Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2066 conjugacy classes of subgroups.
The subgroup lattice has 512 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #85847 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #85828 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#2875 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83806 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #83797 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #78575 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #78563 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #78528 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #78527 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #78497 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×#4714 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #60625 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×#1010 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#1009 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×#131 | C22 | 1 | 2 | yes | — |
| 16 | C3×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 17 | #5827 | C22 | 1 | 2 | yes | — |
| 18 | #5576 | — | 2 | 1 | no | — |
| 19 | #5576 | — | 2 | 1 | no | — |
| 20 | #5570 | — | 2 | 1 | no | — |
| 21 | Q8×Dic6 | — | 2 | 1 | no | — |
| 22 | #5554 | — | 2 | 3 | no | — |
| 23 | #5554 | — | 2 | 3 | no | — |
| 24 | #5543 | — | 2 | 3 | no | — |
| 25 | D4×Dic6 | — | 2 | 3 | no | — |
| 26 | #5526 | C22 | 1 | 3 | yes | — |
| 27 | #5525 | C22 | 1 | 3 | yes | — |
| 28 | #5519 | C22 | 1 | 6 | yes | complemented |
| 29 | #5477 | C22 | 1 | 3 | yes | — |
| 30 | C2×#875 | C22 | 1 | 3 | yes | — |
| 31 | #5470 | C22 | 1 | 3 | yes | complemented |
| 32 | C2×#869 | C22 | 1 | 3 | yes | complemented |
| 33 | C3×#405 | C22 | 1 | 6 | yes | complemented |
| 34 | C3×C4×M16 | C22 | 1 | 3 | yes | complemented |
| 35 | C2×C3×#97 | C22 | 1 | 3 | yes | complemented |
| 36 | #5133 | C22 | 1 | 6 | yes | — |
| 37 | #5133 | C22 | 1 | 6 | yes | complemented |
| 38 | #5131 | C22 | 1 | 6 | yes | — |
| 39 | #5120 | C22 | 1 | 6 | yes | complemented |
| 40 | #5113 | C22 | 1 | 6 | yes | — |
| 41 | #5113 | C22 | 1 | 6 | yes | complemented |
| 42 | C2×#821 | C22 | 1 | 6 | yes | — |
| 43 | C2×#816 | C22 | 1 | 6 | yes | complemented |
| 44 | #4714 | C22 | 1 | 3 | yes | complemented |
| 45 | #4714 | C22 | 1 | 6 | yes | complemented |
| 46 | #4714 | C22 | 1 | 12 | yes | complemented |
| 47 | #4714 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #4714 | C22 | 1 | 3 | yes | complemented |
| 49 | #4714 | C22 | 1 | 3 | yes | complemented |
| 50 | #4713 | C22 | 1 | 6 | yes | complemented |
| 51 | #4703 | C22 | 1 | 6 | yes | complemented |
| 52 | #4697 | C22 | 1 | 12 | yes | complemented |
| 53 | #4694 | C22 | 1 | 6 | yes | complemented |
| 54 | #4681 | C22 | 1 | 6 | yes | complemented |
| 55 | #3503 | — | 3 | 1 | no | — |
| 56 | #3500 | — | 3 | 1 | no | — |
| 57 | #3141 | — | 3 | 3 | no | — |
| 58 | #3140 | — | 3 | 3 | no | — |
| 59 | #3137 | — | 3 | 6 | no | — |
| 60 | #3136 | — | 3 | 6 | no | — |
| 61 | #3135 | — | 3 | 3 | no | — |
| 62 | C2×#489 | — | 3 | 3 | no | — |
| 63 | #2898 | — | 3 | 2 | no | — |
| 64 | #2897 | — | 3 | 2 | no | — |
| 65 | #2875 | D3 | 1 | 1 | yes | characteristic, complemented |
| 66 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 67 | #1010 | — | 2 | 8 | no | — |
| 68 | #1009 | — | 2 | 8 | no | — |
| 69 | C2×#239 | — | 2 | 1 | no | — |
| 70 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 71 | C2×#237 | — | 2 | 3 | no | — |
| 72 | C2×D3×D4 | — | 2 | 3 | no | — |
| 73 | C2×#235 | C23 | 1 | 3 | yes | — |
| 74 | C2×#235 | C23 | 1 | 3 | yes | — |
| 75 | C22×D12 | C23 | 1 | 3 | yes | — |
| 76 | C22×Dic6 | — | 2 | 3 | no | — |
| 77 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 78 | C3×#131 | — | 2 | 8 | no | — |
| 79 | C2×C3×M16 | C23 | 1 | 6 | yes | — |
| 80 | C22×C3×C8 | C23 | 1 | 6 | yes | — |
| 81 | C3×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 82 | C3×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 83 | C3×C4×D4 | D4 | 1 | 3 | yes | — |
| 84 | C3×C4×D4 | D4 | 1 | 3 | yes | — |
| 85 | C3×#117 | C23 | 1 | 3 | yes | — |
| 86 | C2×C3×C42 | C23 | 1 | 3 | yes | — |
| 87 | Q8×Dic3 | — | 2 | 2 | no | — |
| 88 | D4×Dic3 | — | 2 | 6 | no | — |
| 89 | #930 | — | 2 | 3 | no | — |
| 90 | #930 | — | 2 | 3 | no | — |
| 91 | C2×(C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 92 | C2×(C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 93 | #926 | C23 | 1 | 6 | yes | — |
| 94 | C2×C4⋊Dic3 | — | 2 | 3 | no | — |
| 95 | C2×C4⋊Dic3 | C23 | 1 | 6 | yes | — |
| 96 | #924 | — | 2 | 3 | no | — |
| 97 | #924 | — | 2 | 3 | no | — |
| 98 | #897 | — | 2 | 3 | no | — |
| 99 | #897 | — | 2 | 3 | no | — |
| 100 | #895 | — | 2 | 3 | no | — |
| 101 | #895 | — | 2 | 3 | no | — |
| 102 | #890 | — | 2 | 6 | no | — |
| 103 | #888 | — | 2 | 6 | no | — |
| 104 | #886 | — | 2 | 6 | no | — |
| 105 | #882 | — | 2 | 6 | no | — |
| 106 | #878 | — | 2 | 12 | no | — |
| 107 | #875 | — | 2 | 3 | no | — |
| 108 | #875 | — | 2 | 3 | no | — |
| 109 | #875 | C23 | 1 | 6 | yes | — |
| 110 | #875 | C23 | 1 | 3 | yes | — |
| 111 | #875 | C23 | 1 | 1 | yes | characteristic |
| 112 | #874 | C23 | 1 | 3 | yes | — |
| 113 | C4×D12 | — | 2 | 3 | no | — |
| 114 | C4×D12 | — | 2 | 3 | no | — |
| 115 | #870 | C23 | 1 | 6 | yes | — |
| 116 | #869 | — | 2 | 3 | no | — |
| 117 | #869 | — | 2 | 3 | no | — |
| 118 | #869 | C23 | 1 | 3 | yes | — |
| 119 | #869 | C23 | 1 | 6 | yes | — |
| 120 | #869 | C23 | 1 | 3 | yes | — |
| 121 | #869 | C23 | 1 | 1 | yes | characteristic |
| 122 | C4×Dic6 | — | 2 | 3 | no | — |
| 123 | C4×Dic6 | — | 2 | 3 | no | — |
| 124 | C3×#97 | C23 | 1 | 6 | yes | — |
| 125 | C3×#97 | C23 | 1 | 1 | yes | characteristic |
| 126 | C3×#97 | C23 | 1 | 3 | yes | — |
| 127 | C3×C4×C8 | C23 | 1 | 6 | yes | — |
| 128 | #821 | C23 | 1 | 6 | yes | — |
| 129 | #821 | C23 | 1 | 12 | yes | — |
| 130 | #821 | C23 | 1 | 6 | yes | — |
| 131 | #821 | C23 | 1 | 2 | yes | — |
| 132 | #821 | C23 | 1 | 6 | yes | — |
| 133 | #816 | C23 | 1 | 6 | yes | — |
| 134 | #816 | C23 | 1 | 12 | yes | — |
| 135 | #816 | C23 | 1 | 6 | yes | — |
| 136 | #816 | C23 | 1 | 2 | yes | — |
| 137 | #816 | C23 | 1 | 6 | yes | — |
| 138 | C2×2−1+4 | — | 3 | 1 | no | — |
| 139 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 140 | C2×#131 | C2×D3 | 1 | 2 | yes | — |
| 141 | Q82 | — | 6 | 1 | no | — |
| 142 | #557 | — | 6 | 1 | no | — |
| 143 | #554 | — | 6 | 3 | no | — |
| 144 | D4×Q8 | — | 6 | 3 | no | — |
| 145 | #548 | — | 6 | 1 | no | — |
| 146 | #548 | — | 6 | 1 | no | — |
| 147 | #546 | — | 6 | 3 | no | — |
| 148 | #546 | — | 6 | 3 | no | — |
| 149 | #544 | — | 3 | 6 | no | — |
| 150 | #536 | — | 3 | 3 | no | — |
| 151 | #535 | — | 3 | 3 | no | — |
| 152 | #533 | — | 3 | 3 | no | — |
| 153 | #532 | — | 3 | 3 | no | — |
| 154 | C2×C4⋊Q8 | — | 3 | 3 | no | — |
| 155 | C2×#124 | — | 3 | 3 | no | — |
| 156 | #520 | — | 3 | 2 | no | — |
| 157 | C4×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 158 | #491 | — | 3 | 6 | no | — |
| 159 | #490 | — | 3 | 6 | no | — |
| 160 | #489 | — | 3 | 3 | no | — |
| 161 | #489 | — | 3 | 12 | no | — |
| 162 | #489 | — | 3 | 6 | no | — |
| 163 | #489 | — | 3 | 1 | no | — |
| 164 | #489 | — | 3 | 3 | no | — |
| 165 | #489 | — | 3 | 3 | no | — |
| 166 | #488 | — | 3 | 12 | no | — |
| 167 | #487 | — | 3 | 6 | no | — |
| 168 | #486 | — | 3 | 6 | no | — |
| 169 | #419 | — | 3 | 6 | no | — |
| 170 | #418 | — | 3 | 6 | no | — |
| 171 | #417 | — | 3 | 6 | no | — |
| 172 | #417 | — | 3 | 6 | no | — |
| 173 | #416 | — | 3 | 6 | no | — |
| 174 | #416 | — | 3 | 6 | no | — |
| 175 | C2×#103 | — | 3 | 6 | no | — |
| 176 | C2×#102 | — | 3 | 6 | no | — |
| 177 | #405 | C2×D3 | 1 | 6 | yes | complemented |
| 178 | C4×M16 | C2×D3 | 1 | 3 | yes | complemented |
| 179 | C2×#97 | C2×D3 | 1 | 3 | yes | complemented |
| 180 | C23×D3 | — | 2 | 3 | no | — |
| 181 | C3×#41 | #41 | 1 | 8 | yes | — |
| 182 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 184 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 185 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 186 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 187 | C2×#67 | — | 2 | 3 | no | — |
| 188 | C2×#67 | — | 2 | 3 | no | — |
| 189 | C22×Dic3 | — | 2 | 3 | no | — |
| 190 | C22×Dic3 | — | 2 | 6 | no | — |
| 191 | #239 | — | 4 | 4 | no | — |
| 192 | D3×Q8 | — | 4 | 4 | no | — |
| 193 | #237 | — | 4 | 12 | no | — |
| 194 | D3×D4 | — | 4 | 12 | no | — |
| 195 | #235 | — | 2 | 12 | no | — |
| 196 | #235 | — | 2 | 12 | no | — |
| 197 | C2×D12 | — | 2 | 12 | no | — |
| 198 | C2×D12 | — | 2 | 3 | no | — |
| 199 | C2×D12 | — | 2 | 3 | no | — |
| 200 | C2×D12 | — | 2 | 3 | no | — |
| 201 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 202 | C2×D12 | C24 | 1 | 3 | yes | — |
| 203 | C2×C4×D3 | — | 2 | 3 | no | — |
| 204 | C2×C4×D3 | — | 2 | 3 | no | — |
| 205 | C2×Dic6 | — | 2 | 12 | no | — |
| 206 | C2×Dic6 | — | 2 | 1 | no | — |
| 207 | C2×Dic6 | — | 2 | 3 | no | — |
| 208 | C2×Dic6 | — | 2 | 3 | no | — |
| 209 | C2×Dic6 | — | 2 | 6 | no | — |
| 210 | C2×Dic6 | — | 8 | 6 | no | — |
| 211 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 212 | C2×Dic6 | C24 | 1 | 3 | yes | — |
| 213 | C3×M16 | — | 2 | 12 | no | — |
| 214 | C2×C3×C8 | — | 2 | 12 | no | — |
| 215 | C2×C3×C8 | C24 | 1 | 6 | yes | — |
| 216 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 217 | C3×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 218 | C3×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 219 | C3×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 220 | C3×C42 | C2×D4 | 1 | 3 | yes | — |
| 221 | C3×C42 | C2×D4 | 1 | 3 | yes | — |
| 222 | C3×C42 | C24 | 1 | 3 | yes | — |
| 223 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 224 | #217 | — | 2 | 6 | no | — |
| 225 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 226 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 227 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 228 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 229 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 230 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 231 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 232 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 233 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 234 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 235 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 236 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 237 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 238 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 239 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 240 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 241 | C4×Dic3 | — | 2 | 6 | no | — |
| 242 | 2−1+4 | — | 6 | 8 | no | — |
| 243 | H(5,𝔽2) | — | 6 | 8 | no | — |
| 244 | C2×#41 | — | 3 | 3 | no | — |
| 245 | C2×#41 | — | 3 | 3 | no | — |
| 246 | C2×#41 | — | 6 | 1 | no | — |
| 247 | C2×#41 | — | 6 | 3 | no | — |
| 248 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 249 | C22×Q8 | — | 3 | 3 | no | — |
| 250 | C22×Q8 | — | 6 | 1 | no | — |
| 251 | C22×Q8 | — | 6 | 3 | no | — |
| 252 | C22×D4 | — | 3 | 3 | no | — |
| 253 | C22×D4 | — | 6 | 3 | no | — |
| 254 | #131 | — | 2 | 8 | no | — |
| 255 | C2×M16 | C22×D3 | 1 | 6 | yes | — |
| 256 | C22×C8 | C22×D3 | 1 | 6 | yes | — |
| 257 | C4⋊Q8 | — | 3 | 3 | no | — |
| 258 | C4⋊Q8 | — | 3 | 6 | no | — |
| 259 | C4⋊Q8 | — | 3 | 1 | no | — |
| 260 | C4⋊Q8 | — | 3 | 3 | no | — |
| 261 | C4⋊Q8 | — | 6 | 6 | no | — |
| 262 | C4⋊Q8 | — | 6 | 3 | no | — |
| 263 | C4⋊Q8 | — | 6 | 3 | no | — |
| 264 | #127 | — | 3 | 3 | no | — |
| 265 | #125 | — | 3 | 6 | no | — |
| 266 | #125 | — | 6 | 6 | no | — |
| 267 | #124 | — | 3 | 3 | no | — |
| 268 | #124 | — | 3 | 6 | no | — |
| 269 | #124 | — | 3 | 1 | no | — |
| 270 | #124 | — | 6 | 3 | no | — |
| 271 | #124 | — | 6 | 3 | no | — |
| 272 | #123 | — | 6 | 6 | no | — |
| 273 | C22⋊Q8 | — | 6 | 3 | no | — |
| 274 | C22⋊Q8 | — | 6 | 3 | no | — |
| 275 | C22⋊Q8 | — | 6 | 3 | no | — |
| 276 | C22⋊Q8 | — | 6 | 3 | no | — |
| 277 | C22⋊Q8 | — | 6 | 12 | no | — |
| 278 | #121 | — | 6 | 3 | no | — |
| 279 | #121 | — | 6 | 3 | no | — |
| 280 | #121 | — | 6 | 3 | no | — |
| 281 | #121 | — | 6 | 3 | no | — |
| 282 | #120 | — | 6 | 6 | no | — |
| 283 | C4×Q8 | — | 6 | 2 | no | — |
| 284 | C4×Q8 | — | 6 | 3 | no | — |
| 285 | C4×Q8 | — | 6 | 3 | no | — |
| 286 | C4×Q8 | D12 | 1 | 1 | yes | characteristic |
| 287 | C4×Q8 | D12 | 1 | 1 | yes | characteristic |
| 288 | C4×D4 | — | 6 | 6 | no | — |
| 289 | C4×D4 | — | 6 | 3 | no | — |
| 290 | C4×D4 | — | 6 | 3 | no | — |
| 291 | C4×D4 | D12 | 1 | 3 | yes | — |
| 292 | C4×D4 | D12 | 1 | 3 | yes | — |
| 293 | #117 | — | 3 | 6 | no | — |
| 294 | #117 | C22×D3 | 1 | 3 | yes | — |
| 295 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 296 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 297 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 298 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 299 | C2×C42 | C22×D3 | 1 | 3 | yes | — |
| 300 | #103 | — | 3 | 6 | no | — |
| 301 | #103 | — | 3 | 12 | no | — |
| 302 | #103 | — | 3 | 2 | no | — |
| 303 | #103 | — | 3 | 6 | no | — |
| 304 | #103 | — | 3 | 6 | no | — |
| 305 | #102 | — | 3 | 6 | no | — |
| 306 | #102 | — | 3 | 12 | no | — |
| 307 | #102 | — | 3 | 2 | no | — |
| 308 | #102 | — | 3 | 6 | no | — |
| 309 | #102 | — | 3 | 6 | no | — |
| 310 | #97 | C22×D3 | 1 | 1 | yes | characteristic |
| 311 | #97 | C22×D3 | 1 | 3 | yes | — |
| 312 | #97 | C22×D3 | 1 | 6 | yes | — |
| 313 | C4×C8 | C22×D3 | 1 | 6 | yes | — |
| 314 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 315 | C22×D3 | — | 2 | 3 | no | — |
| 316 | C22×D3 | — | 2 | 1 | no | — |
| 317 | C22×D3 | — | 4 | 6 | no | — |
| 318 | C22×D3 | — | 8 | 3 | no | — |
| 319 | C22×D3 | — | 8 | 3 | no | — |
| 320 | C3×Q8 | #124 | 1 | 4 | yes | — |
| 321 | C3×D4 | #124 | 1 | 12 | yes | — |
| 322 | C2×C3×C4 | — | 4 | 3 | no | — |
| 323 | C2×C3×C4 | — | 4 | 3 | no | — |
| 324 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 325 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 326 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 327 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 328 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 329 | C2×C3×C4 | C2×#41 | 1 | 12 | yes | — |
| 330 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 331 | #67 | — | 4 | 6 | no | — |
| 332 | #67 | — | 4 | 6 | no | — |
| 333 | C2×Dic3 | — | 2 | 2 | no | — |
| 334 | C2×Dic3 | — | 2 | 6 | no | — |
| 335 | C2×Dic3 | — | 2 | 1 | no | — |
| 336 | C2×Dic3 | — | 2 | 3 | no | — |
| 337 | C2×Dic3 | — | 4 | 6 | no | — |
| 338 | C2×Dic3 | — | 8 | 6 | no | — |
| 339 | D12 | — | 2 | 6 | no | — |
| 340 | D12 | — | 2 | 2 | no | — |
| 341 | D12 | — | 4 | 6 | no | — |
| 342 | D12 | — | 8 | 3 | no | — |
| 343 | D12 | — | 8 | 3 | no | — |
| 344 | C4×D3 | — | 4 | 6 | no | — |
| 345 | C4×D3 | — | 4 | 6 | no | — |
| 346 | Dic6 | — | 2 | 6 | no | — |
| 347 | Dic6 | — | 2 | 2 | no | — |
| 348 | Dic6 | — | 4 | 2 | no | — |
| 349 | Dic6 | — | 4 | 6 | no | — |
| 350 | Dic6 | — | 4 | 6 | no | — |
| 351 | Dic6 | — | 8 | 6 | no | — |
| 352 | C3×C8 | — | 2 | 2 | no | — |
| 353 | C3×C8 | — | 2 | 6 | no | — |
| 354 | C24 | — | 6 | 3 | no | — |
| 355 | #41 | — | 6 | 12 | no | — |
| 356 | #41 | — | 6 | 12 | no | — |
| 357 | #41 | — | 12 | 4 | no | — |
| 358 | #41 | — | 12 | 12 | no | — |
| 359 | #41 | #235 | 1 | 8 | yes | — |
| 360 | C2×Q8 | — | 3 | 3 | no | — |
| 361 | C2×Q8 | — | 3 | 1 | no | — |
| 362 | C2×Q8 | — | 6 | 1 | no | — |
| 363 | C2×Q8 | — | 6 | 3 | no | — |
| 364 | C2×Q8 | — | 6 | 3 | no | — |
| 365 | C2×Q8 | — | 6 | 6 | no | — |
| 366 | C2×Q8 | — | 6 | 12 | no | — |
| 367 | C2×Q8 | — | 12 | 4 | no | — |
| 368 | C2×Q8 | — | 24 | 6 | no | — |
| 369 | C2×Q8 | C2×D12 | 1 | 1 | yes | characteristic |
| 370 | C2×D4 | — | 3 | 3 | no | — |
| 371 | C2×D4 | — | 3 | 1 | no | — |
| 372 | C2×D4 | — | 6 | 3 | no | — |
| 373 | C2×D4 | — | 6 | 3 | no | — |
| 374 | C2×D4 | — | 6 | 3 | no | — |
| 375 | C2×D4 | — | 6 | 3 | no | — |
| 376 | C2×D4 | — | 6 | 3 | no | — |
| 377 | C2×D4 | — | 6 | 12 | no | — |
| 378 | C2×D4 | — | 12 | 12 | no | — |
| 379 | C2×D4 | C2×D12 | 1 | 3 | yes | — |
| 380 | C22×C4 | — | 6 | 3 | no | — |
| 381 | C22×C4 | — | 6 | 6 | no | — |
| 382 | C22×C4 | — | 6 | 3 | no | — |
| 383 | C22×C4 | — | 6 | 3 | no | — |
| 384 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 385 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 386 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 387 | M16 | — | 2 | 12 | no | — |
| 388 | C2×C8 | — | 2 | 12 | no | — |
| 389 | C2×C8 | C23×D3 | 1 | 6 | yes | — |
| 390 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 391 | C4⋊C4 | — | 3 | 6 | no | — |
| 392 | C4⋊C4 | — | 3 | 2 | no | — |
| 393 | C4⋊C4 | — | 6 | 6 | no | — |
| 394 | C4⋊C4 | — | 6 | 3 | no | — |
| 395 | C4⋊C4 | — | 6 | 6 | no | — |
| 396 | C4⋊C4 | — | 6 | 3 | no | — |
| 397 | C4⋊C4 | — | 6 | 3 | no | — |
| 398 | C4⋊C4 | — | 6 | 1 | no | — |
| 399 | C4⋊C4 | — | 6 | 6 | no | — |
| 400 | C4⋊C4 | — | 6 | 6 | no | — |
| 401 | C4⋊C4 | C2×D12 | 1 | 3 | yes | — |
| 402 | C4⋊C4 | C2×D12 | 1 | 3 | yes | — |
| 403 | C22⋊C4 | — | 6 | 6 | no | — |
| 404 | C22⋊C4 | — | 6 | 3 | no | — |
| 405 | C22⋊C4 | — | 6 | 3 | no | — |
| 406 | C22⋊C4 | — | 6 | 6 | no | — |
| 407 | C22⋊C4 | — | 6 | 6 | no | — |
| 408 | C22⋊C4 | — | 6 | 1 | no | — |
| 409 | C22⋊C4 | — | 6 | 1 | no | — |
| 410 | C22⋊C4 | C2×D12 | 1 | 6 | yes | — |
| 411 | C42 | — | 6 | 6 | no | — |
| 412 | C42 | C2×D12 | 1 | 3 | yes | — |
| 413 | C42 | C2×D12 | 1 | 3 | yes | — |
| 414 | C42 | C23×D3 | 1 | 3 | yes | — |
| 415 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 416 | C22×C3 | — | 2 | 3 | no | — |
| 417 | C22×C3 | — | 2 | 3 | no | — |
| 418 | C22×C3 | C2×#124 | 1 | 6 | yes | — |
| 419 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 420 | C2×D3 | — | 4 | 1 | no | — |
| 421 | C2×D3 | — | 4 | 3 | no | — |
| 422 | C2×D3 | — | 4 | 1 | no | — |
| 423 | C2×D3 | — | 4 | 3 | no | — |
| 424 | C2×D3 | — | 4 | 1 | no | — |
| 425 | C2×D3 | — | 4 | 3 | no | — |
| 426 | C2×D3 | — | 16 | 6 | no | — |
| 427 | C3×C4 | — | 2 | 1 | no | — |
| 428 | C3×C4 | — | 2 | 3 | no | — |
| 429 | C3×C4 | — | 2 | 1 | no | — |
| 430 | C3×C4 | — | 2 | 3 | no | — |
| 431 | C3×C4 | C2×#124 | 1 | 6 | yes | — |
| 432 | C3×C4 | C22×#41 | 1 | 2 | yes | — |
| 433 | Dic3 | — | 4 | 6 | no | — |
| 434 | Dic3 | — | 4 | 2 | no | — |
| 435 | Dic3 | — | 4 | 3 | no | — |
| 436 | Dic3 | — | 4 | 1 | no | — |
| 437 | C23 | — | 6 | 3 | no | — |
| 438 | C23 | — | 6 | 1 | no | — |
| 439 | C23 | — | 12 | 6 | no | — |
| 440 | C23 | — | 24 | 3 | no | — |
| 441 | C23 | — | 24 | 3 | no | — |
| 442 | C23 | C22×D12 | 1 | 3 | yes | — |
| 443 | Q8 | — | 6 | 6 | no | — |
| 444 | Q8 | — | 6 | 2 | no | — |
| 445 | Q8 | — | 12 | 6 | no | — |
| 446 | Q8 | — | 12 | 2 | no | — |
| 447 | Q8 | — | 12 | 6 | no | — |
| 448 | Q8 | — | 24 | 6 | no | — |
| 449 | Q8 | #875 | 1 | 4 | yes | — |
| 450 | D4 | — | 6 | 6 | no | — |
| 451 | D4 | — | 6 | 2 | no | — |
| 452 | D4 | — | 12 | 6 | no | — |
| 453 | D4 | — | 12 | 6 | no | — |
| 454 | D4 | — | 12 | 6 | no | — |
| 455 | D4 | — | 24 | 3 | no | — |
| 456 | D4 | — | 24 | 3 | no | — |
| 457 | D4 | #875 | 1 | 12 | yes | — |
| 458 | C2×C4 | — | 4 | 3 | no | — |
| 459 | C2×C4 | — | 4 | 3 | no | — |
| 460 | C2×C4 | — | 6 | 2 | no | — |
| 461 | C2×C4 | — | 6 | 6 | no | — |
| 462 | C2×C4 | — | 6 | 3 | no | — |
| 463 | C2×C4 | — | 6 | 1 | no | — |
| 464 | C2×C4 | — | 12 | 6 | no | — |
| 465 | C2×C4 | — | 12 | 6 | no | — |
| 466 | C2×C4 | — | 12 | 6 | no | — |
| 467 | C2×C4 | — | 24 | 6 | no | — |
| 468 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 469 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 470 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 471 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 472 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 473 | C2×C4 | C2×#235 | 1 | 12 | yes | — |
| 474 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 475 | C8 | — | 2 | 2 | no | — |
| 476 | C8 | — | 2 | 6 | no | — |
| 477 | C2×C3 | — | 2 | 6 | no | — |
| 478 | C2×C3 | C22×#124 | 1 | 1 | yes | characteristic |
| 479 | C2×C3 | #3585 | 1 | 1 | yes | characteristic |
| 480 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 481 | D3 | — | 8 | 1 | no | — |
| 482 | D3 | — | 8 | 3 | no | — |
| 483 | C22 | — | 2 | 3 | no | — |
| 484 | C22 | — | 2 | 3 | no | — |
| 485 | C22 | — | 12 | 1 | no | — |
| 486 | C22 | — | 12 | 3 | no | — |
| 487 | C22 | — | 12 | 1 | no | — |
| 488 | C22 | — | 12 | 3 | no | — |
| 489 | C22 | — | 12 | 1 | no | — |
| 490 | C22 | — | 12 | 3 | no | — |
| 491 | C22 | — | 48 | 6 | no | — |
| 492 | C22 | C2×#875 | 1 | 6 | yes | — |
| 493 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 494 | C4 | — | 2 | 1 | no | — |
| 495 | C4 | — | 2 | 3 | no | — |
| 496 | C4 | — | 2 | 1 | no | — |
| 497 | C4 | — | 2 | 3 | no | — |
| 498 | C4 | — | 12 | 6 | no | — |
| 499 | C4 | — | 12 | 2 | no | — |
| 500 | C4 | — | 12 | 1 | no | — |
| 501 | C4 | — | 12 | 3 | no | — |
| 502 | C4 | C2×#875 | 1 | 6 | yes | — |
| 503 | C4 | C22×#235 | 1 | 2 | yes | — |
| 504 | C3 | #60625 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 505 | C2 | — | 2 | 6 | no | — |
| 506 | C2 | — | 24 | 3 | no | — |
| 507 | C2 | — | 24 | 1 | no | — |
| 508 | C2 | C22×#875 | 1 | 1 | yes | characteristic |
| 509 | C2 | #87167 | 1 | 1 | yes | characteristic |
| 510 | C2 | #87168 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #85828 | C2 | semidirect |
| 3. C3×#2875 | C2 | semidirect |
| 4. #83806 | C2 | semidirect |
| 5. #83797 | C2 | semidirect |
| 6. #78575 | C2 | semidirect |
| 7. #78563 | C2 | semidirect |
| 8. #78528 | C2 | semidirect |
| 9. #78527 | C2 | semidirect |
| 10. #78497 | C2 | semidirect |
| 11. C2×#4714 | C2 | semidirect |
| 28. #5519 | C22 | semidirect |
| 31. #5470 | C22 | semidirect |
| 32. C2×#869 | C22 | semidirect |
| 33. C3×#405 | C22 | semidirect |
| 34. C3×C4×M16 | C22 | semidirect |
| 35. C2×C3×#97 | C22 | semidirect |
| 37. #5133 | C22 | semidirect |
| 39. #5120 | C22 | semidirect |
| 41. #5113 | C22 | semidirect |
| 43. C2×#816 | C22 | semidirect |
| 44. #4714 | C22 | semidirect |
| 45. #4714 | C22 | semidirect |
| 46. #4714 | C22 | semidirect |
| 47. #4714 | C22 | semidirect |
| 48. #4714 | C22 | semidirect |
| 49. #4714 | C22 | semidirect |
| 50. #4713 | C22 | semidirect |
| 51. #4703 | C22 | semidirect |
| 52. #4697 | C22 | semidirect |
| 53. #4694 | C22 | semidirect |
| 54. #4681 | C22 | semidirect |
| 65. #2875 | D3 | semidirect |
| 177. #405 | C2×D3 | semidirect |
| 178. C4×M16 | C2×D3 | semidirect |
| 179. C2×#97 | C2×D3 | semidirect |
| 504. C3 | #60625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #85847 | 2 |
| #85828 | 2 |
| C3×#2875 | 2 |
| #83806 | 2 |
| #83797 | 2 |
| #78575 | 2 |
| #78563 | 2 |
| #78528 | 2 |
| #78527 | 2 |
| #78497 | 2 |
| C2×#4714 | 2 |
| #60625 | 3 |