Subgroups — C₃⋊D₃×C₁₉×D₄₇ #44565342

Order 32148.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₃×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×C₃⋊D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₉×D₄₇	—	3	4	no	maximal
5	C₃²×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₁₄₁	—	3	4	no	—
7	D₃×C₁₉×C₄₇	—	3	4	no	—
8	C₃×C₁₉×D₄₇	D₃	1	4	yes	complemented
9	C₂×C₁₉×D₄₇	—	9	1	no	Hall
10	C₃×C₁₉×C₄₇	C₂×D₃	1	4	yes	complemented
11	C₂×C₁₉×C₄₇	—	9	1	no	—
12	C₁₉×D₄₇	—	9	1	no	—
13	C₁₉×D₄₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
14	C₃⋊D₃×D₄₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₁₉×C₄₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
16	C₃⋊D₁₄₁	C₂×C₁₉	1	1	yes	characteristic, complemented
17	C₃⋊D₃×C₄₇	C₂×C₁₉	1	1	yes	characteristic, complemented
18	C₃²×D₄₇	C₂×C₁₉	1	1	yes	characteristic, complemented
19	C₂×C₃⋊D₃×C₁₉	—	47	1	no	maximal, Hall
20	D₃×D₄₇	—	3	4	no	—
21	C₃²×C₄₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃²×C₁₉	—	47	1	no	—
23	C₃⋊D₃×C₁₉	—	47	1	no	—
24	C₃⋊D₃×C₁₉	D₄₇	1	1	yes	characteristic, direct product factor
25	D₁₄₁	—	3	4	no	—
26	C₃×D₄₇	D₃×C₁₉	1	4	yes	complemented
27	D₃×C₄₇	—	3	4	no	—
28	C₂×D₃×C₁₉	—	141	4	no	—
29	C₂×D₄₇	—	9	1	no	Hall
30	C₃²×C₁₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄₇	C₂×D₃×C₁₉	1	4	yes	complemented
32	C₂×C₃×C₁₉	—	47	4	no	—
33	D₃×C₁₉	—	3	4	no	—
34	D₃×C₁₉	—	141	4	no	—
35	C₂×C₄₇	—	9	1	no	—
36	D₄₇	—	9	1	no	—
37	D₄₇	C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor
38	C₂²×C₁₉	—	423	1	no	Hall
39	C₃×C₁₉	D₃×D₄₇	1	4	yes	complemented
40	C₄₇	C₂×C₃⋊D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₁₉	—	9	1	no	—
42	C₂×C₁₉	—	47	1	no	—
43	C₂×C₁₉	—	423	1	no	—
44	C₂×C₃⋊D₃	—	47	1	no	Hall
45	C₁₉	C₃⋊D₃×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₃²	—	47	1	no	—
47	C₃⋊D₃	—	47	1	no	—
48	C₃⋊D₃	C₁₉×D₄₇	1	1	yes	characteristic, direct product factor
49	C₂×D₃	—	141	4	no	—
50	C₃²	C₂×C₁₉×D₄₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	47	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	141	4	no	—
54	C₂²	—	423	1	no	Sylow
55	C₃	D₃×C₁₉×D₄₇	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	47	1	no	—
58	C₂	—	423	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊D₃×D₄₇
commutator, cosocle, hypocenter	C₃²×C₄₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₉×C₄₇	C₂²
LCS	G ▷ C₃²×C₄₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₉×D₄₇	C₂	semidirect
2. C₃⋊D₃×C₁₉×C₄₇	C₂	semidirect
3. C₁₉×C₃⋊D₁₄₁	C₂	semidirect
5. C₃²×C₁₉×C₄₇	C₂²	semidirect
8. C₃×C₁₉×D₄₇	D₃	semidirect
10. C₃×C₁₉×C₄₇	C₂×D₃	semidirect
13. C₁₉×D₄₇	C₃⋊D₃	direct (N × H)
14. C₃⋊D₃×D₄₇	C₁₉	direct (N × H)
15. C₁₉×C₄₇	C₂×C₃⋊D₃	semidirect
16. C₃⋊D₁₄₁	C₂×C₁₉	semidirect
17. C₃⋊D₃×C₄₇	C₂×C₁₉	semidirect
18. C₃²×D₄₇	C₂×C₁₉	semidirect
21. C₃²×C₄₇	C₂²×C₁₉	semidirect
24. C₃⋊D₃×C₁₉	D₄₇	direct (N × H)
26. C₃×D₄₇	D₃×C₁₉	semidirect
30. C₃²×C₁₉	C₂×D₄₇	semidirect
31. C₃×C₄₇	C₂×D₃×C₁₉	semidirect
37. D₄₇	C₃⋊D₃×C₁₉	direct (N × H)
39. C₃×C₁₉	D₃×D₄₇	semidirect
40. C₄₇	C₂×C₃⋊D₃×C₁₉	semidirect
45. C₁₉	C₃⋊D₃×D₄₇	direct (N × H)
48. C₃⋊D₃	C₁₉×D₄₇	direct (N × H)
50. C₃²	C₂×C₁₉×D₄₇	semidirect
55. C₃	D₃×C₁₉×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₉×D₄₇	2
C₃⋊D₃×C₁₉×C₄₇	2
C₁₉×C₃⋊D₁₄₁	2
D₃×C₁₉×D₄₇	3
C₃⋊D₃×D₄₇	19
C₂×C₃⋊D₃×C₁₉	47

Subgroups — C3⋊D3×C19×D47 #44565342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×C₁₉×D₄₇ #44565342