Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
826 conjugacy classes of subgroups.
The subgroup lattice has 434 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#4916 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#4912 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #81820 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #81782 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2250 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71482 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #71466 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #71322 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #71292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #69084 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D3×#346 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #33716 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×#919 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#916 | — | 2 | 1 | no | — |
| 15 | C2×#912 | — | 2 | 1 | no | — |
| 16 | C2×#912 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#912 | C22 | 1 | 2 | yes | — |
| 18 | #5716 | — | 2 | 1 | no | — |
| 19 | #5668 | — | 2 | 1 | no | — |
| 20 | C2×C3×SD32 | C22 | 1 | 2 | yes | — |
| 21 | C2×C3×D16 | C22 | 1 | 2 | yes | — |
| 22 | C3×#495 | C22 | 1 | 1 | yes | characteristic |
| 23 | C3×#493 | C22 | 1 | 1 | yes | characteristic |
| 24 | #5183 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#829 | C22 | 1 | 2 | yes | — |
| 26 | #5175 | — | 2 | 1 | no | — |
| 27 | #5155 | — | 2 | 1 | no | — |
| 28 | #5155 | C22 | 1 | 2 | yes | — |
| 29 | #5151 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#827 | C22 | 1 | 2 | yes | — |
| 31 | C2×#827 | C22 | 1 | 2 | yes | — |
| 32 | C2×#826 | C22 | 1 | 2 | yes | — |
| 33 | #5076 | — | 2 | 1 | no | — |
| 34 | #5059 | — | 2 | 1 | no | — |
| 35 | #4916 | — | 2 | 8 | no | — |
| 36 | #4912 | — | 2 | 8 | no | — |
| 37 | C2×Dic24 | C22 | 1 | 2 | yes | — |
| 38 | C2×#800 | C22 | 1 | 2 | yes | — |
| 39 | C2×D3×C16 | C22 | 1 | 2 | yes | — |
| 40 | #4699 | C22 | 1 | 1 | yes | characteristic |
| 41 | #4696 | C22 | 1 | 1 | yes | characteristic |
| 42 | C4×D3×C8 | C22 | 1 | 1 | yes | characteristic |
| 43 | C3×#346 | C22 | 1 | 1 | yes | characteristic |
| 44 | #4502 | C22 | 1 | 2 | yes | — |
| 45 | #4461 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×#508 | — | 3 | 2 | no | — |
| 47 | C2×#508 | — | 3 | 2 | no | — |
| 48 | #3147 | — | 3 | 1 | no | — |
| 49 | #3147 | — | 3 | 1 | no | — |
| 50 | #2251 | — | 3 | 2 | no | — |
| 51 | #2251 | — | 3 | 1 | no | — |
| 52 | #2251 | — | 3 | 1 | no | — |
| 53 | #2250 | — | 3 | 2 | no | — |
| 54 | #2250 | — | 3 | 1 | no | — |
| 55 | #2250 | D3 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×#346 | — | 3 | 1 | no | — |
| 57 | C2×#239 | — | 2 | 1 | no | — |
| 58 | C2×#237 | — | 2 | 1 | no | — |
| 59 | C2×#237 | — | 2 | 2 | no | — |
| 60 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 62 | C2×C3×D8 | — | 2 | 1 | no | — |
| 63 | C2×C3×D8 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C3×D8 | C23 | 1 | 2 | yes | — |
| 65 | C3×#127 | — | 2 | 1 | no | — |
| 66 | C3×#124 | — | 2 | 1 | no | — |
| 67 | #944 | — | 2 | 1 | no | — |
| 68 | C2×#216 | — | 2 | 1 | no | — |
| 69 | C2×#215 | — | 2 | 1 | no | — |
| 70 | #940 | — | 2 | 1 | no | — |
| 71 | #938 | — | 4 | 2 | no | — |
| 72 | #936 | — | 2 | 2 | no | — |
| 73 | D4×Dic3 | — | 4 | 2 | no | — |
| 74 | C2×#214 | — | 2 | 2 | no | — |
| 75 | C2×#214 | — | 2 | 2 | no | — |
| 76 | C2×#214 | — | 2 | 1 | no | — |
| 77 | C2×#213 | — | 2 | 1 | no | — |
| 78 | #919 | — | 2 | 4 | no | — |
| 79 | #916 | — | 4 | 4 | no | — |
| 80 | #912 | — | 2 | 4 | no | — |
| 81 | #912 | — | 2 | 4 | no | — |
| 82 | #912 | — | 2 | 4 | no | — |
| 83 | #912 | — | 4 | 4 | no | — |
| 84 | C2×Dic12 | — | 2 | 1 | no | — |
| 85 | C2×Dic12 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 87 | C2×D24 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#204 | — | 2 | 1 | no | — |
| 89 | C2×D3×C8 | D4 | 1 | 1 | yes | characteristic |
| 90 | C2×D3×C8 | C23 | 1 | 1 | yes | characteristic |
| 91 | #884 | — | 4 | 2 | no | — |
| 92 | #67⋊C4 | — | 4 | 2 | no | — |
| 93 | #875 | — | 2 | 1 | no | — |
| 94 | C42×D3 | D4 | 1 | 1 | yes | characteristic |
| 95 | #869 | — | 2 | 1 | no | — |
| 96 | C3×SD32 | — | 2 | 4 | no | — |
| 97 | C3×D16 | — | 2 | 4 | no | — |
| 98 | C2×C3×C16 | C23 | 1 | 2 | yes | — |
| 99 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 100 | #829 | — | 2 | 4 | no | — |
| 101 | #827 | — | 2 | 4 | no | — |
| 102 | #827 | — | 2 | 4 | no | — |
| 103 | #826 | — | 2 | 4 | no | — |
| 104 | C8×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 105 | C8×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×C3⋊C16 | C23 | 1 | 2 | yes | — |
| 107 | C4×C3⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 108 | Dic24 | — | 2 | 4 | no | — |
| 109 | #800 | — | 2 | 4 | no | — |
| 110 | D3×C16 | D4 | 1 | 8 | yes | complemented |
| 111 | C2×#135 | — | 3 | 1 | no | — |
| 112 | C2×#135 | — | 3 | 1 | no | — |
| 113 | C2×#135 | — | 3 | 2 | no | — |
| 114 | C2×#135 | — | 6 | 1 | no | — |
| 115 | C2×#135 | — | 6 | 1 | no | — |
| 116 | #532 | — | 6 | 1 | no | — |
| 117 | #532 | — | 6 | 1 | no | — |
| 118 | #508 | — | 6 | 8 | no | — |
| 119 | #508 | — | 6 | 8 | no | — |
| 120 | C2×Q32 | — | 3 | 2 | no | — |
| 121 | C2×Q32 | — | 3 | 2 | no | — |
| 122 | C2×SD32 | — | 3 | 2 | no | — |
| 123 | C2×SD32 | — | 3 | 2 | no | — |
| 124 | C2×SD32 | — | 3 | 2 | no | — |
| 125 | C2×SD32 | C2×D3 | 1 | 2 | yes | — |
| 126 | C2×D16 | — | 3 | 2 | no | — |
| 127 | C2×D16 | C2×D3 | 1 | 2 | yes | — |
| 128 | C22×C16 | — | 3 | 2 | no | — |
| 129 | #495 | — | 3 | 2 | no | — |
| 130 | #495 | — | 3 | 1 | no | — |
| 131 | #495 | — | 6 | 1 | no | — |
| 132 | #495 | — | 6 | 1 | no | — |
| 133 | #495 | C2×D3 | 1 | 1 | yes | characteristic |
| 134 | #494 | — | 3 | 1 | no | — |
| 135 | #494 | — | 3 | 1 | no | — |
| 136 | #493 | — | 3 | 1 | no | — |
| 137 | #493 | C2×D3 | 1 | 1 | yes | characteristic |
| 138 | #492 | — | 6 | 1 | no | — |
| 139 | #492 | — | 6 | 1 | no | — |
| 140 | C2×C4×C8 | — | 3 | 1 | no | — |
| 141 | #346 | — | 3 | 2 | no | — |
| 142 | #346 | — | 3 | 1 | no | — |
| 143 | #346 | C2×D3 | 1 | 1 | yes | characteristic |
| 144 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 145 | C2×C3×D4 | — | 2 | 1 | no | — |
| 146 | C2×C3×D4 | — | 2 | 2 | no | — |
| 147 | C2×C3×D4 | — | 4 | 2 | no | — |
| 148 | C2×#67 | — | 4 | 1 | no | — |
| 149 | C2×#67 | — | 4 | 2 | no | — |
| 150 | C2×#67 | — | 4 | 2 | no | — |
| 151 | C22×Dic3 | — | 4 | 1 | no | — |
| 152 | C22×Dic3 | — | 4 | 2 | no | — |
| 153 | #239 | — | 4 | 2 | no | — |
| 154 | #239 | — | 4 | 2 | no | — |
| 155 | #237 | — | 4 | 2 | no | — |
| 156 | #237 | — | 4 | 4 | no | — |
| 157 | #237 | — | 4 | 4 | no | — |
| 158 | #237 | — | 4 | 2 | no | — |
| 159 | C2×D12 | — | 2 | 1 | no | — |
| 160 | C2×D12 | — | 4 | 1 | no | — |
| 161 | C2×C4×D3 | — | 4 | 1 | no | — |
| 162 | C2×C4×D3 | D8 | 1 | 2 | yes | — |
| 163 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×Dic6 | — | 2 | 2 | no | — |
| 165 | C2×Dic6 | — | 2 | 1 | no | — |
| 166 | C3×Q16 | — | 2 | 2 | no | — |
| 167 | C3×SD16 | — | 4 | 2 | no | — |
| 168 | C3×D8 | — | 2 | 2 | no | — |
| 169 | C3×D8 | — | 2 | 2 | no | — |
| 170 | C3×D8 | — | 2 | 2 | no | — |
| 171 | C3×D8 | — | 4 | 2 | no | — |
| 172 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 174 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 175 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | #217 | — | 4 | 4 | no | — |
| 177 | #216 | — | 4 | 2 | no | — |
| 178 | #215 | — | 4 | 2 | no | — |
| 179 | #214 | — | 4 | 2 | no | — |
| 180 | #214 | — | 4 | 4 | no | — |
| 181 | #214 | — | 4 | 4 | no | — |
| 182 | #213 | — | 4 | 2 | no | — |
| 183 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 184 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 185 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 186 | C4×Dic3 | D8 | 1 | 2 | yes | — |
| 187 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | Dic12 | — | 2 | 2 | no | — |
| 191 | Dic12 | — | 2 | 2 | no | — |
| 192 | Dic12 | — | 2 | 2 | no | — |
| 193 | Dic12 | — | 4 | 2 | no | — |
| 194 | D24 | — | 2 | 2 | no | — |
| 195 | #204 | — | 4 | 2 | no | — |
| 196 | D3×C8 | D8 | 1 | 4 | yes | — |
| 197 | D3×C8 | C2×D4 | 1 | 4 | yes | — |
| 198 | C3×C16 | C2×D4 | 1 | 4 | yes | — |
| 199 | C3⋊C16 | C2×D4 | 1 | 4 | yes | — |
| 200 | C2×#41 | — | 6 | 1 | no | — |
| 201 | C2×#41 | — | 6 | 2 | no | — |
| 202 | C2×#41 | — | 6 | 1 | no | — |
| 203 | #135 | — | 6 | 4 | no | — |
| 204 | #135 | — | 6 | 4 | no | — |
| 205 | #135 | — | 6 | 4 | no | — |
| 206 | #135 | — | 6 | 4 | no | — |
| 207 | #135 | — | 12 | 4 | no | — |
| 208 | #135 | — | 12 | 4 | no | — |
| 209 | C2×Q16 | — | 3 | 1 | no | — |
| 210 | C2×Q16 | — | 3 | 2 | no | — |
| 211 | C2×Q16 | — | 6 | 1 | no | — |
| 212 | C2×Q16 | — | 6 | 1 | no | — |
| 213 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic |
| 214 | C2×SD16 | — | 2 | 1 | no | — |
| 215 | C2×SD16 | — | 6 | 1 | no | — |
| 216 | C2×SD16 | — | 6 | 2 | no | — |
| 217 | C2×SD16 | — | 6 | 2 | no | — |
| 218 | C2×SD16 | — | 6 | 1 | no | — |
| 219 | C2×SD16 | — | 6 | 1 | no | — |
| 220 | C2×D8 | — | 2 | 1 | no | — |
| 221 | C2×D8 | — | 3 | 1 | no | — |
| 222 | C2×D8 | — | 6 | 1 | no | — |
| 223 | C2×D8 | C22×D3 | 1 | 1 | yes | characteristic |
| 224 | C2×D8 | C22×D3 | 1 | 2 | yes | — |
| 225 | C22×C8 | — | 3 | 1 | no | — |
| 226 | C22×C8 | — | 3 | 1 | no | — |
| 227 | C4⋊Q8 | — | 6 | 1 | no | — |
| 228 | C4⋊Q8 | — | 6 | 1 | no | — |
| 229 | #127 | — | 2 | 1 | no | — |
| 230 | #127 | — | 6 | 1 | no | — |
| 231 | #124 | — | 2 | 1 | no | — |
| 232 | #124 | — | 6 | 2 | no | — |
| 233 | #124 | — | 6 | 1 | no | — |
| 234 | #121 | — | 12 | 2 | no | — |
| 235 | #121 | — | 12 | 2 | no | — |
| 236 | C4×D4 | — | 12 | 2 | no | — |
| 237 | C4×D4 | — | 12 | 2 | no | — |
| 238 | C2×C42 | — | 3 | 1 | no | — |
| 239 | Q32 | — | 6 | 4 | no | — |
| 240 | Q32 | — | 6 | 4 | no | — |
| 241 | SD32 | — | 2 | 4 | no | — |
| 242 | SD32 | — | 6 | 4 | no | — |
| 243 | SD32 | — | 6 | 4 | no | — |
| 244 | SD32 | — | 6 | 4 | no | — |
| 245 | D16 | — | 2 | 4 | no | — |
| 246 | D16 | — | 6 | 4 | no | — |
| 247 | C2×C16 | — | 3 | 2 | no | — |
| 248 | C2×C16 | — | 3 | 8 | no | — |
| 249 | C2×C16 | C22×D3 | 1 | 2 | yes | — |
| 250 | C4×C8 | — | 3 | 1 | no | — |
| 251 | C4×C8 | — | 3 | 1 | no | — |
| 252 | C4×C8 | — | 3 | 1 | no | — |
| 253 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 254 | C23×C3 | — | 4 | 2 | no | — |
| 255 | C23×C3 | — | 4 | 1 | no | — |
| 256 | C22×D3 | — | 4 | 1 | no | — |
| 257 | C22×D3 | C2×D8 | 1 | 1 | yes | characteristic |
| 258 | C3×Q8 | — | 4 | 1 | no | — |
| 259 | C3×Q8 | — | 4 | 1 | no | — |
| 260 | C3×D4 | — | 4 | 2 | no | — |
| 261 | C3×D4 | — | 4 | 1 | no | — |
| 262 | C3×D4 | — | 4 | 1 | no | — |
| 263 | C3×D4 | — | 4 | 2 | no | — |
| 264 | C3×D4 | — | 8 | 4 | no | — |
| 265 | C2×C3×C4 | — | 4 | 1 | no | — |
| 266 | C2×C3×C4 | C2×D8 | 1 | 2 | yes | — |
| 267 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 268 | #67 | — | 8 | 4 | no | — |
| 269 | #67 | — | 8 | 4 | no | — |
| 270 | #67 | — | 8 | 2 | no | — |
| 271 | C2×Dic3 | — | 4 | 1 | no | — |
| 272 | C2×Dic3 | — | 4 | 2 | no | — |
| 273 | C2×Dic3 | — | 8 | 4 | no | — |
| 274 | C2×Dic3 | — | 8 | 2 | no | — |
| 275 | C2×Dic3 | C2×D8 | 1 | 2 | yes | — |
| 276 | C2×Dic3 | C2×D8 | 1 | 1 | yes | characteristic |
| 277 | D12 | — | 4 | 1 | no | — |
| 278 | D12 | — | 4 | 1 | no | — |
| 279 | D12 | — | 8 | 2 | no | — |
| 280 | C4×D3 | — | 4 | 2 | no | — |
| 281 | C4×D3 | — | 8 | 2 | no | — |
| 282 | C4×D3 | #127 | 1 | 2 | yes | — |
| 283 | C4×D3 | C2×D8 | 1 | 2 | yes | — |
| 284 | Dic6 | — | 4 | 2 | no | — |
| 285 | Dic6 | — | 4 | 1 | no | — |
| 286 | Dic6 | — | 4 | 1 | no | — |
| 287 | Dic6 | — | 4 | 2 | no | — |
| 288 | C3×C8 | C2×D8 | 1 | 2 | yes | — |
| 289 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 290 | C3⋊C8 | #127 | 1 | 2 | yes | — |
| 291 | C3⋊C8 | C2×D8 | 1 | 2 | yes | — |
| 292 | #41 | — | 12 | 2 | no | — |
| 293 | #41 | — | 12 | 4 | no | — |
| 294 | #41 | — | 12 | 4 | no | — |
| 295 | #41 | — | 12 | 2 | no | — |
| 296 | #41 | — | 12 | 2 | no | — |
| 297 | #41 | — | 12 | 2 | no | — |
| 298 | C2×Q8 | — | 2 | 1 | no | — |
| 299 | C2×Q8 | — | 6 | 2 | no | — |
| 300 | C2×Q8 | — | 6 | 1 | no | — |
| 301 | C2×D4 | — | 2 | 1 | no | — |
| 302 | C2×D4 | — | 2 | 2 | no | — |
| 303 | C2×D4 | — | 4 | 2 | no | — |
| 304 | C2×D4 | — | 6 | 1 | no | — |
| 305 | C2×D4 | — | 12 | 2 | no | — |
| 306 | C2×D4 | — | 12 | 1 | no | — |
| 307 | C2×D4 | — | 12 | 1 | no | — |
| 308 | C2×D4 | — | 12 | 2 | no | — |
| 309 | C22×C4 | — | 3 | 1 | no | — |
| 310 | C22×C4 | — | 3 | 2 | no | — |
| 311 | C22×C4 | — | 12 | 1 | no | — |
| 312 | C22×C4 | — | 12 | 1 | no | — |
| 313 | C22×C4 | — | 12 | 2 | no | — |
| 314 | Q16 | — | 2 | 2 | no | — |
| 315 | Q16 | — | 6 | 2 | no | — |
| 316 | Q16 | — | 6 | 2 | no | — |
| 317 | Q16 | — | 6 | 2 | no | — |
| 318 | Q16 | — | 12 | 2 | no | — |
| 319 | Q16 | — | 12 | 2 | no | — |
| 320 | SD16 | — | 4 | 2 | no | — |
| 321 | SD16 | — | 12 | 2 | no | — |
| 322 | SD16 | — | 12 | 4 | no | — |
| 323 | SD16 | — | 12 | 4 | no | — |
| 324 | SD16 | — | 12 | 2 | no | — |
| 325 | SD16 | — | 12 | 2 | no | — |
| 326 | D8 | — | 2 | 2 | no | — |
| 327 | D8 | — | 2 | 2 | no | — |
| 328 | D8 | — | 2 | 2 | no | — |
| 329 | D8 | — | 4 | 2 | no | — |
| 330 | D8 | — | 6 | 2 | no | — |
| 331 | D8 | — | 12 | 2 | no | — |
| 332 | C2×C8 | — | 3 | 1 | no | — |
| 333 | C2×C8 | — | 3 | 1 | no | — |
| 334 | C2×C8 | — | 3 | 4 | no | — |
| 335 | C2×C8 | — | 3 | 4 | no | — |
| 336 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 337 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 338 | C4⋊C4 | — | 12 | 2 | no | — |
| 339 | C4⋊C4 | — | 12 | 2 | no | — |
| 340 | C22⋊C4 | — | 4 | 2 | no | — |
| 341 | C22⋊C4 | — | 12 | 4 | no | — |
| 342 | C22⋊C4 | — | 12 | 2 | no | — |
| 343 | C42 | — | 3 | 2 | no | — |
| 344 | C42 | — | 3 | 1 | no | — |
| 345 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 346 | C16 | — | 3 | 4 | no | — |
| 347 | C16 | D3×D4 | 1 | 4 | yes | — |
| 348 | C22×C3 | — | 8 | 1 | no | — |
| 349 | C22×C3 | — | 8 | 2 | no | — |
| 350 | C22×C3 | — | 8 | 2 | no | — |
| 351 | C22×C3 | — | 8 | 4 | no | — |
| 352 | C22×C3 | C22×D8 | 1 | 1 | yes | characteristic |
| 353 | C2×D3 | — | 2 | 2 | no | — |
| 354 | C2×D3 | — | 8 | 1 | no | — |
| 355 | C2×D3 | — | 8 | 2 | no | — |
| 356 | C2×D3 | #493 | 1 | 2 | yes | — |
| 357 | C3×C4 | — | 2 | 2 | no | — |
| 358 | C3×C4 | — | 8 | 1 | no | — |
| 359 | C3×C4 | C2×#127 | 1 | 1 | yes | characteristic |
| 360 | C3×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 361 | Dic3 | — | 2 | 2 | no | — |
| 362 | Dic3 | — | 8 | 1 | no | — |
| 363 | Dic3 | — | 8 | 2 | no | — |
| 364 | Dic3 | #493 | 1 | 2 | yes | — |
| 365 | C23 | — | 3 | 1 | no | — |
| 366 | C23 | — | 4 | 1 | no | — |
| 367 | C23 | — | 4 | 2 | no | — |
| 368 | C23 | — | 12 | 1 | no | — |
| 369 | Q8 | — | 4 | 1 | no | — |
| 370 | Q8 | — | 4 | 1 | no | — |
| 371 | Q8 | — | 12 | 1 | no | — |
| 372 | Q8 | — | 12 | 2 | no | — |
| 373 | Q8 | — | 12 | 2 | no | — |
| 374 | Q8 | — | 12 | 1 | no | — |
| 375 | D4 | — | 4 | 1 | no | — |
| 376 | D4 | — | 4 | 2 | no | — |
| 377 | D4 | — | 4 | 2 | no | — |
| 378 | D4 | — | 4 | 1 | no | — |
| 379 | D4 | — | 8 | 4 | no | — |
| 380 | D4 | — | 12 | 1 | no | — |
| 381 | D4 | — | 12 | 1 | no | — |
| 382 | D4 | — | 24 | 4 | no | — |
| 383 | D4 | — | 24 | 2 | no | — |
| 384 | D4 | — | 24 | 4 | no | — |
| 385 | D4 | — | 24 | 2 | no | — |
| 386 | C2×C4 | — | 3 | 1 | no | — |
| 387 | C2×C4 | — | 3 | 2 | no | — |
| 388 | C2×C4 | — | 3 | 2 | no | — |
| 389 | C2×C4 | — | 3 | 2 | no | — |
| 390 | C2×C4 | — | 4 | 1 | no | — |
| 391 | C2×C4 | — | 12 | 2 | no | — |
| 392 | C2×C4 | — | 12 | 2 | no | — |
| 393 | C2×C4 | — | 12 | 1 | no | — |
| 394 | C2×C4 | — | 24 | 2 | no | — |
| 395 | C2×C4 | — | 24 | 4 | no | — |
| 396 | C2×C4 | — | 24 | 2 | no | — |
| 397 | C2×C4 | D3×D8 | 1 | 2 | yes | — |
| 398 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 399 | C8 | — | 3 | 2 | no | — |
| 400 | C8 | — | 3 | 2 | no | — |
| 401 | C8 | D3×D8 | 1 | 2 | yes | — |
| 402 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 403 | C2×C3 | — | 16 | 1 | no | — |
| 404 | C2×C3 | — | 16 | 2 | no | — |
| 405 | C2×C3 | C2×#493 | 1 | 1 | yes | characteristic |
| 406 | C2×C3 | #3414 | 1 | 2 | yes | — |
| 407 | D3 | — | 2 | 2 | no | — |
| 408 | D3 | — | 16 | 1 | no | — |
| 409 | C22 | — | 3 | 2 | no | — |
| 410 | C22 | — | 6 | 2 | no | — |
| 411 | C22 | — | 8 | 4 | no | — |
| 412 | C22 | — | 8 | 2 | no | — |
| 413 | C22 | — | 8 | 2 | no | — |
| 414 | C22 | — | 8 | 1 | no | — |
| 415 | C22 | — | 24 | 2 | no | — |
| 416 | C22 | — | 24 | 1 | no | — |
| 417 | C22 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 418 | C4 | — | 2 | 2 | no | — |
| 419 | C4 | — | 3 | 2 | no | — |
| 420 | C4 | — | 6 | 2 | no | — |
| 421 | C4 | — | 8 | 1 | no | — |
| 422 | C4 | — | 24 | 2 | no | — |
| 423 | C4 | — | 24 | 1 | no | — |
| 424 | C4 | D3×#127 | 1 | 1 | yes | characteristic |
| 425 | C4 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 426 | C3 | #33716 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 427 | C2 | — | 6 | 2 | no | — |
| 428 | C2 | — | 16 | 2 | no | — |
| 429 | C2 | — | 16 | 1 | no | — |
| 430 | C2 | — | 48 | 1 | no | — |
| 431 | C2 | D3×#493 | 1 | 1 | yes | characteristic |
| 432 | C2 | #82035 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4916 | C2 | semidirect |
| 2. C2×#4912 | C2 | semidirect |
| 3. #81820 | C2 | semidirect |
| 4. #81782 | C2 | semidirect |
| 5. C3×#2250 | C2 | semidirect |
| 6. #71482 | C2 | semidirect |
| 7. #71466 | C2 | semidirect |
| 8. #71322 | C2 | semidirect |
| 9. #71292 | C2 | semidirect |
| 10. #69084 | C2 | semidirect |
| 11. D3×#346 | C2 | semidirect |
| 55. #2250 | D3 | semidirect |
| 110. D3×C16 | D4 | semidirect |
| 426. C3 | #33716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4916 | 2 |
| C2×#4912 | 2 |
| #81820 | 2 |
| #81782 | 2 |
| C3×#2250 | 2 |
| #71482 | 2 |
| #71466 | 2 |
| #71322 | 2 |
| #71292 | 2 |
| #69084 | 2 |
| D3×#346 | 2 |
| #33716 | 3 |