Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D19 |
| commutator, socle, cosocle | C22×C19 | C24 |
| Fitting | C19×C22⋊Q8 | C2 |
| prime radical | #10597330 | C2 |
| hypercenter | C22⋊Q8 | D19 |
| hypocenter | C19 | #539 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×C22⋊Q8 | C2 | semidirect |
| 2. #10597392 | C2 | semidirect |
| 3. #10597392 | C2 | semidirect |
| 4. #10597375 | C2 | semidirect |
| 5. C4×C22⋊D19 | C2 | semidirect |
| 6. #10597344 | C2 | semidirect |
| 7. #10597340 | C2 | semidirect |
| 8. #10597339 | C2 | semidirect |
| 9. C4⋊C4×D19 | C2 | semidirect |
| 10. #10597335 | C2 | semidirect |
| 11. #10597335 | C2 | semidirect |
| 13. #10597329 | C2 | semidirect |
| 14. #10597329 | C2 | semidirect |
| 15. #10597325 | C2 | semidirect |
| 114. C22⋊Q8 | D19 | semidirect |
| 119. C19 | #539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×C22⋊Q8 | 2 |
| #10597392 | 2 |
| #10597375 | 2 |
| C4×C22⋊D19 | 2 |
| #10597344 | 2 |
| #10597340 | 2 |
| #10597339 | 2 |
| C4⋊C4×D19 | 2 |
| #10597335 | 2 |
| #10597330 | 2 |
| #10597329 | 2 |
| #10597325 | 2 |
| #539 | 19 |