Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
2448 conjugacy classes of subgroups.
The subgroup lattice has 573 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, commutator | C2×C4 | C23×C42 |
| Frattini, cosocle | C4×C8 | C25 |
| socle | C22 | C23×#97 |
| prime radical | #3444 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ 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. #479981 | C2 | semidirect |
| 5. #479977 | C2 | semidirect |
| 6. #479976 | C2 | semidirect |
| 7. #479973 | C2 | semidirect |
| 8. #479968 | C2 | semidirect |
| 9. C2×#11415 | C2 | semidirect |
| 37. #11416 | C22 | semidirect |
| 42. #11415 | C22 | semidirect |
| 43. #11414 | C22 | semidirect |
| 44. #11414 | C22 | semidirect |
| 47. #11413 | C22 | semidirect |
| 48. #11413 | C22 | semidirect |
| 49. #11406 | C22 | semidirect |
| 50. #11405 | C22 | semidirect |
| 51. #11404 | C22 | semidirect |
| 54. C2×#1313 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7622738 | 2 |
| #6342482 | 2 |
| #479981 | 2 |
| #479977 | 2 |
| #479976 | 2 |
| #479973 | 2 |
| #479968 | 2 |
| C2×#11415 | 2 |