Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
42862 conjugacy classes of subgroups; only the 7902 normal subgroups are shown.
This group has 42862 conjugacy classes of subgroups — too many to draw. Only its 7902 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C19 | C23 |
| commutator, Frattini, cosocle | C22 | C26×C19 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C27×C19 | C2 | semidirect |
| 2. C24×D4×C19 | C2 | semidirect |
| 3. C22×C19×#120 | C2 | direct (N × H) |
| 4. C23×C22⋊C4×C19 | C2 | semidirect |
| 7. C26×C19 | C22 | semidirect |
| 8. C26×C19 | C22 | semidirect |
| 10. C23×D4×C19 | C22 | semidirect |
| 11. C24×C4×C19 | C22 | semidirect |
| 12. C2×C19×#120 | C22 | direct (N × H) |
| 13. C22×C22⋊C4×C19 | C22 | semidirect |
| 18. C25×C19 | D4 | semidirect |
| 21. C25×C19 | C23 | semidirect |
| 22. C25×C19 | C23 | semidirect |
| 24. C22×D4×C19 | C23 | semidirect |
| 26. C23×C4×C19 | C23 | semidirect |
| 27. C19×#120 | C23 | direct (N × H) |
| 28. C2×C22⋊C4×C19 | C23 | semidirect |
| 36. C24×C19 | C2×D4 | semidirect |
| 39. C24×C19 | C24 | semidirect |
| 40. C24×C19 | C24 | semidirect |
| 42. C2×D4×C19 | C24 | semidirect |
| 44. C22×C4×C19 | C24 | semidirect |
| 45. C22⋊C4×C19 | C24 | semidirect |
| 46. C23×#120 | C19 | direct (N × H) |
| 53. C23×C19 | #120 | direct (N × H) |
| 55. C23×C19 | C22×D4 | semidirect |
| 58. C23×C19 | C25 | semidirect |
| 61. C2×C4×C19 | C25 | semidirect |
| 62. C27 | C2×C19 | semidirect |
| 63. C24×D4 | C2×C19 | semidirect |
| 64. C22×#120 | C2×C19 | direct (N × H) |
| 65. C23×C22⋊C4 | C2×C19 | semidirect |
| 71. C22×C19 | C2×#120 | direct (N × H) |
| 73. C22×C19 | C23×D4 | semidirect |
| 78. C26 | C22×C19 | semidirect |
| 79. C26 | C22×C19 | semidirect |
| 81. C23×D4 | C22×C19 | semidirect |
| 82. C24×C4 | C22×C19 | semidirect |
| 83. C2×#120 | C22×C19 | direct (N × H) |
| 84. C22×C22⋊C4 | C22×C19 | semidirect |
| 87. C2×C19 | C22×#120 | direct (N × H) |
| 93. C25 | D4×C19 | semidirect |
| 96. C25 | C23×C19 | semidirect |
| 97. C25 | C23×C19 | semidirect |
| 99. C22×D4 | C23×C19 | semidirect |
| 101. C23×C4 | C23×C19 | semidirect |
| 102. #120 | C23×C19 | direct (N × H) |
| 103. C2×C22⋊C4 | C23×C19 | semidirect |
| 104. C19 | C23×#120 | direct (N × H) |
| 112. C24 | C2×D4×C19 | semidirect |
| 115. C24 | C24×C19 | semidirect |
| 116. C24 | C24×C19 | semidirect |
| 118. C2×D4 | C24×C19 | semidirect |
| 120. C22×C4 | C24×C19 | semidirect |
| 121. C22⋊C4 | C24×C19 | semidirect |
| 128. C23 | C19×#120 | direct (N × H) |
| 130. C23 | C22×D4×C19 | semidirect |
| 133. C23 | C25×C19 | semidirect |
| 136. C2×C4 | C25×C19 | semidirect |
| 142. C22 | C2×C19×#120 | direct (N × H) |
| 144. C22 | C23×D4×C19 | semidirect |
| 149. C2 | C22×C19×#120 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×C19 | 2 |
| C24×D4×C19 | 2 |
| C22×C19×#120 | 2 |
| C23×C22⋊C4×C19 | 2 |
| C23×#120 | 19 |