Subgroups — C₃×D₃₉×D₄₇ #36347252

Order 21996.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄₇×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₈₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉×D₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₁₃×D₄₇	—	3	1	no	maximal
6	C₃²×C₁₃×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₁₈₃₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₄₇×D₃₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₆₁₁	—	3	1	no	—
10	C₃×D₁₃×C₄₇	—	3	1	no	—
11	C₃×C₁₃×D₄₇	—	2	1	no	—
12	C₃×C₁₃×D₄₇	D₃	1	1	yes	characteristic, complemented
13	C₃×C₁₃×D₄₇	C₂×C₃	1	1	yes	characteristic, complemented
14	D₁₃×D₄₇	—	3	1	no	Hall
15	C₃×C₁₃×C₄₇	—	2	1	no	—
16	C₃×C₁₃×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₄₇	—	13	1	no	maximal, Hall
19	D₆₁₁	—	3	1	no	—
20	C₁₃×D₄₇	C₃×D₃	1	1	yes	characteristic, complemented
21	D₁₃×C₄₇	—	3	1	no	—
22	C₃×D₁₄₁	—	13	1	no	—
23	C₃×D₃×C₄₇	—	13	1	no	—
24	C₃²×D₄₇	D₁₃	1	1	yes	characteristic, complemented
25	C₁₃×C₄₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×D₄₇	—	39	1	no	—
27	D₃×D₄₇	—	13	1	no	—
28	C₂×C₃×D₃₉	—	47	1	no	maximal, Hall
29	C₃²×C₄₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₄₇	—	39	1	no	—
31	D₁₄₁	—	13	1	no	—
32	C₃×D₄₇	—	2	1	no	—
33	C₃×D₄₇	—	39	1	no	—
34	C₃×D₄₇	C₃×D₁₃	1	1	yes	characteristic, complemented
35	C₃×D₄₇	D₃₉	1	1	yes	characteristic, direct product factor
36	D₃×C₄₇	—	13	1	no	—
37	C₂×C₃²×C₁₃	—	47	1	no	—
38	C₃×D₃₉	—	47	1	no	—
39	C₃×D₃₉	D₄₇	1	1	yes	characteristic, direct product factor
40	C₂×D₄₇	—	39	1	no	Hall
41	C₂×D₃₉	—	47	1	no	—
42	C₂×C₃×D₁₃	—	141	1	no	—
43	C₃×C₄₇	—	2	1	no	—
44	C₃×C₄₇	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
45	C₃×C₄₇	C₂×D₃₉	1	1	yes	characteristic, complemented
46	C₃²×C₁₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
47	C₂×C₄₇	—	39	1	no	—
48	D₄₇	—	39	1	no	—
49	D₄₇	C₃×D₃₉	1	1	yes	characteristic, direct product factor
50	C₂×C₃×C₁₃	—	47	1	no	—
51	C₂×C₃×C₁₃	—	47	1	no	—
52	C₂×C₃×C₁₃	—	94	1	no	—
53	D₃₉	—	47	1	no	—
54	D₃₉	C₃×D₄₇	1	1	yes	characteristic, direct product factor
55	C₃×D₁₃	—	3	1	no	—
56	C₃×D₁₃	—	141	1	no	—
57	C₂×D₁₃	—	141	1	no	Hall
58	C₄₇	C₂×C₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₁₃	—	2	1	no	—
60	C₃×C₁₃	D₃×D₄₇	1	1	yes	characteristic, complemented
61	C₃×C₁₃	C₂×C₃×D₄₇	1	1	yes	characteristic, complemented
62	C₂×C₃×D₃	—	611	1	no	Hall
63	C₂×C₁₃	—	47	1	no	—
64	D₁₃	—	3	1	no	—
65	D₁₃	—	141	1	no	—
66	C₂×C₃²	—	47	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	—	611	1	no	—
69	C₁₃	C₃×D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	1833	1	no	—
71	C₂×D₃	—	611	1	no	—
72	C₃²	D₁₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	39	1	no	—
74	C₂×C₃	—	1833	1	no	—
75	C₂×C₃	—	47	1	no	—
76	C₂×C₃	—	47	1	no	—
77	C₂×C₃	—	94	1	no	—
78	D₃	—	13	1	no	—
79	D₃	—	611	1	no	—
80	C₂²	—	1833	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₁₃×D₄₇	1	1	yes	characteristic, complemented
83	C₃	D₃₉×D₄₇	1	1	yes	characteristic, direct product factor
84	C₂	—	39	1	no	—
85	C₂	—	1833	1	no	—
86	C₂	—	47	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃₉×D₄₇
commutator, cosocle, hypocenter	C₃×C₁₃×C₄₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₄₇	C₂²
LCS	G ▷ C₃×C₁₃×C₄₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×D₄₇	C₂	semidirect
2. C₃×C₄₇×D₃₉	C₂	semidirect
3. C₃×D₁₈₃₃	C₂	semidirect
4. D₃₉×D₄₇	C₃	direct (N × H)
6. C₃²×C₁₃×C₄₇	C₂²	semidirect
7. D₁₈₃₃	C₂×C₃	semidirect
8. C₄₇×D₃₉	C₂×C₃	semidirect
12. C₃×C₁₃×D₄₇	D₃	semidirect
13. C₃×C₁₃×D₄₇	C₂×C₃	semidirect
16. C₃×C₁₃×C₄₇	C₂×D₃	semidirect
17. C₃×C₁₃×C₄₇	C₂²×C₃	semidirect
20. C₁₃×D₄₇	C₃×D₃	semidirect
24. C₃²×D₄₇	D₁₃	semidirect
25. C₁₃×C₄₇	C₂×C₃×D₃	semidirect
29. C₃²×C₄₇	C₂×D₁₃	semidirect
34. C₃×D₄₇	C₃×D₁₃	semidirect
35. C₃×D₄₇	D₃₉	direct (N × H)
39. C₃×D₃₉	D₄₇	direct (N × H)
44. C₃×C₄₇	C₂×C₃×D₁₃	semidirect
45. C₃×C₄₇	C₂×D₃₉	semidirect
46. C₃²×C₁₃	C₂×D₄₇	semidirect
49. D₄₇	C₃×D₃₉	direct (N × H)
54. D₃₉	C₃×D₄₇	direct (N × H)
58. C₄₇	C₂×C₃×D₃₉	semidirect
60. C₃×C₁₃	D₃×D₄₇	semidirect
61. C₃×C₁₃	C₂×C₃×D₄₇	semidirect
69. C₁₃	C₃×D₃×D₄₇	semidirect
72. C₃²	D₁₃×D₄₇	semidirect
82. C₃	C₃×D₁₃×D₄₇	semidirect
83. C₃	D₃₉×D₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×D₄₇	2
C₃×C₄₇×D₃₉	2
C₃×D₁₈₃₃	2
D₃₉×D₄₇	3
C₃×D₁₃×D₄₇	3
C₃×D₃×D₄₇	13
C₂×C₃×D₃₉	47

Subgroups — C3×D39×D47 #36347252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₉×D₄₇ #36347252