Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
786 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 270 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C41 |
| prime radical | C22×D8×C41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C43×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#2860 | C2 | semidirect |
| 3. C41×#1942 | C2 | semidirect |
| 4. C41×#1934 | C2 | semidirect |
| 5. C42×C8×C41 | C2 | semidirect |
| 54. C42×C41 | D8 | semidirect |
| 73. C8×C41 | #126 | semidirect |
| 74. #33266 | C41 | direct (N × H) |
| 86. #2860 | C2×C41 | semidirect |
| 88. #1942 | C2×C41 | semidirect |
| 89. #1934 | C2×C41 | semidirect |
| 90. C42×C8 | C2×C41 | semidirect |
| 106. C41 | #33266 | direct (N × H) |
| 144. C42 | D8×C41 | semidirect |
| 163. C8 | #126×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2860 | 2 |
| C41×#1970 | 2 |
| C41×#1942 | 2 |
| C41×#1934 | 2 |
| C42×C8×C41 | 2 |
| #33266 | 41 |