Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C22⋊D19 |
| commutator, cosocle | C4×C19 | C24 |
| Frattini | C4 | C23×D19 |
| Fitting | C19×2−1+4 | C2 |
| socle | C2×C19 | C22×D4 |
| hypercenter | 2−1+4 | D19 |
| hypocenter | C19 | #577 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×2−1+4 | C2 | semidirect |
| 2. #10597435 | C2 | semidirect |
| 3. #10597396 | C2 | semidirect |
| 4. #10597395 | C2 | semidirect |
| 5. #10597394 | C2 | semidirect |
| 6. #10597388 | C2 | semidirect |
| 7. C2×#64527 | C2 | semidirect |
| 10. #41×C19 | C22 | semidirect |
| 12. C2×Q8×C19 | C22 | semidirect |
| 17. #64528 | C22 | semidirect |
| 18. #64527 | C22 | semidirect |
| 19. #64527 | C22 | semidirect |
| 20. #64526 | C22 | semidirect |
| 21. #64525 | C22 | semidirect |
| 22. #64520 | C22 | semidirect |
| 23. C2×C19⋊C8 | C22 | semidirect |
| 54. 2−1+4 | D19 | semidirect |
| 61. C19 | #577 | semidirect |
| 66. #41 | C2×D19 | semidirect |
| 68. C2×Q8 | C2×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×2−1+4 | 2 |
| #10597435 | 2 |
| #10597396 | 2 |
| #10597395 | 2 |
| #10597394 | 2 |
| #10597388 | 2 |
| C2×#64527 | 2 |
| #577 | 19 |