Subgroups — C₃×(C₄₃⋊C₃)⋊Dic₁₉ #44440930

Order 29412.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	(C₄₃⋊C₃)⋊Dic₁₉	C₃	1	3	yes	maximal, direct product factor
3	C₃×Dic₈₁₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₄₃⋊C₃	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₁₉×C₄₃	C₂×C₃	1	1	yes	characteristic
7	Dic₈₁₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented
9	C₁₉×C₄₃⋊C₃	C₃×C₄	1	3	yes	complemented
10	C₂×C₁₉×C₄₃	C₂×C₃²	1	1	yes	characteristic
11	C₃×(C₄₃⋊C₃)⋊C₄	—	19	1	no	maximal, Hall
12	C₁₉×C₄₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₄₃⋊C₃	D₁₉	1	1	yes	characteristic
14	C₃²×Dic₁₉	—	43	1	no	maximal, Hall
15	C₃×Dic₄₃	—	19	1	no	—
16	(C₄₃⋊C₃)⋊C₄	—	19	3	no	—
17	C₃×C₄₃⋊C₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₁₉	—	43	1	no	—
19	C₂×C₃×C₄₃	C₃×D₁₉	1	1	yes	characteristic
20	C₂×C₄₃⋊C₃	C₃×D₁₉	1	3	yes	—
21	C₃×Dic₁₉	—	43	3	no	—
22	C₃×Dic₁₉	—	129	1	no	—
23	Dic₄₃	—	19	1	no	Hall
24	C₃²×C₁₉	—	43	1	no	Hall
25	C₃×C₄₃	C₃×Dic₁₉	1	1	yes	characteristic, complemented
26	C₄₃⋊C₃	C₃×Dic₁₉	1	3	yes	complemented
27	C₂×C₃×C₁₉	—	43	3	no	—
28	C₂×C₃×C₁₉	D₄₃⋊C₃	1	1	yes	characteristic
29	C₂×C₄₃	C₃²×D₁₉	1	1	yes	characteristic
30	Dic₁₉	—	129	1	no	Hall
31	C₃×C₁₉	—	43	3	no	—
32	C₃×C₁₉	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
33	C₄₃	C₃²×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₁₉	C₃×D₄₃⋊C₃	1	1	yes	characteristic
35	C₃²×C₄	—	817	1	no	Hall
36	C₁₉	C₃×(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²	—	43	1	no	—
38	C₃×C₄	—	817	3	no	—
39	C₃×C₄	—	2451	1	no	—
40	C₃²	—	43	1	no	Sylow
41	C₂×C₃	—	43	3	no	—
42	C₂×C₃	(C₄₃⋊C₃)⋊D₁₉	1	1	yes	characteristic
43	C₄	—	2451	1	no	Sylow
44	C₃	—	43	3	no	—
45	C₃	(C₄₃⋊C₃)⋊Dic₁₉	1	1	yes	characteristic, direct product factor
46	C₂	C₃×(C₄₃⋊C₃)⋊D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₄₃⋊C₃)⋊D₁₉
commutator, hypocenter	C₁₉×C₄₃	C₃²×C₄
Frattini	C₂	C₃×(C₄₃⋊C₃)⋊D₁₉
Fitting, socle	C₂×C₃×C₁₉×C₄₃	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₄₃⋊C₃	C₂
cosocle	C₂×C₁₉×C₄₃	C₂×C₃²
LCS	G ▷ C₁₉×C₄₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. (C₄₃⋊C₃)⋊Dic₁₉	C₃	direct (N × H)
3. C₃×Dic₈₁₇	C₃	semidirect
4. C₃×C₁₉×C₄₃⋊C₃	C₄	semidirect
7. Dic₈₁₇	C₃²	semidirect
8. C₃×C₁₉×C₄₃	C₃×C₄	semidirect
9. C₁₉×C₄₃⋊C₃	C₃×C₄	semidirect
12. C₁₉×C₄₃	C₃²×C₄	semidirect
17. C₃×C₄₃⋊C₃	Dic₁₉	semidirect
25. C₃×C₄₃	C₃×Dic₁₉	semidirect
26. C₄₃⋊C₃	C₃×Dic₁₉	semidirect
32. C₃×C₁₉	(C₄₃⋊C₃)⋊C₄	semidirect
33. C₄₃	C₃²×Dic₁₉	semidirect
36. C₁₉	C₃×(C₄₃⋊C₃)⋊C₄	semidirect
45. C₃	(C₄₃⋊C₃)⋊Dic₁₉	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×C₁₉×C₄₃⋊C₃	2
(C₄₃⋊C₃)⋊Dic₁₉	3
C₃×Dic₈₁₇	3
C₃×(C₄₃⋊C₃)⋊C₄	19
C₃²×Dic₁₉	43

Subgroups — C3×(C43⋊C3)⋊Dic19 #44440930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₄₃⋊C₃)⋊Dic₁₉ #44440930