Subgroups — C₉×D₇²×C₁₉ #45691663

Order 33516.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₉×D₇×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₃×D₇²×C₁₉	C₃	1	1	yes	maximal, characteristic
4	C₇²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	C₃×C₇×D₇×C₁₉	C₂×C₃	1	2	yes	—
7	C₂×C₉×D₇×C₁₉	—	7	2	no	maximal
8	D₇²×C₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
10	C₉×D₇×C₁₉	—	7	2	no	—
11	C₉×D₇×C₁₉	—	14	3	no	—
12	C₉×D₇×C₁₉	D₇	1	2	yes	direct product factor
13	C₂×C₇×C₉×C₁₉	—	7	2	no	—
14	C₁₉×C₇⋊D₇	C₂×C₉	1	1	yes	characteristic, complemented
15	C₇×D₇×C₁₉	C₂×C₉	1	2	yes	complemented
16	C₉×D₇²	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×D₇×C₁₉	—	7	2	no	—
18	C₇×C₉×C₁₉	—	2	3	no	—
19	C₇×C₉×C₁₉	C₂×D₇	1	2	yes	complemented
20	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₉×C₇⋊D₇	C₂×C₁₉	1	1	yes	characteristic, complemented
22	C₇×C₉×D₇	C₂×C₁₉	1	2	yes	complemented
23	C₂×C₃×C₇×C₁₉	—	7	2	no	—
24	C₃×D₇×C₁₉	—	7	2	no	—
25	C₃×D₇×C₁₉	—	14	3	no	—
26	C₃×D₇×C₁₉	C₃×D₇	1	2	yes	—
27	C₂²×C₉×C₁₉	—	49	1	no	Hall
28	C₃×D₇²	C₃×C₁₉	1	1	yes	characteristic
29	C₂×D₇×C₁₉	—	7	2	no	—
30	C₇²×C₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
31	C₃×C₇×C₁₉	—	2	3	no	—
32	C₃×C₇×C₁₉	C₂×C₃×D₇	1	2	yes	—
33	C₂×C₉×C₁₉	—	7	2	no	—
34	C₂×C₉×C₁₉	—	49	1	no	—
35	C₃×C₇⋊D₇	C₂×C₃×C₁₉	1	1	yes	characteristic
36	C₃×C₇×D₇	C₂×C₃×C₁₉	1	2	yes	—
37	C₂×C₇×C₁₉	—	7	2	no	—
38	D₇×C₁₉	—	7	2	no	—
39	D₇×C₁₉	—	14	3	no	—
40	D₇×C₁₉	C₉×D₇	1	2	yes	direct product factor
41	C₂×C₉×D₇	—	7	2	no	—
42	C₂²×C₃×C₁₉	—	49	1	no	—
43	D₇²	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
44	C₉×C₁₉	D₇²	1	1	yes	characteristic, direct product factor, Hall
45	C₃×C₇²	C₂²×C₃×C₁₉	1	1	yes	characteristic
46	C₇×C₁₉	—	2	3	no	—
47	C₇×C₁₉	C₂×C₉×D₇	1	2	yes	complemented
48	C₂×C₇×C₉	—	7	2	no	—
49	C₉×D₇	—	7	2	no	—
50	C₉×D₇	—	14	3	no	—
51	C₉×D₇	D₇×C₁₉	1	2	yes	direct product factor
52	C₂×C₃×C₁₉	—	7	2	no	—
53	C₂×C₃×C₁₉	—	49	1	no	—
54	C₇⋊D₇	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented
55	C₇×D₇	C₂×C₉×C₁₉	1	2	yes	complemented
56	C₂×C₃×D₇	—	7	2	no	—
57	C₂²×C₁₉	—	49	1	no	Hall
58	C₇×C₉	—	2	3	no	—
59	C₇×C₉	C₂×D₇×C₁₉	1	2	yes	complemented
60	C₃×C₁₉	C₃×D₇²	1	1	yes	characteristic
61	C₇²	C₂²×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₃×C₇	—	7	2	no	—
63	C₃×D₇	—	7	2	no	—
64	C₃×D₇	—	14	3	no	—
65	C₃×D₇	C₃×D₇×C₁₉	1	2	yes	—
66	C₂×C₁₉	—	7	2	no	—
67	C₂×C₁₉	—	49	1	no	—
68	C₂²×C₉	—	49	1	no	Hall
69	C₂×D₇	—	7	2	no	—
70	C₃×C₇	—	2	3	no	—
71	C₃×C₇	C₂×C₃×D₇×C₁₉	1	2	yes	—
72	C₁₉	C₉×D₇²	1	1	yes	characteristic, direct product factor, Sylow
73	C₂×C₉	—	7	2	no	—
74	C₂×C₉	—	49	1	no	—
75	C₂×C₇	—	7	2	no	—
76	D₇	—	7	2	no	—
77	D₇	—	14	3	no	—
78	D₇	C₉×D₇×C₁₉	1	2	yes	direct product factor
79	C₂²×C₃	—	49	1	no	—
80	C₉	D₇²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₇	—	2	3	no	—
82	C₇	C₂×C₉×D₇×C₁₉	1	2	yes	complemented
83	C₂×C₃	—	7	2	no	—
84	C₂×C₃	—	49	1	no	—
85	C₂²	—	49	1	no	Sylow
86	C₃	C₃×D₇²×C₁₉	1	1	yes	characteristic
87	C₂	—	7	2	no	—
88	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₇²
commutator, hypocenter	C₇²	C₂²×C₉×C₁₉
Frattini	C₃	C₃×D₇²×C₁₉
Fitting	C₇²×C₉×C₁₉	C₂²
socle	C₃×C₇²×C₁₉	C₂²×C₃
prime radical	C₃×D₇²×C₁₉	C₃
cosocle	C₃×C₇²	C₂²×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₉×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₉×C₇⋊D₇	C₂	semidirect
2. C₇×C₉×D₇×C₁₉	C₂	semidirect
4. C₇²×C₉×C₁₉	C₂²	semidirect
8. D₇²×C₁₉	C₉	direct (N × H)
12. C₉×D₇×C₁₉	D₇	direct (N × H)
14. C₁₉×C₇⋊D₇	C₂×C₉	semidirect
15. C₇×D₇×C₁₉	C₂×C₉	semidirect
16. C₉×D₇²	C₁₉	direct (N × H)
19. C₇×C₉×C₁₉	C₂×D₇	semidirect
20. C₇²×C₁₉	C₂²×C₉	semidirect
21. C₉×C₇⋊D₇	C₂×C₁₉	semidirect
22. C₇×C₉×D₇	C₂×C₁₉	semidirect
30. C₇²×C₉	C₂²×C₁₉	semidirect
40. D₇×C₁₉	C₉×D₇	direct (N × H)
43. D₇²	C₉×C₁₉	direct (N × H)
44. C₉×C₁₉	D₇²	direct (N × H)
47. C₇×C₁₉	C₂×C₉×D₇	semidirect
51. C₉×D₇	D₇×C₁₉	direct (N × H)
54. C₇⋊D₇	C₂×C₉×C₁₉	semidirect
55. C₇×D₇	C₂×C₉×C₁₉	semidirect
59. C₇×C₉	C₂×D₇×C₁₉	semidirect
61. C₇²	C₂²×C₉×C₁₉	semidirect
72. C₁₉	C₉×D₇²	direct (N × H)
78. D₇	C₉×D₇×C₁₉	direct (N × H)
80. C₉	D₇²×C₁₉	direct (N × H)
82. C₇	C₂×C₉×D₇×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₁₉×C₇⋊D₇	2
C₇×C₉×D₇×C₁₉	2
C₃×D₇²×C₁₉	3
C₂×C₉×D₇×C₁₉	7
C₉×D₇²	19

Subgroups — C9×D72×C19 #45691663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₇²×C₁₉ #45691663