Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
474 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #353 |
| commutator | C42 | C22×C4×C43 |
| Frattini, cosocle | #127 | C23×C43 |
| prime radical | C2×#127×C43 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C23×C43 ◁ C22×C4×C43 ◁ C2×#127×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C43×#1409 | C2 | direct (N × H) |
| 5. C2×C4⋊Q8×C43 | C4 | semidirect |
| 8. C43×#492 | C4 | semidirect |
| 11. C2×C4×C8×C43 | C4 | semidirect |
| 24. C4⋊Q8×C43 | C2×C4 | semidirect |
| 35. C4×C8×C43 | C2×C4 | semidirect |
| 93. C2×#1409 | C43 | direct (N × H) |
| 112. #1409 | C2×C43 | direct (N × H) |
| 117. C2×C43 | #1409 | direct (N × H) |
| 120. C2×C4⋊Q8 | C4×C43 | semidirect |
| 123. #492 | C4×C43 | semidirect |
| 126. C2×C4×C8 | C4×C43 | semidirect |
| 129. C43 | C2×#1409 | direct (N × H) |
| 140. C4⋊Q8 | C2×C4×C43 | semidirect |
| 151. C4×C8 | C2×C4×C43 | semidirect |
| 229. C2 | C43×#1409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×#492 | 2 |
| C2×C43×#353 | 2 |
| C43×#1409 | 2 |
| C2×#1409 | 43 |