Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
416 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | #353 |
| commutator | C42 | C22×C4×C41 |
| Frattini, cosocle | #127 | C23×C41 |
| socle | C2×C41 | C2×#353 |
| prime radical | C41×#3147 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C2×C4×C41 ◁ C22×C4×C41 ◁ C41×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2126 | C2 | semidirect |
| 3. C41×#1409 | C2 | semidirect |
| 4. C41×#1408 | C2 | semidirect |
| 6. C41×#532 | C4 | semidirect |
| 9. C41×#494 | C4 | semidirect |
| 11. C41×#492 | C4 | semidirect |
| 14. C2×C4×C8×C41 | C4 | semidirect |
| 104. #13583 | C41 | direct (N × H) |
| 121. #2126 | C2×C41 | semidirect |
| 122. #1409 | C2×C41 | semidirect |
| 123. #1408 | C2×C41 | semidirect |
| 130. #532 | C4×C41 | semidirect |
| 133. #494 | C4×C41 | semidirect |
| 135. #492 | C4×C41 | semidirect |
| 138. C2×C4×C8 | C4×C41 | semidirect |
| 141. C41 | #13583 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3147 | 2 |
| C41×#2126 | 2 |
| C41×#1409 | 2 |
| C41×#1408 | 2 |
| #13583 | 41 |