Subgroups — C₁₉×D₆₃⋊D₇ #45691683

Order 33516.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×D₆₃	C₂	1	2	yes	maximal, complemented
2	C₉×C₁₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×D₂₁⋊D₇	—	3	1	no	maximal
4	C₇²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₉×D₂₁	—	3	2	no	—
6	C₃×C₁₉×C₇⋊D₇	D₃	1	1	yes	characteristic
7	D₇×D₉×C₁₉	—	7	2	no	maximal
8	D₇²×C₁₉	—	9	1	no	Hall
9	C₃×C₇²×C₁₉	C₂×D₃	1	1	yes	characteristic
10	C₁₉×D₆₃	D₇	1	2	yes	complemented
11	C₇×D₉×C₁₉	—	7	2	no	—
12	C₉×D₇×C₁₉	—	7	2	no	—
13	C₉×D₇×C₁₉	—	14	3	no	—
14	C₁₉×C₇⋊D₇	D₉	1	1	yes	characteristic, complemented
15	C₇×D₇×C₁₉	—	9	2	no	—
16	D₆₃⋊D₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	D₃×D₇×C₁₉	—	21	2	no	—
18	C₇×C₉×C₁₉	—	2	3	no	—
19	C₇×C₉×C₁₉	C₂×D₇	1	2	yes	complemented
20	C₇²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
21	C₇×D₆₃	C₂×C₁₉	1	2	yes	complemented
22	C₉×C₇⋊D₇	C₂×C₁₉	1	1	yes	characteristic, complemented
23	C₁₉×D₂₁	—	3	2	no	—
24	D₃×C₇×C₁₉	—	21	2	no	—
25	C₃×D₇×C₁₉	—	7	2	no	—
26	C₃×D₇×C₁₉	—	14	3	no	—
27	C₂×D₉×C₁₉	—	49	1	no	Hall
28	D₂₁⋊D₇	—	3	1	no	—
29	C₂×D₇×C₁₉	—	63	2	no	—
30	C₇²×C₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
31	C₃×C₇×C₁₉	—	2	3	no	—
32	C₃×C₇×C₁₉	D₃×D₇	1	2	yes	—
33	C₂×C₉×C₁₉	—	49	1	no	—
34	D₉×C₁₉	—	7	2	no	—
35	C₇×D₂₁	—	3	2	no	—
36	C₃×C₇⋊D₇	D₃×C₁₉	1	1	yes	characteristic
37	C₂×C₇×C₁₉	—	63	2	no	—
38	D₇×C₁₉	—	7	2	no	—
39	D₇×C₁₉	—	9	2	no	—
40	D₇×C₁₉	—	14	3	no	—
41	D₇×D₉	—	7	2	no	—
42	C₂×D₃×C₁₉	—	147	1	no	—
43	D₇²	—	9	1	no	Hall
44	C₉×C₁₉	D₇²	1	1	yes	characteristic, complemented, Hall
45	C₃×C₇²	C₂×D₃×C₁₉	1	1	yes	characteristic
46	C₇×C₁₉	—	2	3	no	—
47	C₇×C₁₉	D₇×D₉	1	2	yes	complemented
48	D₆₃	D₇×C₁₉	1	2	yes	complemented
49	C₉×D₇	—	7	2	no	—
50	C₉×D₇	—	14	3	no	—
51	C₇×D₉	—	7	2	no	—
52	C₂×C₃×C₁₉	—	49	1	no	—
53	D₃×C₁₉	—	21	2	no	—
54	C₇⋊D₇	D₉×C₁₉	1	1	yes	characteristic, complemented
55	C₇×D₇	—	9	2	no	—
56	D₃×D₇	—	21	2	no	—
57	C₂²×C₁₉	—	441	1	no	Hall
58	C₇×C₉	—	2	3	no	—
59	C₇×C₉	C₂×D₇×C₁₉	1	2	yes	complemented
60	C₃×C₁₉	D₂₁⋊D₇	1	1	yes	characteristic
61	C₇²	C₂×D₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
62	D₂₁	—	3	2	no	—
63	C₃×D₇	—	7	2	no	—
64	C₃×D₇	—	14	3	no	—
65	D₃×C₇	—	21	2	no	—
66	C₂×C₁₉	—	49	1	no	—
67	C₂×C₁₉	—	63	2	no	—
68	C₂×D₉	—	49	1	no	Hall
69	C₂×D₇	—	63	2	no	—
70	C₃×C₇	—	2	3	no	—
71	C₃×C₇	D₃×D₇×C₁₉	1	2	yes	—
72	C₁₉	D₆₃⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
73	C₂×C₉	—	49	1	no	—
74	D₉	—	7	2	no	—
75	C₂×C₇	—	63	2	no	—
76	D₇	—	7	2	no	—
77	D₇	—	9	2	no	—
78	D₇	—	14	3	no	—
79	C₂×D₃	—	147	1	no	—
80	C₉	D₇²×C₁₉	1	1	yes	characteristic, complemented, Sylow
81	C₇	—	2	3	no	—
82	C₇	D₇×D₉×C₁₉	1	2	yes	complemented
83	C₂×C₃	—	49	1	no	—
84	D₃	—	21	2	no	—
85	C₂²	—	441	1	no	Sylow
86	C₃	C₁₉×D₂₁⋊D₇	1	1	yes	characteristic
87	C₂	—	49	1	no	—
88	C₂	—	63	2	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₆₃⋊D₇
commutator, cosocle, hypocenter	C₇²×C₉	C₂²×C₁₉
Frattini	C₃	C₁₉×D₂₁⋊D₇
Fitting	C₇²×C₉×C₁₉	C₂²
socle	C₃×C₇²×C₁₉	C₂×D₃
LCS	G ▷ C₇²×C₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×D₆₃	C₂	semidirect
2. C₉×C₁₉×C₇⋊D₇	C₂	semidirect
4. C₇²×C₉×C₁₉	C₂²	semidirect
10. C₁₉×D₆₃	D₇	semidirect
14. C₁₉×C₇⋊D₇	D₉	semidirect
16. D₆₃⋊D₇	C₁₉	direct (N × H)
19. C₇×C₉×C₁₉	C₂×D₇	semidirect
20. C₇²×C₁₉	C₂×D₉	semidirect
21. C₇×D₆₃	C₂×C₁₉	semidirect
22. C₉×C₇⋊D₇	C₂×C₁₉	semidirect
30. C₇²×C₉	C₂²×C₁₉	semidirect
44. C₉×C₁₉	D₇²	semidirect
47. C₇×C₁₉	D₇×D₉	semidirect
48. D₆₃	D₇×C₁₉	semidirect
54. C₇⋊D₇	D₉×C₁₉	semidirect
59. C₇×C₉	C₂×D₇×C₁₉	semidirect
61. C₇²	C₂×D₉×C₁₉	semidirect
72. C₁₉	D₆₃⋊D₇	direct (N × H)
80. C₉	D₇²×C₁₉	semidirect
82. C₇	D₇×D₉×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₉×D₆₃	2
C₉×C₁₉×C₇⋊D₇	2
C₁₉×D₂₁⋊D₇	3
D₇×D₉×C₁₉	7
D₆₃⋊D₇	19

Subgroups — C19×D63⋊D7 #45691683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₆₃⋊D₇ #45691683