Subgroups — C₉×C₁₉×C₇⋊D₇ #30660626

Order 16758.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
4	C₉×D₇×C₁₉	—	7	8	no	maximal
5	C₁₉×C₇⋊D₇	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₇×C₉×C₁₉	D₇	1	8	yes	complemented
7	C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₉×C₇⋊D₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×D₇×C₁₉	—	7	8	no	—
10	C₇²×C₉	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₉	C₃×D₇	1	8	yes	—
12	C₂×C₉×C₁₉	—	49	1	no	Hall
13	C₃×C₇⋊D₇	C₃×C₁₉	1	1	yes	characteristic
14	D₇×C₁₉	—	7	8	no	—
15	C₉×C₁₉	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
17	C₇×C₁₉	C₉×D₇	1	8	yes	complemented
18	C₉×D₇	—	7	8	no	—
19	C₂×C₃×C₁₉	—	49	1	no	—
20	C₇⋊D₇	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
21	C₇×C₉	D₇×C₁₉	1	8	yes	complemented
22	C₃×C₁₉	C₃×C₇⋊D₇	1	1	yes	characteristic
23	C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
24	C₃×D₇	—	7	8	no	—
25	C₂×C₁₉	—	49	1	no	Hall
26	C₃×C₇	C₃×D₇×C₁₉	1	8	yes	—
27	C₁₉	C₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	—	49	1	no	Hall
29	D₇	—	7	8	no	—
30	C₉	C₁₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₇	C₉×D₇×C₁₉	1	8	yes	complemented
32	C₂×C₃	—	49	1	no	—
33	C₃	C₃×C₁₉×C₇⋊D₇	1	1	yes	characteristic
34	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₁₉	C₇⋊D₇
commutator, hypocenter	C₇²	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×C₇⋊D₇
Fitting	C₇²×C₉×C₁₉	C₂
socle	C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₃×C₁₉×C₇⋊D₇	C₃
cosocle	C₃×C₇²	C₂×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. C₇²×C₉×C₁₉	C₂	semidirect
5. C₁₉×C₇⋊D₇	C₉	direct (N × H)
6. C₇×C₉×C₁₉	D₇	semidirect
7. C₇²×C₁₉	C₂×C₉	semidirect
8. C₉×C₇⋊D₇	C₁₉	direct (N × H)
10. C₇²×C₉	C₂×C₁₉	semidirect
15. C₉×C₁₉	C₇⋊D₇	direct (N × H)
17. C₇×C₁₉	C₉×D₇	semidirect
20. C₇⋊D₇	C₉×C₁₉	direct (N × H)
21. C₇×C₉	D₇×C₁₉	semidirect
23. C₇²	C₂×C₉×C₁₉	semidirect
27. C₁₉	C₉×C₇⋊D₇	direct (N × H)
30. C₉	C₁₉×C₇⋊D₇	direct (N × H)
31. 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
C₇²×C₉×C₁₉	2
C₃×C₁₉×C₇⋊D₇	3
C₉×D₇×C₁₉	7
C₉×C₇⋊D₇	19

Subgroups — C9×C19×C7⋊D7 #30660626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₉×C₇⋊D₇ #30660626