Group #14545013 — subgroups

Subgroups — #14545013

Order 2176.

260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587538	C₂	1	2	yes	maximal, complemented
2	#11763704	C₂	1	4	yes	maximal, complemented
3	C₂²×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×D₁₇	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₇	C₄	1	1	yes	characteristic
6	C₂²×#3622	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₁₇	—	2	4	no	—
8	C₂×C₈×D₁₇	C₄	1	2	yes	—
9	C₂×C₈×D₁₇	C₂²	1	2	yes	—
10	#10587538	—	2	4	no	—
11	C₂×#63216	C₂²	1	4	yes	complemented
12	C₂³×D₁₇	C₈	1	1	yes	characteristic
13	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₁₇	C₈	1	1	yes	characteristic
15	C₂×C₄×D₁₇	—	2	2	no	—
16	C₂×C₄×D₁₇	—	2	2	no	—
17	C₂×C₄×D₁₇	C₈	1	2	yes	—
18	C₂×C₄×D₁₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₇	—	2	2	no	—
20	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
21	C₂×#3622	C₂×C₄	1	1	yes	characteristic
22	C₂×#3622	D₄	1	4	yes	—
23	C₂×#3622	C₂³	1	1	yes	characteristic
24	C₈×D₁₇	—	2	4	no	—
25	C₈×D₁₇	—	2	4	no	—
26	#63216	—	2	4	no	—
27	C₂³×C₁₇	C₂×C₈	1	1	yes	characteristic
28	C₂²×D₁₇	—	2	2	no	—
29	C₂²×D₁₇	—	2	4	no	—
30	C₂²×D₁₇	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₁₇	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
34	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₁₇	—	2	2	no	—
36	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
37	C₄×D₁₇	—	2	4	no	—
38	C₄×D₁₇	—	2	2	no	—
39	C₄×D₁₇	—	2	2	no	—
40	C₈×C₁₇	—	2	2	no	—
41	#3622	C₂²⋊C₄	1	2	yes	—
42	#3622	C₂×D₄	1	2	yes	—
43	#2112	—	17	1	no	maximal, Sylow
44	C₂²×C₁₇	—	2	2	no	—
45	C₂²×C₁₇	C₂²⋊C₈	1	2	yes	—
46	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
47	C₂×D₁₇	—	2	8	no	—
48	C₂×D₁₇	—	2	2	no	—
49	C₂×D₁₇	—	2	2	no	—
50	C₂×D₁₇	M₃₂	1	4	yes	complemented
51	C₄×C₁₇	C₂²⋊C₈	1	2	yes	—
52	C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
54	Dic₁₇	—	2	2	no	—
55	C₂³×C₈	—	17	1	no	—
56	C₂×M₃₂	—	17	2	no	—
57	C₂²⋊C₁₆	—	17	4	no	—
58	C₂×C₁₇	—	2	2	no	—
59	C₂×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
60	C₂×C₁₇	C₂×M₃₂	1	2	yes	—
61	D₁₇	—	2	4	no	—
62	C₂³×C₄	—	17	1	no	—
63	C₂²×C₈	—	17	1	no	—
64	C₂²×C₈	—	17	2	no	—
65	C₂²×C₈	—	17	2	no	—
66	C₂²×C₈	—	34	4	no	—
67	C₂²×C₈	#595	1	1	yes	characteristic
68	M₃₂	—	34	4	no	—
69	C₂×C₁₆	—	17	4	no	—
70	C₁₇	#2112	1	1	yes	characteristic, complemented, Sylow
71	C₂⁴	—	17	1	no	—
72	C₂²×C₄	—	17	1	no	—
73	C₂²×C₄	—	17	2	no	—
74	C₂²×C₄	—	17	2	no	—
75	C₂²×C₄	—	34	2	no	—
76	C₂²×C₄	—	34	2	no	—
77	C₂²×C₄	C₂×#595	1	1	yes	characteristic
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	17	4	no	—
80	C₂×C₈	—	17	1	no	—
81	C₂×C₈	—	17	1	no	—
82	C₂×C₈	—	34	4	no	—
83	C₂×C₈	—	34	4	no	—
84	C₂×C₈	C₂×#595	1	2	yes	—
85	C₁₆	—	34	4	no	—
86	C₂³	—	17	2	no	—
87	C₂³	—	34	4	no	—
88	C₂³	—	34	2	no	—
89	C₂³	#63242	1	1	yes	characteristic
90	C₂×C₄	—	17	2	no	—
91	C₂×C₄	—	34	2	no	—
92	C₂×C₄	—	34	2	no	—
93	C₂×C₄	—	34	2	no	—
94	C₂×C₄	—	34	4	no	—
95	C₂×C₄	#63242	1	1	yes	characteristic
96	C₂×C₄	#63243	1	2	yes	—
97	C₂×C₄	C₂²⋊#595	1	2	yes	—
98	C₂×C₄	C₂²×#595	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	—	17	2	no	—
101	C₈	—	17	2	no	—
102	C₂²	—	2	2	no	—
103	C₂²	—	17	4	no	—
104	C₂²	—	34	8	no	—
105	C₂²	—	34	2	no	—
106	C₂²	—	34	2	no	—
107	C₂²	#10587543	1	2	yes	—
108	C₂²	C₂×#63242	1	1	yes	characteristic
109	C₄	—	34	2	no	—
110	C₄	#10587543	1	2	yes	—
111	C₄	C₂×#63243	1	1	yes	characteristic
112	C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
113	C₂	—	2	2	no	—
114	C₂	—	34	4	no	—
115	C₂	C₂×#10587543	1	1	yes	characteristic
116	C₂	#11763865	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587538

C₂

yes

maximal, complemented

#11763704

C₂

yes

maximal, complemented

C₂²×C₈×D₁₇

C₂

yes

maximal, characteristic

C₂²×C₄×D₁₇

C₄

yes

characteristic

C₂²×C₈×C₁₇

C₄

yes

characteristic

C₂²×#3622

C₂²

yes

characteristic

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

C₄

yes

—

C₂×C₈×D₁₇

C₂²

yes

—

#10587538

—

C₂×#63216

C₂²

yes

complemented

C₂³×D₁₇

C₈

yes

characteristic

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₈

yes

characteristic

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₈

yes

—

C₂×C₄×D₁₇

C₂×C₄

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

D₄

yes

—

C₂×#3622

C₂³

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

—

#63216

—

C₂³×C₁₇

C₂×C₈

yes

characteristic

C₂²×D₁₇

—

C₂²×D₁₇

—

C₂²×D₁₇

C₂×C₈

yes

—

C₂×C₄×C₁₇

C₂²⋊C₄

yes

—

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

M₁₆

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂×C₈

yes

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

C₈×C₁₇

—

#3622

C₂²⋊C₄

yes

—

#3622

C₂×D₄

yes

—

#2112

—

maximal, Sylow

C₂²×C₁₇

—

C₂²×C₁₇

C₂²⋊C₈

yes

—

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

M₃₂

yes

complemented

C₄×C₁₇

C₂²⋊C₈

yes

—

C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₇

C₂×M₁₆

yes

characteristic

Dic₁₇

—

C₂³×C₈

—

C₂×M₃₂

—

C₂²⋊C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₁₇

C₂×M₃₂

yes

—

D₁₇

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

#595

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₁₇

#2112

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#595

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

—

C₁₆

—

C₂³

—

C₂³

—

C₂³

—

C₂³

#63242

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#63242

yes

characteristic

C₂×C₄

#63243

yes

—

C₂×C₄

C₂²⋊#595

yes

—

C₂×C₄

C₂²×#595

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

#10587543

yes

—

108

C₂²

C₂×#63242

yes

characteristic

109

C₄

—

110

C₄

#10587543

yes

—

111

C₄

C₂×#63243

yes

characteristic

112

C₄

C₂×C₂²⋊#595

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

C₂×#10587543

yes

characteristic

116

C₂

#11763865

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₈
Fitting	C₂²×C₈×C₁₇	C₄
prime radical	C₂³×D₁₇	C₈
cosocle	C₂×#3622	C₂³
hypercenter	C₂²×C₈	#595
hypocenter	C₁₇	#2112
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂²×C₈

Fitting

C₂²×C₈×C₁₇

C₄

prime radical

C₂³×D₁₇

C₈

C₂³

C₂²×C₈

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
1. C₂×#10587538	C₂	semidirect
2. #11763704	C₂	semidirect
11. C₂×#63216	C₂²	semidirect
50. C₂×D₁₇	M₃₂	semidirect
70. C₁₇	#2112	semidirect

H ≅ G/N

type

1. C₂×#10587538

C₂

semidirect

2. #11763704

C₂

semidirect

11. C₂×#63216

C₂²

semidirect

50. C₂×D₁₇

M₃₂

semidirect

70. C₁₇

#2112

semidirect

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

subgroup	index
C₂×#10587538	2
#11763704	2
C₂²×C₈×D₁₇	2
#2112	17

subgroup

index

C₂×#10587538

#11763704

C₂²×C₈×D₁₇

#2112

Subgroups — #14545013

Conjugacy classes of subgroups

Complements

Maximal subgroups