Subgroups — C₁₇×#64418⋊C₂ #23756200

Order 9996.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#64418	C₂	1	2	yes	maximal, complemented
2	C₁₇×#64425	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇²×C₁₇	—	3	1	no	maximal, Hall
4	C₁₇×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×C₇⋊D₇	D₃	1	1	yes	characteristic, complemented
6	C₇×D₇×C₁₇	—	3	2	no	—
7	C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₁₇×AGL(1,𝔽₇)	—	14	1	no	—
9	#64418⋊C₂	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×D₇×C₁₇	—	21	2	no	—
11	C₁₇×ΓL(1,𝔽₈)	—	14	1	no	—
12	#64425	C₂×C₁₇	1	1	yes	characteristic, complemented
13	#64418	C₂×C₁₇	1	2	yes	complemented
14	C₂×C₇×C₁₇	—	21	2	no	—
15	D₇×C₁₇	—	3	2	no	—
16	D₇×C₁₇	—	14	1	no	—
17	D₇×C₁₇	—	21	2	no	—
18	C₂×D₃×C₁₇	—	49	1	no	maximal, Hall
19	D₇²	—	3	1	no	Hall
20	#3862	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₇×C₁₇	—	2	1	no	—
22	C₇×C₁₇	—	3	2	no	—
23	C₂×C₃×C₁₇	—	49	1	no	—
24	D₃×C₁₇	—	49	2	no	—
25	C₇⋊D₇	D₃×C₁₇	1	1	yes	characteristic, complemented
26	C₇×D₇	—	3	2	no	—
27	C₂²×C₁₇	—	147	1	no	Hall
28	C₃×C₁₇	—	49	1	no	Hall
29	C₇²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
30	AGL(1,𝔽₇)	—	14	1	no	—
31	C₂×C₁₇	—	21	2	no	—
32	C₂×C₁₇	—	49	1	no	—
33	C₂×D₇	—	21	2	no	—
34	ΓL(1,𝔽₈)	—	14	1	no	—
35	C₁₇	#64418⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₇	—	21	2	no	—
37	D₇	—	3	2	no	—
38	D₇	—	14	1	no	—
39	D₇	—	21	2	no	—
40	C₂×D₃	—	49	1	no	Hall
41	C₇	—	2	1	no	—
42	C₇	—	3	2	no	—
43	C₂×C₃	—	49	1	no	—
44	D₃	—	49	2	no	—
45	C₂²	—	147	1	no	Sylow
46	C₃	—	49	1	no	Sylow
47	C₂	—	21	2	no	—
48	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	#64418⋊C₂
commutator, cosocle, hypocenter	#3862	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₇²×C₁₇	C₂×D₃
LCS	G ▷ #3862
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×#64418	C₂	semidirect
2. C₁₇×#64425	C₂	semidirect
4. C₁₇×#3862	C₂²	semidirect
5. C₁₇×C₇⋊D₇	D₃	semidirect
7. C₇²×C₁₇	C₂×D₃	semidirect
9. #64418⋊C₂	C₁₇	direct (N × H)
12. #64425	C₂×C₁₇	semidirect
13. #64418	C₂×C₁₇	semidirect
20. #3862	C₂²×C₁₇	semidirect
25. C₇⋊D₇	D₃×C₁₇	semidirect
29. C₇²	C₂×D₃×C₁₇	semidirect
35. C₁₇	#64418⋊C₂	direct (N × H)

Subgroups — C17×#64418⋊C2 #23756200

Conjugacy classes of subgroups

Complements

Subgroups — C₁₇×#64418⋊C₂ #23756200