Subgroups — C₂×C₁₇×#64418 #23756228

Order 9996.

68 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	C₁₇×#64418	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₇×C₁₇	—	3	1	no	maximal, Hall
4	C₁₇×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₇	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	C₂×C₁₇×ΓL(1,𝔽₈)	—	14	1	no	—
9	C₂×#64418	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₇×C₁₇	—	21	1	no	—
11	C₂×D₇×C₁₇	—	3	1	no	—
12	C₁₇×ΓL(1,𝔽₈)	—	14	1	no	—
13	C₂×#3862	C₂×C₁₇	1	1	yes	characteristic, complemented
14	#64418	C₂×C₁₇	1	2	yes	direct product factor
15	C₂×C₇×C₁₇	—	2	1	no	—
16	C₂×C₇×C₁₇	—	3	1	no	—
17	C₂×C₇×C₁₇	—	3	1	no	—
18	C₂×C₇×C₁₇	—	21	2	no	—
19	D₇×C₁₇	—	3	2	no	—
20	C₂×D₃×C₁₇	—	49	1	no	maximal, Hall
21	C₂×C₇×D₇	—	3	1	no	Hall
22	#3862	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
23	C₇×C₁₇	—	2	1	no	—
24	C₇×C₁₇	—	3	1	no	—
25	C₇×C₁₇	—	3	1	no	—
26	C₂×C₃×C₁₇	—	49	1	no	—
27	D₃×C₁₇	—	49	2	no	—
28	C₂×C₇²	D₃×C₁₇	1	1	yes	characteristic, complemented
29	C₇×D₇	—	3	2	no	—
30	C₂²×C₁₇	—	21	1	no	Hall
31	C₃×C₁₇	—	49	1	no	Hall
32	C₇²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
33	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
34	C₂×C₁₇	—	21	2	no	—
35	C₂×C₁₇	#64418	1	1	yes	characteristic, direct product factor
36	C₂²×C₇	—	21	1	no	—
37	C₂×D₇	—	3	1	no	—
38	ΓL(1,𝔽₈)	—	14	1	no	—
39	C₁₇	C₂×#64418	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	—	2	1	no	—
41	C₂×C₇	—	3	1	no	—
42	C₂×C₇	—	3	1	no	—
43	C₂×C₇	—	21	2	no	—
44	D₇	—	3	2	no	—
45	C₂×D₃	—	49	1	no	Hall
46	C₇	—	2	1	no	—
47	C₇	—	3	1	no	—
48	C₇	—	3	1	no	—
49	C₂×C₃	—	49	1	no	—
50	D₃	—	49	2	no	—
51	C₂²	—	21	1	no	Sylow
52	C₃	—	49	1	no	Sylow
53	C₂	—	21	2	no	—
54	C₂	C₁₇×#64418	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#3862	C₂	semidirect
2. C₁₇×#64418	C₂	direct (N × H)
4. C₁₇×#3862	C₂²	semidirect
5. C₂×C₇²×C₁₇	D₃	semidirect
7. C₇²×C₁₇	C₂×D₃	semidirect
9. C₂×#64418	C₁₇	direct (N × H)
13. C₂×#3862	C₂×C₁₇	semidirect
14. #64418	C₂×C₁₇	direct (N × H)
22. #3862	C₂²×C₁₇	semidirect
28. C₂×C₇²	D₃×C₁₇	semidirect
32. C₇²	C₂×D₃×C₁₇	semidirect
35. C₂×C₁₇	#64418	direct (N × H)
39. C₁₇	C₂×#64418	direct (N × H)
54. C₂	C₁₇×#64418	direct (N × H)

Subgroups — C2×C17×#64418 #23756228

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₇×#64418 #23756228