Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
3790 conjugacy classes of subgroups.
The subgroup lattice has 2164 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#99 |
| commutator | C22×C4 | C22×C42 |
| Frattini, cosocle | C2×C4×D4 | C24 |
| socle | C22 | C22×#342 |
| prime radical | C23×#41 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C42 ◁ C22×C4×#41 ◁ G | |
| LECS | G ▷ C2×C4×D4 ▷ C23 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #127143 | C2 | semidirect |
| 5. #127126 | C2 | semidirect |
| 6. #127110 | C2 | semidirect |
| 9. C2×#2920 | C4 | semidirect |
| 10. C22×C4×M16 | C4 | semidirect |
| 12. #21380 | C4 | semidirect |
| 18. #21373 | C4 | semidirect |
| 20. #21303 | C4 | semidirect |
| 41. #17366 | C4 | semidirect |
| 42. #17365 | C4 | semidirect |
| 49. #17361 | C4 | semidirect |
| 51. #17357 | C4 | semidirect |
| 54. #7205 | C22 | semidirect |
| 110. C2×#432 | C2×C4 | semidirect |
| 114. C2×#431 | C2×C4 | semidirect |
| 132. C2×C4×M16 | C2×C4 | semidirect |
| 134. C22×C4×C8 | C2×C4 | semidirect |
| 152. #1984 | C2×C4 | semidirect |
| 153. #1984 | C2×C4 | semidirect |
| 203. #1467 | C2×C4 | semidirect |
| 213. #1464 | C2×C4 | semidirect |
| 219. #1461 | C2×C4 | semidirect |
| 229. #1458 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6372358 | 2 |
| C2×#20723 | 2 |
| #6342561 | 2 |
| #127143 | 2 |
| #127126 | 2 |
| #127110 | 2 |