Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
810 conjugacy classes of subgroups; only the 443 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 443 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C23×D41 |
| commutator, socle, cosocle | C2×C41 | C25 |
| Frattini | C2 | C24×D41 |
| Fitting | C2×#41×C41 | C2 |
| hypercenter | C2×#41 | D41 |
| hypocenter | C41 | #585 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13050212 | C2 | semidirect |
| 2. #13050211 | C2 | semidirect |
| 3. #13050210 | C2 | semidirect |
| 4. #13050209 | C2 | semidirect |
| 5. C2×#10620306 | C2 | semidirect |
| 6. #41×D41 | C2 | semidirect |
| 7. C2×#41×C41 | C2 | semidirect |
| 8. #41×C41 | C22 | semidirect |
| 9. #41×C41 | C22 | semidirect |
| 10. C2×Q8×C41 | C22 | semidirect |
| 11. C2×D4×C41 | C22 | semidirect |
| 12. C22×C4×C41 | C22 | semidirect |
| 13. C2×C22⋊D41 | C22 | semidirect |
| 14. #10620310 | C22 | semidirect |
| 15. Q8×D41 | C22 | semidirect |
| 16. #10620308 | C22 | semidirect |
| 17. D4×D41 | C22 | semidirect |
| 18. #10620306 | C22 | semidirect |
| 19. #10620306 | C22 | semidirect |
| 20. #10620306 | C22 | semidirect |
| 21. #10620306 | C22 | semidirect |
| 22. C2×D164 | C22 | semidirect |
| 23. C2×C4×D41 | C22 | semidirect |
| 24. C2×Dic82 | C22 | semidirect |
| 56. C41 | #585 | semidirect |
| 63. C2×#41 | D41 | semidirect |
| 70. #41 | C2×D41 | semidirect |
| 71. #41 | C2×D41 | semidirect |
| 74. C2×Q8 | C2×D41 | semidirect |
| 78. C2×D4 | C2×D41 | semidirect |
| 80. C22×C4 | C2×D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050212 | 2 |
| #13050211 | 2 |
| #13050210 | 2 |
| #13050209 | 2 |
| C2×#10620306 | 2 |
| #41×D41 | 2 |
| C2×#41×C41 | 2 |
| #585 | 41 |