Subgroups — C₃×C₁₇×C₇⋊#595 #37566261

Order 24276.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₇⋊#595	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₁₇×D₁₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₇×#595	—	7	1	no	maximal, Hall
6	C₇×C₁₇²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₇×D₁₇	D₇	1	1	yes	characteristic
8	C₃×C₇⋊#595	C₁₇	1	1	yes	maximal, characteristic, direct product factor
9	C₃×C₁₇×Dic₇	—	17	1	no	maximal
10	C₁₇×#595	—	7	1	no	Hall
11	C₃×C₁₇²	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₇×C₁₇	—	17	1	no	—
13	C₃×C₇×D₁₇	C₂×C₁₇	1	1	yes	characteristic
14	C₁₇×D₁₇	C₃×D₇	1	1	yes	characteristic
15	C₇⋊#595	C₃×C₁₇	1	1	yes	characteristic, direct product factor
16	C₁₇×Dic₇	—	17	1	no	—
17	C₃×C₇×C₁₇	—	4	4	no	—
18	C₃×C₇×C₁₇	C₄×C₁₇	1	1	yes	characteristic, complemented
19	C₃×C₇×C₁₇	#595	1	1	yes	characteristic, complemented
20	C₁₇²	C₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₇×C₁₇	—	17	1	no	—
22	C₇×D₁₇	C₂×C₃×C₁₇	1	1	yes	characteristic
23	C₃×#595	—	7	1	no	—
24	C₃×C₄×C₁₇	—	119	1	no	—
25	C₇×C₁₇	—	4	4	no	—
26	C₇×C₁₇	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented
27	C₇×C₁₇	C₃×#595	1	1	yes	characteristic, complemented
28	C₂×C₃×C₁₇	—	17	1	no	—
29	C₃×D₁₇	D₇×C₁₇	1	1	yes	characteristic
30	C₃×Dic₇	—	17	1	no	Hall
31	#595	—	7	1	no	—
32	C₄×C₁₇	—	119	1	no	—
33	C₃×C₁₇	—	4	4	no	—
34	C₃×C₁₇	C₁₇×Dic₇	1	1	yes	characteristic, complemented
35	C₃×C₁₇	C₇⋊#595	1	1	yes	characteristic, direct product factor
36	C₂×C₃×C₇	—	17	1	no	—
37	C₂×C₁₇	—	17	1	no	—
38	D₁₇	C₃×D₇×C₁₇	1	1	yes	characteristic
39	Dic₇	—	17	1	no	Hall
40	C₃×C₇	C₁₇×#595	1	1	yes	characteristic, complemented, Hall
41	C₁₇	—	4	4	no	—
42	C₁₇	C₃×C₁₇×Dic₇	1	1	yes	characteristic, complemented
43	C₁₇	C₃×C₇⋊#595	1	1	yes	characteristic, direct product factor
44	C₂×C₇	—	17	1	no	—
45	C₃×C₄	—	119	1	no	Hall
46	C₇	C₃×C₁₇×#595	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	17	1	no	—
48	C₄	—	119	1	no	Sylow
49	C₃	C₁₇×C₇⋊#595	1	1	yes	characteristic, direct product factor, Sylow
50	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₇⋊#595
commutator, hypocenter	C₇×C₁₇	C₃×C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇²	C₄
prime radical	C₃×C₇×C₁₇×D₁₇	C₂
cosocle	C₇×D₁₇	C₂×C₃×C₁₇
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₁₇×C₇⋊#595	C₃	direct (N × H)
3. C₃×C₇×C₁₇²	C₄	semidirect
6. C₇×C₁₇²	C₃×C₄	semidirect
8. C₃×C₇⋊#595	C₁₇	direct (N × H)
11. C₃×C₁₇²	Dic₇	semidirect
15. C₇⋊#595	C₃×C₁₇	direct (N × H)
18. C₃×C₇×C₁₇	C₄×C₁₇	semidirect
19. C₃×C₇×C₁₇	#595	semidirect
20. C₁₇²	C₃×Dic₇	semidirect
26. C₇×C₁₇	C₃×C₄×C₁₇	semidirect
27. C₇×C₁₇	C₃×#595	semidirect
34. C₃×C₁₇	C₁₇×Dic₇	semidirect
35. C₃×C₁₇	C₇⋊#595	direct (N × H)
40. C₃×C₇	C₁₇×#595	semidirect
42. C₁₇	C₃×C₁₇×Dic₇	semidirect
43. C₁₇	C₃×C₇⋊#595	direct (N × H)
46. C₇	C₃×C₁₇×#595	semidirect
49. C₃	C₁₇×C₇⋊#595	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₇×C₁₇×D₁₇	2
C₁₇×C₇⋊#595	3
C₃×C₁₇×#595	7
C₃×C₇⋊#595	17
C₃×C₁₇×Dic₇	17

Subgroups — C3×C17×C7⋊#595 #37566261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×C₇⋊#595 #37566261