Subgroups — D₇×C₁₉×C₇⋊C₉ #30660604

Order 16758.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₇×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
4	C₉×D₇×C₁₉	—	7	1	no	maximal
5	C₂×C₁₉×C₇⋊C₉	—	7	1	no	maximal
6	C₇×D₇×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	C₇×C₉×C₁₉	—	7	1	no	—
8	C₁₉×C₇⋊C₉	D₇	1	1	yes	characteristic, direct product factor
9	C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	D₇×C₇⋊C₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₁₉	—	7	1	no	—
12	C₃×D₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₇×C₇⋊C₉	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₇×C₁₉	—	6	1	no	—
15	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₃×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic
17	C₂×C₉×C₁₉	—	49	1	no	Hall
18	C₃×C₇×D₇	C₃×C₁₉	1	1	yes	characteristic
19	C₂×C₇×C₁₉	—	7	1	no	—
20	D₇×C₁₉	C₇⋊C₉	1	1	yes	characteristic, direct product factor
21	C₉×C₁₉	—	7	1	no	Hall
22	C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
23	C₇×C₁₉	—	6	1	no	—
24	C₇×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
25	C₇×C₁₉	C₉×D₇	1	1	yes	characteristic, complemented
26	C₉×D₇	—	7	1	no	—
27	C₂×C₇⋊C₉	—	7	1	no	—
28	C₂×C₃×C₁₉	—	7	1	no	—
29	C₇×D₇	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₇×C₉	—	7	1	no	—
31	C₇⋊C₉	D₇×C₁₉	1	1	yes	characteristic, direct product factor
32	C₃×C₁₉	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₇	—	7	1	no	—
35	C₃×D₇	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
36	C₂×C₁₉	—	7	1	no	Hall
37	C₃×C₇	—	6	1	no	—
38	C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
39	C₃×C₇	C₃×D₇×C₁₉	1	1	yes	characteristic
40	C₁₉	D₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₉	—	49	1	no	Hall
42	C₂×C₇	—	7	1	no	—
43	D₇	C₁₉×C₇⋊C₉	1	1	yes	characteristic, direct product factor
44	C₉	—	7	1	no	Sylow
45	C₇	—	6	1	no	—
46	C₇	C₂×C₁₉×C₇⋊C₉	1	1	yes	characteristic, complemented
47	C₇	C₉×D₇×C₁₉	1	1	yes	characteristic, complemented
48	C₂×C₃	—	7	1	no	—
49	C₃	D₇×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
50	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₇×ΓL(1,𝔽₈)
commutator, hypocenter	C₇²	C₂×C₉×C₁₉
Frattini	C₃	D₇×C₁₉×ΓL(1,𝔽₈)
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₃×C₇×D₇×C₁₉	C₃
cosocle	C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×C₇⋊C₉	C₂	semidirect
6. C₇×D₇×C₁₉	C₉	semidirect
8. C₁₉×C₇⋊C₉	D₇	direct (N × H)
9. C₇²×C₁₉	C₂×C₉	semidirect
10. D₇×C₇⋊C₉	C₁₉	direct (N × H)
13. C₇×C₇⋊C₉	C₂×C₁₉	semidirect
20. D₇×C₁₉	C₇⋊C₉	direct (N × H)
24. C₇×C₁₉	C₂×C₇⋊C₉	semidirect
25. C₇×C₁₉	C₉×D₇	semidirect
29. C₇×D₇	C₉×C₁₉	semidirect
31. C₇⋊C₉	D₇×C₁₉	direct (N × H)
33. C₇²	C₂×C₉×C₁₉	semidirect
40. C₁₉	D₇×C₇⋊C₉	direct (N × H)
43. D₇	C₁₉×C₇⋊C₉	direct (N × H)
46. C₇	C₂×C₁₉×C₇⋊C₉	semidirect
47. C₇	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
C₇×C₁₉×C₇⋊C₉	2
C₃×C₇×D₇×C₁₉	3
C₉×D₇×C₁₉	7
C₂×C₁₉×C₇⋊C₉	7
D₇×C₇⋊C₉	19

Subgroups — D7×C19×C7⋊C9 #30660604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₁₉×C₇⋊C₉ #30660604