Subgroups — C₉⋊(C₁₉⋊#5997) #45691687

Order 33516.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊#5997)	—	3	1	no	maximal
3	C₇²×C₉×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×C₇⋊D₇	D₃	1	1	yes	characteristic
5	C₁₉⋊#5997	—	9	1	no	Hall
6	C₃×C₇²×C₁₉	Dic₃	1	1	yes	characteristic
7	C₉×D₇×C₁₉	—	14	4	no	—
8	C₁₉×C₇⋊D₇	D₉	1	1	yes	characteristic
9	C₉⋊#5997	—	19	1	no	maximal, Hall
10	C₇×C₉×C₁₉	—	2	4	no	—
11	C₇²×C₁₉	Dic₉	1	1	yes	characteristic, complemented, Hall
12	C₉×C₇⋊D₇	D₁₉	1	1	yes	characteristic
13	C₃×D₇×C₁₉	—	14	4	no	—
14	Dic₁₇₁	—	49	1	no	maximal, Hall
15	C₃⋊#5997	—	57	1	no	—
16	C₇²×C₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇×C₁₉	—	2	4	no	—
18	C₂×C₉×C₁₉	—	49	1	no	—
19	C₃×C₇⋊D₇	D₅₇	1	1	yes	characteristic
20	D₇×C₁₉	—	14	4	no	—
21	Dic₅₇	—	147	1	no	—
22	#5997	—	171	1	no	Hall
23	C₉×C₁₉	#5997	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇²	Dic₅₇	1	1	yes	characteristic
25	C₇×C₁₉	—	2	4	no	—
26	C₉×D₇	—	14	4	no	—
27	C₂×C₃×C₁₉	—	49	1	no	—
28	C₇⋊D₇	D₁₇₁	1	1	yes	characteristic
29	Dic₁₉	—	441	1	no	Hall
30	C₇×C₉	—	2	4	no	—
31	C₃×C₁₉	C₃⋊#5997	1	1	yes	characteristic
32	C₇²	Dic₁₇₁	1	1	yes	characteristic, complemented, Sylow
33	C₃×D₇	—	14	4	no	—
34	C₂×C₁₉	—	49	1	no	—
35	Dic₉	—	931	1	no	Hall
36	C₃×C₇	—	2	4	no	—
37	C₁₉	C₉⋊#5997	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₉	—	49	1	no	—
39	D₇	—	14	4	no	—
40	Dic₃	—	2793	1	no	—
41	C₉	C₁₉⋊#5997	1	1	yes	characteristic, complemented, Sylow
42	C₇	—	2	4	no	—
43	C₂×C₃	—	49	1	no	—
44	C₄	—	8379	1	no	Sylow
45	C₃	C₃⋊(C₁₉⋊#5997)	1	1	yes	characteristic
46	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₇²×C₉×C₁₉	C₄
Frattini	C₃	C₃⋊(C₁₉⋊#5997)
socle	C₃×C₇²×C₁₉	Dic₃
prime radical	C₃×C₁₉×C₇⋊D₇	D₃
cosocle	C₉×C₁₉×C₇⋊D₇	C₂
LCS	G ▷ C₇²×C₉×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₇²×C₉×C₁₉	C₄	semidirect
11. C₇²×C₁₉	Dic₉	semidirect
16. C₇²×C₉	Dic₁₉	semidirect
23. C₉×C₁₉	#5997	semidirect
32. C₇²	Dic₁₇₁	semidirect
37. C₁₉	C₉⋊#5997	semidirect
41. C₉	C₁₉⋊#5997	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₁₉×C₇⋊D₇	2
C₃⋊(C₁₉⋊#5997)	3
C₉⋊#5997	19
Dic₁₇₁	49

Subgroups — C9⋊(C19⋊#5997) #45691687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊(C₁₉⋊#5997) #45691687