Order 2048.
20292 conjugacy classes of subgroups.
The subgroup lattice has 4666 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×#120 |
| commutator | C2×C42 | C22×C42 |
| Frattini, cosocle | C23×C42 | C24 |
| socle | C23 | C2×#1436 |
| prime radical | C26 | #124 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C23×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #72240023 | C2 | semidirect |
| 21. C2×#21994 | C4 | semidirect |
| 22. C2×#21970 | C4 | semidirect |
| 34. C2×#8094 | C4 | semidirect |
| 35. C2×#8093 | C4 | semidirect |
| 53. C2×#7867 | C4 | semidirect |
| 54. C2×#7867 | C4 | semidirect |
| 236. C2×#1950 | C2×C4 | semidirect |
| 254. C2×#1303 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6375061 | 2 |
| #72240023 | 2 |
| #72239964 | 2 |
| C2×#181727 | 2 |
| C2×#180904 | 2 |
| C2×#353780 | 2 |
| C22×#7867 | 2 |