Subgroups — C₂×D₁₇×#3862 #23756225

Order 9996.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#3862	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₇×#3862	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²×D₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₇×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇²×D₁₇	C₂×C₃	1	2	yes	complemented
7	C₂×ΓL(1,𝔽₈)×D₁₇	—	7	2	no	maximal
8	C₇²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₇×ΓL(1,𝔽₈)	—	7	2	no	—
10	ΓL(1,𝔽₈)×D₁₇	—	7	4	no	—
11	C₂²×#3862	—	17	1	no	maximal, Hall
12	C₂×C₇×D₁₇	—	3	2	no	—
13	C₂×C₇×D₁₇	ΓL(1,𝔽₈)	1	2	yes	complemented
14	C₁₇×ΓL(1,𝔽₈)	—	7	2	no	—
15	C₂×#3862	—	17	2	no	—
16	C₂×#3862	D₁₇	1	1	yes	characteristic, direct product factor
17	C₂×C₇×C₁₇	—	3	2	no	—
18	C₂×C₇×C₁₇	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
19	C₇×D₁₇	—	3	4	no	—
20	C₇×D₁₇	C₂×ΓL(1,𝔽₈)	1	4	yes	complemented
21	C₂×C₃×D₁₇	—	49	1	no	Hall
22	C₂²×C₇²	—	17	1	no	Hall
23	#3862	C₂×D₁₇	1	1	yes	characteristic, direct product factor, Hall
24	C₇×C₁₇	—	3	2	no	—
25	C₇×C₁₇	C₂²×ΓL(1,𝔽₈)	1	2	yes	complemented
26	C₂×C₃×C₁₇	—	49	1	no	—
27	C₃×D₁₇	—	49	2	no	—
28	C₂×C₇²	—	17	2	no	—
29	C₂×C₇²	C₃×D₁₇	1	1	yes	characteristic, complemented
30	C₂²×ΓL(1,𝔽₈)	—	119	2	no	—
31	C₂×D₁₇	#3862	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₇	—	49	1	no	Hall
33	C₇²	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
34	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
35	C₂×ΓL(1,𝔽₈)	—	119	4	no	—
36	C₂×C₁₇	C₂×#3862	1	1	yes	characteristic, complemented
37	D₁₇	C₂×#3862	1	2	yes	direct product factor
38	C₂²×C₇	—	17	2	no	—
39	C₂²×C₇	—	51	2	no	—
40	ΓL(1,𝔽₈)	—	7	2	no	—
41	C₁₇	C₂²×#3862	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₇	—	3	2	no	—
43	C₂×C₇	—	17	4	no	—
44	C₂×C₇	—	51	4	no	—
45	C₂×C₇	ΓL(1,𝔽₈)×D₁₇	1	2	yes	complemented
46	C₂²×C₃	—	833	1	no	Hall
47	C₇	—	3	2	no	—
48	C₇	C₂×ΓL(1,𝔽₈)×D₁₇	1	2	yes	complemented
49	C₂×C₃	—	49	1	no	—
50	C₂×C₃	—	833	2	no	—
51	C₂²	—	17	1	no	Sylow
52	C₃	—	49	1	no	Sylow
53	C₂	—	17	2	no	—
54	C₂	D₁₇×#3862	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₇×#3862
commutator, cosocle, hypocenter	C₇²×C₁₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₇	C₂×C₃
LCS	G ▷ C₇²×C₁₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#3862	C₂	semidirect
2. D₁₇×#3862	C₂	direct (N × H)
3. C₂×C₇²×D₁₇	C₃	semidirect
4. C₁₇×#3862	C₂²	semidirect
5. C₂×C₇²×C₁₇	C₂×C₃	semidirect
6. C₇²×D₁₇	C₂×C₃	semidirect
8. C₇²×C₁₇	C₂²×C₃	semidirect
13. C₂×C₇×D₁₇	ΓL(1,𝔽₈)	semidirect
16. C₂×#3862	D₁₇	direct (N × H)
18. C₂×C₇×C₁₇	C₂×ΓL(1,𝔽₈)	semidirect
20. C₇×D₁₇	C₂×ΓL(1,𝔽₈)	semidirect
23. #3862	C₂×D₁₇	direct (N × H)
25. C₇×C₁₇	C₂²×ΓL(1,𝔽₈)	semidirect
29. C₂×C₇²	C₃×D₁₇	semidirect
31. C₂×D₁₇	#3862	direct (N × H)
33. C₇²	C₂×C₃×D₁₇	semidirect
36. C₂×C₁₇	C₂×#3862	semidirect
37. D₁₇	C₂×#3862	direct (N × H)
41. C₁₇	C₂²×#3862	semidirect
45. C₂×C₇	ΓL(1,𝔽₈)×D₁₇	semidirect
48. C₇	C₂×ΓL(1,𝔽₈)×D₁₇	semidirect
54. C₂	D₁₇×#3862	direct (N × H)

Subgroups — C2×D17×#3862 #23756225

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₁₇×#3862 #23756225