Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
18788 conjugacy classes of subgroups.
The subgroup lattice has 4625 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | #394 |
| commutator | C2×C42 | C22×C42 |
| Frattini, cosocle | C23×C42 | C24 |
| socle | C23 | C2×#1442 |
| prime radical | C26 | #124 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C23×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #72239971 | C2 | semidirect |
| 31. #181727 | C4 | semidirect |
| 40. C2×#8128 | C4 | semidirect |
| 41. C2×#8128 | C4 | semidirect |
| 48. C2×#7867 | C4 | semidirect |
| 231. C2×#1309 | C2×C4 | semidirect |
| 235. #8094 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#181415 | 2 |
| #72239971 | 2 |
| C2×#181727 | 2 |
| #72239950 | 2 |
| C2×#353780 | 2 |
| C22×#7867 | 2 |