yes | complemented |
| 41 | #4715 | C22 | 1 | 8 | yes | complemented |
| 42 | #4715 | C22 | 1 | 16 | yes | complemented |
| 43 | #4712 | C22 | 1 | 8 | yes | complemented |
| 44 | #4699 | C22 | 1 | 8 | yes | complemented |
| 45 | #4696 | C22 | 1 | 16 | yes | complemented |
| 46 | #4693 | C22 | 1 | 8 | yes | complemented |
| 47 | C2×#575 | — | 3 | 2 | no | — |
| 48 | C22×#137 | — | 3 | 2 | no | — |
| 49 | #3449 | — | 3 | 1 | no | — |
| 50 | C2×#536 | — | 3 | 1 | no | — |
| 51 | #3156 | — | 3 | 8 | no | — |
| 52 | #3154 | — | 3 | 8 | no | — |
| 53 | #3153 | — | 3 | 4 | no | — |
| 54 | #3152 | — | 3 | 4 | no | — |
| 55 | #2873 | D3 | 1 | 1 | yes | characteristic, complemented |
| 56 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×#67 | — | 2 | 1 | no | — |
| 58 | C22×#67 | — | 2 | 2 | no | — |
| 59 | C23×Dic3 | — | 2 | 1 | no | — |
| 60 | C2×#235 | — | 2 | 2 | no | — |
| 61 | C2×#235 | — | 2 | 2 | no | — |
| 62 | C2×#235 | — | 2 | 2 | no | — |
| 63 | C2×#235 | — | 2 | 8 | no | — |
| 64 | C2×#235 | — | 2 | 8 | no | — |
| 65 | C2×#235 | — | 2 | 8 | no | — |
| 66 | C2×#235 | C23 | 1 | 4 | yes | — |
| 67 | C2×#235 | C23 | 1 | 4 | yes | — |
| 68 | C2×#235 | C23 | 1 | 4 | yes | — |
| 69 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×D12 | C23 | 1 | 2 | yes | — |
| 71 | C22×C4×D3 | — | 2 | 1 | no | — |
| 72 | C22×C4×D3 | — | 2 | 2 | no | — |
| 73 | C22×Dic6 | — | 2 | 8 | no | — |
| 74 | C22×Dic6 | — | 2 | 1 | no | — |
| 75 | C22×Dic6 | — | 2 | 2 | no | — |
| 76 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 77 | C22×Dic6 | C23 | 1 | 4 | yes | — |
| 78 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 79 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 80 | C2×C3×M16 | D4 | 1 | 16 | yes | complemented |
| 81 | C2×C3×M16 | C23 | 1 | 4 | yes | — |
| 82 | C2×C3×M16 | C23 | 1 | 4 | yes | — |
| 83 | C22×C3×C8 | C23 | 1 | 4 | yes | — |
| 84 | C3×#117 | D4 | 1 | 4 | yes | — |
| 85 | C3×#117 | C23 | 1 | 4 | yes | — |
| 86 | C2×C3×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 87 | C2×C3×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 88 | C2×C3×C42 | C23 | 1 | 2 | yes | — |
| 89 | #930 | — | 2 | 8 | no | — |
| 90 | C2×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 91 | C2×C4⋊Dic3 | — | 2 | 4 | no | — |
| 92 | #909 | — | 2 | 32 | no | — |
| 93 | #909 | — | 2 | 32 | no | — |
| 94 | #909 | — | 2 | 16 | no | — |
| 95 | #909 | — | 2 | 16 | no | — |
| 96 | #908 | — | 2 | 16 | no | — |
| 97 | #908 | — | 2 | 16 | no | — |
| 98 | C2×Dic12 | — | 2 | 16 | no | — |
| 99 | C2×Dic12 | C23 | 1 | 16 | yes | — |
| 100 | C2×Dic12 | C23 | 1 | 8 | yes | — |
| 101 | #904 | — | 2 | 32 | no | — |
| 102 | C2×D24 | C23 | 1 | 8 | yes | — |
| 103 | C2×#204 | — | 2 | 16 | no | — |
| 104 | C2×#204 | C23 | 1 | 8 | yes | — |
| 105 | C2×#204 | C23 | 1 | 16 | yes | — |
| 106 | C2×#204 | C23 | 1 | 8 | yes | — |
| 107 | #897 | — | 2 | 16 | no | — |
| 108 | #897 | — | 2 | 8 | no | — |
| 109 | #895 | — | 2 | 8 | no | — |
| 110 | #886 | — | 2 | 16 | no | — |
| 111 | #886 | — | 2 | 8 | no | — |
| 112 | #882 | — | 2 | 8 | no | — |
| 113 | #875 | — | 2 | 4 | no | — |
| 114 | #875 | C23 | 1 | 8 | yes | — |
| 115 | #875 | C23 | 1 | 8 | yes | — |
| 116 | #874 | C23 | 1 | 4 | yes | — |
| 117 | C4×D12 | — | 2 | 8 | no | — |
| 118 | #869 | — | 2 | 4 | no | — |
| 119 | #869 | C23 | 1 | 8 | yes | — |
| 120 | #869 | C23 | 1 | 4 | yes | — |
| 121 | C3×#97 | C23 | 1 | 8 | yes | — |
| 122 | C3×C4×C8 | C23 | 1 | 8 | yes | — |
| 123 | C22×#41 | — | 3 | 1 | no | — |
| 124 | C22×#41 | — | 3 | 2 | no | — |
| 125 | C23×Q8 | — | 3 | 1 | no | — |
| 126 | #575 | — | 6 | 16 | no | — |
| 127 | C2×#137 | — | 3 | 4 | no | — |
| 128 | C2×#137 | — | 3 | 8 | no | — |
| 129 | C2×#137 | — | 3 | 8 | no | — |
| 130 | C2×#137 | — | 3 | 4 | no | — |
| 131 | C2×#137 | — | 6 | 16 | no | — |
| 132 | C2×AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 133 | C2×AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 134 | C2×#135 | — | 3 | 8 | no | — |
| 135 | C22×Q16 | — | 3 | 4 | no | — |
| 136 | C22×SD16 | — | 3 | 4 | no | — |
| 137 | C22×M16 | C2×D3 | 1 | 2 | yes | — |
| 138 | #537 | — | 6 | 2 | no | — |
| 139 | #536 | — | 3 | 8 | no | — |
| 140 | #536 | — | 3 | 4 | no | — |
| 141 | #536 | — | 6 | 4 | no | — |
| 142 | #535 | — | 3 | 4 | no | — |
| 143 | #534 | — | 6 | 2 | no | — |
| 144 | #532 | — | 3 | 4 | no | — |
| 145 | C2×C4⋊Q8 | — | 3 | 2 | no | — |
| 146 | C2×#124 | — | 3 | 2 | no | — |
| 147 | #525 | — | 6 | 4 | no | — |
| 148 | C2×#123 | — | 6 | 2 | no | — |
| 149 | C2×C22⋊Q8 | — | 6 | 2 | no | — |
| 150 | C2×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 151 | #497 | — | 3 | 16 | no | — |
| 152 | #497 | — | 3 | 8 | no | — |
| 153 | #496 | — | 3 | 8 | no | — |
| 154 | #495 | — | 3 | 16 | no | — |
| 155 | #494 | — | 3 | 8 | no | — |
| 156 | #492 | — | 3 | 8 | no | — |
| 157 | #405 | C2×D3 | 1 | 8 | yes | complemented |
| 158 | C4×M16 | C2×D3 | 1 | 4 | yes | complemented |
| 159 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C23×D3 | — | 2 | 1 | no | — |
| 161 | C23×D3 | — | 2 | 2 | no | — |
| 162 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 163 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 165 | C22×C3×C4 | C2×D4 | 1 | 8 | yes | — |
| 166 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 167 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 168 | C2×#67 | — | 2 | 4 | no | — |
| 169 | C2×#67 | — | 2 | 4 | no | — |
| 170 | C2×#67 | — | 2 | 4 | no | — |
| 171 | C2×#67 | — | 4 | 8 | no | — |
| 172 | C2×#67 | — | 4 | 4 | no | — |
| 173 | C22×Dic3 | — | 2 | 4 | no | — |
| 174 | C22×Dic3 | — | 2 | 2 | no | — |
| 175 | C22×Dic3 | — | 2 | 1 | no | — |
| 176 | C22×Dic3 | — | 2 | 2 | no | — |
| 177 | C22×Dic3 | — | 4 | 4 | no | — |
| 178 | #235 | — | 2 | 8 | no | — |
| 179 | #235 | — | 2 | 8 | no | — |
| 180 | #235 | — | 2 | 8 | no | — |
| 181 | #235 | — | 2 | 8 | no | — |
| 182 | #235 | — | 2 | 8 | no | — |
| 183 | #235 | — | 2 | 8 | no | — |
| 184 | #235 | — | 4 | 8 | no | — |
| 185 | #235 | — | 4 | 8 | no | — |
| 186 | #235 | — | 4 | 8 | no | — |
| 187 | C2×D12 | — | 2 | 4 | no | — |
| 188 | C2×D12 | — | 2 | 4 | no | — |
| 189 | C2×D12 | — | 2 | 4 | no | — |
| 190 | C2×D12 | — | 2 | 1 | no | — |
| 191 | C2×D12 | — | 2 | 2 | no | — |
| 192 | C2×D12 | — | 2 | 8 | no | — |
| 193 | C2×D12 | C24 | 1 | 4 | yes | — |
| 194 | C2×D12 | C24 | 1 | 2 | yes | — |
| 195 | C2×C4×D3 | — | 2 | 4 | no | — |
| 196 | C2×C4×D3 | — | 2 | 4 | no | — |
| 197 | C2×C4×D3 | — | 2 | 4 | no | — |
| 198 | C2×C4×D3 | — | 4 | 4 | no | — |
| 199 | C2×C4×D3 | — | 4 | 8 | no | — |
| 200 | C2×Dic6 | — | 2 | 8 | no | — |
| 201 | C2×Dic6 | — | 2 | 4 | no | — |
| 202 | C2×Dic6 | — | 2 | 8 | no | — |
| 203 | C2×Dic6 | — | 2 | 8 | no | — |
| 204 | C2×Dic6 | — | 2 | 4 | no | — |
| 205 | C2×Dic6 | — | 2 | 4 | no | — |
| 206 | C2×Dic6 | — | 2 | 1 | no | — |
| 207 | C2×Dic6 | — | 2 | 2 | no | — |
| 208 | C2×Dic6 | — | 2 | 4 | no | — |
| 209 | C2×Dic6 | — | 2 | 2 | no | — |
| 210 | C2×Dic6 | — | 4 | 4 | no | — |
| 211 | C2×Dic6 | — | 4 | 8 | no | — |
| 212 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 213 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 214 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 215 | C3×M16 | C2×D4 | 1 | 16 | yes | — |
| 216 | C3×M16 | C2×D4 | 1 | 16 | yes | — |
| 217 | C2×C3×C8 | C2×D4 | 1 | 16 | yes | — |
| 218 | C2×C3×C8 | C24 | 1 | 8 | yes | — |
| 219 | C3×C4⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 220 | C3×C22⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 221 | C3×C42 | C2×D4 | 1 | 4 | yes | — |
| 222 | C3×C42 | C24 | 1 | 4 | yes | — |
| 223 | (C2×D3)⋊C4 | — | 2 | 16 | no | — |
| 224 | (C2×D3)⋊C4 | — | 2 | 16 | no | — |
| 225 | C4⋊Dic3 | — | 2 | 16 | no | — |
| 226 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 227 | Dic12 | — | 2 | 16 | no | — |
| 228 | Dic12 | — | 2 | 32 | no | — |
| 229 | D24 | — | 2 | 16 | no | — |
| 230 | #204 | — | 2 | 32 | no | — |
| 231 | #204 | — | 2 | 16 | no | — |
| 232 | #204 | — | 2 | 16 | no | — |
| 233 | C2×#41 | — | 3 | 4 | no | — |
| 234 | C2×#41 | — | 3 | 4 | no | — |
| 235 | C2×#41 | — | 3 | 4 | no | — |
| 236 | C2×#41 | — | 6 | 2 | no | — |
| 237 | C2×#41 | — | 6 | 2 | no | — |
| 238 | C2×#41 | — | 6 | 2 | no | — |
| 239 | C2×#41 | — | 6 | 8 | no | — |
| 240 | C2×#41 | — | 6 | 8 | no | — |
| 241 | C2×#41 | — | 6 | 8 | no | — |
| 242 | C22×Q8 | — | 3 | 2 | no | — |
| 243 | C22×Q8 | — | 3 | 1 | no | — |
| 244 | C22×Q8 | — | 3 | 4 | no | — |
| 245 | C22×Q8 | — | 3 | 2 | no | — |
| 246 | C22×Q8 | — | 6 | 1 | no | — |
| 247 | C22×Q8 | — | 6 | 2 | no | — |
| 248 | C22×Q8 | — | 6 | 8 | no | — |
| 249 | C22×D4 | — | 3 | 1 | no | — |
| 250 | C22×D4 | — | 3 | 2 | no | — |
| 251 | C22×D4 | — | 6 | 1 | no | — |
| 252 | C22×D4 | — | 6 | 2 | no | — |
| 253 | C23×C4 | — | 6 | 1 | no | — |
| 254 | C23×C4 | — | 6 | 1 | no | — |
| 255 | C23×C4 | — | 6 | 2 | no | — |
| 256 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 257 | #137 | — | 6 | 32 | no | — |
| 258 | #137 | — | 6 | 32 | no | — |
| 259 | #137 | — | 6 | 16 | no | — |
| 260 | #137 | — | 6 | 16 | no | — |
| 261 | AGL(1,ℤ/8) | — | 6 | 16 | no | — |
| 262 | AGL(1,ℤ/8) | — | 6 | 16 | no | — |
| 263 | #135 | — | 6 | 32 | no | — |
| 264 | C2×Q16 | — | 3 | 16 | no | — |
| 265 | C2×Q16 | — | 3 | 8 | no | — |
| 266 | C2×Q16 | — | 6 | 16 | no | — |
| 267 | C2×SD16 | — | 3 | 16 | no | — |
| 268 | C2×SD16 | — | 3 | 8 | no | — |
| 269 | C2×SD16 | — | 3 | 8 | no | — |
| 270 | C2×SD16 | — | 6 | 16 | no | — |
| 271 | C2×D8 | — | 3 | 8 | no | — |
| 272 | C2×M16 | D12 | 1 | 16 | yes | complemented |
| 273 | C2×M16 | C22×D3 | 1 | 4 | yes | — |
| 274 | C2×M16 | C22×D3 | 1 | 4 | yes | — |
| 275 | C22×C8 | C22×D3 | 1 | 4 | yes | — |
| 276 | C4⋊Q8 | — | 3 | 8 | no | — |
| 277 | C4⋊Q8 | — | 3 | 4 | no | — |
| 278 | C4⋊Q8 | — | 6 | 4 | no | — |
| 279 | #127 | — | 3 | 4 | no | — |
| 280 | #124 | — | 3 | 8 | no | — |
| 281 | #124 | — | 3 | 8 | no | — |
| 282 | #124 | — | 6 | 4 | no | — |
| 283 | #123 | — | 6 | 16 | no | — |
| 284 | #123 | — | 6 | 8 | no | — |
| 285 | C22⋊Q8 | — | 6 | 16 | no | — |
| 286 | C22⋊Q8 | — | 6 | 8 | no | — |
| 287 | #121 | — | 6 | 8 | no | — |
| 288 | #121 | — | 6 | 8 | no | — |
| 289 | #120 | — | 6 | 8 | no | — |
| 290 | C4×D4 | — | 6 | 8 | no | — |
| 291 | #117 | D12 | 1 | 4 | yes | — |
| 292 | #117 | C22×D3 | 1 | 4 | yes | — |
| 293 | C2×C4⋊C4 | — | 6 | 4 | no | — |
| 294 | C2×C4⋊C4 | D12 | 1 | 2 | yes | — |
| 295 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 296 | C2×C22⋊C4 | D12 | 1 | 2 | yes | — |
| 297 | C2×C42 | C22×D3 | 1 | 2 | yes | — |
| 298 | #97 | C22×D3 | 1 | 8 | yes | — |
| 299 | C4×C8 | C22×D3 | 1 | 8 | yes | — |
| 300 | C23×C3 | — | 4 | 2 | no | — |
| 301 | C23×C3 | #127 | 1 | 4 | yes | — |
| 302 | C23×C3 | C22×D4 | 1 | 2 | yes | — |
| 303 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 304 | C22×D3 | — | 2 | 2 | no | — |
| 305 | C22×D3 | — | 2 | 4 | no | — |
| 306 | C22×D3 | — | 4 | 4 | no | — |
| 307 | C22×D3 | — | 4 | 2 | no | — |
| 308 | C22×D3 | — | 4 | 4 | no | — |
| 309 | C22×D3 | — | 8 | 4 | no | — |
| 310 | C2×C3×C4 | — | 4 | 4 | no | — |
| 311 | C2×C3×C4 | #127 | 1 | 4 | yes | — |
| 312 | C2×C3×C4 | #127 | 1 | 8 | yes | — |
| 313 | C2×C3×C4 | C22×D4 | 1 | 8 | yes | — |
| 314 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 315 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 316 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 317 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 318 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 319 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 320 | #67 | — | 4 | 8 | no | — |
| 321 | #67 | — | 4 | 8 | no | — |
| 322 | #67 | — | 4 | 8 | no | — |
| 323 | C2×Dic3 | — | 2 | 2 | no | — |
| 324 | C2×Dic3 | — | 2 | 4 | no | — |
| 325 | C2×Dic3 | — | 2 | 4 | no | — |
| 326 | C2×Dic3 | — | 4 | 8 | no | — |
| 327 | C2×Dic3 | — | 4 | 4 | no | — |
| 328 | C2×Dic3 | — | 4 | 4 | no | — |
| 329 | C2×Dic3 | — | 4 | 2 | no | — |
| 330 | D12 | — | 2 | 4 | no | — |
| 331 | D12 | — | 2 | 4 | no | — |
| 332 | D12 | — | 2 | 4 | no | — |
| 333 | D12 | — | 4 | 4 | no | — |
| 334 | D12 | — | 4 | 2 | no | — |
| 335 | D12 | — | 8 | 8 | no | — |
| 336 | C4×D3 | — | 4 | 8 | no | — |
| 337 | C4×D3 | — | 4 | 8 | no | — |
| 338 | C4×D3 | — | 4 | 8 | no | — |
| 339 | Dic6 | — | 2 | 8 | no | — |
| 340 | Dic6 | — | 2 | 4 | no | — |
| 341 | Dic6 | — | 2 | 4 | no | — |
| 342 | Dic6 | — | 2 | 4 | no | — |
| 343 | Dic6 | — | 4 | 8 | no | — |
| 344 | Dic6 | — | 4 | 4 | no | — |
| 345 | Dic6 | — | 4 | 4 | no | — |
| 346 | Dic6 | — | 4 | 2 | no | — |
| 347 | C3×C8 | C22×D4 | 1 | 16 | yes | — |
| 348 | C24 | — | 6 | 1 | no | — |
| 349 | C24 | — | 6 | 2 | no | — |
| 350 | C24 | C2×D12 | 1 | 1 | yes | characteristic |
| 351 | #41 | — | 6 | 8 | no | — |
| 352 | #41 | — | 6 | 8 | no | — |
| 353 | #41 | — | 6 | 8 | no | — |
| 354 | #41 | — | 6 | 8 | no | — |
| 355 | #41 | — | 6 | 8 | no | — |
| 356 | #41 | — | 6 | 8 | no | — |
| 357 | #41 | — | 12 | 8 | no | — |
| 358 | #41 | — | 12 | 8 | no | — |
| 359 | #41 | — | 12 | 8 | no | — |
| 360 | C2×Q8 | — | 3 | 4 | no | — |
| 361 | C2×Q8 | — | 3 | 4 | no | — |
| 362 | C2×Q8 | — | 3 | 2 | no | — |
| 363 | C2×Q8 | — | 6 | 4 | no | — |
| 364 | C2×Q8 | — | 6 | 2 | no | — |
| 365 | C2×Q8 | — | 6 | 2 | no | — |
| 366 | C2×Q8 | — | 6 | 1 | no | — |
| 367 | C2×Q8 | — | 6 | 8 | no | — |
| 368 | C2×Q8 | — | 6 | 4 | no | — |
| 369 | C2×Q8 | — | 6 | 8 | no | — |
| 370 | C2×Q8 | — | 6 | 8 | no | — |
| 371 | C2×Q8 | — | 6 | 4 | no | — |
| 372 | C2×Q8 | — | 6 | 4 | no | — |
| 373 | C2×Q8 | — | 12 | 4 | no | — |
| 374 | C2×Q8 | — | 12 | 8 | no | — |
| 375 | C2×D4 | — | 3 | 2 | no | — |
| 376 | C2×D4 | — | 3 | 4 | no | — |
| 377 | C2×D4 | — | 6 | 4 | no | — |
| 378 | C2×D4 | — | 6 | 4 | no | — |
| 379 | C2×D4 | — | 6 | 4 | no | — |
| 380 | C2×D4 | — | 6 | 4 | no | — |
| 381 | C2×D4 | — | 6 | 4 | no | — |
| 382 | C2×D4 | — | 6 | 4 | no | — |
| 383 | C2×D4 | — | 6 | 2 | no | — |
| 384 | C2×D4 | — | 6 | 1 | no | — |
| 385 | C2×D4 | — | 6 | 8 | no | — |
| 386 | C2×D4 | — | 12 | 4 | no | — |
| 387 | C2×D4 | — | 12 | 8 | no | — |
| 388 | C22×C4 | — | 6 | 2 | no | — |
| 389 | C22×C4 | — | 6 | 1 | no | — |
| 390 | C22×C4 | — | 6 | 2 | no | — |
| 391 | C22×C4 | — | 6 | 4 | no | — |
| 392 | C22×C4 | — | 6 | 4 | no | — |
| 393 | C22×C4 | — | 6 | 4 | no | — |
| 394 | C22×C4 | — | 6 | 4 | no | — |
| 395 | C22×C4 | — | 12 | 4 | no | — |
| 396 | C22×C4 | — | 12 | 4 | no | — |
| 397 | C22×C4 | — | 12 | 8 | no | — |
| 398 | C22×C4 | C2×D12 | 1 | 4 | yes | — |
| 399 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 400 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 401 | C22×C4 | C2×D12 | 1 | 8 | yes | — |
| 402 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 403 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 404 | Q16 | — | 6 | 32 | no | — |
| 405 | Q16 | — | 6 | 16 | no | — |
| 406 | SD16 | — | 6 | 32 | no | — |
| 407 | SD16 | — | 6 | 16 | no | — |
| 408 | SD16 | — | 6 | 16 | no | — |
| 409 | D8 | — | 6 | 16 | no | — |
| 410 | M16 | C2×D12 | 1 | 16 | yes | — |
| 411 | M16 | C2×D12 | 1 | 16 | yes | — |
| 412 | C2×C8 | C2×D12 | 1 | 16 | yes | — |
| 413 | C2×C8 | C23×D3 | 1 | 8 | yes | — |
| 414 | C4⋊C4 | — | 6 | 16 | no | — |
| 415 | C4⋊C4 | — | 6 | 8 | no | — |
| 416 | C4⋊C4 | C2×D12 | 1 | 8 | yes | — |
| 417 | C22⋊C4 | — | 6 | 16 | no | — |
| 418 | C22⋊C4 | — | 6 | 16 | no | — |
| 419 | C22⋊C4 | C2×D12 | 1 | 8 | yes | — |
| 420 | C42 | C2×D12 | 1 | 4 | yes | — |
| 421 | C42 | C23×D3 | 1 | 4 | yes | — |
| 422 | C22×C3 | — | 2 | 2 | no | — |
| 423 | C22×C3 | — | 2 | 4 | no | — |
| 424 | C22×C3 | — | 4 | 4 | no | — |
| 425 | C22×C3 | C2×#127 | 1 | 4 | yes | — |
| 426 | C22×C3 | C2×#127 | 1 | 2 | yes | — |
| 427 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 428 | C2×D3 | — | 4 | 8 | no | — |
| 429 | C2×D3 | — | 4 | 4 | no | — |
| 430 | C2×D3 | — | 4 | 4 | no | — |
| 431 | C2×D3 | — | 4 | 2 | no | — |
| 432 | C2×D3 | — | 8 | 4 | no | — |
| 433 | C2×D3 | — | 8 | 8 | no | — |
| 434 | C3×C4 | — | 2 | 8 | no | — |
| 435 | C3×C4 | C2×#127 | 1 | 2 | yes | — |
| 436 | C3×C4 | C2×#127 | 1 | 4 | yes | — |
| 437 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 438 | Dic3 | — | 4 | 4 | no | — |
| 439 | Dic3 | — | 4 | 2 | no | — |
| 440 | Dic3 | — | 4 | 4 | no | — |
| 441 | C23 | — | 4 | 2 | no | — |
| 442 | C23 | — | 6 | 2 | no | — |
| 443 | C23 | — | 6 | 4 | no | — |
| 444 | C23 | — | 12 | 4 | no | — |
| 445 | C23 | — | 12 | 2 | no | — |
| 446 | C23 | — | 12 | 4 | no | — |
| 447 | C23 | — | 24 | 4 | no | — |
| 448 | C23 | #874 | 1 | 4 | yes | — |
| 449 | C23 | C22×D12 | 1 | 2 | yes | — |
| 450 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 451 | Q8 | — | 6 | 8 | no | — |
| 452 | Q8 | — | 6 | 4 | no | — |
| 453 | Q8 | — | 6 | 4 | no | — |
| 454 | Q8 | — | 6 | 4 | no | — |
| 455 | Q8 | — | 12 | 8 | no | — |
| 456 | Q8 | — | 12 | 4 | no | — |
| 457 | Q8 | — | 12 | 4 | no | — |
| 458 | Q8 | — | 12 | 2 | no | — |
| 459 | D4 | — | 6 | 4 | no | — |
| 460 | D4 | — | 6 | 4 | no | — |
| 461 | D4 | — | 6 | 4 | no | — |
| 462 | D4 | — | 12 | 8 | no | — |
| 463 | D4 | — | 12 | 8 | no | — |
| 464 | D4 | — | 12 | 8 | no | — |
| 465 | D4 | — | 12 | 4 | no | — |
| 466 | D4 | — | 12 | 2 | no | — |
| 467 | D4 | — | 24 | 8 | no | — |
| 468 | C2×C4 | — | 4 | 4 | no | — |
| 469 | C2×C4 | — | 6 | 4 | no | — |
| 470 | C2×C4 | — | 6 | 4 | no | — |
| 471 | C2×C4 | — | 6 | 2 | no | — |
| 472 | C2×C4 | — | 12 | 2 | no | — |
| 473 | C2×C4 | — | 12 | 4 | no | — |
| 474 | C2×C4 | — | 12 | 4 | no | — |
| 475 | C2×C4 | — | 12 | 8 | no | — |
| 476 | C2×C4 | — | 12 | 8 | no | — |
| 477 | C2×C4 | — | 12 | 8 | no | — |
| 478 | C2×C4 | — | 12 | 8 | no | — |
| 479 | C2×C4 | #874 | 1 | 4 | yes | — |
| 480 | C2×C4 | #874 | 1 | 8 | yes | — |
| 481 | C2×C4 | C22×D12 | 1 | 8 | yes | — |
| 482 | C2×C4 | C22×D12 | 1 | 4 | yes | — |
| 483 | C2×C4 | C22×D12 | 1 | 4 | yes | — |
| 484 | C2×C4 | C22×D12 | 1 | 4 | yes | — |
| 485 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 486 | C2×C4 | C22×D12 | 1 | 2 | yes | — |
| 487 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 488 | C8 | C22×D12 | 1 | 16 | yes | — |
| 489 | C2×C3 | — | 2 | 2 | no | — |
| 490 | C2×C3 | — | 2 | 4 | no | — |
| 491 | C2×C3 | C22×#127 | 1 | 1 | yes | characteristic |
| 492 | C2×C3 | #3586 | 1 | 2 | yes | — |
| 493 | D3 | — | 8 | 4 | no | — |
| 494 | D3 | — | 8 | 2 | no | — |
| 495 | C22 | — | 2 | 2 | no | — |
| 496 | C22 | — | 2 | 4 | no | — |
| 497 | C22 | — | 4 | 4 | no | — |
| 498 | C22 | — | 12 | 8 | no | — |
| 499 | C22 | — | 12 | 4 | no | — |
| 500 | C22 | — | 12 | 2 | no | — |
| 501 | C22 | — | 12 | 4 | no | — |
| 502 | C22 | — | 24 | 4 | no | — |
| 503 | C22 | — | 24 | 8 | no | — |
| 504 | C22 | C2×#874 | 1 | 4 | yes | — |
| 505 | C22 | C2×#874 | 1 | 2 | yes | — |
| 506 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 507 | C4 | — | 2 | 8 | no | — |
| 508 | C4 | — | 12 | 4 | no | — |
| 509 | C4 | — | 12 | 2 | no | — |
| 510 | C4 | — | 12 | 4 | no | — |
| 511 | C4 | C2×#874 | 1 | 4 | yes | — |
| 512 | C4 | C2×#874 | 1 | 2 | yes | — |
| 513 | C4 | C23×D12 | 1 | 2 | yes | — |
| 514 | C3 | #60645 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 515 | C2 | — | 2 | 2 | no | — |
| 516 | C2 | — | 2 | 4 | no | — |
| 517 | C2 | — | 24 | 4 | no | — |
| 518 | C2 | — | 24 | 2 | no | — |
| 519 | C2 | C22×#874 | 1 | 1 | yes | characteristic |
| 520 | C2 | #87168 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#909 | C2 | semidirect |
| 2. C2×#5748 | C2 | semidirect |
| 3. #85735 | C2 | semidirect |
| 4. C2×#5526 | C2 | semidirect |
| 5. C3×#2873 | C2 | semidirect |
| 6. #78576 | C2 | semidirect |
| 7. #78564 | C2 | semidirect |
| 8. #78538 | C2 | semidirect |
| 9. #78531 | C2 | semidirect |
| 18. C2×#909 | C22 | semidirect |
| 19. C2×#909 | C22 | semidirect |
| 20. C2×#909 | C22 | semidirect |
| 21. C2×#909 | C22 | semidirect |
| 22. C2×#908 | C22 | semidirect |
| 23. C2×#908 | C22 | semidirect |
| 24. C22×Dic12 | C22 | semidirect |
| 26. C22×#204 | C22 | semidirect |
| 28. #5526 | C22 | semidirect |
| 29. #5526 | C22 | semidirect |
| 30. #5525 | C22 | semidirect |
| 37. C2×#875 | C22 | semidirect |
| 38. C2×#869 | C22 | semidirect |
| 39. C3×#405 | C22 | semidirect |
| 40. C3×C4×M16 | C22 | semidirect |
| 41. #4715 | C22 | semidirect |
| 42. #4715 | C22 | semidirect |
| 43. #4712 | C22 | semidirect |
| 44. #4699 | C22 | semidirect |
| 45. #4696 | C22 | semidirect |
| 46. #4693 | C22 | semidirect |
| 55. #2873 | D3 | semidirect |
| 80. C2×C3×M16 | D4 | semidirect |
| 157. #405 | C2×D3 | semidirect |
| 158. C4×M16 | C2×D3 | semidirect |
| 272. C2×M16 | D12 | semidirect |
| 514. C3 | #60645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#909 | 2 |
| C2×#5748 | 2 |
| #85735 | 2 |
| C2×#5526 | 2 |
| C3×#2873 | 2 |
| #78576 | 2 |
| #78564 | 2 |
| #78538 | 2 |
| #78531 | 2 |
| #60645 | 3 |