Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
3702 conjugacy classes of subgroups.
The subgroup lattice has 2192 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#99 |
| commutator | C24 | C22×C42 |
| Frattini, cosocle | C2×C4×D4 | C24 |
| socle | C22 | C22×#342 |
| prime radical | C23×#41 | C2×C4 |
| LCS | G ▷ C24 ▷ 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. #127141 | C2 | semidirect |
| 5. #127124 | C2 | semidirect |
| 6. #127106 | C2 | semidirect |
| 9. C2×#2920 | C4 | semidirect |
| 10. C22×#423 | C4 | semidirect |
| 14. #21851 | C4 | semidirect |
| 18. #21847 | C4 | semidirect |
| 22. #20898 | C4 | semidirect |
| 45. #17363 | C4 | semidirect |
| 47. #17362 | C4 | semidirect |
| 49. #17361 | C4 | semidirect |
| 51. #17357 | C4 | semidirect |
| 54. #7204 | C22 | semidirect |
| 110. C2×#432 | C2×C4 | semidirect |
| 114. C2×#431 | C2×C4 | semidirect |
| 125. C22×C4⋊C8 | C2×C4 | semidirect |
| 126. C22×C4⋊C8 | C2×C4 | semidirect |
| 163. #1869 | C2×C4 | semidirect |
| 164. #1869 | C2×C4 | semidirect |
| 209. #1465 | C2×C4 | semidirect |
| 213. #1464 | C2×C4 | semidirect |
| 225. #1459 | 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 |
|---|---|
| #6374537 | 2 |
| C2×#20723 | 2 |
| #6342561 | 2 |
| #127141 | 2 |
| #127124 | 2 |
| #127106 | 2 |