Subgroups — C₃×C₄×C₄₃×C₁₉⋊C₃ #44440950

Order 29412.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₃×C₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₄×C₁₉×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄₃×C₁₉⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₄₃×C₁₉⋊C₃	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₁₉×C₄₃	C₂×C₃	1	1	yes	characteristic
7	C₄×C₁₉×C₄₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented
9	C₄₃×C₁₉⋊C₃	C₃×C₄	1	3	yes	direct product factor
10	C₂×C₁₉×C₄₃	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₄×C₄₃	—	19	1	no	maximal, Hall
12	C₁₉×C₄₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃²×C₄₃	—	19	1	no	—
14	C₃×C₄×C₁₉⋊C₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₄×C₄₃	—	19	3	no	—
16	C₃×C₄×C₄₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
17	C₃²×C₄₃	—	19	1	no	Hall
18	C₂×C₃×C₁₉⋊C₃	C₂×C₄₃	1	1	yes	characteristic
19	C₂×C₃×C₄₃	—	19	3	no	—
20	C₂×C₃×C₄₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
21	C₃×C₄×C₁₉	C₃×C₄₃	1	1	yes	characteristic, complemented
22	C₄×C₁₉⋊C₃	C₃×C₄₃	1	3	yes	direct product factor
23	C₄×C₄₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₁₉⋊C₃	C₄×C₄₃	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₄₃	—	19	3	no	—
26	C₃×C₄₃	C₄×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
27	C₂×C₃×C₁₉	C₂×C₃×C₄₃	1	1	yes	characteristic
28	C₂×C₁₉⋊C₃	C₂×C₃×C₄₃	1	3	yes	—
29	C₂×C₄₃	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic
30	C₄×C₁₉	C₃²×C₄₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₉	C₃×C₄×C₄₃	1	1	yes	characteristic, complemented
32	C₁₉⋊C₃	C₃×C₄×C₄₃	1	3	yes	direct product factor
33	C₄₃	C₃×C₄×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₁₉	C₂×C₃²×C₄₃	1	1	yes	characteristic
35	C₃²×C₄	—	19	1	no	Hall
36	C₁₉	C₃²×C₄×C₄₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²	—	19	1	no	—
38	C₃×C₄	—	19	3	no	—
39	C₃×C₄	C₄₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
40	C₃²	—	19	1	no	Sylow
41	C₂×C₃	—	19	3	no	—
42	C₂×C₃	C₂×C₄₃×C₁₉⋊C₃	1	1	yes	characteristic
43	C₄	C₃×C₄₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	19	3	no	—
45	C₃	C₄×C₄₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂	C₂×C₃×C₄₃×C₁₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₄₃	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₃²×C₄×C₄₃
Frattini	C₂	C₂×C₃×C₄₃×C₁₉⋊C₃
Fitting	C₃×C₄×C₁₉×C₄₃	C₃
socle	C₂×C₃×C₁₉×C₄₃	C₂×C₃
prime radical	C₂×C₃×C₄₃×C₁₉⋊C₃	C₂
cosocle	C₂×C₁₉	C₂×C₃²×C₄₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₄×C₄₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄×C₄₃×C₁₉⋊C₃	C₃	direct (N × H)
3. C₃×C₄×C₁₉×C₄₃	C₃	semidirect
4. C₃×C₄₃×C₁₉⋊C₃	C₄	direct (N × H)
7. C₄×C₁₉×C₄₃	C₃²	semidirect
8. C₃×C₁₉×C₄₃	C₃×C₄	semidirect
9. C₄₃×C₁₉⋊C₃	C₃×C₄	direct (N × H)
12. C₁₉×C₄₃	C₃²×C₄	semidirect
14. C₃×C₄×C₁₉⋊C₃	C₄₃	direct (N × H)
16. C₃×C₄×C₄₃	C₁₉⋊C₃	direct (N × H)
21. C₃×C₄×C₁₉	C₃×C₄₃	semidirect
22. C₄×C₁₉⋊C₃	C₃×C₄₃	direct (N × H)
23. C₄×C₄₃	C₃×C₁₉⋊C₃	direct (N × H)
24. C₃×C₁₉⋊C₃	C₄×C₄₃	direct (N × H)
26. C₃×C₄₃	C₄×C₁₉⋊C₃	direct (N × H)
30. C₄×C₁₉	C₃²×C₄₃	semidirect
31. C₃×C₁₉	C₃×C₄×C₄₃	semidirect
32. C₁₉⋊C₃	C₃×C₄×C₄₃	direct (N × H)
33. C₄₃	C₃×C₄×C₁₉⋊C₃	direct (N × H)
36. C₁₉	C₃²×C₄×C₄₃	semidirect
39. C₃×C₄	C₄₃×C₁₉⋊C₃	direct (N × H)
43. C₄	C₃×C₄₃×C₁₉⋊C₃	direct (N × H)
45. C₃	C₄×C₄₃×C₁₉⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₄₃×C₁₉⋊C₃	2
C₄×C₄₃×C₁₉⋊C₃	3
C₃×C₄×C₁₉×C₄₃	3
C₃²×C₄×C₄₃	19
C₃×C₄×C₁₉⋊C₃	43

Subgroups — C3×C4×C43×C19⋊C3 #44440950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₄₃×C₁₉⋊C₃ #44440950