Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
184 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 86 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 | C2×D16 |
| commutator | C16 | C22×C4×C41 |
| Frattini, cosocle | C2×C16 | C23×C41 |
| socle | C2×C41 | C4×D16 |
| prime radical | C41×#2262 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C2×C8×C41 ◁ C4×C8×C41 ◁ C4×C16×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2178 | C2 | semidirect |
| 3. C41×#1425 | C2 | semidirect |
| 4. C41×#1417 | C2 | semidirect |
| 5. C41×#1397 | C2 | semidirect |
| 8. C41×Q64 | C4 | semidirect |
| 9. C41×SD64 | C4 | semidirect |
| 10. C41×D32 | C4 | semidirect |
| 52. #13656 | C41 | direct (N × H) |
| 60. #2178 | C2×C41 | semidirect |
| 61. #1425 | C2×C41 | semidirect |
| 62. #1417 | C2×C41 | semidirect |
| 63. #1397 | C2×C41 | semidirect |
| 69. Q64 | C4×C41 | semidirect |
| 70. SD64 | C4×C41 | semidirect |
| 71. D32 | C4×C41 | semidirect |
| 77. C41 | #13656 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2262 | 2 |
| C41×#2178 | 2 |
| C41×#1425 | 2 |
| C41×#1417 | 2 |
| C41×#1397 | 2 |
| #13656 | 41 |