Subgroups — D₃×C₁₉⋊C₃×D₄₇ #44565310

Order 32148.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₄₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉⋊C₃×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₉×D₄₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉⋊C₃×D₄₇	—	3	1	no	maximal
6	C₃×C₄₇×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₁₉⋊C₃×D₄₇	—	2	1	no	—
8	C₁₉⋊C₃×D₄₇	—	3	1	no	—
9	C₁₉⋊C₃×D₄₇	D₃	1	1	yes	characteristic, direct product factor
10	C₁₉×D₁₄₁	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₁₉×D₄₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₄₇×C₁₉⋊C₃	—	3	1	no	—
14	C₂×C₁₉×D₄₇	—	3	1	no	Hall
15	C₃×C₁₉×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₄₇×C₁₉⋊C₃	—	2	1	no	—
17	C₄₇×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₁₉×C₄₇	—	3	1	no	—
19	C₁₉×D₄₇	—	3	1	no	—
20	C₁₉×D₄₇	C₃×D₃	1	1	yes	characteristic, complemented
21	C₃×D₃×D₄₇	—	19	1	no	maximal, Hall
22	C₁₉×C₄₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
23	C₃×D₁₄₁	—	19	1	no	—
24	C₃×D₃×C₄₇	—	19	1	no	—
25	C₃²×D₄₇	—	19	1	no	—
26	C₂×D₃×C₁₉⋊C₃	—	47	1	no	maximal, Hall
27	C₂×C₃×D₄₇	—	57	1	no	—
28	D₃×D₄₇	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
29	C₃²×C₄₇	—	19	1	no	Hall
30	C₂×C₃×C₁₉⋊C₃	—	47	1	no	—
31	D₃×C₁₉⋊C₃	—	47	1	no	—
32	D₃×C₁₉⋊C₃	D₄₇	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₄₇	—	57	1	no	—
34	D₁₄₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
35	C₃×D₄₇	—	19	1	no	—
36	C₃×D₄₇	—	38	1	no	—
37	C₃×D₄₇	—	57	1	no	—
38	C₃×D₄₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
39	D₃×C₄₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
40	C₂×D₃×C₁₉	—	47	1	no	—
41	C₂²×C₁₉⋊C₃	—	141	1	no	—
42	C₂×D₄₇	—	3	1	no	Hall
43	C₃×C₁₉⋊C₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
44	C₃×C₄₇	—	19	1	no	—
45	C₃×C₄₇	—	38	1	no	—
46	C₃×C₄₇	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
47	C₂×C₃×C₁₉	—	47	1	no	—
48	D₃×C₁₉	—	47	1	no	—
49	D₃×C₁₉	C₃×D₄₇	1	1	yes	characteristic, complemented
50	C₂×C₁₉⋊C₃	—	3	1	no	—
51	C₂×C₁₉⋊C₃	—	47	1	no	—
52	C₂×C₁₉⋊C₃	—	94	1	no	—
53	C₂×C₁₉⋊C₃	—	141	1	no	—
54	C₂×C₄₇	—	3	1	no	—
55	D₄₇	—	3	1	no	—
56	D₄₇	D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
57	C₂²×C₁₉	—	141	1	no	Hall
58	C₃×C₁₉	C₂×C₃×D₄₇	1	1	yes	characteristic, complemented
59	C₁₉⋊C₃	—	2	1	no	—
60	C₁₉⋊C₃	D₃×D₄₇	1	1	yes	characteristic, direct product factor
61	C₄₇	C₂×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₁₉	—	3	1	no	—
63	C₂×C₁₉	—	47	1	no	—
64	C₂×C₁₉	—	141	1	no	—
65	C₂×C₃×D₃	—	893	1	no	Hall
66	C₁₉	C₃×D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃²	—	893	1	no	—
68	C₃×D₃	—	19	1	no	—
69	C₃×D₃	—	893	1	no	—
70	C₂²×C₃	—	2679	1	no	—
71	C₂×D₃	—	47	1	no	—
72	C₃²	—	19	1	no	Sylow
73	C₂×C₃	—	47	1	no	—
74	C₂×C₃	—	57	1	no	—
75	C₂×C₃	—	2679	1	no	—
76	C₂×C₃	—	893	1	no	—
77	C₂×C₃	—	1786	1	no	—
78	D₃	—	47	1	no	—
79	D₃	C₁₉⋊C₃×D₄₇	1	1	yes	characteristic, direct product factor
80	C₂²	—	141	1	no	Sylow
81	C₃	—	19	1	no	—
82	C₃	—	38	1	no	—
83	C₃	C₂×C₁₉⋊C₃×D₄₇	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	47	1	no	—
86	C₂	—	141	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₉⋊C₃×D₁₄₁	C₂	semidirect
2. D₃×C₄₇×C₁₉⋊C₃	C₂	semidirect
3. C₃×C₁₉⋊C₃×D₄₇	C₂	semidirect
4. D₃×C₁₉×D₄₇	C₃	semidirect
6. C₃×C₄₇×C₁₉⋊C₃	C₂²	semidirect
9. C₁₉⋊C₃×D₄₇	D₃	direct (N × H)
10. C₁₉×D₁₄₁	C₂×C₃	semidirect
11. D₃×C₁₉×C₄₇	C₂×C₃	semidirect
12. C₃×C₁₉×D₄₇	C₂×C₃	semidirect
15. C₃×C₁₉×C₄₇	C₂²×C₃	semidirect
17. C₄₇×C₁₉⋊C₃	C₂×D₃	semidirect
20. C₁₉×D₄₇	C₃×D₃	semidirect
22. C₁₉×C₄₇	C₂×C₃×D₃	semidirect
28. D₃×D₄₇	C₁₉⋊C₃	direct (N × H)
32. D₃×C₁₉⋊C₃	D₄₇	direct (N × H)
34. D₁₄₁	C₂×C₁₉⋊C₃	semidirect
38. C₃×D₄₇	C₂×C₁₉⋊C₃	semidirect
39. D₃×C₄₇	C₂×C₁₉⋊C₃	semidirect
43. C₃×C₁₉⋊C₃	C₂×D₄₇	semidirect
46. C₃×C₄₇	C₂²×C₁₉⋊C₃	semidirect
49. D₃×C₁₉	C₃×D₄₇	semidirect
56. D₄₇	D₃×C₁₉⋊C₃	direct (N × H)
58. C₃×C₁₉	C₂×C₃×D₄₇	semidirect
60. C₁₉⋊C₃	D₃×D₄₇	direct (N × H)
61. C₄₇	C₂×D₃×C₁₉⋊C₃	semidirect
66. C₁₉	C₃×D₃×D₄₇	semidirect
79. D₃	C₁₉⋊C₃×D₄₇	direct (N × H)
83. C₃	C₂×C₁₉⋊C₃×D₄₇	semidirect

Maximal subgroups

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

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

Subgroups — D3×C19⋊C3×D47 #44565310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₉⋊C₃×D₄₇ #44565310