Subgroups — C₁₉×D₂₁⋊D₇ #26014024

Order 11172.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×D₂₁	C₂	1	2	yes	maximal, complemented
2	C₃×C₁₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇²×C₁₉	—	3	1	no	maximal, Hall
4	C₃×C₇²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₉×C₇⋊D₇	D₃	1	1	yes	characteristic, complemented
6	C₇×D₇×C₁₉	—	3	2	no	—
7	D₃×D₇×C₁₉	—	7	2	no	maximal
8	C₇²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₁₉×D₂₁	D₇	1	2	yes	complemented
10	D₃×C₇×C₁₉	—	7	2	no	—
11	C₃×D₇×C₁₉	—	7	2	no	—
12	C₃×D₇×C₁₉	—	14	3	no	—
13	D₂₁⋊D₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×D₇×C₁₉	—	21	2	no	—
15	C₃×C₇×C₁₉	—	2	3	no	—
16	C₃×C₇×C₁₉	C₂×D₇	1	2	yes	complemented
17	C₇×D₂₁	C₂×C₁₉	1	2	yes	complemented
18	C₃×C₇⋊D₇	C₂×C₁₉	1	1	yes	characteristic, complemented
19	C₂×C₇×C₁₉	—	21	2	no	—
20	D₇×C₁₉	—	3	2	no	—
21	D₇×C₁₉	—	7	2	no	—
22	D₇×C₁₉	—	14	3	no	—
23	C₂×D₃×C₁₉	—	49	1	no	Hall
24	D₇²	—	3	1	no	Hall
25	C₃×C₇²	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
26	C₇×C₁₉	—	2	3	no	—
27	C₇×C₁₉	D₃×D₇	1	2	yes	complemented
28	C₂×C₃×C₁₉	—	49	1	no	—
29	D₃×C₁₉	—	7	2	no	—
30	C₇⋊D₇	D₃×C₁₉	1	1	yes	characteristic, complemented
31	C₇×D₇	—	3	2	no	—
32	D₃×D₇	—	7	2	no	—
33	C₂²×C₁₉	—	147	1	no	Hall
34	C₃×C₁₉	D₇²	1	1	yes	characteristic, complemented, Hall
35	C₇²	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
36	D₂₁	D₇×C₁₉	1	2	yes	complemented
37	C₃×D₇	—	7	2	no	—
38	C₃×D₇	—	14	3	no	—
39	D₃×C₇	—	7	2	no	—
40	C₂×C₁₉	—	21	2	no	—
41	C₂×C₁₉	—	49	1	no	—
42	C₂×D₇	—	21	2	no	—
43	C₃×C₇	—	2	3	no	—
44	C₃×C₇	C₂×D₇×C₁₉	1	2	yes	complemented
45	C₁₉	D₂₁⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₇	—	21	2	no	—
47	D₇	—	3	2	no	—
48	D₇	—	7	2	no	—
49	D₇	—	14	3	no	—
50	C₂×D₃	—	49	1	no	Hall
51	C₇	—	2	3	no	—
52	C₇	D₃×D₇×C₁₉	1	2	yes	complemented
53	C₂×C₃	—	49	1	no	—
54	D₃	—	7	2	no	—
55	C₂²	—	147	1	no	Sylow
56	C₃	D₇²×C₁₉	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	21	2	no	—
58	C₂	—	49	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×D₂₁	C₂	semidirect
2. C₃×C₁₉×C₇⋊D₇	C₂	semidirect
4. C₃×C₇²×C₁₉	C₂²	semidirect
5. C₁₉×C₇⋊D₇	D₃	semidirect
8. C₇²×C₁₉	C₂×D₃	semidirect
9. C₁₉×D₂₁	D₇	semidirect
13. D₂₁⋊D₇	C₁₉	direct (N × H)
16. C₃×C₇×C₁₉	C₂×D₇	semidirect
17. C₇×D₂₁	C₂×C₁₉	semidirect
18. C₃×C₇⋊D₇	C₂×C₁₉	semidirect
25. C₃×C₇²	C₂²×C₁₉	semidirect
27. C₇×C₁₉	D₃×D₇	semidirect
30. C₇⋊D₇	D₃×C₁₉	semidirect
34. C₃×C₁₉	D₇²	semidirect
35. C₇²	C₂×D₃×C₁₉	semidirect
36. D₂₁	D₇×C₁₉	semidirect
44. C₃×C₇	C₂×D₇×C₁₉	semidirect
45. C₁₉	D₂₁⋊D₇	direct (N × H)
52. C₇	D₃×D₇×C₁₉	semidirect
56. C₃	D₇²×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×D₂₁	2
C₃×C₁₉×C₇⋊D₇	2
D₇²×C₁₉	3
D₃×D₇×C₁₉	7
D₂₁⋊D₇	19

Subgroups — C19×D21⋊D7 #26014024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₂₁⋊D₇ #26014024