Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
229876716 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C2 | C210 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ G | |
| LECS | G ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72258201 | C2 | semidirect |
| 2. C2×2−1+8 | C2 | semidirect |
| 3. 2−1+8 | C22 | semidirect |
| 4. H(9,𝔽2) | C22 | semidirect |
| 5. C2×#63103 | C22 | semidirect |
| 6. C22×2−1+6 | C22 | semidirect |
| 7. #63103 | C23 | semidirect |
| 8. C2×2−1+6 | C23 | semidirect |
| 9. C2×H(7,𝔽2) | C23 | semidirect |
| 10. C22×#585 | C23 | semidirect |
| 11. C23×2−1+4 | C23 | semidirect |
| 12. 2−1+6 | C24 | semidirect |
| 13. H(7,𝔽2) | C24 | semidirect |
| 14. C2×#585 | C24 | semidirect |
| 15. C22×2−1+4 | C24 | semidirect |
| 16. C22×H(5,𝔽2) | C24 | semidirect |
| 17. C23×#41 | C24 | semidirect |
| 18. C24×Q8 | C24 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72258201 | 2 |
| C2×2−1+8 | 2 |