Finite Group DatabasebetaFinite Group DatabasebetaOrder 25856.
576 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 118 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×C101 | #386 |
| commutator | C42 | C22×C4×C101 |
| Frattini, cosocle | C2×C42 | C23×C101 |
| prime radical | C101×#3153 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C101×#2372 | C2 | semidirect |
| 3. C101×#1533 | C2 | semidirect |
| 4. C101×#1505 | C2 | semidirect |
| 5. C101×#1300 | C2 | semidirect |
| 10. #497×C101 | C4 | semidirect |
| 11. #496×C101 | C4 | semidirect |
| 36. C4⋊Q8×C101 | C2×C4 | semidirect |
| 37. #127×C101 | C2×C4 | semidirect |
| 54. #97×C101 | C2×C4 | semidirect |
| 164. #9441 | C101 | direct (N × H) |
| 172. #2372 | C2×C101 | semidirect |
| 173. #1533 | C2×C101 | semidirect |
| 174. #1505 | C2×C101 | semidirect |
| 175. #1300 | C2×C101 | semidirect |
| 176. C101 | #9441 | direct (N × H) |
| 181. #497 | C4×C101 | semidirect |
| 182. #496 | C4×C101 | semidirect |
| 207. C4⋊Q8 | C2×C4×C101 | semidirect |
| 208. #127 | C2×C4×C101 | semidirect |
| 225. #97 | C2×C4×C101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C101×#3153 | 2 |
| C101×#2372 | 2 |
| C101×#1533 | 2 |
| C101×#1505 | 2 |
| C101×#1300 | 2 |
| #9441 | 101 |