Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
476 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C23×C43 |
| prime radical | C22×D4×C43 | C23 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C23×C43 ◁ C22×D4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 177. #13462 | C43 | direct (N × H) |
| 244. C43 | #13462 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#2748 | 2 |
| C43×#1867 | 2 |
| C43×#1856 | 2 |
| C43×#1393 | 2 |
| C43×#1390 | 2 |
| #13462 | 43 |