Group #14545117 — subgroups

Subgroups — #14545117

Order 2176.

172 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 82 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×#10587530	C₂	1	2	yes	maximal
2	#11763730	C₂	1	2	yes	maximal, complemented
3	C₄⋊#63216	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
6	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
7	C₄²×D₁₇	C₄	1	1	yes	characteristic
8	C₂×#63216	C₂²	1	4	yes	—
9	#10587530	—	2	4	no	—
10	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
11	C₈×Dic₁₇	C₄	1	1	yes	characteristic
12	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₄×#3622	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₇	C₈	1	1	yes	characteristic
15	C₂×C₄×D₁₇	C₈	1	1	yes	characteristic
16	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₁₇	C₈	1	1	yes	characteristic
21	C₄×Dic₁₇	C₈	1	1	yes	characteristic
22	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂×#3622	C₂×C₄	1	1	yes	characteristic
24	C₂×#3622	C₂³	1	1	yes	characteristic
25	C₈×D₁₇	—	2	2	no	—
26	C₈×D₁₇	D₄	1	2	yes	—
27	C₈×D₁₇	Q₈	1	2	yes	—
28	#63216	—	2	4	no	—
29	C₂²×D₁₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
34	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
35	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
36	C₄×D₁₇	—	2	2	no	—
37	C₄×D₁₇	—	2	2	no	—
38	C₄×D₁₇	C₄⋊C₄	1	2	yes	—
39	C₄×D₁₇	M₁₆	1	2	yes	—
40	C₈×C₁₇	—	2	1	no	—
41	C₈×C₁₇	C₄⋊C₄	1	2	yes	—
42	#3622	—	2	1	no	—
43	#3622	C₂×D₄	1	1	yes	characteristic
44	#3622	C₂×Q₈	1	1	yes	characteristic
45	#2150	—	17	1	no	maximal, Sylow
46	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
47	C₂×D₁₇	—	2	1	no	—
48	C₂×D₁₇	—	2	1	no	—
49	C₂×D₁₇	C₄⋊C₈	1	2	yes	—
50	C₄×C₁₇	—	2	1	no	—
51	C₄×C₁₇	M₃₂	1	2	yes	complemented
52	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
54	Dic₁₇	—	2	1	no	—
55	Dic₁₇	C₄⋊C₈	1	2	yes	—
56	Dic₁₇	M₃₂	1	2	yes	complemented
57	C₂×M₃₂	—	17	2	no	—
58	C₂×C₄×C₈	—	17	1	no	—
59	C₄⋊C₁₆	—	17	2	no	—
60	C₄⋊C₁₆	—	17	2	no	—
61	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
62	C₂×C₁₇	C₂×M₃₂	1	1	yes	characteristic
63	C₂×C₁₇	C₂×M₃₂	1	1	yes	characteristic
64	D₁₇	—	2	2	no	—
65	C₂²×C₈	—	17	1	no	—
66	C₂²×C₈	—	17	1	no	—
67	C₂×C₄²	—	17	1	no	—
68	M₃₂	—	34	4	no	—
69	C₂×C₁₆	—	17	4	no	—
70	C₄×C₈	—	17	1	no	—
71	C₄×C₈	—	17	1	no	—
72	C₄×C₈	—	17	1	no	—
73	C₄×C₈	#595	1	1	yes	characteristic
74	C₁₇	#2150	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	17	1	no	—
76	C₂²×C₄	—	17	1	no	—
77	C₂²×C₄	—	17	1	no	—
78	C₂×C₈	—	17	1	no	—
79	C₂×C₈	—	17	2	no	—
80	C₂×C₈	—	17	2	no	—
81	C₂×C₈	—	17	1	no	—
82	C₂×C₈	—	34	2	no	—
83	C₂×C₈	C₂×#595	1	1	yes	characteristic
84	C₂×C₈	C₂×#595	1	1	yes	characteristic
85	C₄²	—	17	1	no	—
86	C₄²	—	17	1	no	—
87	C₄²	—	17	1	no	—
88	C₄²	C₂×#595	1	1	yes	characteristic
89	C₁₆	—	34	4	no	—
90	C₂³	—	17	1	no	—
91	C₂×C₄	—	17	1	no	—
92	C₂×C₄	—	17	1	no	—
93	C₂×C₄	—	17	2	no	—
94	C₂×C₄	—	17	2	no	—
95	C₂×C₄	—	17	1	no	—
96	C₂×C₄	—	34	2	no	—
97	C₂×C₄	—	34	2	no	—
98	C₂×C₄	#63242	1	1	yes	characteristic
99	C₂×C₄	#63242	1	1	yes	characteristic
100	C₂×C₄	C₂²×#595	1	1	yes	characteristic
101	C₈	—	2	1	no	—
102	C₈	—	17	1	no	—
103	C₈	—	17	1	no	—
104	C₈	—	34	1	no	—
105	C₈	C₄⋊#595	1	2	yes	—
106	C₂²	—	17	2	no	—
107	C₂²	—	34	1	no	—
108	C₂²	—	34	1	no	—
109	C₂²	C₂×#63242	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	17	2	no	—
112	C₄	—	17	2	no	—
113	C₄	—	34	1	no	—
114	C₄	#10587530	1	2	yes	complemented
115	C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
116	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
117	C₂	—	34	2	no	—
118	C₂	#11763810	1	1	yes	characteristic
119	C₂	#11763865	1	1	yes	characteristic
120	C₂	C₂×#10587530	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587530

C₂

yes

maximal

#11763730

C₂

yes

maximal, complemented

C₄⋊#63216

C₂

yes

maximal, complemented

C₄×C₈×D₁₇

C₂

yes

maximal, characteristic

C₂×C₈×D₁₇

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

C₄²×D₁₇

C₄

yes

characteristic

C₂×#63216

C₂²

yes

—

#10587530

—

C₄×C₈×C₁₇

C₄

yes

characteristic

C₈×Dic₁₇

C₄

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₄×#3622

C₂²

yes

characteristic

C₂×C₄×D₁₇

C₈

yes

characteristic

C₂×C₄×D₁₇

C₈

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₈

yes

characteristic

C₄×Dic₁₇

C₈

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂³

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

D₄

yes

—

C₈×D₁₇

Q₈

yes

—

#63216

—

C₂²×D₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

C₄⋊C₄

yes

—

C₄×D₁₇

M₁₆

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₄⋊C₄

yes

—

#3622

—

#3622

C₂×D₄

yes

characteristic

#3622

C₂×Q₈

yes

characteristic

#2150

—

maximal, Sylow

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

C₄⋊C₈

yes

—

C₄×C₁₇

—

C₄×C₁₇

M₃₂

yes

complemented

C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₇

C₂×M₁₆

yes

characteristic

Dic₁₇

—

Dic₁₇

C₄⋊C₈

yes

—

Dic₁₇

M₃₂

yes

complemented

C₂×M₃₂

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₇

C₂×M₃₂

yes

characteristic

C₂×C₁₇

C₂×M₃₂

yes

characteristic

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#595

yes

characteristic

C₁₇

#2150

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

100

C₂×C₄

C₂²×#595

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

C₄⋊#595

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×#63242

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

#10587530

yes

complemented

115

C₄

D₁₇⋊M₁₆

yes

characteristic

116

C₄

C₂×C₄⋊#595

yes

characteristic

117

C₂

—

118

C₂

#11763810

yes

characteristic

119

C₂

#11763865

yes

characteristic

120

C₂

C₂×#10587530

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₈
Fitting	C₄×C₈×C₁₇	C₄
prime radical	C₂²×D₁₇	C₂×C₈
cosocle	C₂×#3622	C₂³
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#2150
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂²×C₈

Fitting

C₄×C₈×C₁₇

C₄

prime radical

C₂²×D₁₇

C₂×C₈

C₂³

C₄×C₈

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ C₄×C₈

N	H ≅ G/N	type
2. #11763730	C₂	semidirect
3. C₄⋊#63216	C₂	semidirect
51. C₄×C₁₇	M₃₂	semidirect
56. Dic₁₇	M₃₂	semidirect
74. C₁₇	#2150	semidirect
114. C₄	#10587530	semidirect

H ≅ G/N

type

2. #11763730

C₂

semidirect

3. C₄⋊#63216

C₂

semidirect

51. C₄×C₁₇

M₃₂

semidirect

56. Dic₁₇

M₃₂

semidirect

74. C₁₇

#2150

semidirect

114. C₄

#10587530

semidirect

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

subgroup	index
C₂×#10587530	2
#11763730	2
C₄⋊#63216	2
C₄×C₈×D₁₇	2
#2150	17

subgroup

index

C₄×C₈×D₁₇

Subgroups — #14545117

Conjugacy classes of subgroups

Complements

Maximal subgroups