Subgroups — #401×#595 #17963117

Order 4352.

1222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543971	C₂	1	7	yes	maximal
2	#95×#595	C₂	1	7	yes	maximal
3	D₁₇×#401	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×#595	C₂²	1	7	yes	—
5	C₂×(C₂×#595)⋊C₄	C₂²	1	21	yes	—
6	C₁₇⋊#401	C₄	1	7	yes	complemented
7	#95×D₁₇	C₂²	1	7	yes	—
8	C₁₇×#401	C₄	1	1	yes	characteristic, complemented
9	C₂³×#595	C₂³	1	7	yes	—
10	C₂³×#595	C₂³	1	1	yes	characteristic
11	C₂²×C₄×D₁₇	C₂³	1	7	yes	—
12	C₂×C₄×#595	—	2	42	no	—
13	(C₂×#595)⋊C₄	—	2	42	no	—
14	C₁₇×#95	C₂×C₄	1	7	yes	—
15	#10587502	C₂×C₄	1	21	yes	—
16	C₂³×D₁₇	C₂⁴	1	1	yes	characteristic
17	C₂²×#595	—	2	21	no	—
18	C₂²×#595	—	2	21	no	—
19	C₂²×#595	#41	1	14	yes	—
20	C₂²×#595	#41	1	14	yes	—
21	C₂²×C₄×C₁₇	C₂²×C₄	1	7	yes	—
22	C₂²×Dic₁₇	C₂²×C₄	1	7	yes	—
23	C₂×C₄×D₁₇	—	2	21	no	—
24	C₂×C₄×D₁₇	—	2	21	no	—
25	C₄×#595	—	4	28	no	—
26	C₄×#401	—	17	1	no	maximal, Sylow
27	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
28	C₂²×D₁₇	C₂×#41	1	7	yes	—
29	C₂²×D₁₇	C₂×#41	1	7	yes	—
30	C₂×#595	—	2	42	no	—
31	C₂×#595	—	4	7	no	—
32	C₂×#595	—	4	21	no	—
33	C₂×#595	#126	1	28	yes	—
34	C₂×C₄×C₁₇	—	2	21	no	—
35	C₂×Dic₁₇	—	2	21	no	—
36	C₄×D₁₇	—	4	7	no	—
37	C₄×D₁₇	—	4	21	no	—
38	C₂×#401	—	17	1	no	—
39	#1443	—	17	7	no	—
40	C₄×#95	—	17	7	no	—
41	C₂²×C₁₇	C₄×#41	1	7	yes	—
42	C₂×D₁₇	C₂×#126	1	7	yes	—
43	C₂×D₁₇	#529	1	21	yes	—
44	#595	—	4	14	no	—
45	#595	#401	1	8	yes	direct product factor
46	C₄×C₁₇	—	4	7	no	—
47	Dic₁₇	—	4	7	no	—
48	C₂²×C₄²	—	17	7	no	—
49	#401	—	17	7	no	—
50	#401	#595	1	1	yes	characteristic, direct product factor
51	C₂×#95	—	17	7	no	—
52	C₂×#95	—	17	21	no	—
53	C₂×C₁₇	C₄×#126	1	7	yes	—
54	D₁₇	C₂×#401	1	1	yes	characteristic
55	D₁₇	#2401	1	7	yes	—
56	C₂³×C₄	—	17	1	no	—
57	C₂³×C₄	—	17	7	no	—
58	C₂³×C₄	—	17	7	no	—
59	C₂×C₄²	—	34	42	no	—
60	#95	—	17	21	no	—
61	#95	—	34	42	no	—
62	#95	C₂×#595	1	7	yes	—
63	C₁₇	C₄×#401	1	1	yes	characteristic, complemented, Sylow
64	C₂⁴	—	17	1	no	—
65	C₂²×C₄	—	17	14	no	—
66	C₂²×C₄	—	17	14	no	—
67	C₂²×C₄	—	17	7	no	—
68	C₂²×C₄	—	34	21	no	—
69	C₂²×C₄	—	34	21	no	—
70	C₂²×C₄	—	34	21	no	—
71	C₂²×C₄	—	34	21	no	—
72	C₂²×C₄	C₂²×#595	1	7	yes	—
73	C₄²	—	68	28	no	—
74	C₂³	—	17	7	no	—
75	C₂³	—	17	7	no	—
76	C₂³	C₂³×#595	1	1	yes	characteristic
77	C₂×C₄	—	2	21	no	—
78	C₂×C₄	—	17	28	no	—
79	C₂×C₄	—	34	42	no	—
80	C₂×C₄	—	34	21	no	—
81	C₂×C₄	—	68	7	no	—
82	C₂×C₄	—	68	21	no	—
83	C₂×C₄	—	68	7	no	—
84	C₂×C₄	—	68	21	no	—
85	C₂²	—	17	7	no	—
86	C₂²	—	17	21	no	—
87	C₂²	#41×#595	1	7	yes	—
88	C₄	—	4	7	no	—
89	C₄	—	17	8	no	—
90	C₄	—	68	14	no	—
91	C₄	—	68	7	no	—
92	C₂	—	17	1	no	—
93	C₂	—	17	7	no	—
94	C₂	#126×#595	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×#595
commutator, socle	C₂³×C₁₇	C₂³×C₄
Fitting	C₁₇×#401	C₄
prime radical, cosocle	C₂³×D₁₇	C₂⁴
hypercenter	#401	#595
hypocenter	C₁₇	C₄×#401
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ #401

Complements

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

N	H ≅ G/N	type
6. C₁₇⋊#401	C₄	semidirect
8. C₁₇×#401	C₄	semidirect
45. #595	#401	direct (N × H)
50. #401	#595	direct (N × H)
63. C₁₇	C₄×#401	semidirect

Maximal subgroups

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

subgroup	index
#14543971	2
#95×#595	2
D₁₇×#401	2
C₄×#401	17