Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3114 conjugacy classes of subgroups.
The subgroup lattice has 462 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×#578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87292 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#5838 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×#5753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83975 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #83972 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #83907 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #83903 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #83881 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C2×#5183 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | Dic3×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #60648 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×C3×2−1+4 | C22 | 1 | 2 | yes | — |
| 14 | C2×#1010 | C22 | 1 | 2 | yes | — |
| 15 | C3×#578 | — | 2 | 8 | no | — |
| 16 | C2×C3×#137 | C22 | 1 | 6 | yes | — |
| 17 | C2×C3×#135 | C22 | 1 | 3 | yes | — |
| 18 | C22×C3×Q16 | C22 | 1 | 3 | yes | — |
| 19 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 20 | #5838 | — | 2 | 16 | no | — |
| 21 | #5832 | C22 | 1 | 6 | yes | — |
| 22 | Dic3×#41 | C22 | 1 | 1 | yes | characteristic |
| 23 | #5825 | C22 | 1 | 6 | yes | — |
| 24 | #5824 | — | 2 | 12 | no | — |
| 25 | C2×#951 | C22 | 1 | 6 | yes | — |
| 26 | C2×#950 | C22 | 1 | 6 | yes | — |
| 27 | C2×#948 | C22 | 1 | 1 | yes | characteristic |
| 28 | #5816 | C22 | 1 | 6 | yes | — |
| 29 | Q8×#67 | — | 2 | 4 | no | — |
| 30 | C2×#944 | C22 | 1 | 6 | yes | — |
| 31 | C22×#216 | C22 | 1 | 6 | yes | — |
| 32 | C2×#942 | C22 | 1 | 6 | yes | — |
| 33 | #5753 | — | 2 | 8 | no | — |
| 34 | C2×#909 | C22 | 1 | 6 | yes | — |
| 35 | C22×Dic12 | C22 | 1 | 3 | yes | — |
| 36 | C2×#904 | C22 | 1 | 3 | yes | — |
| 37 | #5191 | C22 | 1 | 3 | yes | — |
| 38 | #5190 | C22 | 1 | 12 | yes | — |
| 39 | #5183 | C22 | 1 | 6 | yes | — |
| 40 | #5183 | C22 | 1 | 6 | yes | — |
| 41 | #5183 | C22 | 1 | 3 | yes | — |
| 42 | #5183 | C22 | 1 | 6 | yes | — |
| 43 | #5175 | C22 | 1 | 6 | yes | — |
| 44 | #5168 | C22 | 1 | 6 | yes | — |
| 45 | #5167 | C22 | 1 | 12 | yes | — |
| 46 | #5155 | C22 | 1 | 3 | yes | — |
| 47 | #5151 | C22 | 1 | 1 | yes | characteristic |
| 48 | #5122 | C22 | 1 | 3 | yes | — |
| 49 | Dic3×M16 | C22 | 1 | 3 | yes | — |
| 50 | #5101 | C22 | 1 | 3 | yes | — |
| 51 | C2×C8×Dic3 | C22 | 1 | 3 | yes | — |
| 52 | C2×#578 | — | 3 | 2 | no | — |
| 53 | C2×#578 | — | 3 | 1 | no | — |
| 54 | C2×#578 | D3 | 1 | 1 | yes | characteristic, complemented |
| 55 | #3499 | — | 3 | 2 | no | — |
| 56 | #3156 | — | 3 | 6 | no | — |
| 57 | #3156 | — | 3 | 3 | no | — |
| 58 | #3156 | — | 3 | 3 | no | — |
| 59 | #3152 | — | 3 | 6 | no | — |
| 60 | #3147 | — | 3 | 3 | no | — |
| 61 | C2×#494 | — | 3 | 3 | no | — |
| 62 | C4×#131 | — | 3 | 1 | no | — |
| 63 | C3×2−1+4 | — | 2 | 8 | no | — |
| 64 | C3×2−1+4 | — | 2 | 8 | no | — |
| 65 | C2×C3×#41 | — | 2 | 6 | no | — |
| 66 | C2×C3×#41 | C23 | 1 | 6 | yes | — |
| 67 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×C3×Q8 | — | 2 | 2 | no | — |
| 69 | C22×C3×Q8 | C23 | 1 | 6 | yes | — |
| 70 | #1010 | — | 2 | 8 | no | — |
| 71 | #1010 | — | 2 | 8 | no | — |
| 72 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 73 | C2×#237 | — | 2 | 6 | no | — |
| 74 | C2×#235 | C23 | 1 | 6 | yes | — |
| 75 | C22×Dic6 | C23 | 1 | 6 | yes | — |
| 76 | C3×#137 | — | 2 | 24 | no | — |
| 77 | C3×#135 | — | 2 | 12 | no | — |
| 78 | C2×C3×Q16 | — | 2 | 12 | no | — |
| 79 | C2×C3×Q16 | C23 | 1 | 3 | yes | — |
| 80 | C2×C3×Q16 | C23 | 1 | 6 | yes | — |
| 81 | C2×C3×SD16 | C23 | 1 | 6 | yes | — |
| 82 | C2×C3×D8 | C23 | 1 | 1 | yes | characteristic |
| 83 | C3×#131 | D4 | 1 | 8 | yes | complemented |
| 84 | C2×C3×M16 | C23 | 1 | 3 | yes | — |
| 85 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 86 | #951 | — | 2 | 24 | no | — |
| 87 | #950 | — | 2 | 24 | no | — |
| 88 | #948 | D4 | 1 | 8 | yes | complemented |
| 89 | #947 | C23 | 1 | 6 | yes | — |
| 90 | #946 | — | 2 | 12 | no | — |
| 91 | Q8×Dic3 | D4 | 1 | 2 | yes | — |
| 92 | #944 | — | 2 | 12 | no | — |
| 93 | #944 | C23 | 1 | 12 | yes | — |
| 94 | #944 | C23 | 1 | 6 | yes | — |
| 95 | C2×#216 | — | 2 | 24 | no | — |
| 96 | C2×#216 | C23 | 1 | 12 | yes | — |
| 97 | C2×#216 | C23 | 1 | 6 | yes | — |
| 98 | #942 | — | 2 | 24 | no | — |
| 99 | C2×#215 | C23 | 1 | 6 | yes | — |
| 100 | #940 | C23 | 1 | 2 | yes | — |
| 101 | #939 | — | 2 | 12 | no | — |
| 102 | #936 | C23 | 1 | 6 | yes | — |
| 103 | #935 | — | 2 | 12 | no | — |
| 104 | D4×Dic3 | D4 | 1 | 6 | yes | — |
| 105 | C2×#214 | C23 | 1 | 6 | yes | — |
| 106 | C2×#213 | C23 | 1 | 2 | yes | — |
| 107 | #929 | — | 2 | 12 | no | — |
| 108 | C4×#67 | — | 2 | 12 | no | — |
| 109 | #926 | C23 | 1 | 3 | yes | — |
| 110 | #924 | — | 2 | 12 | no | — |
| 111 | C2×Dic3⋊C4 | — | 2 | 12 | no | — |
| 112 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 113 | C2×#208 | C23 | 1 | 3 | yes | — |
| 114 | C22×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 115 | #909 | — | 2 | 24 | no | — |
| 116 | C2×Dic12 | — | 2 | 12 | no | — |
| 117 | C2×Dic12 | C23 | 1 | 3 | yes | — |
| 118 | C2×Dic12 | C23 | 1 | 6 | yes | — |
| 119 | #904 | — | 2 | 12 | no | — |
| 120 | C2×D24 | C23 | 1 | 1 | yes | characteristic |
| 121 | C2×#204 | C23 | 1 | 6 | yes | — |
| 122 | #815 | C23 | 1 | 6 | yes | — |
| 123 | C8×Dic3 | C23 | 1 | 3 | yes | — |
| 124 | C8×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 125 | C8×Dic3 | C23 | 1 | 3 | yes | — |
| 126 | C8×Dic3 | C23 | 1 | 3 | yes | — |
| 127 | C2×2−1+4 | — | 3 | 2 | no | — |
| 128 | C2×2−1+4 | C2×D3 | 1 | 2 | yes | — |
| 129 | #578 | — | 2 | 8 | no | — |
| 130 | #578 | — | 6 | 16 | no | — |
| 131 | #578 | — | 6 | 8 | no | — |
| 132 | C2×#137 | — | 3 | 6 | no | — |
| 133 | C2×#137 | — | 3 | 6 | no | — |
| 134 | C2×#137 | — | 3 | 6 | no | — |
| 135 | C2×#137 | C2×D3 | 1 | 6 | yes | — |
| 136 | C2×#135 | — | 3 | 6 | no | — |
| 137 | C2×#135 | — | 3 | 3 | no | — |
| 138 | C2×#135 | C2×D3 | 1 | 3 | yes | — |
| 139 | C22×Q16 | — | 3 | 6 | no | — |
| 140 | C22×Q16 | — | 3 | 3 | no | — |
| 141 | C22×Q16 | C2×D3 | 1 | 3 | yes | — |
| 142 | C2×#131 | — | 3 | 1 | no | — |
| 143 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 144 | D4×Q8 | — | 6 | 4 | no | — |
| 145 | #547 | — | 6 | 12 | no | — |
| 146 | #536 | — | 3 | 6 | no | — |
| 147 | #536 | — | 3 | 6 | no | — |
| 148 | #532 | — | 3 | 6 | no | — |
| 149 | C2×C4⋊Q8 | — | 3 | 6 | no | — |
| 150 | C4×#41 | — | 3 | 1 | no | — |
| 151 | #497 | — | 3 | 12 | no | — |
| 152 | #497 | — | 3 | 12 | no | — |
| 153 | #495 | — | 3 | 3 | no | — |
| 154 | #495 | — | 3 | 6 | no | — |
| 155 | #495 | — | 3 | 3 | no | — |
| 156 | #494 | — | 3 | 3 | no | — |
| 157 | #494 | — | 3 | 6 | no | — |
| 158 | #494 | — | 3 | 6 | no | — |
| 159 | #494 | — | 3 | 6 | no | — |
| 160 | #493 | — | 3 | 1 | no | — |
| 161 | #492 | — | 3 | 6 | no | — |
| 162 | #405 | — | 3 | 3 | no | — |
| 163 | #405 | — | 3 | 3 | no | — |
| 164 | C4×M16 | — | 3 | 3 | no | — |
| 165 | C2×C4×C8 | — | 3 | 3 | no | — |
| 166 | C3×#41 | — | 2 | 12 | no | — |
| 167 | C3×#41 | — | 2 | 12 | no | — |
| 168 | C3×#41 | — | 4 | 24 | no | — |
| 169 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 170 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 171 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 172 | C2×C3×Q8 | — | 2 | 12 | no | — |
| 173 | C2×C3×Q8 | — | 2 | 12 | no | — |
| 174 | C2×C3×Q8 | — | 4 | 8 | no | — |
| 175 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C2×C3×Q8 | C24 | 1 | 6 | yes | — |
| 177 | C2×C3×D4 | — | 2 | 6 | no | — |
| 178 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 179 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 180 | C22×C3×C4 | — | 2 | 6 | no | — |
| 181 | C22×C3×C4 | — | 2 | 6 | no | — |
| 182 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 183 | C2×#67 | — | 2 | 6 | no | — |
| 184 | C2×#67 | — | 2 | 4 | no | — |
| 185 | C22×Dic3 | — | 2 | 6 | no | — |
| 186 | C22×Dic3 | C2×D4 | 1 | 6 | yes | — |
| 187 | D3×Q8 | — | 4 | 8 | no | — |
| 188 | #237 | — | 4 | 24 | no | — |
| 189 | #235 | — | 2 | 12 | no | — |
| 190 | #235 | — | 2 | 12 | no | — |
| 191 | C2×D12 | C24 | 1 | 2 | yes | — |
| 192 | C2×C4×D3 | — | 2 | 6 | no | — |
| 193 | C2×Dic6 | — | 2 | 12 | no | — |
| 194 | C2×Dic6 | — | 2 | 12 | no | — |
| 195 | C2×Dic6 | — | 2 | 6 | no | — |
| 196 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 197 | C3×Q16 | — | 2 | 6 | no | — |
| 198 | C3×Q16 | — | 2 | 12 | no | — |
| 199 | C3×SD16 | — | 2 | 12 | no | — |
| 200 | C3×D8 | — | 2 | 2 | no | — |
| 201 | C3×M16 | C2×D4 | 1 | 12 | yes | — |
| 202 | C2×C3×C8 | C2×D4 | 1 | 12 | yes | — |
| 203 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 204 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 205 | #217 | — | 2 | 12 | no | — |
| 206 | #217 | C2×D4 | 1 | 6 | yes | — |
| 207 | #216 | — | 2 | 24 | no | — |
| 208 | #216 | — | 2 | 12 | no | — |
| 209 | #215 | — | 2 | 12 | no | — |
| 210 | #214 | — | 2 | 12 | no | — |
| 211 | #213 | — | 2 | 4 | no | — |
| 212 | (C2×D3)⋊C4 | — | 2 | 12 | no | — |
| 213 | C4⋊Dic3 | C2×D4 | 1 | 6 | yes | — |
| 214 | Dic3⋊C4 | — | 2 | 12 | no | — |
| 215 | Dic3⋊C4 | — | 2 | 24 | no | — |
| 216 | C4×Dic3 | C2×D4 | 1 | 6 | yes | — |
| 217 | C4×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 218 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 219 | #208 | C2×D4 | 1 | 12 | yes | — |
| 220 | C2×C3⋊C8 | C2×D4 | 1 | 12 | yes | — |
| 221 | C2×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 222 | C2×C3⋊C8 | C24 | 1 | 3 | yes | — |
| 223 | Dic12 | — | 2 | 6 | no | — |
| 224 | Dic12 | — | 2 | 12 | no | — |
| 225 | D24 | — | 2 | 2 | no | — |
| 226 | #204 | — | 2 | 12 | no | — |
| 227 | 2−1+4 | — | 2 | 8 | no | — |
| 228 | 2−1+4 | — | 2 | 8 | no | — |
| 229 | 2−1+4 | — | 6 | 8 | no | — |
| 230 | 2−1+4 | — | 6 | 8 | no | — |
| 231 | C2×#41 | — | 2 | 6 | no | — |
| 232 | C2×#41 | — | 3 | 6 | no | — |
| 233 | C2×#41 | — | 6 | 6 | no | — |
| 234 | C2×#41 | C22×D3 | 1 | 6 | yes | — |
| 235 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 236 | C22×Q8 | — | 2 | 2 | no | — |
| 237 | C22×Q8 | — | 3 | 6 | no | — |
| 238 | C22×Q8 | — | 6 | 2 | no | — |
| 239 | C22×Q8 | C22×D3 | 1 | 6 | yes | — |
| 240 | #137 | — | 2 | 24 | no | — |
| 241 | #137 | — | 6 | 24 | no | — |
| 242 | #137 | — | 6 | 24 | no | — |
| 243 | #137 | — | 6 | 24 | no | — |
| 244 | #135 | — | 2 | 12 | no | — |
| 245 | #135 | — | 6 | 24 | no | — |
| 246 | #135 | — | 6 | 12 | no | — |
| 247 | C2×Q16 | — | 2 | 12 | no | — |
| 248 | C2×Q16 | — | 3 | 6 | no | — |
| 249 | C2×Q16 | — | 3 | 12 | no | — |
| 250 | C2×Q16 | — | 3 | 3 | no | — |
| 251 | C2×Q16 | — | 3 | 6 | no | — |
| 252 | C2×Q16 | — | 6 | 24 | no | — |
| 253 | C2×Q16 | — | 6 | 12 | no | — |
| 254 | C2×Q16 | C22×D3 | 1 | 3 | yes | — |
| 255 | C2×Q16 | C22×D3 | 1 | 6 | yes | — |
| 256 | C2×SD16 | — | 3 | 6 | no | — |
| 257 | C2×SD16 | — | 3 | 6 | no | — |
| 258 | C2×SD16 | — | 3 | 6 | no | — |
| 259 | C2×SD16 | C22×D3 | 1 | 6 | yes | — |
| 260 | C2×D8 | — | 3 | 2 | no | — |
| 261 | C2×D8 | — | 3 | 1 | no | — |
| 262 | C2×D8 | C22×D3 | 1 | 1 | yes | characteristic |
| 263 | #131 | — | 3 | 8 | no | — |
| 264 | #131 | #67 | 1 | 8 | yes | complemented |
| 265 | C2×M16 | — | 3 | 3 | no | — |
| 266 | C2×M16 | C22×D3 | 1 | 3 | yes | — |
| 267 | C22×C8 | — | 3 | 3 | no | — |
| 268 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 269 | C4⋊Q8 | — | 3 | 6 | no | — |
| 270 | C4⋊Q8 | — | 3 | 12 | no | — |
| 271 | C4⋊Q8 | — | 6 | 12 | no | — |
| 272 | #127 | — | 3 | 2 | no | — |
| 273 | #124 | — | 3 | 6 | no | — |
| 274 | #124 | — | 3 | 6 | no | — |
| 275 | #123 | — | 6 | 12 | no | — |
| 276 | #123 | — | 6 | 12 | no | — |
| 277 | C22⋊Q8 | — | 6 | 12 | no | — |
| 278 | C22⋊Q8 | — | 6 | 12 | no | — |
| 279 | #121 | — | 6 | 12 | no | — |
| 280 | C4×Q8 | — | 3 | 2 | no | — |
| 281 | C4×D4 | — | 3 | 6 | no | — |
| 282 | C4×D4 | — | 6 | 12 | no | — |
| 283 | #117 | — | 3 | 3 | no | — |
| 284 | C2×C4⋊C4 | — | 6 | 12 | no | — |
| 285 | C2×C42 | — | 3 | 3 | no | — |
| 286 | #97 | — | 3 | 6 | no | — |
| 287 | C4×C8 | — | 3 | 1 | no | — |
| 288 | C4×C8 | — | 3 | 3 | no | — |
| 289 | C4×C8 | — | 3 | 3 | no | — |
| 290 | C4×C8 | — | 3 | 3 | no | — |
| 291 | C23×C3 | — | 2 | 2 | no | — |
| 292 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 293 | C22×D3 | — | 2 | 2 | no | — |
| 294 | C3×Q8 | — | 2 | 6 | no | — |
| 295 | C3×Q8 | — | 2 | 6 | no | — |
| 296 | C3×Q8 | — | 4 | 12 | no | — |
| 297 | C3×Q8 | #127 | 1 | 4 | yes | — |
| 298 | C3×D4 | — | 2 | 2 | no | — |
| 299 | C3×D4 | — | 2 | 2 | no | — |
| 300 | C3×D4 | — | 4 | 12 | no | — |
| 301 | C3×D4 | #127 | 1 | 12 | yes | — |
| 302 | C2×C3×C4 | — | 2 | 6 | no | — |
| 303 | C2×C3×C4 | — | 4 | 12 | no | — |
| 304 | C2×C3×C4 | — | 4 | 12 | no | — |
| 305 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 306 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 307 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 308 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 309 | #67 | — | 4 | 12 | no | — |
| 310 | #67 | — | 4 | 8 | no | — |
| 311 | C2×Dic3 | — | 2 | 12 | no | — |
| 312 | C2×Dic3 | — | 2 | 6 | no | — |
| 313 | C2×Dic3 | — | 4 | 12 | no | — |
| 314 | C2×Dic3 | C22×D4 | 1 | 6 | yes | — |
| 315 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 316 | D12 | — | 2 | 2 | no | — |
| 317 | D12 | — | 2 | 2 | no | — |
| 318 | C4×D3 | — | 4 | 12 | no | — |
| 319 | Dic6 | — | 2 | 6 | no | — |
| 320 | Dic6 | — | 2 | 6 | no | — |
| 321 | Dic6 | — | 4 | 12 | no | — |
| 322 | C3×C8 | C22×D4 | 1 | 6 | yes | — |
| 323 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 324 | C3⋊C8 | C22×D4 | 1 | 2 | yes | — |
| 325 | C3⋊C8 | C22×D4 | 1 | 6 | yes | — |
| 326 | #41 | — | 2 | 12 | no | — |
| 327 | #41 | — | 2 | 12 | no | — |
| 328 | #41 | — | 4 | 24 | no | — |
| 329 | #41 | — | 6 | 12 | no | — |
| 330 | #41 | — | 6 | 12 | no | — |
| 331 | #41 | — | 12 | 24 | no | — |
| 332 | #41 | D3×D4 | 1 | 4 | yes | — |
| 333 | #41 | C2×#67 | 1 | 4 | yes | — |
| 334 | C2×Q8 | — | 2 | 6 | no | — |
| 335 | C2×Q8 | — | 2 | 12 | no | — |
| 336 | C2×Q8 | — | 2 | 12 | no | — |
| 337 | C2×Q8 | — | 3 | 6 | no | — |
| 338 | C2×Q8 | — | 4 | 8 | no | — |
| 339 | C2×Q8 | — | 6 | 6 | no | — |
| 340 | C2×Q8 | — | 6 | 12 | no | — |
| 341 | C2×Q8 | — | 6 | 12 | no | — |
| 342 | C2×Q8 | — | 12 | 8 | no | — |
| 343 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 344 | C2×Q8 | C23×D3 | 1 | 6 | yes | — |
| 345 | C2×D4 | — | 2 | 6 | no | — |
| 346 | C2×D4 | — | 3 | 2 | no | — |
| 347 | C2×D4 | — | 6 | 4 | no | — |
| 348 | C2×D4 | — | 6 | 6 | no | — |
| 349 | C2×D4 | D3×D4 | 1 | 3 | yes | — |
| 350 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 351 | C22×C4 | — | 2 | 6 | no | — |
| 352 | C22×C4 | — | 2 | 6 | no | — |
| 353 | C22×C4 | — | 3 | 6 | no | — |
| 354 | C22×C4 | — | 6 | 6 | no | — |
| 355 | C22×C4 | — | 6 | 6 | no | — |
| 356 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 357 | Q16 | — | 2 | 6 | no | — |
| 358 | Q16 | — | 2 | 12 | no | — |
| 359 | Q16 | — | 6 | 12 | no | — |
| 360 | Q16 | — | 6 | 24 | no | — |
| 361 | Q16 | — | 6 | 6 | no | — |
| 362 | Q16 | — | 6 | 12 | no | — |
| 363 | SD16 | — | 2 | 12 | no | — |
| 364 | SD16 | — | 6 | 12 | no | — |
| 365 | SD16 | — | 6 | 12 | no | — |
| 366 | SD16 | — | 6 | 12 | no | — |
| 367 | D8 | — | 2 | 2 | no | — |
| 368 | D8 | — | 6 | 4 | no | — |
| 369 | D8 | — | 6 | 2 | no | — |
| 370 | M16 | — | 3 | 12 | no | — |
| 371 | M16 | C2×#67 | 1 | 12 | yes | — |
| 372 | C2×C8 | — | 3 | 12 | no | — |
| 373 | C2×C8 | — | 3 | 1 | no | — |
| 374 | C2×C8 | — | 3 | 3 | no | — |
| 375 | C2×C8 | C2×#67 | 1 | 12 | yes | — |
| 376 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 377 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 378 | C4⋊C4 | — | 3 | 6 | no | — |
| 379 | C4⋊C4 | — | 6 | 12 | no | — |
| 380 | C4⋊C4 | — | 6 | 24 | no | — |
| 381 | C22⋊C4 | — | 3 | 6 | no | — |
| 382 | C22⋊C4 | — | 6 | 12 | no | — |
| 383 | C22⋊C4 | — | 6 | 12 | no | — |
| 384 | C42 | — | 3 | 6 | no | — |
| 385 | C42 | — | 3 | 1 | no | — |
| 386 | C42 | — | 3 | 3 | no | — |
| 387 | C22×C3 | — | 2 | 6 | no | — |
| 388 | C22×C3 | — | 4 | 2 | no | — |
| 389 | C22×C3 | — | 4 | 4 | no | — |
| 390 | C22×C3 | C2×#127 | 1 | 6 | yes | — |
| 391 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 392 | C2×D3 | — | 4 | 2 | no | — |
| 393 | C2×D3 | — | 4 | 4 | no | — |
| 394 | C3×C4 | — | 4 | 6 | no | — |
| 395 | C3×C4 | C2×#127 | 1 | 6 | yes | — |
| 396 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 397 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 398 | Dic3 | — | 2 | 6 | no | — |
| 399 | Dic3 | — | 4 | 6 | no | — |
| 400 | Dic3 | #578 | 1 | 4 | yes | complemented |
| 401 | C23 | — | 2 | 2 | no | — |
| 402 | C23 | — | 6 | 2 | no | — |
| 403 | C23 | C2×D3×D4 | 1 | 3 | yes | — |
| 404 | Q8 | — | 2 | 6 | no | — |
| 405 | Q8 | — | 2 | 6 | no | — |
| 406 | Q8 | — | 4 | 12 | no | — |
| 407 | Q8 | — | 6 | 6 | no | — |
| 408 | Q8 | — | 6 | 6 | no | — |
| 409 | Q8 | — | 12 | 12 | no | — |
| 410 | Q8 | #940 | 1 | 4 | yes | — |
| 411 | D4 | — | 2 | 2 | no | — |
| 412 | D4 | — | 2 | 2 | no | — |
| 413 | D4 | — | 4 | 12 | no | — |
| 414 | D4 | — | 6 | 2 | no | — |
| 415 | D4 | — | 6 | 2 | no | — |
| 416 | D4 | — | 12 | 8 | no | — |
| 417 | D4 | — | 12 | 12 | no | — |
| 418 | D4 | #940 | 1 | 12 | yes | — |
| 419 | C2×C4 | — | 2 | 6 | no | — |
| 420 | C2×C4 | — | 3 | 2 | no | — |
| 421 | C2×C4 | — | 3 | 6 | no | — |
| 422 | C2×C4 | — | 4 | 12 | no | — |
| 423 | C2×C4 | — | 4 | 12 | no | — |
| 424 | C2×C4 | — | 6 | 12 | no | — |
| 425 | C2×C4 | — | 6 | 6 | no | — |
| 426 | C2×C4 | — | 12 | 12 | no | — |
| 427 | C2×C4 | — | 12 | 12 | no | — |
| 428 | C2×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 429 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 430 | C2×C4 | C22×#67 | 1 | 6 | yes | — |
| 431 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 432 | C8 | — | 3 | 2 | no | — |
| 433 | C8 | — | 3 | 6 | no | — |
| 434 | C8 | C22×#67 | 1 | 2 | yes | — |
| 435 | C8 | C22×#67 | 1 | 6 | yes | — |
| 436 | C2×C3 | — | 2 | 6 | no | — |
| 437 | C2×C3 | — | 8 | 2 | no | — |
| 438 | C2×C3 | C22×#127 | 1 | 1 | yes | characteristic |
| 439 | C2×C3 | C2×#578 | 1 | 2 | yes | — |
| 440 | D3 | — | 8 | 2 | no | — |
| 441 | C22 | — | 2 | 6 | no | — |
| 442 | C22 | — | 4 | 4 | no | — |
| 443 | C22 | — | 4 | 2 | no | — |
| 444 | C22 | — | 12 | 4 | no | — |
| 445 | C22 | — | 12 | 2 | no | — |
| 446 | C22 | C2×#940 | 1 | 6 | yes | — |
| 447 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 448 | C4 | — | 3 | 4 | no | — |
| 449 | C4 | — | 4 | 6 | no | — |
| 450 | C4 | — | 6 | 6 | no | — |
| 451 | C4 | — | 12 | 6 | no | — |
| 452 | C4 | C2×#940 | 1 | 6 | yes | — |
| 453 | C4 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 454 | C4 | C23×#67 | 1 | 1 | yes | characteristic |
| 455 | C3 | #60648 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 456 | C2 | — | 2 | 6 | no | — |
| 457 | C2 | — | 8 | 2 | no | — |
| 458 | C2 | — | 24 | 2 | no | — |
| 459 | C2 | D3×#578 | 1 | 2 | yes | — |
| 460 | C2 | C22×#940 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#578 | C2 | semidirect |
| 2. #87292 | C2 | semidirect |
| 3. C2×#5838 | C2 | semidirect |
| 4. C2×#5753 | C2 | semidirect |
| 5. #83975 | C2 | semidirect |
| 6. #83972 | C2 | semidirect |
| 7. #83907 | C2 | semidirect |
| 8. #83903 | C2 | semidirect |
| 9. #83881 | C2 | semidirect |
| 10. C2×#5183 | C2 | semidirect |
| 11. Dic3×#131 | C2 | semidirect |
| 54. C2×#578 | D3 | semidirect |
| 83. C3×#131 | D4 | semidirect |
| 88. #948 | D4 | semidirect |
| 264. #131 | #67 | semidirect |
| 400. Dic3 | #578 | semidirect |
| 455. C3 | #60648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#578 | 2 |
| #87292 | 2 |
| C2×#5838 | 2 |
| C2×#5753 | 2 |
| #83975 | 2 |
| #83972 | 2 |
| #83907 | 2 |
| #83903 | 2 |
| #83881 | 2 |
| C2×#5183 | 2 |
| Dic3×#131 | 2 |
| #60648 | 3 |