Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
14188 conjugacy classes of subgroups.
The subgroup lattice has 570 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C42 | C26 |
| commutator, socle | C22 | C24×C42 |
| prime radical | #412 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #6342516 | C2 | semidirect |
| 4. #6342511 | C2 | semidirect |
| 5. #6342509 | C2 | semidirect |
| 6. #6342500 | C2 | semidirect |
| 7. #6342499 | C2 | semidirect |
| 8. #6342482 | C2 | semidirect |
| 9. C2×#17320 | C2 | semidirect |
| 28. #17342 | C22 | semidirect |
| 29. #17337 | C22 | semidirect |
| 30. #17336 | C22 | semidirect |
| 31. #17336 | C22 | semidirect |
| 32. M162 | C22 | semidirect |
| 33. #17331 | C22 | semidirect |
| 34. #17330 | C22 | semidirect |
| 35. #17329 | C22 | semidirect |
| 36. #17329 | C22 | semidirect |
| 37. #17329 | C22 | semidirect |
| 38. #17327 | C22 | semidirect |
| 39. #17326 | C22 | semidirect |
| 40. #17325 | C22 | semidirect |
| 41. #17323 | C22 | semidirect |
| 42. #17323 | C22 | semidirect |
| 47. #17320 | C22 | semidirect |
| 48. #17320 | C22 | semidirect |
| 49. #17320 | C22 | semidirect |
| 50. #17320 | C22 | semidirect |
| 51. C2×#1452 | C22 | semidirect |
| 52. C2×#1451 | C22 | semidirect |
| 53. C2×#1451 | C22 | semidirect |
| 55. #17316 | C22 | semidirect |
| 56. C22×#322 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10574593 | 2 |
| #41×#131 | 2 |
| #6342516 | 2 |
| #6342511 | 2 |
| #6342509 | 2 |
| #6342500 | 2 |
| #6342499 | 2 |
| #6342482 | 2 |
| C2×#17320 | 2 |