Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
280 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #11715906 |
| commutator, hypocenter | C97 | C2×C82 |
| Frattini | C4 | C22×#11715906 |
| Fitting | C2×C8×C97 | C8 |
| socle | C22×C97 | C4×C8 |
| prime radical | C22×D97 | C42 |
| cosocle | C4×#87604 | C23 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×#11715906 | C2 | direct (N × H) |
| 12. C2×#11715906 | C8 | direct (N × H) |
| 15. #13095519 | C8 | semidirect |
| 17. C2×#11715897 | C8 | semidirect |
| 22. C2×#11715895 | C8 | semidirect |
| 23. C8×D97 | C8 | semidirect |
| 25. C2×C8×C97 | C8 | semidirect |
| 30. #11715906 | C2×C8 | direct (N × H) |
| 37. #11715897 | C2×C8 | semidirect |
| 38. C8×C97 | C2×C8 | semidirect |
| 39. #11715895 | C2×C8 | semidirect |
| 50. C2×C97 | C82 | semidirect |
| 52. D97 | C82 | semidirect |
| 55. C97 | C2×C82 | semidirect |
| 77. C2×C8 | #11715906 | direct (N × H) |
| 94. C8 | C2×#11715906 | direct (N × H) |
| 107. C2 | C8×#11715906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11715906 | 2 |
| C8×#11715906 | 2 |
| C2×C8×#87604 | 2 |
| C2×C82 | 97 |