Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
620 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 136 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×C47 | #120 |
| commutator | C2×C4 | C22×C4×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| prime radical | C2×H(5,𝔽2)×C47 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#104×C47 | C2 | semidirect |
| 3. C47×#417 | C2 | semidirect |
| 4. C2×#100×C47 | C2 | semidirect |
| 5. C47×#390 | C2 | semidirect |
| 8. H(5,𝔽2)×C47 | C4 | semidirect |
| 14. C2×M16×C47 | C22 | semidirect |
| 15. C2×C4⋊C4×C47 | C22 | semidirect |
| 17. C2×C42×C47 | C22 | semidirect |
| 64. Q8×C47 | C22⋊C4 | semidirect |
| 71. D4×C47 | C22⋊C4 | semidirect |
| 105. #1792 | C47 | direct (N × H) |
| 114. C2×#104 | C2×C47 | semidirect |
| 115. #417 | C2×C47 | semidirect |
| 116. C2×#100 | C2×C47 | semidirect |
| 117. #390 | C2×C47 | semidirect |
| 118. C47 | #1792 | direct (N × H) |
| 121. H(5,𝔽2) | C4×C47 | semidirect |
| 127. C2×M16 | C22×C47 | semidirect |
| 128. C2×C4⋊C4 | C22×C47 | semidirect |
| 130. C2×C42 | C22×C47 | semidirect |
| 177. Q8 | C22⋊C4×C47 | semidirect |
| 184. D4 | C22⋊C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×H(5,𝔽2)×C47 | 2 |
| C2×#104×C47 | 2 |
| C47×#417 | 2 |
| C2×#100×C47 | 2 |
| C47×#390 | 2 |
| #1792 | 47 |