Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
636 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C41 |
| socle | C22×C41 | #392 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#3150 | C2 | semidirect |
| 2. C41×#3100 | C2 | semidirect |
| 3. C41×#1955 | C2 | semidirect |
| 4. C41×#1480 | C2 | semidirect |
| 5. C41×#1275 | C2 | semidirect |
| 81. C2×C8×C41 | D8 | semidirect |
| 123. #10032 | C41 | direct (N × H) |
| 143. #3150 | C2×C41 | semidirect |
| 144. #3100 | C2×C41 | semidirect |
| 145. #1955 | C2×C41 | semidirect |
| 146. #1480 | C2×C41 | semidirect |
| 147. #1275 | C2×C41 | semidirect |
| 169. C41 | #10032 | direct (N × H) |
| 230. C2×C8 | D8×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3150 | 2 |
| C41×#3100 | 2 |
| C41×#1955 | 2 |
| C41×#1480 | 2 |
| C41×#1275 | 2 |
| #10032 | 41 |