Subgroups — C₇×D₂₁×C₁₉⋊C₃ #30660817

Order 16758.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₉×D₂₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×D₇×C₁₉⋊C₃	—	3	1	no	maximal
4	C₇²×C₁₉⋊C₃	—	2	1	no	—
5	C₇²×C₁₉⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₂₁×C₁₉⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor
8	D₃×C₇×C₁₉⋊C₃	—	7	1	no	maximal
9	C₇×D₇×C₁₉	—	3	1	no	Hall
10	C₃×C₇×C₁₉⋊C₃	—	2	3	no	—
11	C₃×C₇×C₁₉⋊C₃	D₇	1	1	yes	characteristic, complemented
12	C₃×C₇×C₁₉⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
13	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₇×D₂₁	—	19	1	no	maximal, Hall
15	C₁₉×D₂₁	C₃×C₇	1	1	yes	characteristic, complemented
16	D₃×C₇×C₁₉	—	7	1	no	—
17	C₂×C₇×C₁₉⋊C₃	—	21	1	no	—
18	D₇×C₁₉⋊C₃	—	3	1	no	—
19	C₃²×C₇²	—	19	1	no	Hall
20	C₃×C₇×C₁₉	—	2	3	no	—
21	C₃×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
22	C₃×C₇×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	C₇×C₁₉⋊C₃	—	2	6	no	—
24	C₇×C₁₉⋊C₃	—	2	3	no	—
25	C₇×C₁₉⋊C₃	—	2	1	no	—
26	C₇×C₁₉⋊C₃	—	2	1	no	—
27	C₇×C₁₉⋊C₃	D₃×C₇	1	1	yes	characteristic, complemented
28	C₇×C₁₉⋊C₃	D₂₁	1	1	yes	characteristic, direct product factor
29	D₃×C₁₉⋊C₃	—	7	1	no	Hall
30	C₇×D₂₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃×C₇×D₇	—	57	1	no	—
32	C₂×C₇×C₁₉	—	21	1	no	—
33	D₇×C₁₉	—	3	1	no	—
34	C₃×C₁₉⋊C₃	C₇×D₇	1	1	yes	characteristic, complemented, Hall
35	C₃×C₇²	—	19	1	no	—
36	C₃×C₇²	—	38	1	no	—
37	C₃×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
38	C₇×C₁₉	—	2	3	no	—
39	C₇×C₁₉	C₃×D₃×C₇	1	1	yes	characteristic, complemented
40	C₇×C₁₉	C₃×D₂₁	1	1	yes	characteristic, complemented
41	C₃×D₂₁	—	19	1	no	—
42	C₃×D₃×C₇	—	133	1	no	—
43	D₃×C₁₉	—	7	1	no	—
44	C₂×C₁₉⋊C₃	—	21	1	no	—
45	C₇×D₇	—	3	1	no	Hall
46	C₃²×C₇	—	19	1	no	—
47	C₃²×C₇	—	19	1	no	—
48	C₃²×C₇	—	38	3	no	—
49	C₃×C₁₉	C₃×C₇×D₇	1	1	yes	characteristic, complemented
50	C₁₉⋊C₃	—	2	1	no	—
51	C₁₉⋊C₃	C₇×D₂₁	1	1	yes	characteristic, direct product factor
52	C₇²	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃×C₇	—	399	1	no	—
54	D₂₁	C₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
55	C₃×D₇	—	57	1	no	—
56	D₃×C₇	—	7	1	no	—
57	C₂×C₁₉	—	21	1	no	Hall
58	C₃×C₇	—	2	3	no	—
59	C₃×C₇	—	19	1	no	—
60	C₃×C₇	—	19	1	no	—
61	C₃×C₇	—	38	3	no	—
62	C₃×C₇	—	38	6	no	—
63	C₃×C₇	—	38	1	no	—
64	C₃×C₇	—	38	1	no	—
65	C₃×C₇	D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
66	C₃×C₇	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
67	C₁₉	C₃×C₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
68	C₃×D₃	—	133	1	no	Hall
69	C₂×C₇	—	21	1	no	—
70	D₇	—	3	1	no	—
71	C₃²	—	19	1	no	Sylow
72	C₇	—	2	3	no	—
73	C₇	D₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
74	C₇	D₂₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
75	C₂×C₃	—	399	1	no	—
76	D₃	—	7	1	no	—
77	C₃	—	19	1	no	—
78	C₃	—	38	1	no	—
79	C₃	C₇×D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
80	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₂₁×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₇×C₁₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₁₉⋊C₃	C₂	semidirect
2. C₇×C₁₉×D₂₁	C₃	semidirect
5. C₇²×C₁₉⋊C₃	D₃	semidirect
6. C₃×C₇²×C₁₉	C₂×C₃	semidirect
7. D₂₁×C₁₉⋊C₃	C₇	direct (N × H)
11. C₃×C₇×C₁₉⋊C₃	D₇	semidirect
12. C₃×C₇×C₁₉⋊C₃	C₂×C₇	semidirect
13. C₇²×C₁₉	C₃×D₃	semidirect
15. C₁₉×D₂₁	C₃×C₇	semidirect
21. C₃×C₇×C₁₉	C₃×D₇	semidirect
22. C₃×C₇×C₁₉	C₂×C₃×C₇	semidirect
27. C₇×C₁₉⋊C₃	D₃×C₇	semidirect
28. C₇×C₁₉⋊C₃	D₂₁	direct (N × H)
30. C₇×D₂₁	C₁₉⋊C₃	direct (N × H)
34. C₃×C₁₉⋊C₃	C₇×D₇	semidirect
37. C₃×C₇²	C₂×C₁₉⋊C₃	semidirect
39. C₇×C₁₉	C₃×D₃×C₇	semidirect
40. C₇×C₁₉	C₃×D₂₁	semidirect
49. C₃×C₁₉	C₃×C₇×D₇	semidirect
51. C₁₉⋊C₃	C₇×D₂₁	direct (N × H)
52. C₇²	D₃×C₁₉⋊C₃	semidirect
54. D₂₁	C₇×C₁₉⋊C₃	direct (N × H)
65. C₃×C₇	D₇×C₁₉⋊C₃	semidirect
66. C₃×C₇	C₂×C₇×C₁₉⋊C₃	semidirect
67. C₁₉	C₃×C₇×D₂₁	semidirect
73. C₇	D₃×C₇×C₁₉⋊C₃	semidirect
74. C₇	D₂₁×C₁₉⋊C₃	direct (N × H)
79. C₃	C₇×D₇×C₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇²×C₁₉⋊C₃	2
C₇×C₁₉×D₂₁	3
C₇×D₇×C₁₉⋊C₃	3
D₂₁×C₁₉⋊C₃	7
D₃×C₇×C₁₉⋊C₃	7
C₃×C₇×D₂₁	19

Subgroups — C7×D21×C19⋊C3 #30660817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₂₁×C₁₉⋊C₃ #30660817