Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
544 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 544 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×C41 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C41 |
| prime radical | C2×#121×C41 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#3095 | C2 | semidirect |
| 4. C41×#1820 | C2 | semidirect |
| 5. C41×#1511 | C2 | semidirect |
| 7. C41×#1306 | C2 | semidirect |
| 179. #9984 | C41 | direct (N × H) |
| 206. #3095 | C2×C41 | semidirect |
| 209. #1820 | C2×C41 | semidirect |
| 210. #1511 | C2×C41 | semidirect |
| 212. #1306 | C2×C41 | semidirect |
| 245. C41 | #9984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3095 | 2 |
| C41×#3094 | 2 |
| C41×#2816 | 2 |
| C41×#1820 | 2 |
| C41×#1511 | 2 |
| C41×#1510 | 2 |
| C41×#1306 | 2 |
| #9984 | 41 |