Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
402 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 402 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, socle | C22×C41 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C41 |
| prime radical | C41×#3213 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#1967 | C2 | semidirect |
| 3. C41×#1569 | C2 | semidirect |
| 4. C41×#1557 | C2 | semidirect |
| 5. C41×#1527 | C2 | semidirect |
| 6. C41×#1525 | C2 | semidirect |
| 7. C41×#1291 | C2 | semidirect |
| 162. #10496 | C41 | direct (N × H) |
| 184. #1967 | C2×C41 | semidirect |
| 185. #1569 | C2×C41 | semidirect |
| 186. #1557 | C2×C41 | semidirect |
| 187. #1527 | C2×C41 | semidirect |
| 188. #1525 | C2×C41 | semidirect |
| 189. #1291 | C2×C41 | semidirect |
| 219. C41 | #10496 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3213 | 2 |
| C41×#1967 | 2 |
| C41×#1569 | 2 |
| C41×#1557 | 2 |
| C41×#1527 | 2 |
| C41×#1525 | 2 |
| C41×#1291 | 2 |
| #10496 | 41 |