Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2234 conjugacy classes of subgroups.
The subgroup lattice has 442 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C22×C4 | C25 |
| commutator | C22 | C23×C42 |
| socle | C23 | C24×C4 |
| prime radical | C25 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #20551 | C2 | semidirect |
| 5. #20545 | C2 | semidirect |
| 6. #20537 | C2 | semidirect |
| 8. #20480 | C2 | semidirect |
| 9. #20479 | C2 | semidirect |
| 10. #20467 | C2 | semidirect |
| 12. #2920 | C4 | semidirect |
| 13. C2×#432 | C4 | semidirect |
| 43. #1771 | C22 | semidirect |
| 44. #1770 | C22 | semidirect |
| 45. C8×C4⋊C4 | C22 | semidirect |
| 46. #1768 | C22 | semidirect |
| 51. #1745 | C22 | semidirect |
| 52. C4×#97 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2920 | 2 |
| C22×#432 | 2 |
| #34012 | 2 |
| #20551 | 2 |
| #20545 | 2 |
| #20537 | 2 |
| #20527 | 2 |
| #20480 | 2 |
| #20479 | 2 |
| #20467 | 2 |