Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2206 conjugacy classes of subgroups.
The subgroup lattice has 416 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5525 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #85725 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#2873 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83768 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#5131 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #78563 | C2 | 1 | 16 | yes | maximal, complemented |
| 7 | #78527 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #78526 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #60619 | — | 3 | 1 | no | maximal, Sylow |
| 10 | C22×#235 | C22 | 1 | 1 | yes | characteristic |
| 11 | C23×D12 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×C3×M16 | C22 | 1 | 2 | yes | — |
| 13 | C2×C3×#117 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#926 | C22 | 1 | 2 | yes | — |
| 15 | #5525 | — | 2 | 4 | no | — |
| 16 | #5525 | C22 | 1 | 8 | yes | — |
| 17 | #5519 | C22 | 1 | 8 | yes | complemented |
| 18 | #5517 | — | 2 | 4 | no | — |
| 19 | C2×#895 | — | 2 | 2 | no | — |
| 20 | #5500 | — | 2 | 2 | no | — |
| 21 | C2×#882 | — | 2 | 2 | no | — |
| 22 | #5483 | — | 2 | 2 | no | — |
| 23 | C2×#875 | C22 | 1 | 2 | yes | — |
| 24 | C2×#874 | C22 | 1 | 2 | yes | — |
| 25 | #5470 | C22 | 1 | 4 | yes | complemented |
| 26 | C3×#405 | C22 | 1 | 8 | yes | complemented |
| 27 | C3×C4×M16 | C22 | 1 | 4 | yes | complemented |
| 28 | #5133 | C22 | 1 | 8 | yes | complemented |
| 29 | #5131 | C22 | 1 | 8 | yes | — |
| 30 | #5131 | C22 | 1 | 8 | yes | complemented |
| 31 | #5131 | C22 | 1 | 4 | yes | complemented |
| 32 | #5120 | C22 | 1 | 4 | yes | complemented |
| 33 | #5113 | C22 | 1 | 8 | yes | complemented |
| 34 | C2×#821 | C22 | 1 | 8 | yes | complemented |
| 35 | #4714 | C22 | 1 | 16 | yes | complemented |
| 36 | #4713 | C22 | 1 | 16 | yes | complemented |
| 37 | #4697 | C22 | 1 | 16 | yes | complemented |
| 38 | #4694 | C22 | 1 | 16 | yes | complemented |
| 39 | #3458 | — | 3 | 1 | no | — |
| 40 | C2×#535 | — | 3 | 1 | no | — |
| 41 | #3140 | — | 3 | 4 | no | — |
| 42 | #3138 | — | 3 | 4 | no | — |
| 43 | #3136 | — | 3 | 16 | no | — |
| 44 | #2896 | — | 3 | 2 | no | — |
| 45 | C2×#418 | — | 3 | 2 | no | — |
| 46 | #2873 | D3 | 1 | 1 | yes | characteristic, complemented |
| 47 | C24×D3 | — | 2 | 1 | no | — |
| 48 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×#67 | — | 2 | 1 | no | — |
| 50 | C2×#235 | — | 2 | 2 | no | — |
| 51 | C2×#235 | — | 2 | 8 | no | — |
| 52 | C2×#235 | C23 | 1 | 4 | yes | — |
| 53 | C22×D12 | — | 2 | 8 | no | — |
| 54 | C22×D12 | — | 2 | 1 | no | — |
| 55 | C22×D12 | — | 2 | 2 | no | — |
| 56 | C22×D12 | — | 2 | 4 | no | — |
| 57 | C22×D12 | C23 | 1 | 2 | yes | — |
| 58 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 59 | C22×D12 | C23 | 1 | 4 | yes | — |
| 60 | C22×C4×D3 | — | 2 | 1 | no | — |
| 61 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C3×M16 | — | 2 | 8 | no | — |
| 63 | C2×C3×M16 | C23 | 1 | 4 | yes | — |
| 64 | C2×C3×M16 | C23 | 1 | 4 | yes | — |
| 65 | C22×C3×C8 | C23 | 1 | 4 | yes | — |
| 66 | C3×#117 | D4 | 1 | 4 | yes | — |
| 67 | C3×#117 | C23 | 1 | 4 | yes | — |
| 68 | C2×C3×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 69 | C2×C3×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 70 | C2×C3×C42 | C23 | 1 | 2 | yes | — |
| 71 | C2×#217 | — | 2 | 2 | no | — |
| 72 | C2×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 73 | #926 | — | 2 | 2 | no | — |
| 74 | #926 | — | 2 | 2 | no | — |
| 75 | #926 | C23 | 1 | 4 | yes | — |
| 76 | #926 | C23 | 1 | 4 | yes | — |
| 77 | C2×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 78 | #924 | — | 2 | 8 | no | — |
| 79 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 80 | #895 | — | 2 | 16 | no | — |
| 81 | #890 | — | 2 | 8 | no | — |
| 82 | #888 | — | 2 | 8 | no | — |
| 83 | #882 | — | 2 | 16 | no | — |
| 84 | #878 | — | 2 | 16 | no | — |
| 85 | #875 | — | 2 | 4 | no | — |
| 86 | #875 | C23 | 1 | 8 | yes | — |
| 87 | #874 | — | 2 | 4 | no | — |
| 88 | #874 | C23 | 1 | 8 | yes | — |
| 89 | #870 | C23 | 1 | 8 | yes | complemented |
| 90 | #869 | C23 | 1 | 8 | yes | complemented |
| 91 | C4×Dic6 | — | 2 | 8 | no | — |
| 92 | C3×#97 | C23 | 1 | 8 | yes | complemented |
| 93 | C3×C4×C8 | C23 | 1 | 8 | yes | complemented |
| 94 | #821 | C23 | 1 | 32 | yes | — |
| 95 | #821 | C23 | 1 | 16 | yes | complemented |
| 96 | #816 | C23 | 1 | 16 | yes | complemented |
| 97 | C22×#41 | — | 3 | 1 | no | — |
| 98 | C23×D4 | — | 3 | 1 | no | — |
| 99 | C22×M16 | C2×D3 | 1 | 2 | yes | — |
| 100 | #544 | — | 3 | 8 | no | — |
| 101 | #544 | — | 6 | 2 | no | — |
| 102 | #543 | — | 6 | 2 | no | — |
| 103 | #535 | — | 3 | 8 | no | — |
| 104 | #535 | — | 6 | 4 | no | — |
| 105 | #533 | — | 3 | 4 | no | — |
| 106 | #533 | — | 6 | 4 | no | — |
| 107 | C2×#127 | — | 3 | 2 | no | — |
| 108 | C2×#124 | — | 3 | 2 | no | — |
| 109 | C2×#121 | — | 6 | 2 | no | — |
| 110 | C2×#120 | — | 6 | 2 | no | — |
| 111 | C2×#117 | — | 3 | 2 | no | — |
| 112 | C2×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 113 | #490 | — | 3 | 16 | no | — |
| 114 | #489 | — | 3 | 16 | no | — |
| 115 | #488 | — | 3 | 16 | no | — |
| 116 | #486 | — | 3 | 16 | no | — |
| 117 | #419 | — | 3 | 4 | no | — |
| 118 | #418 | — | 3 | 8 | no | — |
| 119 | #418 | — | 3 | 8 | no | — |
| 120 | #418 | — | 3 | 4 | no | — |
| 121 | #417 | — | 3 | 8 | no | — |
| 122 | #416 | — | 3 | 8 | no | — |
| 123 | C2×#102 | — | 3 | 8 | no | — |
| 124 | #405 | C2×D3 | 1 | 8 | yes | complemented |
| 125 | C4×M16 | C2×D3 | 1 | 4 | yes | complemented |
| 126 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C23×D3 | — | 2 | 2 | no | — |
| 128 | C23×D3 | — | 2 | 1 | no | — |
| 129 | C23×D3 | — | 2 | 4 | no | — |
| 130 | C23×D3 | — | 4 | 4 | no | — |
| 131 | C23×D3 | — | 8 | 4 | no | — |
| 132 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 133 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 134 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C22×C3×C4 | #41 | 1 | 8 | yes | — |
| 136 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 137 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 138 | C2×#67 | — | 2 | 4 | no | — |
| 139 | C2×#67 | — | 4 | 4 | no | — |
| 140 | C22×Dic3 | — | 2 | 1 | no | — |
| 141 | C22×Dic3 | — | 2 | 4 | no | — |
| 142 | #235 | — | 2 | 8 | no | — |
| 143 | #235 | — | 2 | 8 | no | — |
| 144 | #235 | — | 4 | 8 | no | — |
| 145 | C2×D12 | — | 2 | 8 | no | — |
| 146 | C2×D12 | — | 2 | 8 | no | — |
| 147 | C2×D12 | — | 2 | 8 | no | — |
| 148 | C2×D12 | — | 2 | 4 | no | — |
| 149 | C2×D12 | — | 2 | 1 | no | — |
| 150 | C2×D12 | — | 2 | 2 | no | — |
| 151 | C2×D12 | — | 2 | 4 | no | — |
| 152 | C2×D12 | — | 2 | 16 | no | — |
| 153 | C2×D12 | — | 4 | 4 | no | — |
| 154 | C2×D12 | — | 4 | 8 | no | — |
| 155 | C2×D12 | — | 8 | 8 | no | — |
| 156 | C2×D12 | C24 | 1 | 4 | yes | — |
| 157 | C2×D12 | C24 | 1 | 2 | yes | — |
| 158 | C2×C4×D3 | — | 2 | 4 | no | — |
| 159 | C2×C4×D3 | — | 4 | 4 | no | — |
| 160 | C2×Dic6 | — | 2 | 4 | no | — |
| 161 | C2×Dic6 | — | 2 | 1 | no | — |
| 162 | C2×Dic6 | — | 2 | 8 | no | — |
| 163 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 164 | C3×M16 | — | 2 | 8 | no | — |
| 165 | C3×M16 | — | 2 | 8 | no | — |
| 166 | C2×C3×C8 | — | 2 | 8 | no | — |
| 167 | C2×C3×C8 | C24 | 1 | 8 | yes | — |
| 168 | C3×C4⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 169 | C3×C22⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 170 | C3×C42 | C2×D4 | 1 | 4 | yes | — |
| 171 | C3×C42 | C24 | 1 | 4 | yes | — |
| 172 | #217 | — | 2 | 4 | no | — |
| 173 | #217 | — | 2 | 4 | no | — |
| 174 | (C2×D3)⋊C4 | — | 2 | 16 | no | — |
| 175 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 176 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 177 | C4⋊Dic3 | C24 | 1 | 8 | yes | — |
| 178 | Dic3⋊C4 | — | 2 | 16 | no | — |
| 179 | C4×Dic3 | — | 2 | 4 | no | — |
| 180 | C4×Dic3 | — | 2 | 4 | no | — |
| 181 | C25 | — | 6 | 1 | no | — |
| 182 | C2×#41 | — | 3 | 4 | no | — |
| 183 | C2×#41 | — | 6 | 2 | no | — |
| 184 | C2×#41 | — | 6 | 8 | no | — |
| 185 | C22×Q8 | — | 3 | 1 | no | — |
| 186 | C22×D4 | — | 3 | 2 | no | — |
| 187 | C22×D4 | — | 3 | 1 | no | — |
| 188 | C22×D4 | — | 3 | 4 | no | — |
| 189 | C22×D4 | — | 6 | 1 | no | — |
| 190 | C22×D4 | — | 6 | 1 | no | — |
| 191 | C22×D4 | — | 6 | 2 | no | — |
| 192 | C22×D4 | — | 6 | 4 | no | — |
| 193 | C22×D4 | — | 6 | 8 | no | — |
| 194 | C23×C4 | — | 6 | 1 | no | — |
| 195 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 196 | C2×M16 | — | 2 | 8 | no | — |
| 197 | C2×M16 | C22×D3 | 1 | 4 | yes | — |
| 198 | C2×M16 | C22×D3 | 1 | 4 | yes | — |
| 199 | C22×C8 | C22×D3 | 1 | 4 | yes | — |
| 200 | C4⋊Q8 | — | 3 | 8 | no | — |
| 201 | C4⋊Q8 | — | 6 | 8 | no | — |
| 202 | #127 | — | 3 | 8 | no | — |
| 203 | #127 | — | 6 | 4 | no | — |
| 204 | #125 | — | 3 | 8 | no | — |
| 205 | #125 | — | 6 | 8 | no | — |
| 206 | #124 | — | 3 | 8 | no | — |
| 207 | #124 | — | 6 | 4 | no | — |
| 208 | C22⋊Q8 | — | 6 | 8 | no | — |
| 209 | C22⋊Q8 | — | 6 | 16 | no | — |
| 210 | #121 | — | 6 | 16 | no | — |
| 211 | #120 | — | 6 | 16 | no | — |
| 212 | C4×Q8 | — | 6 | 8 | no | — |
| 213 | #117 | — | 3 | 4 | no | — |
| 214 | #117 | — | 3 | 4 | no | — |
| 215 | #117 | — | 6 | 2 | no | — |
| 216 | #117 | — | 6 | 2 | no | — |
| 217 | #117 | D12 | 1 | 4 | yes | — |
| 218 | #117 | C22×D3 | 1 | 4 | yes | — |
| 219 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 220 | C2×C4⋊C4 | D12 | 1 | 2 | yes | — |
| 221 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 222 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 223 | C2×C22⋊C4 | D12 | 1 | 2 | yes | — |
| 224 | C2×C42 | — | 6 | 2 | no | — |
| 225 | C2×C42 | C22×D3 | 1 | 2 | yes | — |
| 226 | #103 | — | 3 | 16 | no | — |
| 227 | #102 | — | 3 | 32 | no | — |
| 228 | #102 | — | 3 | 16 | no | — |
| 229 | #97 | C22×D3 | 1 | 8 | yes | complemented |
| 230 | C4×C8 | C22×D3 | 1 | 8 | yes | complemented |
| 231 | C23×C3 | — | 4 | 2 | no | — |
| 232 | C23×C3 | #124 | 1 | 4 | yes | — |
| 233 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 234 | C23×C3 | C22×D4 | 1 | 2 | yes | — |
| 235 | C22×D3 | — | 2 | 4 | no | — |
| 236 | C22×D3 | — | 2 | 2 | no | — |
| 237 | C22×D3 | — | 4 | 4 | no | — |
| 238 | C22×D3 | — | 4 | 8 | no | — |
| 239 | C22×D3 | — | 4 | 2 | no | — |
| 240 | C22×D3 | — | 4 | 4 | no | — |
| 241 | C22×D3 | — | 4 | 8 | no | — |
| 242 | C22×D3 | — | 8 | 8 | no | — |
| 243 | C22×D3 | — | 8 | 16 | no | — |
| 244 | C2×C3×C4 | — | 4 | 4 | no | — |
| 245 | C2×C3×C4 | #124 | 1 | 4 | yes | — |
| 246 | C2×C3×C4 | #124 | 1 | 8 | yes | — |
| 247 | C2×C3×C4 | C22×D4 | 1 | 8 | yes | — |
| 248 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 249 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 250 | C2×C3×C4 | C2×#41 | 1 | 4 | yes | — |
| 251 | C2×C3×C4 | C2×#41 | 1 | 4 | yes | — |
| 252 | C2×C3×C4 | C2×#41 | 1 | 4 | yes | — |
| 253 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 254 | #67 | — | 4 | 8 | no | — |
| 255 | C2×Dic3 | — | 2 | 8 | no | — |
| 256 | C2×Dic3 | — | 2 | 2 | no | — |
| 257 | C2×Dic3 | — | 4 | 2 | no | — |
| 258 | C2×Dic3 | — | 8 | 4 | no | — |
| 259 | D12 | — | 2 | 8 | no | — |
| 260 | D12 | — | 2 | 4 | no | — |
| 261 | D12 | — | 4 | 4 | no | — |
| 262 | D12 | — | 4 | 8 | no | — |
| 263 | D12 | — | 4 | 2 | no | — |
| 264 | D12 | — | 8 | 16 | no | — |
| 265 | C4×D3 | — | 4 | 8 | no | — |
| 266 | Dic6 | — | 2 | 4 | no | — |
| 267 | Dic6 | — | 4 | 2 | no | — |
| 268 | Dic6 | — | 8 | 8 | no | — |
| 269 | C3×C8 | — | 2 | 8 | no | — |
| 270 | C24 | — | 6 | 2 | no | — |
| 271 | C24 | — | 6 | 1 | no | — |
| 272 | C24 | — | 6 | 4 | no | — |
| 273 | C24 | — | 12 | 4 | no | — |
| 274 | C24 | — | 24 | 4 | no | — |
| 275 | C24 | C2×D12 | 1 | 1 | yes | characteristic |
| 276 | #41 | — | 6 | 8 | no | — |
| 277 | #41 | — | 6 | 8 | no | — |
| 278 | #41 | — | 12 | 8 | no | — |
| 279 | C2×Q8 | — | 3 | 2 | no | — |
| 280 | C2×Q8 | — | 6 | 1 | no | — |
| 281 | C2×Q8 | — | 6 | 8 | no | — |
| 282 | C2×Q8 | — | 6 | 4 | no | — |
| 283 | C2×D4 | — | 3 | 4 | no | — |
| 284 | C2×D4 | — | 3 | 2 | no | — |
| 285 | C2×D4 | — | 6 | 4 | no | — |
| 286 | C2×D4 | — | 6 | 4 | no | — |
| 287 | C2×D4 | — | 6 | 2 | no | — |
| 288 | C2×D4 | — | 6 | 1 | no | — |
| 289 | C2×D4 | — | 6 | 16 | no | — |
| 290 | C2×D4 | — | 6 | 8 | no | — |
| 291 | C2×D4 | — | 6 | 8 | no | — |
| 292 | C2×D4 | — | 6 | 8 | no | — |
| 293 | C2×D4 | — | 6 | 4 | no | — |
| 294 | C2×D4 | — | 12 | 4 | no | — |
| 295 | C2×D4 | — | 12 | 4 | no | — |
| 296 | C2×D4 | — | 12 | 8 | no | — |
| 297 | C2×D4 | — | 24 | 8 | no | — |
| 298 | C22×C4 | — | 6 | 1 | no | — |
| 299 | C22×C4 | — | 6 | 4 | no | — |
| 300 | C22×C4 | — | 6 | 4 | no | — |
| 301 | C22×C4 | — | 12 | 4 | no | — |
| 302 | C22×C4 | C2×D12 | 1 | 4 | yes | — |
| 303 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 304 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 305 | C22×C4 | #235 | 1 | 8 | yes | — |
| 306 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 307 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 308 | M16 | — | 2 | 8 | no | — |
| 309 | M16 | — | 2 | 8 | no | — |
| 310 | C2×C8 | — | 2 | 8 | no | — |
| 311 | C2×C8 | C23×D3 | 1 | 8 | yes | — |
| 312 | C4⋊C4 | — | 3 | 8 | no | — |
| 313 | C4⋊C4 | — | 6 | 4 | no | — |
| 314 | C4⋊C4 | — | 6 | 16 | no | — |
| 315 | C4⋊C4 | — | 6 | 8 | no | — |
| 316 | C4⋊C4 | C2×D12 | 1 | 8 | yes | — |
| 317 | C22⋊C4 | — | 6 | 4 | no | — |
| 318 | C22⋊C4 | — | 6 | 4 | no | — |
| 319 | C22⋊C4 | — | 6 | 16 | no | — |
| 320 | C22⋊C4 | C2×D12 | 1 | 8 | yes | — |
| 321 | C42 | — | 6 | 4 | no | — |
| 322 | C42 | — | 6 | 4 | no | — |
| 323 | C42 | C2×D12 | 1 | 4 | yes | — |
| 324 | C42 | C23×D3 | 1 | 4 | yes | — |
| 325 | C22×C3 | — | 2 | 4 | no | — |
| 326 | C22×C3 | — | 2 | 2 | no | — |
| 327 | C22×C3 | — | 4 | 4 | no | — |
| 328 | C22×C3 | C2×#124 | 1 | 2 | yes | — |
| 329 | C22×C3 | C2×#124 | 1 | 4 | yes | — |
| 330 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 331 | C2×D3 | — | 4 | 4 | no | — |
| 332 | C2×D3 | — | 4 | 8 | no | — |
| 333 | C2×D3 | — | 4 | 2 | no | — |
| 334 | C2×D3 | — | 4 | 4 | no | — |
| 335 | C2×D3 | — | 8 | 4 | no | — |
| 336 | C2×D3 | — | 8 | 8 | no | — |
| 337 | C2×D3 | — | 8 | 16 | no | — |
| 338 | C3×C4 | — | 2 | 8 | no | — |
| 339 | C3×C4 | C2×#124 | 1 | 2 | yes | — |
| 340 | C3×C4 | C2×#124 | 1 | 4 | yes | — |
| 341 | C3×C4 | C22×#41 | 1 | 2 | yes | — |
| 342 | Dic3 | — | 4 | 8 | no | — |
| 343 | Dic3 | — | 4 | 2 | no | — |
| 344 | C23 | — | 4 | 2 | no | — |
| 345 | C23 | — | 6 | 4 | no | — |
| 346 | C23 | — | 6 | 2 | no | — |
| 347 | C23 | — | 12 | 4 | no | — |
| 348 | C23 | — | 12 | 8 | no | — |
| 349 | C23 | — | 12 | 2 | no | — |
| 350 | C23 | — | 12 | 4 | no | — |
| 351 | C23 | — | 12 | 8 | no | — |
| 352 | C23 | — | 24 | 8 | no | — |
| 353 | C23 | — | 24 | 16 | no | — |
| 354 | C23 | #875 | 1 | 4 | yes | — |
| 355 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 356 | C23 | C22×D12 | 1 | 2 | yes | — |
| 357 | Q8 | — | 6 | 4 | no | — |
| 358 | Q8 | — | 12 | 2 | no | — |
| 359 | Q8 | — | 24 | 8 | no | — |
| 360 | D4 | — | 6 | 8 | no | — |
| 361 | D4 | — | 6 | 4 | no | — |
| 362 | D4 | — | 12 | 8 | no | — |
| 363 | D4 | — | 12 | 8 | no | — |
| 364 | D4 | — | 12 | 4 | no | — |
| 365 | D4 | — | 12 | 2 | no | — |
| 366 | D4 | — | 24 | 16 | no | — |
| 367 | C2×C4 | — | 4 | 4 | no | — |
| 368 | C2×C4 | — | 6 | 8 | no | — |
| 369 | C2×C4 | — | 6 | 2 | no | — |
| 370 | C2×C4 | — | 12 | 2 | no | — |
| 371 | C2×C4 | — | 12 | 8 | no | — |
| 372 | C2×C4 | — | 24 | 4 | no | — |
| 373 | C2×C4 | #875 | 1 | 4 | yes | — |
| 374 | C2×C4 | #875 | 1 | 8 | yes | — |
| 375 | C2×C4 | C22×D12 | 1 | 8 | yes | — |
| 376 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 377 | C2×C4 | C22×D12 | 1 | 2 | yes | — |
| 378 | C2×C4 | C2×#235 | 1 | 4 | yes | — |
| 379 | C2×C4 | C2×#235 | 1 | 4 | yes | — |
| 380 | C2×C4 | C2×#235 | 1 | 4 | yes | — |
| 381 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 382 | C8 | — | 2 | 8 | no | — |
| 383 | C2×C3 | — | 2 | 2 | no | — |
| 384 | C2×C3 | — | 2 | 4 | no | — |
| 385 | C2×C3 | C22×#124 | 1 | 1 | yes | characteristic |
| 386 | C2×C3 | #3585 | 1 | 2 | yes | — |
| 387 | D3 | — | 8 | 2 | no | — |
| 388 | D3 | — | 8 | 4 | no | — |
| 389 | C22 | — | 2 | 2 | no | — |
| 390 | C22 | — | 2 | 4 | no | — |
| 391 | C22 | — | 4 | 4 | no | — |
| 392 | C22 | — | 12 | 4 | no | — |
| 393 | C22 | — | 12 | 8 | no | — |
| 394 | C22 | — | 12 | 2 | no | — |
| 395 | C22 | — | 12 | 4 | no | — |
| 396 | C22 | — | 24 | 8 | no | — |
| 397 | C22 | — | 24 | 4 | no | — |
| 398 | C22 | — | 24 | 16 | no | — |
| 399 | C22 | C2×#875 | 1 | 2 | yes | — |
| 400 | C22 | C2×#875 | 1 | 4 | yes | — |
| 401 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 402 | C4 | — | 2 | 8 | no | — |
| 403 | C4 | — | 12 | 8 | no | — |
| 404 | C4 | — | 12 | 2 | no | — |
| 405 | C4 | C2×#875 | 1 | 4 | yes | — |
| 406 | C4 | C2×#875 | 1 | 2 | yes | — |
| 407 | C4 | C22×#235 | 1 | 2 | yes | — |
| 408 | C3 | #60619 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 409 | C2 | — | 2 | 2 | no | — |
| 410 | C2 | — | 2 | 4 | no | — |
| 411 | C2 | — | 24 | 4 | no | — |
| 412 | C2 | — | 24 | 2 | no | — |
| 413 | C2 | C22×#875 | 1 | 1 | yes | characteristic |
| 414 | C2 | #87167 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #85725 | C2 | semidirect |
| 3. C3×#2873 | C2 | semidirect |
| 4. #83768 | C2 | semidirect |
| 5. C2×#5131 | C2 | semidirect |
| 6. #78563 | C2 | semidirect |
| 7. #78527 | C2 | semidirect |
| 8. #78526 | C2 | semidirect |
| 17. #5519 | C22 | semidirect |
| 25. #5470 | C22 | semidirect |
| 26. C3×#405 | C22 | semidirect |
| 27. C3×C4×M16 | C22 | semidirect |
| 28. #5133 | C22 | semidirect |
| 30. #5131 | C22 | semidirect |
| 31. #5131 | C22 | semidirect |
| 32. #5120 | C22 | semidirect |
| 33. #5113 | C22 | semidirect |
| 34. C2×#821 | C22 | semidirect |
| 35. #4714 | C22 | semidirect |
| 36. #4713 | C22 | semidirect |
| 37. #4697 | C22 | semidirect |
| 38. #4694 | C22 | semidirect |
| 46. #2873 | D3 | semidirect |
| 89. #870 | C23 | semidirect |
| 90. #869 | C23 | semidirect |
| 92. C3×#97 | C23 | semidirect |
| 93. C3×C4×C8 | C23 | semidirect |
| 95. #821 | C23 | semidirect |
| 96. #816 | C23 | semidirect |
| 124. #405 | C2×D3 | semidirect |
| 125. C4×M16 | C2×D3 | semidirect |
| 229. #97 | C22×D3 | semidirect |
| 230. C4×C8 | C22×D3 | semidirect |
| 408. C3 | #60619 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5525 | 2 |
| #85725 | 2 |
| C3×#2873 | 2 |
| #83768 | 2 |
| C2×#5131 | 2 |
| #78563 | 2 |
| #78527 | 2 |
| #78526 | 2 |
| #60619 | 3 |