Subgroups — D₉×D₁₉×C₄₇ #44565261

Order 32148.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×D₁₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₉×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₉×C₄₇	—	3	1	no	maximal
5	C₉×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₄₇×D₅₇	—	3	1	no	—
7	D₃×C₁₉×C₄₇	—	3	1	no	—
8	C₃×D₁₉×C₄₇	D₃	1	1	yes	characteristic
9	C₂×D₁₉×C₄₇	—	9	1	no	Hall
10	C₃×C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic
11	C₂×C₁₉×C₄₇	—	9	1	no	—
12	D₁₉×C₄₇	—	9	1	no	—
13	D₁₉×C₄₇	D₉	1	1	yes	characteristic, direct product factor
14	C₂×D₉×C₄₇	—	19	1	no	maximal, Hall
15	C₁₉×C₄₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₉×C₄₇	—	19	1	no	—
17	D₉×C₄₇	—	19	1	no	—
18	D₉×C₄₇	D₁₉	1	1	yes	characteristic, direct product factor
19	D₉×D₁₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×D₃×C₄₇	—	57	1	no	—
21	C₉×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
22	D₁₇₁	C₂×C₄₇	1	1	yes	characteristic, complemented
23	C₉×D₁₉	C₂×C₄₇	1	1	yes	characteristic, complemented
24	D₉×C₁₉	C₂×C₄₇	1	1	yes	characteristic, complemented
25	C₂×C₃×C₄₇	—	19	1	no	—
26	D₃×C₄₇	—	3	1	no	—
27	D₃×C₄₇	—	57	1	no	—
28	D₃×D₁₉	—	3	1	no	—
29	C₂²×C₄₇	—	171	1	no	Hall
30	C₉×C₁₉	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄₇	D₃×D₁₉	1	1	yes	characteristic
32	D₅₇	—	3	1	no	—
33	C₃×D₁₉	D₃×C₄₇	1	1	yes	characteristic
34	D₃×C₁₉	—	3	1	no	—
35	C₂×C₄₇	—	9	1	no	—
36	C₂×C₄₇	—	19	1	no	—
37	C₂×C₄₇	—	171	1	no	—
38	C₂×D₁₉	—	9	1	no	Hall
39	C₃×C₁₉	C₂×D₃×C₄₇	1	1	yes	characteristic
40	C₄₇	D₉×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₁₉	—	9	1	no	—
42	D₁₉	—	9	1	no	—
43	D₁₉	D₉×C₄₇	1	1	yes	characteristic, direct product factor
44	C₂×D₉	—	19	1	no	Hall
45	C₁₉	C₂×D₉×C₄₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₉	—	19	1	no	—
47	D₉	—	19	1	no	—
48	D₉	D₁₉×C₄₇	1	1	yes	characteristic, direct product factor
49	C₂×D₃	—	57	1	no	—
50	C₉	C₂×D₁₉×C₄₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	19	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	57	1	no	—
54	C₂²	—	171	1	no	Sylow
55	C₃	D₃×D₁₉×C₄₇	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	19	1	no	—
58	C₂	—	171	1	no	—

	subgroup	G/H
center, hypercenter	C₄₇	D₉×D₁₉
commutator, cosocle, hypocenter	C₉×C₁₉	C₂²×C₄₇
Frattini	C₃	D₃×D₁₉×C₄₇
Fitting	C₉×C₁₉×C₄₇	C₂²
socle	C₃×C₁₉×C₄₇	C₂×D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₄₇

Complements

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

N	H ≅ G/N	type
1. C₄₇×D₁₇₁	C₂	semidirect
2. D₉×C₁₉×C₄₇	C₂	semidirect
3. C₉×D₁₉×C₄₇	C₂	semidirect
5. C₉×C₁₉×C₄₇	C₂²	semidirect
13. D₁₉×C₄₇	D₉	direct (N × H)
15. C₁₉×C₄₇	C₂×D₉	semidirect
18. D₉×C₄₇	D₁₉	direct (N × H)
19. D₉×D₁₉	C₄₇	direct (N × H)
21. C₉×C₄₇	C₂×D₁₉	semidirect
22. D₁₇₁	C₂×C₄₇	semidirect
23. C₉×D₁₉	C₂×C₄₇	semidirect
24. D₉×C₁₉	C₂×C₄₇	semidirect
30. C₉×C₁₉	C₂²×C₄₇	semidirect
40. C₄₇	D₉×D₁₉	direct (N × H)
43. D₁₉	D₉×C₄₇	direct (N × H)
45. C₁₉	C₂×D₉×C₄₇	semidirect
48. D₉	D₁₉×C₄₇	direct (N × H)
50. C₉	C₂×D₁₉×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×D₁₇₁	2
D₉×C₁₉×C₄₇	2
C₉×D₁₉×C₄₇	2
D₃×D₁₉×C₄₇	3
C₂×D₉×C₄₇	19
D₉×D₁₉	47

Subgroups — D9×D19×C47 #44565261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×D₁₉×C₄₇ #44565261