Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
408 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #87604 |
| commutator, hypocenter | C97 | C42×C8 |
| Frattini | C2×C4 | C22×#87604 |
| Fitting | C4×C8×C97 | C4 |
| socle | C22×C97 | C2×C42 |
| prime radical | C22×D97 | C22×C4 |
| cosocle | C2×C4×D97 | C23 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C4×#11715897 | C4 | semidirect |
| 9. C8×#87604 | C4 | direct (N × H) |
| 12. C4×#11715895 | C4 | semidirect |
| 13. C8×Dic97 | C4 | semidirect |
| 14. C4×C8×C97 | C4 | semidirect |
| 18. C4×#87604 | C8 | direct (N × H) |
| 37. #11715897 | C42 | semidirect |
| 38. C8×C97 | C42 | semidirect |
| 39. #11715895 | C42 | semidirect |
| 43. #87604 | C4×C8 | direct (N × H) |
| 44. C4×C97 | C4×C8 | semidirect |
| 46. Dic97 | C4×C8 | semidirect |
| 52. C97 | C42×C8 | semidirect |
| 66. C4×C8 | #87604 | direct (N × H) |
| 91. C8 | C4×#87604 | direct (N × H) |
| 98. C4 | C8×#87604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095519 | 2 |
| C2×C8×#87604 | 2 |
| C42×#87604 | 2 |
| C4×C8×D97 | 2 |
| C42×C8 | 97 |