Subgroups — C₄³×#595 #17962907

Order 4352.

3966 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×#595	C₂	1	14	yes	maximal
2	C₄³×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×#595	C₂²	1	28	yes	—
4	C₄²×#595	C₄	1	112	yes	direct product factor
5	C₂×C₄²×D₁₇	C₂²	1	7	yes	—
6	C₄²×Dic₁₇	C₄	1	7	yes	complemented
7	C₄³×C₁₇	C₄	1	1	yes	characteristic, complemented
8	C₂³×#595	C₂³	1	8	yes	—
9	C₂²×C₄×D₁₇	C₂³	1	7	yes	—
10	C₂×C₄×#595	C₂×C₄	1	336	yes	—
11	C₂×C₄²×C₁₇	C₂×C₄	1	7	yes	—
12	C₂×C₄×Dic₁₇	C₂×C₄	1	21	yes	—
13	C₄²×D₁₇	C₂×C₄	1	56	yes	—
14	C₂³×D₁₇	C₂⁴	1	1	yes	characteristic
15	C₂²×#595	C₂²×C₄	1	112	yes	—
16	C₂²×C₄×C₁₇	C₂²×C₄	1	7	yes	—
17	C₂²×Dic₁₇	C₂²×C₄	1	7	yes	—
18	C₂×C₄×D₁₇	C₂²×C₄	1	84	yes	—
19	C₄×#595	C₄²	1	448	yes	direct product factor
20	C₄²×C₁₇	C₄²	1	28	yes	complemented
21	C₄×Dic₁₇	C₄²	1	84	yes	complemented
22	C₄⁴	—	17	1	no	maximal, Sylow
23	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
24	C₂²×D₁₇	C₂³×C₄	1	14	yes	—
25	C₂×#595	C₂×C₄²	1	224	yes	—
26	C₂×C₄×C₁₇	C₂×C₄²	1	42	yes	—
27	C₂×Dic₁₇	C₂×C₄²	1	42	yes	—
28	C₄×D₁₇	C₂×C₄²	1	112	yes	—
29	C₂×C₄³	—	17	14	no	—
30	C₂×C₄³	—	17	1	no	—
31	C₂²×C₁₇	C₂²×C₄²	1	7	yes	—
32	C₂×D₁₇	C₂²×C₄²	1	28	yes	—
33	#595	C₄³	1	64	yes	direct product factor
34	C₄×C₁₇	C₄³	1	28	yes	complemented
35	Dic₁₇	C₄³	1	28	yes	complemented
36	C₂²×C₄²	—	17	28	no	—
37	C₂²×C₄²	—	17	7	no	—
38	C₄³	—	17	112	no	—
39	C₄³	—	17	7	no	—
40	C₄³	#595	1	1	yes	characteristic, direct product factor
41	C₂×C₁₇	C₂×C₄³	1	7	yes	—
42	D₁₇	C₂×C₄³	1	8	yes	—
43	C₂³×C₄	—	17	8	no	—
44	C₂³×C₄	—	17	7	no	—
45	C₂×C₄²	—	17	336	no	—
46	C₂×C₄²	—	17	21	no	—
47	C₂×C₄²	—	17	56	no	—
48	C₂×C₄²	C₂×#595	1	7	yes	—
49	C₁₇	C₄⁴	1	1	yes	characteristic, complemented, Sylow
50	C₂⁴	—	17	1	no	—
51	C₂²×C₄	—	17	112	no	—
52	C₂²×C₄	—	17	7	no	—
53	C₂²×C₄	—	17	84	no	—
54	C₂²×C₄	C₂²×#595	1	7	yes	—
55	C₄²	—	17	448	no	—
56	C₄²	—	17	84	no	—
57	C₄²	C₄×#595	1	28	yes	direct product factor
58	C₂³	—	17	14	no	—
59	C₂³	C₂³×#595	1	1	yes	characteristic
60	C₂×C₄	—	17	224	no	—
61	C₂×C₄	—	17	42	no	—
62	C₂×C₄	—	17	112	no	—
63	C₂×C₄	C₂×C₄×#595	1	42	yes	—
64	C₂²	—	17	28	no	—
65	C₂²	C₂²×C₄×#595	1	7	yes	—
66	C₄	—	17	64	no	—
67	C₄	—	17	28	no	—
68	C₄	C₄²×#595	1	28	yes	direct product factor
69	C₂	—	17	8	no	—
70	C₂	C₂×C₄²×#595	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	#595
commutator, hypocenter	C₁₇	C₄⁴
Frattini	C₂³	C₂³×#595
Fitting	C₄³×C₁₇	C₄
socle	C₂³×C₁₇	C₂³×C₄
prime radical, cosocle	C₂³×D₁₇	C₂⁴
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
4. C₄²×#595	C₄	direct (N × H)
6. C₄²×Dic₁₇	C₄	semidirect
7. C₄³×C₁₇	C₄	semidirect
19. C₄×#595	C₄²	direct (N × H)
20. C₄²×C₁₇	C₄²	semidirect
21. C₄×Dic₁₇	C₄²	semidirect
33. #595	C₄³	direct (N × H)
34. C₄×C₁₇	C₄³	semidirect
35. Dic₁₇	C₄³	semidirect
40. C₄³	#595	direct (N × H)
49. C₁₇	C₄⁴	semidirect
57. C₄²	C₄×#595	direct (N × H)
68. C₄	C₄²×#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
C₂×C₄²×#595	2
C₄³×D₁₇	2
C₄⁴	17

Subgroups — C43×#595 #17962907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×#595 #17962907