Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
4619 conjugacy classes of subgroups.
The subgroup lattice has 422 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C32 | C24 |
| socle, prime radical | C24 | C2×C4×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C2×C4×C32 ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C4×C8×C64 | C2 | direct (N × H) |
| 14. C2×C8×C64 | C4 | direct (N × H) |
| 29. C2×C4×C64 | C8 | direct (N × H) |
| 46. C8×C64 | C2×C4 | direct (N × H) |
| 94. C4×C64 | C2×C8 | direct (N × H) |
| 153. C2×C64 | C4×C8 | direct (N × H) |
| 194. C2×C4×C8 | C64 | direct (N × H) |
| 250. C64 | C2×C4×C8 | direct (N × H) |
| 306. C4×C8 | C2×C64 | direct (N × H) |
| 338. C2×C8 | C4×C64 | direct (N × H) |
| 379. C2×C4 | C8×C64 | direct (N × H) |
| 399. C8 | C2×C4×C64 | direct (N × H) |
| 411. C4 | C2×C8×C64 | direct (N × H) |
| 417. C2 | C4×C8×C64 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C8×C32 | 2 |
| C2×C42×C64 | 2 |
| C22×C8×C64 | 2 |
| C4×C8×C64 | 2 |