Subgroups — C₂×D₁₇×#401 #17200617

Order 4352.

2942 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇⋊#401	C₂	1	7	yes	maximal, complemented
2	D₁₇×#401	C₂	1	16	yes	maximal, direct product factor
3	C₂×#95×D₁₇	C₂	1	7	yes	maximal
4	C₂×C₁₇×#401	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₄×D₁₇	C₂²	1	7	yes	—
6	C₁₇⋊#401	C₂²	1	56	yes	complemented
7	C₂×#10587502	C₂²	1	21	yes	—
8	#95×D₁₇	C₂²	1	56	yes	—
9	C₁₇×#401	C₂²	1	8	yes	complemented
10	C₂×C₁₇×#95	C₂²	1	7	yes	—
11	C₂⁴×D₁₇	C₂³	1	1	yes	characteristic
12	C₂³×C₄×C₁₇	C₂³	1	7	yes	—
13	C₂³×Dic₁₇	C₂³	1	7	yes	—
14	C₂²×C₄×D₁₇	—	2	84	no	—
15	C₂²×C₄×D₁₇	C₂³	1	28	yes	—
16	C₁₇×#95	C₂³	1	28	yes	—
17	#10587502	C₂³	1	84	yes	—
18	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
19	C₂³×D₁₇	#41	1	28	yes	—
20	C₂³×D₁₇	C₂⁴	1	2	yes	—
21	C₂²×C₄×C₁₇	—	2	42	no	—
22	C₂²×C₄×C₁₇	C₂⁴	1	14	yes	—
23	C₂²×Dic₁₇	—	2	42	no	—
24	C₂²×Dic₁₇	C₂⁴	1	14	yes	—
25	C₂×C₄×D₁₇	—	2	168	no	—
26	C₂×C₄×D₁₇	—	4	112	no	—
27	C₂²×#401	—	17	1	no	maximal, Sylow
28	C₂³×C₁₇	C₂×#41	1	14	yes	—
29	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
30	C₂²×D₁₇	#126	1	112	yes	—
31	C₂²×D₁₇	C₂×#41	1	28	yes	—
32	C₂×C₄×C₁₇	—	2	42	no	—
33	C₂×C₄×C₁₇	—	4	28	no	—
34	C₂×Dic₁₇	—	2	42	no	—
35	C₂×Dic₁₇	—	4	28	no	—
36	C₄×D₁₇	—	4	112	no	—
37	C₂×#401	—	17	16	no	—
38	C₂×#401	—	17	7	no	—
39	C₂×#401	D₁₇	1	1	yes	characteristic, direct product factor
40	C₂²×#95	—	17	7	no	—
41	C₂²×C₁₇	C₂×#126	1	28	yes	—
42	C₂²×C₁₇	C₂²×#41	1	7	yes	—
43	C₂×D₁₇	#401	1	64	yes	direct product factor
44	C₂×D₁₇	C₂×#126	1	56	yes	—
45	C₄×C₁₇	—	4	14	no	—
46	Dic₁₇	—	4	14	no	—
47	C₂⁴×C₄	—	17	7	no	—
48	#401	—	17	56	no	—
49	#401	C₂×D₁₇	1	8	yes	direct product factor
50	C₂×#95	—	17	21	no	—
51	C₂×#95	—	17	56	no	—
52	C₂×#95	C₂×D₁₇	1	7	yes	—
53	C₂×C₁₇	C₂×#401	1	8	yes	complemented
54	C₂×C₁₇	C₂²×#126	1	7	yes	—
55	D₁₇	C₂×#401	1	16	yes	direct product factor
56	C₂⁵	—	17	1	no	—
57	C₂³×C₄	—	17	7	no	—
58	C₂³×C₄	—	17	28	no	—
59	C₂³×C₄	—	34	84	no	—
60	C₂³×C₄	C₂²×D₁₇	1	7	yes	—
61	#95	—	17	84	no	—
62	#95	C₂²×D₁₇	1	28	yes	—
63	C₁₇	C₂²×#401	1	1	yes	characteristic, complemented, Sylow
64	C₂⁴	—	17	28	no	—
65	C₂⁴	—	17	2	no	—
66	C₂⁴	C₂³×D₁₇	1	1	yes	characteristic
67	C₂²×C₄	—	2	42	no	—
68	C₂²×C₄	—	17	14	no	—
69	C₂²×C₄	—	34	168	no	—
70	C₂²×C₄	—	34	42	no	—
71	C₂²×C₄	—	68	112	no	—
72	C₂²×C₄	C₂³×D₁₇	1	14	yes	—
73	C₂³	—	17	112	no	—
74	C₂³	—	17	28	no	—
75	C₂³	#41×D₁₇	1	14	yes	—
76	C₂³	C₂⁴×D₁₇	1	1	yes	characteristic
77	C₂×C₄	—	2	42	no	—
78	C₂×C₄	—	4	28	no	—
79	C₂×C₄	—	34	42	no	—
80	C₂×C₄	—	68	112	no	—
81	C₂×C₄	—	68	28	no	—
82	C₂²	—	17	56	no	—
83	C₂²	—	17	64	no	—
84	C₂²	#126×D₁₇	1	28	yes	—
85	C₂²	C₂×#41×D₁₇	1	7	yes	—
86	C₄	—	4	14	no	—
87	C₄	—	68	14	no	—
88	C₂	—	17	16	no	—
89	C₂	D₁₇×#401	1	8	yes	direct product factor
90	C₂	C₂×#126×D₁₇	1	7	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₇
commutator, cosocle	C₂³×C₁₇	C₂⁵
Frattini	C₂³	C₂⁴×D₁₇
Fitting	C₂×C₁₇×#401	C₂
socle	C₂⁴×C₁₇	C₂⁴
prime radical	C₂⁴×D₁₇	C₂³
hypercenter	C₂×#401	D₁₇
hypocenter	C₁₇	C₂²×#401
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#401

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇⋊#401	C₂	semidirect
2. D₁₇×#401	C₂	direct (N × H)
4. C₂×C₁₇×#401	C₂	semidirect
6. C₁₇⋊#401	C₂²	semidirect
9. C₁₇×#401	C₂²	semidirect
39. C₂×#401	D₁₇	direct (N × H)
43. C₂×D₁₇	#401	direct (N × H)
49. #401	C₂×D₁₇	direct (N × H)
53. C₂×C₁₇	C₂×#401	semidirect
55. D₁₇	C₂×#401	direct (N × H)
63. C₁₇	C₂²×#401	semidirect
89. C₂	D₁₇×#401	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×C₁₇⋊#401	2
D₁₇×#401	2
C₂×#95×D₁₇	2
C₂×C₁₇×#401	2
C₂²×#401	17

Subgroups — C2×D17×#401 #17200617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₇×#401 #17200617