Finite Group DatabasebetaFinite Group DatabasebetaOrder 25856.
568 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 568 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×C101 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C101 |
| socle | C2×C101 | #1999 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C101 ◁ C22×C4×C101 ◁ C23×C8×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C101×#3414 | C2 | semidirect |
| 2. C101×#3050 | C2 | semidirect |
| 3. C101×#2145 | C2 | semidirect |
| 4. C101×#2112 | C2 | semidirect |
| 5. C101×#1384 | C2 | semidirect |
| 27. C2×Q16×C101 | D4 | semidirect |
| 29. C2×D8×C101 | D4 | semidirect |
| 48. C2×C16×C101 | D4 | semidirect |
| 50. #106×C101 | D4 | semidirect |
| 137. #13309 | C101 | direct (N × H) |
| 143. #3414 | C2×C101 | semidirect |
| 144. #3050 | C2×C101 | semidirect |
| 145. #2145 | C2×C101 | semidirect |
| 146. #2112 | C2×C101 | semidirect |
| 147. #1384 | C2×C101 | semidirect |
| 148. C101 | #13309 | direct (N × H) |
| 170. C2×Q16 | D4×C101 | semidirect |
| 172. C2×D8 | D4×C101 | semidirect |
| 191. C2×C16 | D4×C101 | semidirect |
| 193. #106 | D4×C101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C101×#3414 | 2 |
| C101×#3050 | 2 |
| C101×#2145 | 2 |
| C101×#2112 | 2 |
| C101×#1384 | 2 |
| #13309 | 101 |