Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1118 conjugacy classes of subgroups.
The subgroup lattice has 436 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5771 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C22×#800 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #79183 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2138 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71409 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70654 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #69223 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #69192 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #33524 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C2×#1010 | — | 2 | 1 | no | — |
| 12 | C2×C3×#135 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#951 | — | 2 | 1 | no | — |
| 14 | #5771 | — | 2 | 4 | no | — |
| 15 | #5771 | — | 2 | 4 | no | — |
| 16 | C2×D3×Q16 | C22 | 1 | 2 | yes | complemented |
| 17 | C2×#915 | — | 2 | 2 | no | — |
| 18 | C2×#912 | C22 | 1 | 2 | yes | complemented |
| 19 | C22×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 20 | C22×D24 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#901 | C22 | 1 | 1 | yes | characteristic |
| 22 | #5525 | — | 2 | 1 | no | — |
| 23 | C22×C3×C16 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#427 | C22 | 1 | 1 | yes | characteristic |
| 25 | #5193 | — | 2 | 4 | no | — |
| 26 | C2×#828 | C22 | 1 | 2 | yes | — |
| 27 | C2×#826 | C22 | 1 | 2 | yes | — |
| 28 | C2×#812 | C22 | 1 | 1 | yes | characteristic |
| 29 | #5001 | — | 2 | 1 | no | — |
| 30 | C2×#800 | — | 2 | 4 | no | — |
| 31 | C2×#800 | C22 | 1 | 4 | yes | — |
| 32 | #4883 | C22 | 1 | 4 | yes | — |
| 33 | #4865 | — | 2 | 2 | no | — |
| 34 | C3×#358 | C22 | 1 | 2 | yes | complemented |
| 35 | C3×#357 | C22 | 1 | 2 | yes | complemented |
| 36 | (C2×D3)⋊C16 | C22 | 1 | 4 | yes | complemented |
| 37 | #4492 | C22 | 1 | 4 | yes | complemented |
| 38 | C2×#578 | — | 3 | 1 | no | — |
| 39 | C2×#509 | — | 3 | 1 | no | — |
| 40 | C22×SD32 | — | 3 | 1 | no | — |
| 41 | #3058 | — | 3 | 1 | no | — |
| 42 | #2186 | — | 3 | 4 | no | — |
| 43 | #2185 | — | 3 | 4 | no | — |
| 44 | #2141 | — | 3 | 1 | no | — |
| 45 | #2138 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | #2113 | — | 3 | 1 | no | — |
| 47 | C2×C3×#41 | — | 2 | 1 | no | — |
| 48 | #1010 | — | 2 | 8 | no | — |
| 49 | #1010 | — | 4 | 4 | no | — |
| 50 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 51 | C2×#237 | — | 2 | 2 | no | — |
| 52 | C2×#237 | — | 4 | 2 | no | — |
| 53 | C2×#235 | — | 4 | 1 | no | — |
| 54 | C2×#235 | D4 | 1 | 1 | yes | characteristic |
| 55 | C22×D12 | — | 2 | 1 | no | — |
| 56 | C22×Dic6 | — | 2 | 1 | no | — |
| 57 | C22×Dic6 | — | 4 | 1 | no | — |
| 58 | C3×#135 | — | 2 | 2 | no | — |
| 59 | C3×#135 | D4 | 1 | 4 | yes | complemented |
| 60 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 62 | C2×C3×D8 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 64 | C3×#117 | — | 2 | 1 | no | — |
| 65 | #951 | — | 2 | 8 | no | — |
| 66 | C2×#216 | — | 2 | 2 | no | — |
| 67 | C2×#214 | — | 2 | 2 | no | — |
| 68 | C2×#208 | D4 | 1 | 1 | yes | characteristic |
| 69 | D3×Q16 | — | 2 | 4 | no | — |
| 70 | D3×Q16 | — | 2 | 4 | no | — |
| 71 | #915 | — | 2 | 16 | no | — |
| 72 | #912 | — | 2 | 4 | no | — |
| 73 | #912 | — | 2 | 4 | no | — |
| 74 | C2×Dic12 | — | 2 | 1 | no | — |
| 75 | C2×Dic12 | — | 2 | 2 | no | — |
| 76 | C2×Dic12 | D4 | 1 | 4 | yes | complemented |
| 77 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 78 | C2×D24 | — | 2 | 2 | no | — |
| 79 | C2×D24 | — | 2 | 2 | no | — |
| 80 | C2×D24 | — | 2 | 1 | no | — |
| 81 | C2×D24 | C23 | 1 | 2 | yes | — |
| 82 | #901 | — | 2 | 2 | no | — |
| 83 | #901 | — | 2 | 2 | no | — |
| 84 | C2×ΓL(1,𝔽25) | D4 | 1 | 2 | yes | — |
| 85 | C2×D3×C8 | C23 | 1 | 2 | yes | — |
| 86 | #895 | — | 2 | 4 | no | — |
| 87 | #882 | — | 4 | 2 | no | — |
| 88 | #875 | — | 4 | 1 | no | — |
| 89 | #874 | — | 4 | 1 | no | — |
| 90 | C2×C3×C16 | — | 2 | 2 | no | — |
| 91 | C2×C3×C16 | C23 | 1 | 2 | yes | — |
| 92 | C3×#107 | C23 | 1 | 2 | yes | — |
| 93 | C3×#106 | — | 2 | 1 | no | — |
| 94 | #828 | — | 2 | 4 | no | — |
| 95 | #826 | — | 2 | 4 | no | — |
| 96 | #812 | — | 2 | 2 | no | — |
| 97 | C2×C3⋊C16 | C23 | 1 | 2 | yes | — |
| 98 | #809 | — | 2 | 4 | no | — |
| 99 | #800 | — | 2 | 8 | no | — |
| 100 | C2×2−1+4 | — | 6 | 1 | no | — |
| 101 | #578 | — | 6 | 4 | no | — |
| 102 | #578 | — | 6 | 4 | no | — |
| 103 | C2×#137 | — | 6 | 2 | no | — |
| 104 | C2×#137 | — | 6 | 1 | no | — |
| 105 | C2×#135 | — | 3 | 2 | no | — |
| 106 | C2×#135 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | C22×Q16 | — | 3 | 2 | no | — |
| 108 | C22×Q16 | — | 3 | 1 | no | — |
| 109 | C22×D8 | — | 3 | 1 | no | — |
| 110 | C2×#131 | — | 3 | 1 | no | — |
| 111 | #535 | — | 6 | 1 | no | — |
| 112 | #509 | — | 6 | 4 | no | — |
| 113 | C2×SD32 | — | 3 | 2 | no | — |
| 114 | C2×SD32 | — | 3 | 4 | no | — |
| 115 | C2×SD32 | — | 6 | 4 | no | — |
| 116 | C2×D16 | — | 3 | 2 | no | — |
| 117 | C2×M32 | — | 3 | 1 | no | — |
| 118 | C22×C16 | C2×D3 | 1 | 1 | yes | characteristic |
| 119 | #469 | — | 6 | 2 | no | — |
| 120 | #466 | — | 3 | 4 | no | — |
| 121 | #427 | C2×D3 | 1 | 1 | yes | characteristic |
| 122 | #418 | — | 6 | 1 | no | — |
| 123 | #358 | — | 3 | 4 | no | — |
| 124 | #358 | C2×D3 | 1 | 2 | yes | complemented |
| 125 | #357 | C2×D3 | 1 | 2 | yes | complemented |
| 126 | C22⋊C16 | — | 3 | 4 | no | — |
| 127 | C23×D3 | — | 4 | 1 | no | — |
| 128 | C3×#41 | — | 2 | 4 | no | — |
| 129 | C3×#41 | — | 4 | 2 | no | — |
| 130 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 131 | C2×C3×D4 | — | 2 | 1 | no | — |
| 132 | C2×C3×D4 | — | 4 | 1 | no | — |
| 133 | C22×C3×C4 | — | 4 | 1 | no | — |
| 134 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×#67 | — | 4 | 2 | no | — |
| 136 | C2×#67 | D8 | 1 | 2 | yes | — |
| 137 | C22×Dic3 | — | 4 | 1 | no | — |
| 138 | C22×Dic3 | — | 4 | 2 | no | — |
| 139 | D3×Q8 | — | 2 | 8 | no | — |
| 140 | D3×Q8 | — | 4 | 4 | no | — |
| 141 | #237 | — | 2 | 8 | no | — |
| 142 | #237 | — | 4 | 4 | no | — |
| 143 | #237 | — | 4 | 16 | no | — |
| 144 | #235 | — | 2 | 2 | no | — |
| 145 | #235 | — | 2 | 2 | no | — |
| 146 | #235 | — | 4 | 8 | no | — |
| 147 | C2×D12 | — | 2 | 2 | no | — |
| 148 | C2×D12 | — | 4 | 2 | no | — |
| 149 | C2×D12 | — | 4 | 2 | no | — |
| 150 | C2×D12 | — | 4 | 1 | no | — |
| 151 | C2×D12 | — | 4 | 4 | no | — |
| 152 | C2×D12 | D8 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×D3 | — | 4 | 2 | no | — |
| 154 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 155 | C2×Dic6 | — | 2 | 4 | no | — |
| 156 | C2×Dic6 | — | 2 | 2 | no | — |
| 157 | C2×Dic6 | — | 4 | 8 | no | — |
| 158 | C2×Dic6 | — | 4 | 1 | no | — |
| 159 | C2×Dic6 | — | 4 | 2 | no | — |
| 160 | C2×Dic6 | — | 4 | 2 | no | — |
| 161 | C2×Dic6 | D8 | 1 | 1 | yes | characteristic |
| 162 | C3×Q16 | — | 2 | 1 | no | — |
| 163 | C3×Q16 | C2×D4 | 1 | 2 | yes | — |
| 164 | C3×SD16 | — | 2 | 4 | no | — |
| 165 | C3×D8 | — | 2 | 1 | no | — |
| 166 | C3×D8 | C2×D4 | 1 | 2 | yes | — |
| 167 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 168 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 171 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 172 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 173 | C3×C42 | — | 4 | 1 | no | — |
| 174 | #216 | — | 2 | 8 | no | — |
| 175 | #214 | — | 2 | 8 | no | — |
| 176 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 177 | #208 | — | 2 | 2 | no | — |
| 178 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 179 | Dic12 | — | 2 | 4 | no | — |
| 180 | Dic12 | — | 2 | 2 | no | — |
| 181 | Dic12 | C2×D4 | 1 | 4 | yes | — |
| 182 | D24 | — | 2 | 2 | no | — |
| 183 | D24 | — | 2 | 2 | no | — |
| 184 | D24 | — | 4 | 2 | no | — |
| 185 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 186 | D3×C8 | — | 2 | 2 | no | — |
| 187 | D3×C8 | — | 2 | 2 | no | — |
| 188 | C3×C16 | — | 2 | 2 | no | — |
| 189 | C3⋊C16 | — | 2 | 2 | no | — |
| 190 | 2−1+4 | — | 6 | 8 | no | — |
| 191 | 2−1+4 | — | 12 | 4 | no | — |
| 192 | C2×#41 | — | 2 | 1 | no | — |
| 193 | C2×#41 | — | 3 | 1 | no | — |
| 194 | C2×#41 | — | 6 | 2 | no | — |
| 195 | C2×#41 | — | 12 | 1 | no | — |
| 196 | C2×#41 | — | 12 | 2 | no | — |
| 197 | C22×Q8 | — | 6 | 2 | no | — |
| 198 | C22×Q8 | — | 6 | 1 | no | — |
| 199 | C22×Q8 | — | 12 | 1 | no | — |
| 200 | C22×D4 | — | 6 | 1 | no | — |
| 201 | #137 | — | 6 | 16 | no | — |
| 202 | #137 | — | 6 | 8 | no | — |
| 203 | #135 | — | 2 | 2 | no | — |
| 204 | #135 | — | 6 | 4 | no | — |
| 205 | #135 | — | 6 | 4 | no | — |
| 206 | #135 | D12 | 1 | 4 | yes | complemented |
| 207 | C2×Q16 | — | 3 | 4 | no | — |
| 208 | C2×Q16 | — | 3 | 2 | no | — |
| 209 | C2×Q16 | — | 6 | 2 | no | — |
| 210 | C2×Q16 | — | 6 | 4 | no | — |
| 211 | C2×Q16 | — | 6 | 4 | no | — |
| 212 | C2×Q16 | — | 6 | 2 | no | — |
| 213 | C2×Q16 | — | 6 | 1 | no | — |
| 214 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic |
| 215 | C2×SD16 | — | 2 | 1 | no | — |
| 216 | C2×SD16 | — | 6 | 2 | no | — |
| 217 | C2×D8 | — | 3 | 2 | no | — |
| 218 | C2×D8 | — | 6 | 2 | no | — |
| 219 | C2×D8 | — | 6 | 2 | no | — |
| 220 | C2×D8 | — | 6 | 1 | no | — |
| 221 | C2×D8 | C22×D3 | 1 | 1 | yes | characteristic |
| 222 | #131 | — | 6 | 2 | no | — |
| 223 | #131 | — | 6 | 2 | no | — |
| 224 | C2×M16 | — | 3 | 1 | no | — |
| 225 | C2×M16 | — | 3 | 2 | no | — |
| 226 | C22×C8 | — | 3 | 2 | no | — |
| 227 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 228 | #127 | — | 12 | 1 | no | — |
| 229 | #124 | — | 12 | 1 | no | — |
| 230 | #121 | — | 6 | 4 | no | — |
| 231 | #120 | — | 12 | 2 | no | — |
| 232 | #117 | — | 2 | 1 | no | — |
| 233 | SD32 | — | 6 | 8 | no | — |
| 234 | SD32 | — | 6 | 4 | no | — |
| 235 | D16 | — | 6 | 4 | no | — |
| 236 | M32 | — | 6 | 2 | no | — |
| 237 | C2×C16 | — | 2 | 2 | no | — |
| 238 | C2×C16 | — | 3 | 2 | no | — |
| 239 | C2×C16 | C22×D3 | 1 | 2 | yes | — |
| 240 | #107 | C22×D3 | 1 | 2 | yes | — |
| 241 | #106 | — | 2 | 1 | no | — |
| 242 | #102 | — | 6 | 4 | no | — |
| 243 | C23×C3 | — | 4 | 1 | no | — |
| 244 | C23×C3 | C2×D8 | 1 | 1 | yes | characteristic |
| 245 | C22×D3 | — | 4 | 2 | no | — |
| 246 | C22×D3 | — | 8 | 2 | no | — |
| 247 | C22×D3 | — | 16 | 2 | no | — |
| 248 | C22×D3 | C2×D8 | 1 | 2 | yes | — |
| 249 | C3×Q8 | — | 2 | 2 | no | — |
| 250 | C3×Q8 | — | 4 | 1 | no | — |
| 251 | C3×D4 | — | 2 | 2 | no | — |
| 252 | C3×D4 | — | 4 | 4 | no | — |
| 253 | C3×D4 | — | 4 | 1 | no | — |
| 254 | C2×C3×C4 | — | 4 | 1 | no | — |
| 255 | C2×C3×C4 | — | 4 | 4 | no | — |
| 256 | C2×C3×C4 | — | 4 | 2 | no | — |
| 257 | C2×C3×C4 | #120 | 1 | 2 | yes | — |
| 258 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 259 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 260 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | #67 | — | 2 | 4 | no | — |
| 262 | #67 | — | 4 | 8 | no | — |
| 263 | C2×Dic3 | — | 4 | 8 | no | — |
| 264 | C2×Dic3 | — | 4 | 2 | no | — |
| 265 | C2×Dic3 | — | 4 | 4 | no | — |
| 266 | C2×Dic3 | C2×D8 | 1 | 2 | yes | — |
| 267 | D12 | — | 2 | 2 | no | — |
| 268 | D12 | — | 4 | 2 | no | — |
| 269 | D12 | — | 4 | 2 | no | — |
| 270 | D12 | — | 8 | 2 | no | — |
| 271 | D12 | — | 16 | 4 | no | — |
| 272 | C4×D3 | — | 2 | 2 | no | — |
| 273 | C4×D3 | — | 2 | 2 | no | — |
| 274 | C4×D3 | — | 4 | 8 | no | — |
| 275 | Dic6 | — | 2 | 2 | no | — |
| 276 | Dic6 | — | 2 | 4 | no | — |
| 277 | Dic6 | — | 4 | 8 | no | — |
| 278 | Dic6 | — | 4 | 2 | no | — |
| 279 | Dic6 | — | 4 | 4 | no | — |
| 280 | C3×C8 | #120 | 1 | 2 | yes | — |
| 281 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 282 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 283 | C3⋊C8 | — | 2 | 2 | no | — |
| 284 | C24 | — | 12 | 1 | no | — |
| 285 | #41 | — | 2 | 4 | no | — |
| 286 | #41 | — | 4 | 2 | no | — |
| 287 | #41 | — | 6 | 2 | no | — |
| 288 | #41 | — | 6 | 2 | no | — |
| 289 | #41 | — | 6 | 8 | no | — |
| 290 | #41 | — | 12 | 8 | no | — |
| 291 | #41 | — | 12 | 4 | no | — |
| 292 | #41 | — | 12 | 16 | no | — |
| 293 | C2×Q8 | — | 2 | 1 | no | — |
| 294 | C2×Q8 | — | 3 | 1 | no | — |
| 295 | C2×Q8 | — | 6 | 8 | no | — |
| 296 | C2×Q8 | — | 6 | 4 | no | — |
| 297 | C2×Q8 | — | 6 | 2 | no | — |
| 298 | C2×Q8 | — | 12 | 2 | no | — |
| 299 | C2×Q8 | — | 12 | 8 | no | — |
| 300 | C2×Q8 | — | 12 | 4 | no | — |
| 301 | C2×Q8 | — | 12 | 1 | no | — |
| 302 | C2×Q8 | — | 12 | 2 | no | — |
| 303 | C2×D4 | — | 2 | 1 | no | — |
| 304 | C2×D4 | — | 3 | 2 | no | — |
| 305 | C2×D4 | — | 3 | 1 | no | — |
| 306 | C2×D4 | — | 4 | 1 | no | — |
| 307 | C2×D4 | — | 6 | 2 | no | — |
| 308 | C2×D4 | — | 12 | 4 | no | — |
| 309 | C2×D4 | — | 12 | 2 | no | — |
| 310 | C2×D4 | — | 12 | 2 | no | — |
| 311 | C2×D4 | — | 12 | 1 | no | — |
| 312 | C2×D4 | — | 12 | 2 | no | — |
| 313 | C22×C4 | — | 3 | 2 | no | — |
| 314 | C22×C4 | — | 4 | 1 | no | — |
| 315 | C22×C4 | — | 12 | 2 | no | — |
| 316 | C22×C4 | — | 12 | 2 | no | — |
| 317 | C22×C4 | — | 12 | 1 | no | — |
| 318 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 319 | Q16 | — | 2 | 1 | no | — |
| 320 | Q16 | — | 3 | 4 | no | — |
| 321 | Q16 | — | 6 | 8 | no | — |
| 322 | Q16 | — | 6 | 4 | no | — |
| 323 | Q16 | — | 6 | 2 | no | — |
| 324 | Q16 | C2×D12 | 1 | 2 | yes | — |
| 325 | SD16 | — | 2 | 4 | no | — |
| 326 | SD16 | — | 6 | 8 | no | — |
| 327 | D8 | — | 2 | 1 | no | — |
| 328 | D8 | — | 6 | 2 | no | — |
| 329 | D8 | — | 6 | 2 | no | — |
| 330 | D8 | — | 12 | 2 | no | — |
| 331 | D8 | C2×D12 | 1 | 2 | yes | — |
| 332 | M16 | — | 6 | 2 | no | — |
| 333 | M16 | — | 6 | 4 | no | — |
| 334 | C2×C8 | — | 3 | 2 | no | — |
| 335 | C2×C8 | — | 6 | 2 | no | — |
| 336 | C2×C8 | — | 6 | 2 | no | — |
| 337 | C2×C8 | C2×D12 | 1 | 2 | yes | — |
| 338 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 339 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 340 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 341 | C4⋊C4 | — | 2 | 2 | no | — |
| 342 | C22⋊C4 | — | 4 | 1 | no | — |
| 343 | C22⋊C4 | — | 12 | 4 | no | — |
| 344 | C42 | — | 4 | 1 | no | — |
| 345 | C16 | — | 2 | 2 | no | — |
| 346 | C16 | — | 6 | 2 | no | — |
| 347 | C22×C3 | — | 2 | 2 | no | — |
| 348 | C22×C3 | — | 4 | 2 | no | — |
| 349 | C22×C3 | — | 8 | 2 | no | — |
| 350 | C22×C3 | #447 | 1 | 2 | yes | — |
| 351 | C22×C3 | C22×D8 | 1 | 1 | yes | characteristic |
| 352 | C2×D3 | — | 2 | 4 | no | — |
| 353 | C2×D3 | — | 2 | 2 | no | — |
| 354 | C2×D3 | — | 8 | 4 | no | — |
| 355 | C2×D3 | — | 8 | 2 | no | — |
| 356 | C2×D3 | — | 16 | 4 | no | — |
| 357 | C3×C4 | — | 4 | 2 | no | — |
| 358 | C3×C4 | — | 8 | 2 | no | — |
| 359 | C3×C4 | #447 | 1 | 2 | yes | — |
| 360 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 361 | C3×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 362 | Dic3 | — | 2 | 2 | no | — |
| 363 | Dic3 | — | 4 | 4 | no | — |
| 364 | C23 | — | 3 | 2 | no | — |
| 365 | C23 | — | 4 | 1 | no | — |
| 366 | C23 | — | 12 | 2 | no | — |
| 367 | C23 | — | 24 | 2 | no | — |
| 368 | C23 | — | 48 | 2 | no | — |
| 369 | C23 | D3×D8 | 1 | 1 | yes | characteristic |
| 370 | Q8 | — | 2 | 2 | no | — |
| 371 | Q8 | — | 4 | 1 | no | — |
| 372 | Q8 | — | 6 | 2 | no | — |
| 373 | Q8 | — | 6 | 4 | no | — |
| 374 | Q8 | — | 12 | 8 | no | — |
| 375 | Q8 | — | 12 | 2 | no | — |
| 376 | Q8 | — | 12 | 4 | no | — |
| 377 | D4 | — | 2 | 2 | no | — |
| 378 | D4 | — | 4 | 4 | no | — |
| 379 | D4 | — | 4 | 1 | no | — |
| 380 | D4 | — | 6 | 4 | no | — |
| 381 | D4 | — | 6 | 2 | no | — |
| 382 | D4 | — | 12 | 8 | no | — |
| 383 | D4 | — | 12 | 2 | no | — |
| 384 | D4 | — | 12 | 2 | no | — |
| 385 | D4 | — | 24 | 2 | no | — |
| 386 | D4 | — | 48 | 4 | no | — |
| 387 | C2×C4 | — | 3 | 2 | no | — |
| 388 | C2×C4 | — | 4 | 1 | no | — |
| 389 | C2×C4 | — | 4 | 4 | no | — |
| 390 | C2×C4 | — | 4 | 2 | no | — |
| 391 | C2×C4 | — | 6 | 2 | no | — |
| 392 | C2×C4 | — | 6 | 2 | no | — |
| 393 | C2×C4 | — | 12 | 8 | no | — |
| 394 | C2×C4 | — | 12 | 8 | no | — |
| 395 | C2×C4 | — | 12 | 2 | no | — |
| 396 | C2×C4 | — | 12 | 4 | no | — |
| 397 | C2×C4 | #882 | 1 | 2 | yes | — |
| 398 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 399 | C2×C4 | #914 | 1 | 2 | yes | — |
| 400 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 401 | C8 | — | 6 | 2 | no | — |
| 402 | C8 | #882 | 1 | 2 | yes | — |
| 403 | C8 | C22×D12 | 1 | 1 | yes | characteristic |
| 404 | C8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 405 | C2×C3 | — | 2 | 2 | no | — |
| 406 | C2×C3 | — | 8 | 2 | no | — |
| 407 | C2×C3 | C2×#447 | 1 | 1 | yes | characteristic |
| 408 | C2×C3 | #3416 | 1 | 2 | yes | — |
| 409 | D3 | — | 4 | 2 | no | — |
| 410 | D3 | — | 16 | 2 | no | — |
| 411 | C22 | — | 2 | 2 | no | — |
| 412 | C22 | — | 4 | 2 | no | — |
| 413 | C22 | — | 6 | 4 | no | — |
| 414 | C22 | — | 6 | 2 | no | — |
| 415 | C22 | — | 8 | 2 | no | — |
| 416 | C22 | — | 24 | 4 | no | — |
| 417 | C22 | — | 24 | 2 | no | — |
| 418 | C22 | — | 48 | 4 | no | — |
| 419 | C22 | #4773 | 1 | 2 | yes | — |
| 420 | C22 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 421 | C4 | — | 4 | 2 | no | — |
| 422 | C4 | — | 6 | 2 | no | — |
| 423 | C4 | — | 8 | 2 | no | — |
| 424 | C4 | — | 12 | 4 | no | — |
| 425 | C4 | #4773 | 1 | 2 | yes | — |
| 426 | C4 | C2×#882 | 1 | 1 | yes | characteristic |
| 427 | C4 | C2×#914 | 1 | 1 | yes | characteristic |
| 428 | C3 | #33524 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 429 | C2 | — | 2 | 2 | no | — |
| 430 | C2 | — | 8 | 2 | no | — |
| 431 | C2 | — | 12 | 2 | no | — |
| 432 | C2 | — | 48 | 2 | no | — |
| 433 | C2 | C2×#4773 | 1 | 1 | yes | characteristic |
| 434 | C2 | #82032 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5771 | C2 | semidirect |
| 2. C2×#5193 | C2 | semidirect |
| 3. C22×#800 | C2 | semidirect |
| 4. #79183 | C2 | semidirect |
| 5. C3×#2138 | C2 | semidirect |
| 6. #71409 | C2 | semidirect |
| 7. #70654 | C2 | semidirect |
| 8. #69223 | C2 | semidirect |
| 9. #69192 | C2 | semidirect |
| 16. C2×D3×Q16 | C22 | semidirect |
| 18. C2×#912 | C22 | semidirect |
| 34. C3×#358 | C22 | semidirect |
| 35. C3×#357 | C22 | semidirect |
| 36. (C2×D3)⋊C16 | C22 | semidirect |
| 37. #4492 | C22 | semidirect |
| 45. #2138 | D3 | semidirect |
| 59. C3×#135 | D4 | semidirect |
| 76. C2×Dic12 | D4 | semidirect |
| 124. #358 | C2×D3 | semidirect |
| 125. #357 | C2×D3 | semidirect |
| 206. #135 | D12 | semidirect |
| 428. C3 | #33524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5771 | 2 |
| C2×#5193 | 2 |
| C22×#800 | 2 |
| #79183 | 2 |
| C3×#2138 | 2 |
| #71409 | 2 |
| #70654 | 2 |
| #69223 | 2 |
| #69192 | 2 |
| #33524 | 3 |