Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
416 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 114 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 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C41 |
| Frattini, cosocle | C2×#41 | C23×C41 |
| socle | C2×C41 | #1867 |
| prime radical | C41×#532 | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C2×C4×C41 ◁ C2×#41×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C41×#1868 | C2 | semidirect |
| 5. C41×#1391 | C2 | semidirect |
| 17. C41×#354 | C4 | semidirect |
| 18. C41×#353 | C4 | semidirect |
| 116. #12969 | C41 | direct (N × H) |
| 136. #1868 | C2×C41 | semidirect |
| 137. #1391 | C2×C41 | semidirect |
| 154. #354 | C4×C41 | semidirect |
| 155. #353 | C4×C41 | semidirect |
| 158. C41 | #12969 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2980 | 2 |
| C41×#2126 | 2 |
| C41×#1884 | 2 |
| C41×#1868 | 2 |
| C41×#1391 | 2 |
| #12969 | 41 |