Finite Group DatabasebetaFinite Group DatabasebetaOrder 25856.
336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 336 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, socle | C2×C101 | #2127 |
| commutator | C42 | C22×C4×C101 |
| Frattini, cosocle | #127 | C23×C101 |
| prime radical | #535×C101 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C101 ◁ C22×C101 ◁ C22×C4×C101 ◁ #535×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C101×#1412 | C2 | semidirect |
| 5. C101×#1409 | C2 | semidirect |
| 6. #541×C101 | C4 | semidirect |
| 8. #497×C101 | C4 | semidirect |
| 11. #488×C101 | C4 | semidirect |
| 16. #433×C101 | C4 | semidirect |
| 29. C4⋊Q8×C101 | C2×C4 | semidirect |
| 34. #125×C101 | C2×C4 | semidirect |
| 54. #97×C101 | C2×C4 | semidirect |
| 55. C4×C8×C101 | C2×C4 | semidirect |
| 147. #13610 | C101 | direct (N × H) |
| 157. #1412 | C2×C101 | semidirect |
| 158. #1409 | C2×C101 | semidirect |
| 159. C101 | #13610 | direct (N × H) |
| 160. #541 | C4×C101 | semidirect |
| 162. #497 | C4×C101 | semidirect |
| 165. #488 | C4×C101 | semidirect |
| 170. #433 | C4×C101 | semidirect |
| 183. C4⋊Q8 | C2×C4×C101 | semidirect |
| 188. #125 | C2×C4×C101 | semidirect |
| 208. #97 | C2×C4×C101 | semidirect |
| 209. C4×C8 | C2×C4×C101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C101×#3222 | 2 |
| C101×#2128 | 2 |
| C101×#2127 | 2 |
| C101×#1412 | 2 |
| C101×#1409 | 2 |
| #13610 | 101 |