Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C47 | #121 |
| commutator | C2×C4 | C22×C4×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| socle | C2×C47 | #386 |
| prime radical | C47×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C47 ◁ C22×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#41×C47 | C2 | semidirect |
| 3. C47×#421 | C2 | semidirect |
| 4. C2×#104×C47 | C2 | semidirect |
| 5. C47×#410 | C2 | semidirect |
| 6. C47×#344 | C2 | semidirect |
| 7. C47×#339 | C2 | semidirect |
| 11. #137×C47 | C4 | semidirect |
| 13. AGL(1,ℤ/8)×C47 | C4 | semidirect |
| 37. C2×Q8×C47 | C2×C4 | semidirect |
| 41. C2×D4×C47 | C2×C4 | semidirect |
| 55. M16×C47 | C2×C4 | semidirect |
| 123. #1906 | C47 | direct (N × H) |
| 131. C4×#41 | C2×C47 | semidirect |
| 132. #421 | C2×C47 | semidirect |
| 133. C2×#104 | C2×C47 | semidirect |
| 134. #410 | C2×C47 | semidirect |
| 135. #344 | C2×C47 | semidirect |
| 136. #339 | C2×C47 | semidirect |
| 137. C47 | #1906 | direct (N × H) |
| 141. #137 | C4×C47 | semidirect |
| 143. AGL(1,ℤ/8) | C4×C47 | semidirect |
| 167. C2×Q8 | C2×C4×C47 | semidirect |
| 171. C2×D4 | C2×C4×C47 | semidirect |
| 185. M16 | C2×C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#575 | 2 |
| C4×#41×C47 | 2 |
| C47×#421 | 2 |
| C2×#104×C47 | 2 |
| C47×#410 | 2 |
| C47×#344 | 2 |
| C47×#339 | 2 |
| #1906 | 47 |