Finite Group DatabasebetaFinite Group DatabasebetaOrder 33300.
160 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | C3⋊#1044 |
| commutator, hypocenter | C3×C52 | C3×C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C37 | C4 |
| prime radical | C32×C37×C5⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C2×C3×C37 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C3×C37 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C37×C3⋊#1044 | C3 | direct (N × H) |
| 4. C32×C52×C37 | C4 | semidirect |
| 13. C3×C52×C37 | Dic3 | semidirect |
| 14. C3×C52×C37 | C3×C4 | semidirect |
| 19. C32×C5×C37 | AGL(1,𝔽5) | semidirect |
| 27. C52×C37 | C3×Dic3 | semidirect |
| 28. C3×C3⋊#1044 | C37 | direct (N × H) |
| 35. C3×C5×C37 | C3×AGL(1,𝔽5) | semidirect |
| 36. C3×C5×C37 | ΓL(1,𝔽16) | semidirect |
| 42. C32×C37 | #1044 | semidirect |
| 43. C3⋊#1044 | C3×C37 | direct (N × H) |
| 45. C32×C52 | C4×C37 | semidirect |
| 50. C5×C37 | C3×ΓL(1,𝔽16) | semidirect |
| 57. C3×C37 | C3×#1044 | semidirect |
| 58. C3×C37 | C3⋊#1044 | direct (N × H) |
| 63. C3×C52 | Dic3×C37 | semidirect |
| 64. C3×C52 | C3×C4×C37 | semidirect |
| 70. C32×C5 | AGL(1,𝔽5)×C37 | semidirect |
| 71. C37 | C3×C3⋊#1044 | direct (N × H) |
| 79. C52 | C3×Dic3×C37 | semidirect |
| 86. C3×C5 | C3×AGL(1,𝔽5)×C37 | semidirect |
| 87. C3×C5 | C37×ΓL(1,𝔽16) | semidirect |
| 92. C32 | C37×#1044 | semidirect |
| 97. C5 | C3×C37×ΓL(1,𝔽16) | semidirect |
| 100. C3 | C3×C37×#1044 | semidirect |
| 101. C3 | C37×C3⋊#1044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C37×C5⋊D5 | 2 |
| C37×C3⋊#1044 | 3 |
| C3×C37×#1044 | 3 |
| C3×C37×ΓL(1,𝔽16) | 5 |
| C3×C3⋊#1044 | 37 |