Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
3464 conjugacy classes of subgroups; only the 600 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 600 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C127 | C23 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C23 | C24×C127 |
| prime radical | C26×C127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊C4×C127 | C2 | semidirect |
| 3. #379×C127 | C2 | direct (N × H) |
| 5. C25×C127 | C4 | semidirect |
| 8. C23×C4×C127 | C22 | semidirect |
| 10. C2×C22⋊C4×C127 | C22 | semidirect |
| 16. C24×C127 | C2×C4 | semidirect |
| 21. C22×C4×C127 | C23 | semidirect |
| 29. C23×C127 | C22⋊C4 | semidirect |
| 42. C22×C127 | C2×C22⋊C4 | semidirect |
| 48. C2×C127 | #379 | direct (N × H) |
| 51. C2×#379 | C127 | direct (N × H) |
| 52. C127 | C2×#379 | direct (N × H) |
| 54. C22×C22⋊C4 | C2×C127 | semidirect |
| 55. #379 | C2×C127 | direct (N × H) |
| 57. C25 | C4×C127 | semidirect |
| 60. C23×C4 | C22×C127 | semidirect |
| 62. C2×C22⋊C4 | C22×C127 | semidirect |
| 68. C24 | C2×C4×C127 | semidirect |
| 73. C22×C4 | C23×C127 | semidirect |
| 81. C23 | C22⋊C4×C127 | semidirect |
| 94. C22 | C2×C22⋊C4×C127 | semidirect |
| 100. C2 | #379×C127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C26×C127 | 2 |
| C22×C22⋊C4×C127 | 2 |
| #379×C127 | 2 |
| C2×#379 | 127 |