Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
238 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| socle | C22×C47 | C2×C22⋊C4 |
| prime radical | #121×C47 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C2×C42×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#431 | C2 | semidirect |
| 3. C47×#376 | C2 | semidirect |
| 4. C47×#328 | C2 | semidirect |
| 7. #125×C47 | C4 | semidirect |
| 8. #124×C47 | C4 | semidirect |
| 12. C4×Q8×C47 | C4 | semidirect |
| 14. C4×D4×C47 | C4 | semidirect |
| 88. #1500 | C47 | direct (N × H) |
| 95. #431 | C2×C47 | semidirect |
| 96. #376 | C2×C47 | semidirect |
| 97. #328 | C2×C47 | semidirect |
| 99. C47 | #1500 | direct (N × H) |
| 101. #125 | C4×C47 | semidirect |
| 102. #124 | C4×C47 | semidirect |
| 106. C4×Q8 | C4×C47 | semidirect |
| 108. C4×D4 | C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#529 | 2 |
| C47×#431 | 2 |
| C47×#376 | 2 |
| C47×#328 | 2 |
| C47×#327 | 2 |
| #1500 | 47 |