Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2042 conjugacy classes of subgroups.
The subgroup lattice has 408 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#3503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #85827 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #83471 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #83337 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #83334 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #83199 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#5093 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #82570 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C4×#948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #60623 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C2×#1010 | C22 | 1 | 2 | yes | — |
| 12 | C3×Q82 | — | 2 | 1 | no | — |
| 13 | C3×#557 | — | 2 | 1 | no | — |
| 14 | C3×#554 | — | 2 | 3 | no | — |
| 15 | C3×D4×Q8 | — | 2 | 3 | no | — |
| 16 | C3×#544 | C22 | 1 | 6 | yes | — |
| 17 | C3×#533 | C22 | 1 | 3 | yes | — |
| 18 | C2×C3×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 19 | C3×#520 | C22 | 1 | 2 | yes | — |
| 20 | C3×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#948 | C22 | 1 | 2 | yes | — |
| 22 | Q8×D12 | — | 2 | 1 | no | — |
| 23 | Q8×D12 | — | 2 | 1 | no | — |
| 24 | #5555 | — | 2 | 3 | no | — |
| 25 | #5555 | — | 2 | 3 | no | — |
| 26 | #5526 | C22 | 1 | 6 | yes | — |
| 27 | #5477 | C22 | 1 | 3 | yes | — |
| 28 | C2×#869 | C22 | 1 | 3 | yes | — |
| 29 | #5093 | C22 | 1 | 12 | yes | — |
| 30 | #5093 | C22 | 1 | 3 | yes | — |
| 31 | #5093 | C22 | 1 | 3 | yes | — |
| 32 | #5093 | C22 | 1 | 6 | yes | — |
| 33 | #5089 | C22 | 1 | 12 | yes | — |
| 34 | #5088 | C22 | 1 | 1 | yes | characteristic |
| 35 | #5088 | C22 | 1 | 3 | yes | — |
| 36 | #5069 | C22 | 1 | 12 | yes | — |
| 37 | #5068 | C22 | 1 | 12 | yes | — |
| 38 | #5004 | C22 | 1 | 12 | yes | — |
| 39 | #5002 | C22 | 1 | 12 | yes | — |
| 40 | #4997 | C22 | 1 | 6 | yes | — |
| 41 | C2×#810 | C22 | 1 | 12 | yes | — |
| 42 | #4966 | C22 | 1 | 12 | yes | — |
| 43 | C4×#208 | C22 | 1 | 3 | yes | — |
| 44 | C2×C4×C3⋊C8 | C22 | 1 | 3 | yes | — |
| 45 | #3503 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | #3499 | — | 3 | 1 | no | — |
| 47 | #3141 | — | 3 | 3 | no | — |
| 48 | #3139 | — | 3 | 3 | no | — |
| 49 | #3137 | — | 3 | 12 | no | — |
| 50 | #3131 | — | 3 | 3 | no | — |
| 51 | C2×#487 | — | 3 | 3 | no | — |
| 52 | #2898 | — | 3 | 4 | no | — |
| 53 | C4×#131 | — | 3 | 1 | no | — |
| 54 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 55 | C22×C3×Q8 | — | 2 | 3 | no | — |
| 56 | #1010 | — | 2 | 16 | no | — |
| 57 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 58 | C2×#237 | — | 2 | 6 | no | — |
| 59 | C2×#235 | C23 | 1 | 6 | yes | — |
| 60 | C22×Dic6 | C23 | 1 | 6 | yes | — |
| 61 | C3×C4⋊Q8 | — | 2 | 6 | no | — |
| 62 | C3×C4⋊Q8 | — | 2 | 3 | no | — |
| 63 | C3×C4⋊Q8 | — | 2 | 3 | no | — |
| 64 | C3×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 65 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 66 | C3×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 67 | C3×#125 | — | 2 | 6 | no | — |
| 68 | C3×#125 | C23 | 1 | 6 | yes | — |
| 69 | C3×C22⋊Q8 | — | 2 | 3 | no | — |
| 70 | C3×C22⋊Q8 | — | 2 | 3 | no | — |
| 71 | C3×C22⋊Q8 | — | 2 | 12 | no | — |
| 72 | C3×C4×Q8 | — | 2 | 2 | no | — |
| 73 | C3×C4×Q8 | — | 2 | 3 | no | — |
| 74 | C3×C4×Q8 | — | 2 | 3 | no | — |
| 75 | C3×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 76 | C3×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 77 | C3×C4×D4 | — | 2 | 6 | no | — |
| 78 | C3×C4×D4 | D4 | 1 | 3 | yes | — |
| 79 | C3×C4×D4 | D4 | 1 | 3 | yes | — |
| 80 | C3×#117 | C23 | 1 | 6 | yes | — |
| 81 | C3×#117 | C23 | 1 | 3 | yes | — |
| 82 | C2×C3×C4⋊C4 | — | 2 | 3 | no | — |
| 83 | C2×C3×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 84 | C2×C3×C42 | C23 | 1 | 3 | yes | — |
| 85 | #948 | — | 2 | 8 | no | — |
| 86 | #930 | — | 2 | 3 | no | — |
| 87 | #930 | — | 2 | 3 | no | — |
| 88 | C2×C4⋊Dic3 | — | 2 | 3 | no | — |
| 89 | C2×C4⋊Dic3 | — | 2 | 3 | no | — |
| 90 | C2×#208 | C23 | 1 | 6 | yes | — |
| 91 | C22×C3⋊C8 | C23 | 1 | 6 | yes | — |
| 92 | #897 | — | 2 | 6 | no | — |
| 93 | #897 | — | 2 | 6 | no | — |
| 94 | #886 | — | 2 | 12 | no | — |
| 95 | #875 | C23 | 1 | 6 | yes | — |
| 96 | #874 | C23 | 1 | 1 | yes | characteristic |
| 97 | C4×D12 | — | 2 | 3 | no | — |
| 98 | C4×D12 | — | 2 | 3 | no | — |
| 99 | #869 | — | 2 | 3 | no | — |
| 100 | #869 | — | 2 | 3 | no | — |
| 101 | #869 | C23 | 1 | 3 | yes | — |
| 102 | #869 | C23 | 1 | 6 | yes | — |
| 103 | #810 | C23 | 1 | 24 | yes | — |
| 104 | #810 | C23 | 1 | 12 | yes | — |
| 105 | #810 | C23 | 1 | 12 | yes | — |
| 106 | #809 | C23 | 1 | 12 | yes | — |
| 107 | #809 | C23 | 1 | 4 | yes | — |
| 108 | #803 | C23 | 1 | 6 | yes | — |
| 109 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 110 | C4×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 111 | C4×C3⋊C8 | C23 | 1 | 6 | yes | — |
| 112 | C2×2−1+4 | — | 3 | 2 | no | — |
| 113 | C2×#131 | — | 3 | 2 | no | — |
| 114 | Q82 | — | 2 | 1 | no | — |
| 115 | #557 | — | 2 | 1 | no | — |
| 116 | #554 | — | 2 | 3 | no | — |
| 117 | D4×Q8 | — | 2 | 3 | no | — |
| 118 | D4×Q8 | — | 6 | 1 | no | — |
| 119 | D4×Q8 | — | 6 | 1 | no | — |
| 120 | #547 | — | 6 | 3 | no | — |
| 121 | #547 | — | 6 | 3 | no | — |
| 122 | #544 | C2×D3 | 1 | 6 | yes | — |
| 123 | #536 | — | 3 | 6 | no | — |
| 124 | #533 | C2×D3 | 1 | 3 | yes | — |
| 125 | #532 | — | 3 | 3 | no | — |
| 126 | C2×C4⋊Q8 | — | 3 | 3 | no | — |
| 127 | C2×C4⋊Q8 | C2×D3 | 1 | 3 | yes | — |
| 128 | #520 | C2×D3 | 1 | 2 | yes | — |
| 129 | C4×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 130 | #491 | — | 3 | 12 | no | — |
| 131 | #489 | — | 3 | 12 | no | — |
| 132 | #488 | — | 3 | 12 | no | — |
| 133 | #487 | — | 3 | 3 | no | — |
| 134 | #487 | — | 3 | 12 | no | — |
| 135 | #487 | — | 3 | 6 | no | — |
| 136 | #487 | — | 3 | 3 | no | — |
| 137 | #486 | — | 3 | 1 | no | — |
| 138 | #486 | — | 3 | 3 | no | — |
| 139 | #419 | — | 3 | 12 | no | — |
| 140 | #417 | — | 3 | 12 | no | — |
| 141 | #416 | — | 3 | 12 | no | — |
| 142 | C2×#103 | — | 3 | 12 | no | — |
| 143 | #405 | — | 3 | 6 | no | — |
| 144 | C4×M16 | — | 3 | 3 | no | — |
| 145 | C2×C4×C8 | — | 3 | 3 | no | — |
| 146 | C3×#41 | #41 | 1 | 8 | yes | — |
| 147 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 148 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 149 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 150 | C2×C3×Q8 | — | 8 | 6 | no | — |
| 151 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 153 | C22×C3×C4 | — | 2 | 6 | no | — |
| 154 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 155 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 156 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 157 | C2×#67 | — | 2 | 6 | no | — |
| 158 | C22×Dic3 | — | 2 | 6 | no | — |
| 159 | D3×Q8 | — | 4 | 8 | no | — |
| 160 | #237 | — | 4 | 24 | no | — |
| 161 | #235 | — | 2 | 24 | no | — |
| 162 | C2×D12 | — | 2 | 1 | no | — |
| 163 | C2×D12 | — | 2 | 1 | no | — |
| 164 | C2×D12 | C24 | 1 | 2 | yes | — |
| 165 | C2×C4×D3 | — | 2 | 6 | no | — |
| 166 | C2×Dic6 | — | 2 | 24 | no | — |
| 167 | C2×Dic6 | — | 2 | 6 | no | — |
| 168 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 169 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 170 | C3×C4⋊C4 | — | 2 | 6 | no | — |
| 171 | C3×C4⋊C4 | — | 2 | 6 | no | — |
| 172 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 173 | C3×C4⋊C4 | — | 2 | 6 | no | — |
| 174 | C3×C4⋊C4 | — | 2 | 6 | no | — |
| 175 | C3×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 176 | C3×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 177 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 178 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 179 | C3×C22⋊C4 | — | 2 | 6 | no | — |
| 180 | C3×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 181 | C3×C42 | — | 2 | 6 | no | — |
| 182 | C3×C42 | C2×D4 | 1 | 3 | yes | — |
| 183 | C3×C42 | C2×D4 | 1 | 3 | yes | — |
| 184 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 185 | C3×C42 | C24 | 1 | 3 | yes | — |
| 186 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 187 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 188 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 189 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 190 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 191 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 192 | #208 | — | 2 | 12 | no | — |
| 193 | C2×C3⋊C8 | — | 2 | 12 | no | — |
| 194 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 195 | C2×C3⋊C8 | C24 | 1 | 6 | yes | — |
| 196 | 2−1+4 | — | 6 | 16 | no | — |
| 197 | C2×#41 | — | 3 | 6 | no | — |
| 198 | C2×#41 | — | 6 | 6 | no | — |
| 199 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 200 | C22×Q8 | — | 2 | 3 | no | — |
| 201 | C22×Q8 | — | 3 | 6 | no | — |
| 202 | C22×Q8 | — | 6 | 2 | no | — |
| 203 | #131 | — | 6 | 8 | no | — |
| 204 | C2×M16 | — | 3 | 6 | no | — |
| 205 | C22×C8 | — | 3 | 6 | no | — |
| 206 | C4⋊Q8 | — | 2 | 6 | no | — |
| 207 | C4⋊Q8 | — | 2 | 3 | no | — |
| 208 | C4⋊Q8 | — | 2 | 3 | no | — |
| 209 | C4⋊Q8 | — | 3 | 3 | no | — |
| 210 | C4⋊Q8 | — | 3 | 6 | no | — |
| 211 | C4⋊Q8 | — | 6 | 3 | no | — |
| 212 | C4⋊Q8 | — | 6 | 3 | no | — |
| 213 | C4⋊Q8 | C22×D3 | 1 | 3 | yes | — |
| 214 | C4⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 215 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 216 | #127 | — | 3 | 1 | no | — |
| 217 | #125 | — | 2 | 6 | no | — |
| 218 | #125 | C22×D3 | 1 | 6 | yes | — |
| 219 | #124 | — | 3 | 6 | no | — |
| 220 | #123 | — | 6 | 12 | no | — |
| 221 | C22⋊Q8 | — | 2 | 3 | no | — |
| 222 | C22⋊Q8 | — | 2 | 3 | no | — |
| 223 | C22⋊Q8 | — | 2 | 12 | no | — |
| 224 | C22⋊Q8 | — | 6 | 6 | no | — |
| 225 | C22⋊Q8 | — | 6 | 6 | no | — |
| 226 | #121 | — | 6 | 3 | no | — |
| 227 | #121 | — | 6 | 3 | no | — |
| 228 | C4×Q8 | — | 2 | 2 | no | — |
| 229 | C4×Q8 | — | 2 | 3 | no | — |
| 230 | C4×Q8 | — | 2 | 3 | no | — |
| 231 | C4×Q8 | #67 | 1 | 1 | yes | characteristic |
| 232 | C4×Q8 | #67 | 1 | 1 | yes | characteristic |
| 233 | C4×D4 | — | 2 | 6 | no | — |
| 234 | C4×D4 | — | 6 | 3 | no | — |
| 235 | C4×D4 | — | 6 | 3 | no | — |
| 236 | C4×D4 | #67 | 1 | 3 | yes | — |
| 237 | C4×D4 | #67 | 1 | 3 | yes | — |
| 238 | #117 | C22×D3 | 1 | 6 | yes | — |
| 239 | #117 | C22×D3 | 1 | 3 | yes | — |
| 240 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 241 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 242 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 243 | C2×C4⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 244 | C2×C42 | C22×D3 | 1 | 3 | yes | — |
| 245 | #103 | — | 3 | 12 | no | — |
| 246 | #103 | — | 3 | 24 | no | — |
| 247 | #103 | — | 3 | 12 | no | — |
| 248 | #102 | — | 3 | 4 | no | — |
| 249 | #102 | — | 3 | 12 | no | — |
| 250 | #97 | — | 3 | 6 | no | — |
| 251 | C4×C8 | — | 3 | 1 | no | — |
| 252 | C4×C8 | — | 3 | 3 | no | — |
| 253 | C4×C8 | — | 3 | 6 | no | — |
| 254 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 255 | C22×D3 | — | 2 | 2 | no | — |
| 256 | C3×Q8 | — | 4 | 6 | no | — |
| 257 | C3×Q8 | — | 4 | 2 | no | — |
| 258 | C3×Q8 | — | 8 | 6 | no | — |
| 259 | C3×Q8 | #124 | 1 | 4 | yes | — |
| 260 | C3×D4 | #124 | 1 | 12 | yes | — |
| 261 | C2×C3×C4 | — | 2 | 6 | no | — |
| 262 | C2×C3×C4 | — | 2 | 6 | no | — |
| 263 | C2×C3×C4 | — | 2 | 2 | no | — |
| 264 | C2×C3×C4 | — | 2 | 6 | no | — |
| 265 | C2×C3×C4 | — | 8 | 6 | no | — |
| 266 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 267 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 268 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 269 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 270 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 271 | C2×C3×C4 | C2×#41 | 1 | 12 | yes | — |
| 272 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 273 | #67 | — | 4 | 12 | no | — |
| 274 | C2×Dic3 | — | 2 | 6 | no | — |
| 275 | C2×Dic3 | — | 4 | 12 | no | — |
| 276 | D12 | — | 2 | 4 | no | — |
| 277 | D12 | — | 4 | 2 | no | — |
| 278 | D12 | — | 4 | 2 | no | — |
| 279 | C4×D3 | — | 4 | 12 | no | — |
| 280 | Dic6 | — | 2 | 12 | no | — |
| 281 | Dic6 | — | 4 | 12 | no | — |
| 282 | C3⋊C8 | — | 2 | 2 | no | — |
| 283 | C3⋊C8 | — | 2 | 6 | no | — |
| 284 | #41 | — | 6 | 24 | no | — |
| 285 | #41 | — | 12 | 24 | no | — |
| 286 | #41 | #239 | 1 | 8 | yes | — |
| 287 | C2×Q8 | — | 2 | 1 | no | — |
| 288 | C2×Q8 | — | 2 | 3 | no | — |
| 289 | C2×Q8 | — | 2 | 6 | no | — |
| 290 | C2×Q8 | — | 3 | 6 | no | — |
| 291 | C2×Q8 | — | 6 | 6 | no | — |
| 292 | C2×Q8 | — | 6 | 24 | no | — |
| 293 | C2×Q8 | — | 8 | 6 | no | — |
| 294 | C2×Q8 | — | 12 | 8 | no | — |
| 295 | C2×Q8 | C2×#67 | 1 | 1 | yes | characteristic |
| 296 | C2×D4 | — | 3 | 2 | no | — |
| 297 | C2×D4 | — | 6 | 6 | no | — |
| 298 | C2×D4 | — | 6 | 1 | no | — |
| 299 | C2×D4 | — | 6 | 1 | no | — |
| 300 | C2×D4 | C2×#67 | 1 | 3 | yes | — |
| 301 | C22×C4 | — | 2 | 6 | no | — |
| 302 | C22×C4 | — | 6 | 6 | no | — |
| 303 | C22×C4 | — | 6 | 6 | no | — |
| 304 | C22×C4 | C2×#67 | 1 | 3 | yes | — |
| 305 | C22×C4 | C2×#67 | 1 | 3 | yes | — |
| 306 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 307 | M16 | — | 6 | 12 | no | — |
| 308 | C2×C8 | — | 3 | 2 | no | — |
| 309 | C2×C8 | — | 3 | 6 | no | — |
| 310 | C2×C8 | — | 6 | 12 | no | — |
| 311 | C4⋊C4 | — | 2 | 3 | no | — |
| 312 | C4⋊C4 | — | 2 | 6 | no | — |
| 313 | C4⋊C4 | — | 2 | 6 | no | — |
| 314 | C4⋊C4 | — | 2 | 1 | no | — |
| 315 | C4⋊C4 | — | 2 | 6 | no | — |
| 316 | C4⋊C4 | — | 2 | 6 | no | — |
| 317 | C4⋊C4 | — | 6 | 3 | no | — |
| 318 | C4⋊C4 | — | 6 | 3 | no | — |
| 319 | C4⋊C4 | — | 6 | 6 | no | — |
| 320 | C4⋊C4 | — | 6 | 6 | no | — |
| 321 | C4⋊C4 | C2×#67 | 1 | 3 | yes | — |
| 322 | C4⋊C4 | C2×#67 | 1 | 3 | yes | — |
| 323 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 324 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 325 | C22⋊C4 | — | 2 | 6 | no | — |
| 326 | C22⋊C4 | — | 6 | 6 | no | — |
| 327 | C22⋊C4 | — | 6 | 6 | no | — |
| 328 | C22⋊C4 | C2×#67 | 1 | 6 | yes | — |
| 329 | C42 | — | 2 | 6 | no | — |
| 330 | C42 | C2×#67 | 1 | 3 | yes | — |
| 331 | C42 | C2×#67 | 1 | 3 | yes | — |
| 332 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 333 | C42 | C23×D3 | 1 | 3 | yes | — |
| 334 | C22×C3 | — | 2 | 3 | no | — |
| 335 | C22×C3 | — | 2 | 3 | no | — |
| 336 | C22×C3 | C2×#124 | 1 | 6 | yes | — |
| 337 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 338 | C2×D3 | — | 4 | 2 | no | — |
| 339 | C2×D3 | — | 4 | 2 | no | — |
| 340 | C2×D3 | — | 4 | 2 | no | — |
| 341 | C3×C4 | — | 2 | 3 | no | — |
| 342 | C3×C4 | — | 2 | 3 | no | — |
| 343 | C3×C4 | — | 4 | 6 | no | — |
| 344 | C3×C4 | — | 4 | 2 | no | — |
| 345 | C3×C4 | C2×#124 | 1 | 6 | yes | — |
| 346 | C3×C4 | #577 | 1 | 2 | yes | — |
| 347 | C3×C4 | #578 | 1 | 2 | yes | — |
| 348 | C3×C4 | C22×#41 | 1 | 2 | yes | — |
| 349 | Dic3 | — | 4 | 6 | no | — |
| 350 | C23 | — | 6 | 2 | no | — |
| 351 | C23 | C22×#67 | 1 | 3 | yes | — |
| 352 | Q8 | — | 4 | 6 | no | — |
| 353 | Q8 | — | 4 | 2 | no | — |
| 354 | Q8 | — | 6 | 12 | no | — |
| 355 | Q8 | — | 8 | 6 | no | — |
| 356 | Q8 | — | 12 | 12 | no | — |
| 357 | Q8 | #947 | 1 | 4 | yes | — |
| 358 | D4 | — | 6 | 4 | no | — |
| 359 | D4 | — | 12 | 12 | no | — |
| 360 | D4 | — | 12 | 2 | no | — |
| 361 | D4 | — | 12 | 2 | no | — |
| 362 | D4 | #947 | 1 | 12 | yes | — |
| 363 | C2×C4 | — | 2 | 6 | no | — |
| 364 | C2×C4 | — | 2 | 6 | no | — |
| 365 | C2×C4 | — | 2 | 2 | no | — |
| 366 | C2×C4 | — | 2 | 6 | no | — |
| 367 | C2×C4 | — | 6 | 6 | no | — |
| 368 | C2×C4 | — | 8 | 6 | no | — |
| 369 | C2×C4 | — | 12 | 12 | no | — |
| 370 | C2×C4 | — | 12 | 12 | no | — |
| 371 | C2×C4 | C2×#239 | 1 | 12 | yes | — |
| 372 | C2×C4 | C22×#67 | 1 | 3 | yes | — |
| 373 | C2×C4 | C22×#67 | 1 | 3 | yes | — |
| 374 | C2×C4 | C22×#67 | 1 | 3 | yes | — |
| 375 | C2×C4 | C22×#67 | 1 | 1 | yes | characteristic |
| 376 | C2×C4 | C22×#67 | 1 | 1 | yes | characteristic |
| 377 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 378 | C8 | — | 6 | 2 | no | — |
| 379 | C8 | — | 6 | 6 | no | — |
| 380 | C2×C3 | — | 2 | 6 | no | — |
| 381 | C2×C3 | C22×#124 | 1 | 1 | yes | characteristic |
| 382 | C2×C3 | C2×#577 | 1 | 1 | yes | characteristic |
| 383 | C2×C3 | C2×#578 | 1 | 1 | yes | characteristic |
| 384 | D3 | — | 8 | 2 | no | — |
| 385 | C22 | — | 2 | 3 | no | — |
| 386 | C22 | — | 2 | 3 | no | — |
| 387 | C22 | — | 12 | 2 | no | — |
| 388 | C22 | — | 12 | 2 | no | — |
| 389 | C22 | — | 12 | 2 | no | — |
| 390 | C22 | C2×#947 | 1 | 6 | yes | — |
| 391 | C22 | C23×#67 | 1 | 1 | yes | characteristic |
| 392 | C4 | — | 2 | 3 | no | — |
| 393 | C4 | — | 2 | 3 | no | — |
| 394 | C4 | — | 4 | 6 | no | — |
| 395 | C4 | — | 4 | 2 | no | — |
| 396 | C4 | — | 12 | 6 | no | — |
| 397 | C4 | C2×#947 | 1 | 6 | yes | — |
| 398 | C4 | #5836 | 1 | 2 | yes | — |
| 399 | C4 | #5838 | 1 | 2 | yes | — |
| 400 | C4 | C22×#239 | 1 | 2 | yes | — |
| 401 | C3 | #60623 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 402 | C2 | — | 2 | 6 | no | — |
| 403 | C2 | — | 24 | 2 | no | — |
| 404 | C2 | C22×#947 | 1 | 1 | yes | characteristic |
| 405 | C2 | C2×#5836 | 1 | 1 | yes | characteristic |
| 406 | C2 | C2×#5838 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3503 | C2 | semidirect |
| 3. #83471 | C2 | semidirect |
| 4. #83337 | C2 | semidirect |
| 5. #83334 | C2 | semidirect |
| 6. #83199 | C2 | semidirect |
| 7. C2×#5093 | C2 | semidirect |
| 8. #82570 | C2 | semidirect |
| 9. C4×#948 | C2 | semidirect |
| 45. #3503 | D3 | semidirect |
| 401. C3 | #60623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3503 | 2 |
| #85827 | 2 |
| #83471 | 2 |
| #83337 | 2 |
| #83334 | 2 |
| #83199 | 2 |
| C2×#5093 | 2 |
| #82570 | 2 |
| C4×#948 | 2 |
| #60623 | 3 |