Subgroups — C₃×C₄₇×Dic₅₇ #44565293

Order 32148.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×Dic₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₄₇×Dic₁₉	—	3	1	no	maximal
4	C₃²×C₁₉×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₉×C₄₇	—	2	1	no	—
6	C₂×C₃×C₁₉×C₄₇	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic
8	C₄₇×Dic₁₉	—	3	1	no	Hall
9	C₃×C₁₉×C₄₇	—	2	1	no	—
10	C₃×C₁₉×C₄₇	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₁₉×C₄₇	C₃×C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₉×C₄₇	C₃×D₃	1	1	yes	characteristic
13	C₃×Dic₃×C₄₇	—	19	1	no	maximal, Hall
14	C₁₉×C₄₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃²×C₄₇	D₁₉	1	1	yes	characteristic
16	C₃×Dic₅₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₄×C₄₇	—	57	1	no	—
18	Dic₃×C₄₇	—	19	1	no	—
19	C₃²×C₄₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃²×C₁₉	C₂×C₄₇	1	1	yes	characteristic
21	C₂×C₃×C₄₇	—	2	1	no	—
22	C₂×C₃×C₄₇	C₃×D₁₉	1	1	yes	characteristic
23	C₂×C₃×C₄₇	D₅₇	1	1	yes	characteristic
24	Dic₅₇	C₃×C₄₇	1	1	yes	characteristic, direct product factor
25	C₃×Dic₁₉	—	3	1	no	—
26	C₄×C₄₇	—	57	1	no	Hall
27	C₃²×C₁₉	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
28	C₃×C₄₇	—	2	1	no	—
29	C₃×C₄₇	C₃×Dic₁₉	1	1	yes	characteristic, complemented
30	C₃×C₄₇	Dic₅₇	1	1	yes	characteristic, direct product factor
31	C₂×C₃×C₁₉	—	2	1	no	—
32	C₂×C₃×C₁₉	D₃×C₄₇	1	1	yes	characteristic
33	C₂×C₃×C₁₉	C₂×C₃×C₄₇	1	1	yes	characteristic
34	C₂×C₄₇	C₃×D₅₇	1	1	yes	characteristic
35	Dic₁₉	—	3	1	no	Hall
36	C₃×C₁₉	—	2	1	no	—
37	C₃×C₁₉	Dic₃×C₄₇	1	1	yes	characteristic, complemented
38	C₃×C₁₉	C₃×C₄×C₄₇	1	1	yes	characteristic, complemented
39	C₄₇	C₃×Dic₅₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₁₉	C₃×D₃×C₄₇	1	1	yes	characteristic
41	C₃×Dic₃	—	19	1	no	Hall
42	C₁₉	C₃×Dic₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃²	D₁₉×C₄₇	1	1	yes	characteristic
44	C₃×C₄	—	57	1	no	—
45	Dic₃	—	19	1	no	—
46	C₃²	C₄₇×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₃×D₁₉×C₄₇	1	1	yes	characteristic
49	C₂×C₃	C₄₇×D₅₇	1	1	yes	characteristic
50	C₄	—	57	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₄₇×Dic₁₉	1	1	yes	characteristic, complemented
53	C₃	C₄₇×Dic₅₇	1	1	yes	characteristic, direct product factor
54	C₂	C₃×C₄₇×D₅₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₇	D₅₇
commutator, hypocenter	C₃×C₁₉	C₃×C₄×C₄₇
Frattini	C₂	C₃×C₄₇×D₅₇
Fitting, socle, prime radical	C₂×C₃²×C₁₉×C₄₇	C₂
cosocle	C₂×C₃×C₁₉	C₂×C₃×C₄₇
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₃×C₄₇

Complements

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

N	H ≅ G/N	type
2. C₄₇×Dic₅₇	C₃	direct (N × H)
4. C₃²×C₁₉×C₄₇	C₄	semidirect
10. C₃×C₁₉×C₄₇	Dic₃	semidirect
11. C₃×C₁₉×C₄₇	C₃×C₄	semidirect
14. C₁₉×C₄₇	C₃×Dic₃	semidirect
16. C₃×Dic₅₇	C₄₇	direct (N × H)
19. C₃²×C₄₇	Dic₁₉	semidirect
24. Dic₅₇	C₃×C₄₇	direct (N × H)
27. C₃²×C₁₉	C₄×C₄₇	semidirect
29. C₃×C₄₇	C₃×Dic₁₉	semidirect
30. C₃×C₄₇	Dic₅₇	direct (N × H)
37. C₃×C₁₉	Dic₃×C₄₇	semidirect
38. C₃×C₁₉	C₃×C₄×C₄₇	semidirect
39. C₄₇	C₃×Dic₅₇	direct (N × H)
42. C₁₉	C₃×Dic₃×C₄₇	semidirect
46. C₃²	C₄₇×Dic₁₉	semidirect
52. C₃	C₃×C₄₇×Dic₁₉	semidirect
53. C₃	C₄₇×Dic₅₇	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×C₃²×C₁₉×C₄₇	2
C₄₇×Dic₅₇	3
C₃×C₄₇×Dic₁₉	3
C₃×Dic₃×C₄₇	19
C₃×Dic₅₇	47

Subgroups — C3×C47×Dic57 #44565293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₇×Dic₅₇ #44565293