Finite Group DatabasebetaFinite Group DatabasebetaOrder 8192.
8142734 conjugacy classes of subgroups.
The subgroup lattice has 228 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C8 | C28 |
| socle, prime radical | C28 | C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C25×C8×C16 | C2 | direct (N × H) |
| 11. C24×C8×C16 | C22 | direct (N × H) |
| 24. C26×C16 | C8 | direct (N × H) |
| 26. C23×C8×C16 | C23 | direct (N × H) |
| 29. C26×C8 | C16 | direct (N × H) |
| 37. C25×C16 | C2×C8 | direct (N × H) |
| 49. C22×C8×C16 | C24 | direct (N × H) |
| 58. C25×C8 | C2×C16 | direct (N × H) |
| 67. C24×C16 | C22×C8 | direct (N × H) |
| 79. C2×C8×C16 | C25 | direct (N × H) |
| 92. C24×C8 | C22×C16 | direct (N × H) |
| 101. C23×C16 | C23×C8 | direct (N × H) |
| 113. C8×C16 | C26 | direct (N × H) |
| 114. C26 | C8×C16 | direct (N × H) |
| 127. C23×C8 | C23×C16 | direct (N × H) |
| 136. C22×C16 | C24×C8 | direct (N × H) |
| 148. C25 | C2×C8×C16 | direct (N × H) |
| 161. C22×C8 | C24×C16 | direct (N × H) |
| 170. C2×C16 | C25×C8 | direct (N × H) |
| 178. C24 | C22×C8×C16 | direct (N × H) |
| 191. C2×C8 | C25×C16 | direct (N × H) |
| 200. C16 | C26×C8 | direct (N × H) |
| 201. C23 | C23×C8×C16 | direct (N × H) |
| 213. C8 | C26×C16 | direct (N × H) |
| 216. C22 | C24×C8×C16 | direct (N × H) |
| 224. C2 | C25×C8×C16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C26×C82 | 2 |
| C26×C4×C16 | 2 |
| C25×C8×C16 | 2 |