Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
2840 conjugacy classes of subgroups.
The subgroup lattice has 601 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×C42 |
| commutator | C2×C4 | C23×C42 |
| Frattini, cosocle | C4×C8 | C25 |
| socle | C22 | C23×#97 |
| prime radical | C22×#41 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C42 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #479979 | C2 | semidirect |
| 5. #479977 | C2 | semidirect |
| 6. #479966 | C2 | semidirect |
| 7. #479962 | C2 | semidirect |
| 8. #479962 | C2 | semidirect |
| 9. C2×#11404 | C2 | semidirect |
| 37. #11415 | C22 | semidirect |
| 38. #11415 | C22 | semidirect |
| 39. #11414 | C22 | semidirect |
| 40. #11414 | C22 | semidirect |
| 41. #11413 | C22 | semidirect |
| 42. #11413 | C22 | semidirect |
| 48. #11404 | C22 | semidirect |
| 49. C2×#1313 | C22 | semidirect |
| 365. M32 | #131 | semidirect |
| 513. C16 | C2×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×M32 | 2 |
| C2×#17320 | 2 |
| #479979 | 2 |
| #479977 | 2 |
| #479966 | 2 |
| #479962 | 2 |
| C2×#11404 | 2 |