Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
332 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 112 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 | #121 |
| commutator | C2×C4 | C22×C4×C101 |
| Frattini, cosocle | C22×C4 | C23×C101 |
| prime radical | C2×AGL(1,ℤ/8)×C101 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C22×C4×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#131×C101 | C2 | semidirect |
| 3. #417×C101 | C2 | semidirect |
| 4. C2×#102×C101 | C2 | semidirect |
| 5. C2×#100×C101 | C2 | semidirect |
| 6. #343×C101 | C2 | semidirect |
| 7. #341×C101 | C2 | semidirect |
| 11. AGL(1,ℤ/8)×C101 | C4 | semidirect |
| 123. #1907 | C101 | direct (N × H) |
| 124. C101 | #1907 | direct (N × H) |
| 126. C2×#131 | C2×C101 | semidirect |
| 127. #417 | C2×C101 | semidirect |
| 128. C2×#102 | C2×C101 | semidirect |
| 129. C2×#100 | C2×C101 | semidirect |
| 130. #343 | C2×C101 | semidirect |
| 131. #341 | C2×C101 | semidirect |
| 135. AGL(1,ℤ/8) | C4×C101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,ℤ/8)×C101 | 2 |
| C2×#131×C101 | 2 |
| #417×C101 | 2 |
| C2×#102×C101 | 2 |
| C2×#100×C101 | 2 |
| #343×C101 | 2 |
| #341×C101 | 2 |
| #1907 | 101 |