Subgroups — C₂×C₁₇×#64424 #23756214

Order 9996.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#3861	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#64424	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₇×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₇×#3861	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₇×C₇⋊D₇	C₂×C₃	1	2	yes	complemented
7	C₂×C₁₇×AGL(1,𝔽₇)	—	7	8	no	maximal
8	C₇²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₇×ΓL(1,𝔽₈)	—	7	8	no	—
10	C₁₇×AGL(1,𝔽₇)	—	7	16	no	—
11	C₂×#64424	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×D₇×C₁₇	—	7	8	no	—
13	C₁₇×ΓL(1,𝔽₈)	—	7	8	no	—
14	C₂×#3861	C₂×C₁₇	1	1	yes	characteristic, complemented
15	#64424	C₂×C₁₇	1	2	yes	direct product factor
16	C₂×C₇×C₁₇	AGL(1,𝔽₇)	1	8	yes	complemented
17	D₇×C₁₇	—	7	16	no	—
18	C₂²×C₃×C₁₇	—	49	1	no	Hall
19	C₂×C₇⋊D₇	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
20	#3861	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₇×C₁₇	C₂×AGL(1,𝔽₇)	1	8	yes	complemented
22	C₂×C₃×C₁₇	—	49	2	no	—
23	C₂×C₃×C₁₇	—	49	1	no	—
24	C₂×C₇²	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
25	C₇⋊D₇	C₂×C₃×C₁₇	1	2	yes	complemented
26	C₂×AGL(1,𝔽₇)	—	7	8	no	—
27	C₂²×C₁₇	—	49	1	no	Hall
28	C₃×C₁₇	—	49	1	no	Hall
29	C₇²	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×ΓL(1,𝔽₈)	—	7	8	no	—
31	AGL(1,𝔽₇)	—	7	16	no	—
32	C₂×C₁₇	—	49	2	no	—
33	C₂×C₁₇	#64424	1	1	yes	characteristic, direct product factor
34	C₂×D₇	—	7	8	no	—
35	ΓL(1,𝔽₈)	—	7	8	no	—
36	C₁₇	C₂×#64424	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₇	C₁₇×AGL(1,𝔽₇)	1	8	yes	complemented
38	D₇	—	7	16	no	—
39	C₂²×C₃	—	49	1	no	Hall
40	C₇	C₂×C₁₇×AGL(1,𝔽₇)	1	8	yes	complemented
41	C₂×C₃	—	49	2	no	—
42	C₂×C₃	—	49	1	no	—
43	C₂²	—	49	1	no	Sylow
44	C₃	—	49	1	no	Sylow
45	C₂	—	49	2	no	—
46	C₂	C₁₇×#64424	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	#64424
commutator, cosocle, hypocenter	C₇²	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₇	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#3861	C₂	semidirect
2. C₁₇×#64424	C₂	direct (N × H)
3. C₂×C₁₇×C₇⋊D₇	C₃	semidirect
4. C₁₇×#3861	C₂²	semidirect
5. C₂×C₇²×C₁₇	C₂×C₃	semidirect
6. C₁₇×C₇⋊D₇	C₂×C₃	semidirect
8. C₇²×C₁₇	C₂²×C₃	semidirect
11. C₂×#64424	C₁₇	direct (N × H)
14. C₂×#3861	C₂×C₁₇	semidirect
15. #64424	C₂×C₁₇	direct (N × H)
16. C₂×C₇×C₁₇	AGL(1,𝔽₇)	semidirect
19. C₂×C₇⋊D₇	C₃×C₁₇	semidirect
20. #3861	C₂²×C₁₇	semidirect
21. C₇×C₁₇	C₂×AGL(1,𝔽₇)	semidirect
24. C₂×C₇²	C₂×C₃×C₁₇	semidirect
25. C₇⋊D₇	C₂×C₃×C₁₇	semidirect
29. C₇²	C₂²×C₃×C₁₇	semidirect
33. C₂×C₁₇	#64424	direct (N × H)
36. C₁₇	C₂×#64424	direct (N × H)
37. C₂×C₇	C₁₇×AGL(1,𝔽₇)	semidirect
40. C₇	C₂×C₁₇×AGL(1,𝔽₇)	semidirect
46. C₂	C₁₇×#64424	direct (N × H)

Subgroups — C2×C17×#64424 #23756214

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₇×#64424 #23756214