Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
204 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 78 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 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C41 |
| prime radical | C41×#2215 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C22×C8×C41 ◁ C22×C16×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C41×SD64 | C2 | semidirect |
| 2. C22×C32×C41 | C2 | semidirect |
| 3. C41×#2216 | C2 | semidirect |
| 5. C41×#1424 | C2 | semidirect |
| 6. C41×#1416 | C2 | semidirect |
| 7. C41×#1415 | C2 | semidirect |
| 39. C32×C41 | D4 | semidirect |
| 77. #13696 | C41 | direct (N × H) |
| 83. C22×C41 | SD64 | semidirect |
| 91. C2×SD64 | C2×C41 | semidirect |
| 92. C22×C32 | C2×C41 | semidirect |
| 93. #2216 | C2×C41 | semidirect |
| 95. #1424 | C2×C41 | semidirect |
| 96. #1416 | C2×C41 | semidirect |
| 97. #1415 | C2×C41 | semidirect |
| 116. C41 | #13696 | direct (N × H) |
| 135. C32 | D4×C41 | semidirect |
| 178. C22 | C41×SD64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×SD64 | 2 |
| C22×C32×C41 | 2 |
| C41×#2216 | 2 |
| C41×#2215 | 2 |
| C41×#1424 | 2 |
| C41×#1416 | 2 |
| C41×#1415 | 2 |
| #13696 | 41 |