Subgroups — C₃×D₄₇×D₅₇ #44565327

Order 32148.

88 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×C₄₇×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₆₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₇×D₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₁₉×D₄₇	—	3	1	no	maximal
6	C₃²×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₆₇₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₄₇×D₅₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₈₉₃	—	3	1	no	—
10	C₃×D₁₉×C₄₇	—	3	1	no	—
11	C₃×C₁₉×D₄₇	—	2	1	no	—
12	C₃×C₁₉×D₄₇	D₃	1	1	yes	characteristic, complemented
13	C₃×C₁₉×D₄₇	C₂×C₃	1	1	yes	characteristic, complemented
14	D₁₉×D₄₇	—	3	1	no	Hall
15	C₃×C₁₉×C₄₇	—	2	1	no	—
16	C₃×C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₉×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented
18	D₈₉₃	—	3	1	no	—
19	C₁₉×D₄₇	C₃×D₃	1	1	yes	characteristic, complemented
20	D₁₉×C₄₇	—	3	1	no	—
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	D₁₉	1	1	yes	characteristic, complemented
26	C₂×C₃×D₅₇	—	47	1	no	maximal, Hall
27	C₂×C₃×D₄₇	—	57	1	no	—
28	D₃×D₄₇	—	19	1	no	—
29	C₃²×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃²×C₁₉	—	47	1	no	—
31	C₃×D₅₇	—	47	1	no	—
32	C₃×D₅₇	D₄₇	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₄₇	—	57	1	no	—
34	D₁₄₁	—	19	1	no	—
35	C₃×D₄₇	—	2	1	no	—
36	C₃×D₄₇	—	57	1	no	—
37	C₃×D₄₇	C₃×D₁₉	1	1	yes	characteristic, complemented
38	C₃×D₄₇	D₅₇	1	1	yes	characteristic, direct product factor
39	D₃×C₄₇	—	19	1	no	—
40	C₂×D₅₇	—	47	1	no	—
41	C₂×C₃×D₁₉	—	141	1	no	—
42	C₂×D₄₇	—	57	1	no	Hall
43	C₃²×C₁₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
44	C₃×C₄₇	—	2	1	no	—
45	C₃×C₄₇	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
46	C₃×C₄₇	C₂×D₅₇	1	1	yes	characteristic, complemented
47	C₂×C₃×C₁₉	—	47	1	no	—
48	C₂×C₃×C₁₉	—	47	1	no	—
49	C₂×C₃×C₁₉	—	94	1	no	—
50	D₅₇	—	47	1	no	—
51	D₅₇	C₃×D₄₇	1	1	yes	characteristic, direct product factor
52	C₃×D₁₉	—	3	1	no	—
53	C₃×D₁₉	—	141	1	no	—
54	C₂×C₄₇	—	57	1	no	—
55	D₄₇	—	57	1	no	—
56	D₄₇	C₃×D₅₇	1	1	yes	characteristic, direct product factor
57	C₂×D₁₉	—	141	1	no	Hall
58	C₃×C₁₉	—	2	1	no	—
59	C₃×C₁₉	D₃×D₄₇	1	1	yes	characteristic, complemented
60	C₃×C₁₉	C₂×C₃×D₄₇	1	1	yes	characteristic, complemented
61	C₄₇	C₂×C₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₁₉	—	47	1	no	—
63	D₁₉	—	3	1	no	—
64	D₁₉	—	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	—	47	1	no	—
68	C₃×D₃	—	19	1	no	—
69	C₃×D₃	—	893	1	no	—
70	C₂²×C₃	—	2679	1	no	—
71	C₂×D₃	—	893	1	no	—
72	C₃²	D₁₉×D₄₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	47	1	no	—
74	C₂×C₃	—	47	1	no	—
75	C₂×C₃	—	57	1	no	—
76	C₂×C₃	—	94	1	no	—
77	C₂×C₃	—	2679	1	no	—
78	D₃	—	19	1	no	—
79	D₃	—	893	1	no	—
80	C₂²	—	2679	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₁₉×D₄₇	1	1	yes	characteristic, complemented
83	C₃	D₄₇×D₅₇	1	1	yes	characteristic, direct product factor
84	C₂	—	47	1	no	—
85	C₂	—	57	1	no	—
86	C₂	—	2679	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₄₇×D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉×C₄₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₉×C₄₇	C₂²
LCS	G ▷ C₃×C₁₉×C₄₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₉×D₄₇	C₂	semidirect
2. C₃×C₄₇×D₅₇	C₂	semidirect
3. C₃×D₂₆₇₉	C₂	semidirect
4. D₄₇×D₅₇	C₃	direct (N × H)
6. C₃²×C₁₉×C₄₇	C₂²	semidirect
7. D₂₆₇₉	C₂×C₃	semidirect
8. C₄₇×D₅₇	C₂×C₃	semidirect
12. C₃×C₁₉×D₄₇	D₃	semidirect
13. C₃×C₁₉×D₄₇	C₂×C₃	semidirect
16. C₃×C₁₉×C₄₇	C₂×D₃	semidirect
17. C₃×C₁₉×C₄₇	C₂²×C₃	semidirect
19. C₁₉×D₄₇	C₃×D₃	semidirect
22. C₁₉×C₄₇	C₂×C₃×D₃	semidirect
25. C₃²×D₄₇	D₁₉	semidirect
29. C₃²×C₄₇	C₂×D₁₉	semidirect
32. C₃×D₅₇	D₄₇	direct (N × H)
37. C₃×D₄₇	C₃×D₁₉	semidirect
38. C₃×D₄₇	D₅₇	direct (N × H)
43. C₃²×C₁₉	C₂×D₄₇	semidirect
45. C₃×C₄₇	C₂×C₃×D₁₉	semidirect
46. C₃×C₄₇	C₂×D₅₇	semidirect
51. D₅₇	C₃×D₄₇	direct (N × H)
56. D₄₇	C₃×D₅₇	direct (N × H)
59. C₃×C₁₉	D₃×D₄₇	semidirect
60. C₃×C₁₉	C₂×C₃×D₄₇	semidirect
61. C₄₇	C₂×C₃×D₅₇	semidirect
66. C₁₉	C₃×D₃×D₄₇	semidirect
72. C₃²	D₁₉×D₄₇	semidirect
82. C₃	C₃×D₁₉×D₄₇	semidirect
83. C₃	D₄₇×D₅₇	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×C₁₉×D₄₇	2
C₃×C₄₇×D₅₇	2
C₃×D₂₆₇₉	2
D₄₇×D₅₇	3
C₃×D₁₉×D₄₇	3
C₃×D₃×D₄₇	19
C₂×C₃×D₅₇	47

Subgroups — C3×D47×D57 #44565327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄₇×D₅₇ #44565327