Subgroups — C₇×C₃⋊(C₇⋊#595) #23756243

Order 9996.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₇⋊#595	—	3	1	no	maximal, Hall
3	C₃×C₇²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇²×D₁₇	D₃	1	1	yes	characteristic
5	C₃⋊(C₇⋊#595)	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×C₃⋊#595	—	7	1	no	maximal
7	C₇²×C₁₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×D₁₇	—	2	3	no	—
9	C₃×C₇×D₁₇	D₇	1	1	yes	characteristic
10	C₃×C₇×D₁₇	C₂×C₇	1	1	yes	characteristic
11	C₇×Dic₂₁	—	17	1	no	maximal, Hall
12	C₇⋊#595	—	3	1	no	—
13	C₇×#595	—	21	1	no	—
14	C₃×C₇×C₁₇	—	2	3	no	—
15	C₃×C₇×C₁₇	Dic₇	1	1	yes	characteristic, complemented
16	C₃×C₇×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented
17	C₂×C₃×C₇²	—	17	1	no	—
18	C₇×D₁₇	—	2	3	no	—
19	C₇×D₁₇	D₃×C₇	1	1	yes	characteristic
20	C₇×D₁₇	D₂₁	1	1	yes	characteristic
21	C₃⋊#595	—	7	1	no	Hall
22	C₇×Dic₇	—	51	1	no	Hall
23	C₃×C₇²	#595	1	1	yes	characteristic, complemented, Hall
24	C₇×C₁₇	—	2	3	no	—
25	C₇×C₁₇	C₇×Dic₃	1	1	yes	characteristic, complemented
26	C₇×C₁₇	Dic₂₁	1	1	yes	characteristic, complemented
27	C₃×D₁₇	C₇×D₇	1	1	yes	characteristic
28	C₂×C₇²	—	17	1	no	—
29	Dic₂₁	—	17	1	no	—
30	C₇×Dic₃	—	119	1	no	—
31	#595	—	21	1	no	Hall
32	C₃×C₁₇	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
33	C₇²	C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₇	—	17	1	no	—
35	C₂×C₃×C₇	—	17	1	no	—
36	C₂×C₃×C₇	—	34	3	no	—
37	D₁₇	C₇×D₂₁	1	1	yes	characteristic
38	C₄×C₇	—	357	1	no	—
39	Dic₇	—	51	1	no	—
40	C₃×C₇	—	2	3	no	—
41	C₃×C₇	C₇×#595	1	1	yes	characteristic, complemented
42	C₃×C₇	C₇⋊#595	1	1	yes	characteristic, complemented
43	C₁₇	C₇×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₇	—	17	1	no	—
45	C₂×C₇	—	17	1	no	—
46	C₂×C₇	—	34	3	no	—
47	Dic₃	—	119	1	no	Hall
48	C₇	—	2	3	no	—
49	C₇	C₇×C₃⋊#595	1	1	yes	characteristic, complemented
50	C₇	C₃⋊(C₇⋊#595)	1	1	yes	characteristic, direct product factor
51	C₂×C₃	—	17	1	no	—
52	C₄	—	357	1	no	Sylow
53	C₃	C₇×C₇⋊#595	1	1	yes	characteristic, complemented, Sylow
54	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₃⋊(C₇⋊#595)
commutator, hypocenter	C₃×C₇×C₁₇	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₇	C₄
prime radical	C₃×C₇²×D₁₇	C₂
cosocle	C₃×C₇×D₁₇	C₂×C₇
LCS	G ▷ C₃×C₇×C₁₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₇²×C₁₇	C₄	semidirect
5. C₃⋊(C₇⋊#595)	C₇	direct (N × H)
7. C₇²×C₁₇	Dic₃	semidirect
15. C₃×C₇×C₁₇	Dic₇	semidirect
16. C₃×C₇×C₁₇	C₄×C₇	semidirect
23. C₃×C₇²	#595	semidirect
25. C₇×C₁₇	C₇×Dic₃	semidirect
26. C₇×C₁₇	Dic₂₁	semidirect
32. C₃×C₁₇	C₇×Dic₇	semidirect
33. C₇²	C₃⋊#595	semidirect
41. C₃×C₇	C₇×#595	semidirect
42. C₃×C₇	C₇⋊#595	semidirect
43. C₁₇	C₇×Dic₂₁	semidirect
49. C₇	C₇×C₃⋊#595	semidirect
50. C₇	C₃⋊(C₇⋊#595)	direct (N × H)
53. C₃	C₇×C₇⋊#595	semidirect

Subgroups — C7×C3⋊(C7⋊#595) #23756243

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₃⋊(C₇⋊#595) #23756243