Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
402 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C43 |
| prime radical | C23×C43 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 71. C42×C43 | Q16 | semidirect |
| 99. #10522 | C43 | direct (N × H) |
| 138. C43 | #10522 | direct (N × H) |
| 191. C42 | Q16×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3249 | 2 |
| C43×#1994 | 2 |
| C43×#1842 | 2 |
| C43×#1550 | 2 |
| C43×#1292 | 2 |
| #10522 | 43 |