Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2050 conjugacy classes of subgroups.
The subgroup lattice has 648 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86257 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #86219 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#3131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83339 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83285 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #81628 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #81593 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #81592 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #81557 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #81556 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #78838 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #78818 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #78463 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×C4×D3×C8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #60673 | — | 3 | 1 | no | maximal, Sylow |
| 16 | C3×#533 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#532 | C22 | 1 | 1 | yes | characteristic |
| 18 | #5828 | C22 | 1 | 2 | yes | — |
| 19 | Dic3×#41 | C22 | 1 | 2 | yes | — |
| 20 | C2×#950 | C22 | 1 | 4 | yes | — |
| 21 | C22×D3×C8 | C22 | 1 | 2 | yes | — |
| 22 | #5728 | C22 | 1 | 2 | yes | — |
| 23 | #5728 | C22 | 1 | 2 | yes | — |
| 24 | #5725 | C22 | 1 | 2 | yes | — |
| 25 | #5716 | C22 | 1 | 2 | yes | — |
| 26 | #5691 | C22 | 1 | 4 | yes | — |
| 27 | #5680 | C22 | 1 | 4 | yes | — |
| 28 | #5627 | — | 2 | 2 | no | — |
| 29 | #5624 | — | 2 | 2 | no | — |
| 30 | #5606 | — | 2 | 2 | no | — |
| 31 | #5600 | — | 2 | 2 | no | — |
| 32 | #5580 | — | 2 | 2 | no | — |
| 33 | C4×#239 | — | 2 | 2 | no | — |
| 34 | #5557 | — | 2 | 2 | no | — |
| 35 | C4×#237 | — | 2 | 2 | no | — |
| 36 | #5524 | C22 | 1 | 2 | yes | — |
| 37 | #5522 | C22 | 1 | 2 | yes | — |
| 38 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 40 | #5470 | C22 | 1 | 1 | yes | characteristic |
| 41 | C3×#488 | C22 | 1 | 4 | yes | complemented |
| 42 | C3×#487 | C22 | 1 | 2 | yes | complemented |
| 43 | C3×#486 | C22 | 1 | 2 | yes | complemented |
| 44 | C3×#416 | C22 | 1 | 4 | yes | — |
| 45 | C2×C3×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 46 | #5113 | C22 | 1 | 4 | yes | — |
| 47 | C2×C8×Dic3 | C22 | 1 | 2 | yes | — |
| 48 | #5092 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #5085 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #5080 | C22 | 1 | 2 | yes | complemented |
| 51 | #5078 | C22 | 1 | 2 | yes | complemented |
| 52 | #5076 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #5073 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #5065 | C22 | 1 | 4 | yes | complemented |
| 55 | #5059 | C22 | 1 | 4 | yes | complemented |
| 56 | #4998 | C22 | 1 | 4 | yes | — |
| 57 | C2×C4×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 58 | #4813 | C22 | 1 | 8 | yes | — |
| 59 | #4807 | C22 | 1 | 8 | yes | — |
| 60 | #4790 | C22 | 1 | 8 | yes | complemented |
| 61 | #4788 | C22 | 1 | 8 | yes | complemented |
| 62 | #4778 | C22 | 1 | 8 | yes | — |
| 63 | #4775 | C22 | 1 | 8 | yes | — |
| 64 | #4758 | C22 | 1 | 8 | yes | complemented |
| 65 | #4756 | C22 | 1 | 8 | yes | complemented |
| 66 | #4697 | C22 | 1 | 4 | yes | complemented |
| 67 | #4694 | C22 | 1 | 2 | yes | complemented |
| 68 | C4×D3×C8 | C22 | 1 | 2 | yes | — |
| 69 | C4×D3×C8 | C22 | 1 | 2 | yes | — |
| 70 | C4×D3×C8 | C22 | 1 | 4 | yes | — |
| 71 | #4681 | C22 | 1 | 2 | yes | complemented |
| 72 | #3444 | — | 3 | 1 | no | — |
| 73 | #3444 | — | 3 | 1 | no | — |
| 74 | #3170 | — | 3 | 2 | no | — |
| 75 | #3169 | — | 3 | 2 | no | — |
| 76 | #3168 | — | 3 | 8 | no | — |
| 77 | #3167 | — | 3 | 2 | no | — |
| 78 | #3167 | — | 3 | 2 | no | — |
| 79 | #3160 | — | 3 | 1 | no | — |
| 80 | #3147 | — | 3 | 1 | no | — |
| 81 | #3131 | — | 3 | 1 | no | — |
| 82 | #3131 | D3 | 1 | 1 | yes | characteristic, complemented |
| 83 | #3050 | — | 3 | 4 | no | — |
| 84 | C4×#135 | — | 3 | 4 | no | — |
| 85 | C22×C4×C8 | — | 3 | 1 | no | — |
| 86 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 87 | C2×#239 | — | 2 | 2 | no | — |
| 88 | C2×#237 | — | 2 | 2 | no | — |
| 89 | C2×#235 | C23 | 1 | 2 | yes | — |
| 90 | C22×C4×D3 | D4 | 1 | 2 | yes | — |
| 91 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 92 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 93 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 94 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 95 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 96 | C3×#125 | C23 | 1 | 2 | yes | — |
| 97 | C3×#124 | C23 | 1 | 2 | yes | — |
| 98 | C3×C22⋊Q8 | — | 2 | 2 | no | — |
| 99 | C3×#121 | — | 2 | 2 | no | — |
| 100 | C3×C4×Q8 | — | 2 | 2 | no | — |
| 101 | C3×C4×D4 | — | 2 | 2 | no | — |
| 102 | C3×#117 | C23 | 1 | 2 | yes | — |
| 103 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 104 | #950 | — | 2 | 16 | no | — |
| 105 | #947 | — | 2 | 2 | no | — |
| 106 | #946 | — | 2 | 2 | no | — |
| 107 | #946 | C23 | 1 | 4 | yes | — |
| 108 | Q8×Dic3 | — | 2 | 2 | no | — |
| 109 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 110 | C2×#216 | C23 | 1 | 4 | yes | — |
| 111 | C2×#215 | C23 | 1 | 4 | yes | — |
| 112 | #938 | — | 2 | 2 | no | — |
| 113 | #938 | C23 | 1 | 4 | yes | — |
| 114 | #937 | — | 2 | 2 | no | — |
| 115 | #936 | — | 2 | 2 | no | — |
| 116 | #935 | — | 2 | 2 | no | — |
| 117 | D4×Dic3 | — | 2 | 4 | no | — |
| 118 | D4×Dic3 | — | 2 | 2 | no | — |
| 119 | D4×Dic3 | C23 | 1 | 4 | yes | — |
| 120 | C2×#214 | C23 | 1 | 4 | yes | — |
| 121 | C2×#213 | C23 | 1 | 4 | yes | — |
| 122 | #930 | — | 2 | 2 | no | — |
| 123 | C4×#67 | — | 2 | 4 | no | — |
| 124 | #926 | — | 2 | 2 | no | — |
| 125 | #926 | C23 | 1 | 2 | yes | — |
| 126 | #924 | — | 2 | 2 | no | — |
| 127 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 128 | C2×C4×Dic3 | D4 | 1 | 2 | yes | — |
| 129 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 130 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 131 | C2×D3×C8 | — | 2 | 8 | no | — |
| 132 | C2×D3×C8 | C23 | 1 | 4 | yes | — |
| 133 | C2×D3×C8 | C23 | 1 | 4 | yes | — |
| 134 | #898 | — | 2 | 4 | no | — |
| 135 | #897 | — | 2 | 2 | no | — |
| 136 | #897 | C23 | 1 | 4 | yes | — |
| 137 | #895 | — | 2 | 2 | no | — |
| 138 | #895 | C23 | 1 | 4 | yes | — |
| 139 | #894 | — | 2 | 4 | no | — |
| 140 | #893 | — | 2 | 4 | no | — |
| 141 | #893 | — | 2 | 2 | no | — |
| 142 | #893 | C23 | 1 | 4 | yes | — |
| 143 | #892 | — | 2 | 2 | no | — |
| 144 | #892 | — | 2 | 2 | no | — |
| 145 | #892 | — | 2 | 4 | no | — |
| 146 | #890 | — | 2 | 2 | no | — |
| 147 | #890 | — | 2 | 2 | no | — |
| 148 | #887 | — | 2 | 2 | no | — |
| 149 | #887 | C23 | 1 | 4 | yes | — |
| 150 | #886 | — | 2 | 2 | no | — |
| 151 | #883 | — | 2 | 4 | no | — |
| 152 | #882 | — | 2 | 2 | no | — |
| 153 | #67⋊C4 | — | 2 | 4 | no | — |
| 154 | #67⋊C4 | — | 2 | 4 | no | — |
| 155 | #879 | — | 2 | 4 | no | — |
| 156 | #877 | — | 2 | 4 | no | — |
| 157 | #875 | C23 | 1 | 2 | yes | — |
| 158 | #874 | C23 | 1 | 1 | yes | characteristic |
| 159 | C4×D12 | — | 2 | 4 | no | — |
| 160 | C4×D12 | — | 2 | 2 | no | — |
| 161 | #872 | — | 2 | 2 | no | — |
| 162 | C42×D3 | — | 2 | 2 | no | — |
| 163 | C42×D3 | D4 | 1 | 2 | yes | — |
| 164 | C42×D3 | D4 | 1 | 2 | yes | — |
| 165 | C42×D3 | C23 | 1 | 2 | yes | — |
| 166 | C42×D3 | C23 | 1 | 2 | yes | — |
| 167 | #870 | C23 | 1 | 2 | yes | — |
| 168 | #869 | C23 | 1 | 1 | yes | characteristic |
| 169 | #869 | C23 | 1 | 2 | yes | — |
| 170 | C4×Dic6 | — | 2 | 2 | no | — |
| 171 | C3×#103 | C23 | 1 | 8 | yes | — |
| 172 | C3×#102 | C23 | 1 | 8 | yes | — |
| 173 | C3×C4×C8 | C23 | 1 | 2 | yes | — |
| 174 | C3×C4×C8 | C23 | 1 | 2 | yes | — |
| 175 | #821 | C23 | 1 | 8 | yes | — |
| 176 | #816 | C23 | 1 | 8 | yes | — |
| 177 | C8×Dic3 | C23 | 1 | 4 | yes | — |
| 178 | C8×Dic3 | C23 | 1 | 4 | yes | — |
| 179 | #808 | C23 | 1 | 8 | yes | — |
| 180 | #807 | C23 | 1 | 8 | yes | — |
| 181 | C4×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 182 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 183 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 184 | C2×#135 | — | 3 | 4 | no | — |
| 185 | C23×C8 | — | 3 | 2 | no | — |
| 186 | #533 | — | 3 | 2 | no | — |
| 187 | #533 | — | 3 | 2 | no | — |
| 188 | #533 | — | 3 | 1 | no | — |
| 189 | #533 | C2×D3 | 1 | 1 | yes | characteristic |
| 190 | #532 | — | 3 | 2 | no | — |
| 191 | #532 | — | 3 | 2 | no | — |
| 192 | #532 | — | 3 | 1 | no | — |
| 193 | #532 | C2×D3 | 1 | 1 | yes | characteristic |
| 194 | #529 | — | 3 | 4 | no | — |
| 195 | #529 | — | 3 | 4 | no | — |
| 196 | #529 | — | 6 | 2 | no | — |
| 197 | #529 | — | 6 | 2 | no | — |
| 198 | #529 | — | 6 | 2 | no | — |
| 199 | #529 | — | 6 | 2 | no | — |
| 200 | #525 | — | 3 | 2 | no | — |
| 201 | #525 | — | 3 | 2 | no | — |
| 202 | #525 | — | 6 | 2 | no | — |
| 203 | #525 | — | 6 | 2 | no | — |
| 204 | C4×#41 | — | 3 | 2 | no | — |
| 205 | C4×#41 | — | 3 | 2 | no | — |
| 206 | C4×#41 | — | 6 | 2 | no | — |
| 207 | C4×#41 | — | 6 | 2 | no | — |
| 208 | C22×C42 | — | 3 | 1 | no | — |
| 209 | #500 | — | 3 | 2 | no | — |
| 210 | #499 | — | 3 | 4 | no | — |
| 211 | #498 | — | 3 | 2 | no | — |
| 212 | #495 | — | 3 | 4 | no | — |
| 213 | #494 | — | 3 | 1 | no | — |
| 214 | #493 | — | 3 | 1 | no | — |
| 215 | #492 | — | 3 | 1 | no | — |
| 216 | #492 | — | 3 | 1 | no | — |
| 217 | #488 | — | 3 | 4 | no | — |
| 218 | #488 | C2×D3 | 1 | 4 | yes | complemented |
| 219 | #487 | — | 3 | 2 | no | — |
| 220 | #487 | C2×D3 | 1 | 2 | yes | complemented |
| 221 | #486 | — | 3 | 2 | no | — |
| 222 | #486 | C2×D3 | 1 | 2 | yes | complemented |
| 223 | #467 | — | 3 | 8 | no | — |
| 224 | #466 | — | 3 | 8 | no | — |
| 225 | #465 | — | 3 | 8 | no | — |
| 226 | #465 | — | 3 | 8 | no | — |
| 227 | C4×Q16 | — | 3 | 8 | no | — |
| 228 | C4×SD16 | — | 3 | 8 | no | — |
| 229 | C4×SD16 | — | 3 | 8 | no | — |
| 230 | C4×D8 | — | 3 | 8 | no | — |
| 231 | #427 | — | 3 | 4 | no | — |
| 232 | #416 | — | 3 | 4 | no | — |
| 233 | #416 | C2×D3 | 1 | 4 | yes | — |
| 234 | C2×C4×C8 | — | 3 | 2 | no | — |
| 235 | C2×C4×C8 | — | 3 | 1 | no | — |
| 236 | C2×C4×C8 | — | 3 | 2 | no | — |
| 237 | C2×C4×C8 | — | 3 | 4 | no | — |
| 238 | C2×C4×C8 | — | 3 | 2 | no | — |
| 239 | C2×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 240 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C3×#41 | — | 2 | 8 | no | — |
| 242 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 243 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 244 | C2×C3×D4 | — | 2 | 2 | no | — |
| 245 | C2×C3×D4 | — | 2 | 2 | no | — |
| 246 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 247 | C22×C3×C4 | — | 2 | 2 | no | — |
| 248 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 249 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 250 | C2×#67 | — | 2 | 2 | no | — |
| 251 | C2×#67 | — | 2 | 4 | no | — |
| 252 | C22×Dic3 | — | 2 | 4 | no | — |
| 253 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 254 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | #239 | — | 4 | 8 | no | — |
| 256 | #237 | — | 4 | 8 | no | — |
| 257 | #235 | — | 2 | 8 | no | — |
| 258 | C2×D12 | — | 2 | 4 | no | — |
| 259 | C2×D12 | — | 2 | 2 | no | — |
| 260 | C2×D12 | C24 | 1 | 2 | yes | — |
| 261 | C2×C4×D3 | — | 2 | 4 | no | — |
| 262 | C2×C4×D3 | — | 2 | 8 | no | — |
| 263 | C2×C4×D3 | — | 2 | 2 | no | — |
| 264 | C2×C4×D3 | — | 2 | 4 | no | — |
| 265 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 266 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 267 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 268 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 269 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 270 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 271 | C2×Dic6 | — | 2 | 2 | no | — |
| 272 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 273 | C2×C3×C8 | — | 2 | 4 | no | — |
| 274 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 275 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 276 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 277 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 278 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 279 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 280 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 281 | C3×C42 | — | 2 | 2 | no | — |
| 282 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 283 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 284 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 285 | #217 | — | 2 | 2 | no | — |
| 286 | #217 | — | 2 | 4 | no | — |
| 287 | #217 | — | 2 | 4 | no | — |
| 288 | #216 | — | 2 | 8 | no | — |
| 289 | #215 | — | 2 | 8 | no | — |
| 290 | #214 | — | 2 | 8 | no | — |
| 291 | #213 | — | 2 | 8 | no | — |
| 292 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 293 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 294 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 295 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 296 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 297 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 298 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 299 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 300 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 301 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 302 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 303 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 304 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 305 | C4×Dic3 | — | 2 | 2 | no | — |
| 306 | C4×Dic3 | — | 2 | 4 | no | — |
| 307 | C4×Dic3 | — | 2 | 4 | no | — |
| 308 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 309 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 310 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 311 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 312 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 313 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 314 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 315 | C2×C3⋊C8 | #41 | 1 | 8 | yes | complemented |
| 316 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 317 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 318 | D3×C8 | — | 2 | 8 | no | — |
| 319 | D3×C8 | — | 2 | 8 | no | — |
| 320 | C2×#41 | — | 3 | 2 | no | — |
| 321 | C2×#41 | — | 6 | 2 | no | — |
| 322 | C2×#41 | — | 6 | 2 | no | — |
| 323 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 324 | C23×C4 | — | 3 | 2 | no | — |
| 325 | C23×C4 | — | 3 | 1 | no | — |
| 326 | #135 | — | 6 | 16 | no | — |
| 327 | C2×Q16 | — | 3 | 4 | no | — |
| 328 | C2×SD16 | — | 3 | 4 | no | — |
| 329 | C2×SD16 | — | 3 | 4 | no | — |
| 330 | C2×D8 | — | 3 | 4 | no | — |
| 331 | C22×C8 | — | 3 | 2 | no | — |
| 332 | C22×C8 | — | 3 | 4 | no | — |
| 333 | C22×C8 | — | 3 | 4 | no | — |
| 334 | C22×C8 | — | 6 | 8 | no | — |
| 335 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 336 | C4⋊Q8 | — | 3 | 2 | no | — |
| 337 | C4⋊Q8 | — | 3 | 1 | no | — |
| 338 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 339 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 340 | #127 | — | 3 | 1 | no | — |
| 341 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 342 | #126 | — | 6 | 4 | no | — |
| 343 | #126 | — | 6 | 4 | no | — |
| 344 | #125 | — | 3 | 2 | no | — |
| 345 | #125 | — | 6 | 2 | no | — |
| 346 | #125 | — | 6 | 2 | no | — |
| 347 | #125 | C22×D3 | 1 | 2 | yes | — |
| 348 | #124 | — | 3 | 2 | no | — |
| 349 | #124 | — | 6 | 2 | no | — |
| 350 | #124 | — | 6 | 2 | no | — |
| 351 | #124 | C22×D3 | 1 | 2 | yes | — |
| 352 | #123 | — | 6 | 2 | no | — |
| 353 | #123 | — | 6 | 4 | no | — |
| 354 | #123 | — | 6 | 4 | no | — |
| 355 | #123 | — | 6 | 2 | no | — |
| 356 | C22⋊Q8 | — | 2 | 2 | no | — |
| 357 | C22⋊Q8 | — | 3 | 4 | no | — |
| 358 | C22⋊Q8 | — | 3 | 4 | no | — |
| 359 | C22⋊Q8 | — | 6 | 2 | no | — |
| 360 | C22⋊Q8 | — | 6 | 2 | no | — |
| 361 | C22⋊Q8 | — | 6 | 2 | no | — |
| 362 | #121 | — | 2 | 2 | no | — |
| 363 | #121 | — | 3 | 4 | no | — |
| 364 | #121 | — | 3 | 4 | no | — |
| 365 | #121 | — | 6 | 2 | no | — |
| 366 | #121 | — | 6 | 2 | no | — |
| 367 | #121 | — | 6 | 2 | no | — |
| 368 | #120 | — | 6 | 2 | no | — |
| 369 | #120 | — | 6 | 2 | no | — |
| 370 | C4×Q8 | — | 2 | 2 | no | — |
| 371 | C4×Q8 | — | 3 | 4 | no | — |
| 372 | C4×Q8 | — | 3 | 4 | no | — |
| 373 | C4×Q8 | — | 6 | 2 | no | — |
| 374 | C4×Q8 | — | 6 | 2 | no | — |
| 375 | C4×Q8 | — | 6 | 2 | no | — |
| 376 | C4×D4 | — | 2 | 2 | no | — |
| 377 | C4×D4 | — | 3 | 4 | no | — |
| 378 | C4×D4 | — | 3 | 4 | no | — |
| 379 | C4×D4 | — | 6 | 4 | no | — |
| 380 | C4×D4 | — | 6 | 2 | no | — |
| 381 | C4×D4 | — | 6 | 2 | no | — |
| 382 | C4×D4 | — | 6 | 4 | no | — |
| 383 | C4×D4 | — | 6 | 4 | no | — |
| 384 | C4×D4 | — | 6 | 4 | no | — |
| 385 | C4×D4 | — | 6 | 4 | no | — |
| 386 | C4×D4 | — | 6 | 4 | no | — |
| 387 | C4×D4 | — | 6 | 2 | no | — |
| 388 | #117 | — | 3 | 2 | no | — |
| 389 | #117 | — | 6 | 2 | no | — |
| 390 | #117 | — | 6 | 4 | no | — |
| 391 | #117 | — | 6 | 4 | no | — |
| 392 | #117 | — | 6 | 2 | no | — |
| 393 | #117 | — | 6 | 2 | no | — |
| 394 | #117 | — | 6 | 2 | no | — |
| 395 | #117 | C22×D3 | 1 | 2 | yes | — |
| 396 | C2×C42 | — | 3 | 2 | no | — |
| 397 | C2×C42 | — | 3 | 1 | no | — |
| 398 | C2×C42 | — | 3 | 2 | no | — |
| 399 | C2×C42 | — | 3 | 2 | no | — |
| 400 | C2×C42 | — | 3 | 2 | no | — |
| 401 | C2×C42 | — | 3 | 2 | no | — |
| 402 | C2×C42 | — | 6 | 2 | no | — |
| 403 | C2×C42 | — | 6 | 2 | no | — |
| 404 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 405 | #107 | — | 3 | 8 | no | — |
| 406 | #106 | — | 3 | 8 | no | — |
| 407 | #103 | — | 3 | 8 | no | — |
| 408 | #103 | C22×D3 | 1 | 8 | yes | — |
| 409 | #102 | — | 3 | 8 | no | — |
| 410 | #102 | C22×D3 | 1 | 8 | yes | — |
| 411 | C4×C8 | — | 3 | 4 | no | — |
| 412 | C4×C8 | — | 3 | 4 | no | — |
| 413 | C4×C8 | — | 3 | 1 | no | — |
| 414 | C4×C8 | — | 3 | 1 | no | — |
| 415 | C4×C8 | — | 3 | 2 | no | — |
| 416 | C4×C8 | C22×D3 | 1 | 2 | yes | — |
| 417 | C4×C8 | C22×D3 | 1 | 2 | yes | — |
| 418 | C23×C3 | — | 2 | 2 | no | — |
| 419 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 420 | C22×D3 | — | 2 | 2 | no | — |
| 421 | C22×D3 | — | 2 | 4 | no | — |
| 422 | C22×D3 | — | 2 | 2 | no | — |
| 423 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 424 | C3×Q8 | — | 2 | 4 | no | — |
| 425 | C3×Q8 | — | 4 | 4 | no | — |
| 426 | C3×D4 | — | 2 | 4 | no | — |
| 427 | C3×D4 | — | 4 | 4 | no | — |
| 428 | C3×D4 | — | 4 | 4 | no | — |
| 429 | C2×C3×C4 | — | 2 | 4 | no | — |
| 430 | C2×C3×C4 | — | 2 | 2 | no | — |
| 431 | C2×C3×C4 | — | 2 | 4 | no | — |
| 432 | C2×C3×C4 | — | 4 | 4 | no | — |
| 433 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 434 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 435 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 436 | C2×C3×C4 | C2×#41 | 1 | 4 | yes | — |
| 437 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 438 | #67 | — | 4 | 4 | no | — |
| 439 | #67 | — | 4 | 8 | no | — |
| 440 | C2×Dic3 | — | 2 | 2 | no | — |
| 441 | C2×Dic3 | — | 2 | 4 | no | — |
| 442 | C2×Dic3 | — | 2 | 4 | no | — |
| 443 | C2×Dic3 | — | 2 | 2 | no | — |
| 444 | C2×Dic3 | — | 4 | 8 | no | — |
| 445 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 446 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 447 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 448 | D12 | — | 2 | 4 | no | — |
| 449 | D12 | — | 4 | 8 | no | — |
| 450 | D12 | — | 4 | 4 | no | — |
| 451 | C4×D3 | — | 2 | 4 | no | — |
| 452 | C4×D3 | — | 2 | 4 | no | — |
| 453 | C4×D3 | — | 2 | 4 | no | — |
| 454 | C4×D3 | — | 2 | 4 | no | — |
| 455 | C4×D3 | — | 2 | 4 | no | — |
| 456 | C4×D3 | — | 4 | 4 | no | — |
| 457 | C4×D3 | — | 4 | 8 | no | — |
| 458 | C4×D3 | #135 | 1 | 8 | yes | complemented |
| 459 | Dic6 | — | 2 | 4 | no | — |
| 460 | Dic6 | — | 4 | 4 | no | — |
| 461 | C3×C8 | — | 2 | 4 | no | — |
| 462 | C3⋊C8 | C2×#41 | 1 | 4 | yes | — |
| 463 | C3⋊C8 | C2×#41 | 1 | 4 | yes | — |
| 464 | C24 | — | 3 | 1 | no | — |
| 465 | #41 | — | 2 | 8 | no | — |
| 466 | #41 | — | 6 | 8 | no | — |
| 467 | #41 | — | 12 | 8 | no | — |
| 468 | #41 | — | 12 | 8 | no | — |
| 469 | C2×Q8 | — | 2 | 2 | no | — |
| 470 | C2×Q8 | — | 3 | 2 | no | — |
| 471 | C2×Q8 | — | 6 | 2 | no | — |
| 472 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 473 | C2×D4 | — | 2 | 2 | no | — |
| 474 | C2×D4 | — | 2 | 2 | no | — |
| 475 | C2×D4 | — | 3 | 2 | no | — |
| 476 | C2×D4 | — | 6 | 4 | no | — |
| 477 | C2×D4 | — | 6 | 4 | no | — |
| 478 | C2×D4 | — | 6 | 2 | no | — |
| 479 | C2×D4 | — | 6 | 2 | no | — |
| 480 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 481 | C22×C4 | — | 2 | 2 | no | — |
| 482 | C22×C4 | — | 3 | 2 | no | — |
| 483 | C22×C4 | — | 3 | 2 | no | — |
| 484 | C22×C4 | — | 3 | 1 | no | — |
| 485 | C22×C4 | — | 3 | 2 | no | — |
| 486 | C22×C4 | — | 3 | 2 | no | — |
| 487 | C22×C4 | — | 3 | 2 | no | — |
| 488 | C22×C4 | — | 3 | 2 | no | — |
| 489 | C22×C4 | — | 3 | 2 | no | — |
| 490 | C22×C4 | — | 6 | 8 | no | — |
| 491 | C22×C4 | — | 6 | 4 | no | — |
| 492 | C22×C4 | — | 6 | 4 | no | — |
| 493 | C22×C4 | — | 6 | 4 | no | — |
| 494 | C22×C4 | — | 6 | 2 | no | — |
| 495 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 496 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 497 | Q16 | — | 6 | 8 | no | — |
| 498 | SD16 | — | 6 | 8 | no | — |
| 499 | SD16 | — | 6 | 8 | no | — |
| 500 | D8 | — | 6 | 8 | no | — |
| 501 | C2×C8 | — | 2 | 4 | no | — |
| 502 | C2×C8 | — | 3 | 8 | no | — |
| 503 | C2×C8 | — | 3 | 2 | no | — |
| 504 | C2×C8 | — | 3 | 2 | no | — |
| 505 | C2×C8 | — | 6 | 8 | no | — |
| 506 | C2×C8 | — | 6 | 8 | no | — |
| 507 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 508 | C4⋊C4 | — | 2 | 2 | no | — |
| 509 | C4⋊C4 | — | 2 | 2 | no | — |
| 510 | C4⋊C4 | — | 2 | 4 | no | — |
| 511 | C4⋊C4 | — | 3 | 4 | no | — |
| 512 | C4⋊C4 | — | 6 | 4 | no | — |
| 513 | C4⋊C4 | — | 6 | 4 | no | — |
| 514 | C4⋊C4 | — | 6 | 4 | no | — |
| 515 | C4⋊C4 | — | 6 | 4 | no | — |
| 516 | C4⋊C4 | — | 6 | 2 | no | — |
| 517 | C4⋊C4 | — | 6 | 2 | no | — |
| 518 | C4⋊C4 | — | 6 | 4 | no | — |
| 519 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 520 | C22⋊C4 | — | 2 | 2 | no | — |
| 521 | C22⋊C4 | — | 2 | 4 | no | — |
| 522 | C22⋊C4 | — | 6 | 4 | no | — |
| 523 | C22⋊C4 | — | 6 | 4 | no | — |
| 524 | C22⋊C4 | — | 6 | 4 | no | — |
| 525 | C22⋊C4 | — | 6 | 4 | no | — |
| 526 | C22⋊C4 | — | 6 | 4 | no | — |
| 527 | C22⋊C4 | — | 6 | 4 | no | — |
| 528 | C22⋊C4 | — | 6 | 2 | no | — |
| 529 | C22⋊C4 | — | 6 | 4 | no | — |
| 530 | C42 | — | 2 | 2 | no | — |
| 531 | C42 | — | 3 | 2 | no | — |
| 532 | C42 | — | 3 | 2 | no | — |
| 533 | C42 | — | 3 | 2 | no | — |
| 534 | C42 | — | 3 | 2 | no | — |
| 535 | C42 | — | 3 | 1 | no | — |
| 536 | C42 | — | 3 | 1 | no | — |
| 537 | C42 | — | 3 | 2 | no | — |
| 538 | C42 | — | 6 | 4 | no | — |
| 539 | C42 | — | 6 | 4 | no | — |
| 540 | C42 | — | 6 | 2 | no | — |
| 541 | C42 | D3×D4 | 1 | 2 | yes | — |
| 542 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 543 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 544 | C22×C3 | — | 2 | 2 | no | — |
| 545 | C22×C3 | — | 4 | 2 | no | — |
| 546 | C22×C3 | — | 4 | 4 | no | — |
| 547 | C22×C3 | #532 | 1 | 2 | yes | — |
| 548 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 549 | C2×D3 | — | 2 | 8 | no | — |
| 550 | C2×D3 | — | 2 | 2 | no | — |
| 551 | C2×D3 | — | 2 | 2 | no | — |
| 552 | C2×D3 | — | 4 | 2 | no | — |
| 553 | C2×D3 | — | 4 | 4 | no | — |
| 554 | C2×D3 | C2×#135 | 1 | 4 | yes | — |
| 555 | C3×C4 | — | 2 | 2 | no | — |
| 556 | C3×C4 | — | 4 | 2 | no | — |
| 557 | C3×C4 | — | 4 | 4 | no | — |
| 558 | C3×C4 | #532 | 1 | 2 | yes | — |
| 559 | C3×C4 | C2×#135 | 1 | 4 | yes | — |
| 560 | C3×C4 | C22×#41 | 1 | 2 | yes | — |
| 561 | Dic3 | — | 2 | 2 | no | — |
| 562 | Dic3 | — | 2 | 2 | no | — |
| 563 | Dic3 | — | 4 | 2 | no | — |
| 564 | Dic3 | — | 4 | 4 | no | — |
| 565 | Dic3 | C2×#135 | 1 | 4 | yes | — |
| 566 | C23 | — | 2 | 2 | no | — |
| 567 | C23 | — | 3 | 2 | no | — |
| 568 | C23 | — | 6 | 4 | no | — |
| 569 | C23 | — | 6 | 2 | no | — |
| 570 | C23 | — | 6 | 2 | no | — |
| 571 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 572 | Q8 | — | 2 | 4 | no | — |
| 573 | Q8 | — | 4 | 4 | no | — |
| 574 | Q8 | — | 6 | 4 | no | — |
| 575 | Q8 | — | 12 | 4 | no | — |
| 576 | D4 | — | 2 | 4 | no | — |
| 577 | D4 | — | 4 | 4 | no | — |
| 578 | D4 | — | 4 | 4 | no | — |
| 579 | D4 | — | 6 | 4 | no | — |
| 580 | D4 | — | 12 | 8 | no | — |
| 581 | D4 | — | 12 | 8 | no | — |
| 582 | D4 | — | 12 | 4 | no | — |
| 583 | D4 | — | 12 | 4 | no | — |
| 584 | C2×C4 | — | 2 | 4 | no | — |
| 585 | C2×C4 | — | 2 | 4 | no | — |
| 586 | C2×C4 | — | 2 | 2 | no | — |
| 587 | C2×C4 | — | 3 | 2 | no | — |
| 588 | C2×C4 | — | 3 | 8 | no | — |
| 589 | C2×C4 | — | 3 | 2 | no | — |
| 590 | C2×C4 | — | 3 | 2 | no | — |
| 591 | C2×C4 | — | 4 | 4 | no | — |
| 592 | C2×C4 | — | 6 | 4 | no | — |
| 593 | C2×C4 | — | 6 | 4 | no | — |
| 594 | C2×C4 | — | 6 | 4 | no | — |
| 595 | C2×C4 | — | 6 | 2 | no | — |
| 596 | C2×C4 | — | 6 | 4 | no | — |
| 597 | C2×C4 | — | 6 | 4 | no | — |
| 598 | C2×C4 | — | 6 | 4 | no | — |
| 599 | C2×C4 | — | 6 | 4 | no | — |
| 600 | C2×C4 | — | 6 | 2 | no | — |
| 601 | C2×C4 | — | 12 | 8 | no | — |
| 602 | C2×C4 | — | 12 | 8 | no | — |
| 603 | C2×C4 | — | 12 | 4 | no | — |
| 604 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 605 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 606 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 607 | C2×C4 | D3×#41 | 1 | 4 | yes | — |
| 608 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 609 | C8 | — | 2 | 4 | no | — |
| 610 | C8 | — | 3 | 4 | no | — |
| 611 | C8 | — | 3 | 4 | no | — |
| 612 | C2×C3 | — | 2 | 2 | no | — |
| 613 | C2×C3 | — | 8 | 2 | no | — |
| 614 | C2×C3 | C2×#532 | 1 | 1 | yes | characteristic |
| 615 | C2×C3 | C22×#135 | 1 | 2 | yes | — |
| 616 | D3 | — | 2 | 4 | no | — |
| 617 | D3 | — | 8 | 2 | no | — |
| 618 | C22 | — | 2 | 2 | no | — |
| 619 | C22 | — | 3 | 4 | no | — |
| 620 | C22 | — | 4 | 2 | no | — |
| 621 | C22 | — | 4 | 4 | no | — |
| 622 | C22 | — | 6 | 8 | no | — |
| 623 | C22 | — | 6 | 2 | no | — |
| 624 | C22 | — | 6 | 2 | no | — |
| 625 | C22 | — | 12 | 2 | no | — |
| 626 | C22 | — | 12 | 4 | no | — |
| 627 | C22 | #5668 | 1 | 2 | yes | — |
| 628 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 629 | C4 | — | 2 | 2 | no | — |
| 630 | C4 | — | 3 | 4 | no | — |
| 631 | C4 | — | 4 | 2 | no | — |
| 632 | C4 | — | 4 | 4 | no | — |
| 633 | C4 | — | 6 | 2 | no | — |
| 634 | C4 | — | 6 | 2 | no | — |
| 635 | C4 | — | 12 | 2 | no | — |
| 636 | C4 | — | 12 | 4 | no | — |
| 637 | C4 | #5668 | 1 | 2 | yes | — |
| 638 | C4 | D3×#135 | 1 | 4 | yes | — |
| 639 | C4 | C2×D3×#41 | 1 | 2 | yes | — |
| 640 | C3 | #60673 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 641 | C2 | — | 2 | 2 | no | — |
| 642 | C2 | — | 6 | 4 | no | — |
| 643 | C2 | — | 8 | 2 | no | — |
| 644 | C2 | — | 24 | 2 | no | — |
| 645 | C2 | C2×#5668 | 1 | 1 | yes | characteristic |
| 646 | C2 | C2×D3×#135 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86257 | C2 | semidirect |
| 2. #86219 | C2 | semidirect |
| 3. C3×#3131 | C2 | semidirect |
| 4. #83339 | C2 | semidirect |
| 5. #83285 | C2 | semidirect |
| 6. #81628 | C2 | semidirect |
| 7. #81593 | C2 | semidirect |
| 8. #81592 | C2 | semidirect |
| 9. #81557 | C2 | semidirect |
| 10. #81556 | C2 | semidirect |
| 11. #78838 | C2 | semidirect |
| 12. #78818 | C2 | semidirect |
| 13. #78463 | C2 | semidirect |
| 14. C2×C4×D3×C8 | C2 | semidirect |
| 41. C3×#488 | C22 | semidirect |
| 42. C3×#487 | C22 | semidirect |
| 43. C3×#486 | C22 | semidirect |
| 48. #5092 | C22 | semidirect |
| 49. #5085 | C22 | semidirect |
| 50. #5080 | C22 | semidirect |
| 51. #5078 | C22 | semidirect |
| 52. #5076 | C22 | semidirect |
| 53. #5073 | C22 | semidirect |
| 54. #5065 | C22 | semidirect |
| 55. #5059 | C22 | semidirect |
| 60. #4790 | C22 | semidirect |
| 61. #4788 | C22 | semidirect |
| 64. #4758 | C22 | semidirect |
| 65. #4756 | C22 | semidirect |
| 66. #4697 | C22 | semidirect |
| 67. #4694 | C22 | semidirect |
| 71. #4681 | C22 | semidirect |
| 82. #3131 | D3 | semidirect |
| 218. #488 | C2×D3 | semidirect |
| 220. #487 | C2×D3 | semidirect |
| 222. #486 | C2×D3 | semidirect |
| 315. C2×C3⋊C8 | #41 | semidirect |
| 458. C4×D3 | #135 | semidirect |
| 640. C3 | #60673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86257 | 2 |
| #86219 | 2 |
| C3×#3131 | 2 |
| #83339 | 2 |
| #83285 | 2 |
| #81628 | 2 |
| #81593 | 2 |
| #81592 | 2 |
| #81557 | 2 |
| #81556 | 2 |
| #78838 | 2 |
| #78818 | 2 |
| #78463 | 2 |
| C2×C4×D3×C8 | 2 |
| #60673 | 3 |