Group #17962871 — subgroups

Subgroups — #17962871

Order 4352.

186 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 76 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	#14545208	C₂	1	2	yes	maximal, complemented
2	#14543943	C₂	1	1	yes	maximal, characteristic, complemented
3	#14543902	C₂	1	2	yes	maximal, complemented
4	C₄×#10587467	C₂	1	1	yes	maximal, characteristic, complemented
5	#14530620	C₂	1	1	yes	maximal, characteristic
6	#11763742	—	2	2	no	—
7	#11763741	C₂²	1	2	yes	—
8	#11763740	—	2	2	no	—
9	C₂×#10587467	C₂²	1	1	yes	characteristic
10	C₂×#10587467	C₂²	1	1	yes	characteristic
11	#11763227	C₂²	1	2	yes	—
12	#11762927	C₄	1	1	yes	characteristic
13	#11762594	C₄	1	2	yes	—
14	C₄×#63214	C₂²	1	1	yes	characteristic
15	C₁₇×#364	C₄	1	1	yes	characteristic
16	#10587590	C₈	1	1	yes	characteristic
17	#10587587	C₂×C₄	1	2	yes	—
18	C₁₇×M₃₂	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
20	#10587490	C₈	1	1	yes	characteristic
21	C₂×#63214	C₂×C₄	1	1	yes	characteristic
22	C₂×#63214	C₂³	1	1	yes	characteristic
23	#10587476	C₈	1	2	yes	—
24	#10587469	—	2	2	no	—
25	C₁₆×D₁₇	—	2	2	no	—
26	#10587467	—	2	2	no	—
27	#10587467	—	2	1	no	—
28	#10587467	D₄	1	1	yes	characteristic
29	#10587467	D₄	1	1	yes	characteristic
30	#63252	C₂×C₈	1	2	yes	—
31	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
34	#63223	C₂×C₈	1	2	yes	—
35	Dic₆₈	C₁₆	1	1	yes	characteristic
36	D₁₃₆	C₁₆	1	1	yes	characteristic
37	#63219	C₁₆	1	2	yes	—
38	#63218	—	2	2	no	—
39	C₈×D₁₇	—	2	2	no	—
40	C₁₆×C₁₇	—	2	2	no	—
41	#63214	—	2	1	no	—
42	#63214	C₂×D₄	1	1	yes	characteristic
43	#63214	#41	1	1	yes	characteristic
44	#13647	—	17	1	no	maximal, Sylow
45	C₂×C₄×C₁₇	—	2	1	no	—
46	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
47	C₂²⋊D₁₇	—	2	2	no	—
48	D₆₈	C₂×C₁₆	1	2	yes	—
49	C₄×D₁₇	—	2	2	no	—
50	Dic₃₄	C₂×C₁₆	1	2	yes	—
51	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
52	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
53	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
54	C₈×C₁₇	#131	1	1	yes	characteristic
55	#3622	—	2	2	no	—
56	#2258	—	17	2	no	—
57	#2170	—	17	1	no	—
58	#1422	—	17	1	no	—
59	#1401	—	17	2	no	—
60	C₄×C₃₂	—	17	1	no	—
61	C₂²×C₁₇	#504	1	1	yes	characteristic
62	C₂×D₁₇	—	2	2	no	—
63	C₄×C₁₇	—	2	2	no	—
64	C₄×C₁₇	C₈×D₄	1	1	yes	characteristic
65	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
66	Dic₁₇	—	2	2	no	—
67	#504	—	17	2	no	—
68	#443	—	17	1	no	—
69	M₆₄	—	17	2	no	—
70	M₆₄	—	34	2	no	—
71	C₂×C₃₂	—	17	1	no	—
72	C₂×C₃₂	—	17	1	no	—
73	C₂×C₃₂	—	34	2	no	—
74	#364	#595	1	1	yes	characteristic
75	#350	—	17	2	no	—
76	C₄×C₁₆	—	17	1	no	—
77	C₂×C₁₇	—	2	1	no	—
78	C₂×C₁₇	D₄×C₁₆	1	1	yes	characteristic
79	D₁₇	—	4	2	no	—
80	#135	—	17	1	no	—
81	#131	—	17	2	no	—
82	M₃₂	—	34	2	no	—
83	M₃₂	C₂×#595	1	2	yes	—
84	C₂×C₁₆	—	17	1	no	—
85	C₂×C₁₆	—	17	1	no	—
86	C₂×C₁₆	—	34	2	no	—
87	#108	—	17	1	no	—
88	#104	—	17	2	no	—
89	C₄×C₈	C₂×#595	1	1	yes	characteristic
90	C₃₂	—	17	1	no	—
91	C₃₂	—	17	1	no	—
92	C₃₂	—	34	1	no	—
93	C₃₂	—	34	2	no	—
94	C₁₇	#13647	1	1	yes	characteristic, complemented, Sylow
95	#41	—	17	2	no	—
96	Q₁₆	—	17	1	no	—
97	SD₁₆	—	17	2	no	—
98	D₈	—	17	1	no	—
99	M₁₆	—	17	2	no	—
100	M₁₆	—	34	2	no	—
101	C₂×C₈	—	34	2	no	—
102	C₂×C₈	#63242	1	1	yes	characteristic
103	C₂×C₈	C₂²×#595	1	1	yes	characteristic
104	C₄²	#63242	1	1	yes	characteristic
105	C₁₆	—	2	2	no	—
106	C₁₆	—	17	1	no	—
107	C₁₆	—	17	1	no	—
108	C₁₆	—	34	1	no	—
109	Q₈	—	17	2	no	—
110	D₄	—	17	2	no	—
111	D₄	—	34	2	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	34	2	no	—
114	C₂×C₄	C₂×#63242	1	1	yes	characteristic
115	C₈	—	34	2	no	—
116	C₈	#10587529	1	1	yes	characteristic
117	C₈	#10587529	1	1	yes	characteristic
118	C₈	D₄×#595	1	1	yes	characteristic
119	C₈	#10587680	1	1	yes	characteristic
120	C₂²	—	34	2	no	—
121	C₂²	#11763868	1	1	yes	characteristic
122	C₄	—	2	2	no	—
123	C₄	—	34	2	no	—
124	C₄	#11763837	1	1	yes	characteristic
125	C₄	C₂×#10587529	1	1	yes	characteristic
126	C₂	—	2	1	no	—
127	C₂	—	68	2	no	—
128	C₂	#14545163	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14545208

C₂

yes

maximal, complemented

#14543943

C₂

yes

maximal, characteristic, complemented

#14543902

C₂

yes

maximal, complemented

C₄×#10587467

C₂

yes

maximal, characteristic, complemented

#14530620

C₂

yes

maximal, characteristic

#11763742

—

#11763741

C₂²

yes

—

#11763740

—

C₂×#10587467

C₂²

yes

characteristic

C₂×#10587467

C₂²

yes

characteristic

#11763227

C₂²

yes

—

#11762927

C₄

yes

characteristic

#11762594

C₄

yes

—

C₄×#63214

C₂²

yes

characteristic

C₁₇×#364

C₄

yes

characteristic

#10587590

C₈

yes

characteristic

#10587587

C₂×C₄

yes

—

C₁₇×M₃₂

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

#10587490

C₈

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₂×#63214

C₂³

yes

characteristic

#10587476

C₈

yes

—

#10587469

—

C₁₆×D₁₇

—

#10587467

—

#10587467

—

#10587467

D₄

yes

characteristic

#10587467

D₄

yes

characteristic

#63252

C₂×C₈

yes

—

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₈

yes

characteristic

#63223

C₂×C₈

yes

—

Dic₆₈

C₁₆

yes

characteristic

D₁₃₆

C₁₆

yes

characteristic

#63219

C₁₆

yes

—

#63218

—

C₈×D₁₇

—

C₁₆×C₁₇

—

#63214

—

#63214

C₂×D₄

yes

yes

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂²⋊D₁₇

—

D₆₈

C₂×C₁₆

yes

—

C₄×D₁₇

—

Dic₃₄

C₂×C₁₆

yes

—

C₈×C₁₇

C₂×C₁₆

yes

characteristic

C₈×C₁₇

C₂×C₁₆

yes

characteristic

C₈×C₁₇

C₄×D₄

yes

C₈×C₁₇

yes

—

—

—

—

—

C₄×C₃₂

—

C₂²×C₁₇

#504

yes

characteristic

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

C₈×D₄

yes

characteristic

C₄×C₁₇

C₂²×C₁₆

yes

characteristic

Dic₁₇

—

#504

—

#443

—

M₆₄

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

yes

—

C₄×C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

D₄×C₁₆

yes

characteristic

D₁₇

—

#135

—

#131

—

M₃₂

—

M₃₂

C₂×#595

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#104

—

C₄×C₈

C₂×#595

yes

characteristic

C₃₂

—

C₃₂

—

C₃₂

—

C₃₂

—

C₁₇

#13647

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

100

M₁₆

—

101

C₂×C₈

—

102

C₂×C₈

#63242

yes

characteristic

103

C₂×C₈

C₂²×#595

yes

characteristic

104

C₄²

#63242

yes

characteristic

105

C₁₆

—

106

C₁₆

—

107

C₁₆

—

108

C₁₆

—

109

Q₈

—

110

D₄

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂×#63242

yes

characteristic

115

C₈

—

116

C₈

#10587529

yes

characteristic

117

C₈

#10587529

yes

characteristic

118

C₈

D₄×#595

yes

characteristic

119

C₈

#10587680

yes

characteristic

120

C₂²

—

121

C₂²

#11763868

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

#11763837

yes

characteristic

125

C₄

C₂×#10587529

yes

characteristic

126

C₂

—

127

C₂

—

128

C₂

#14545163

yes

characteristic

	subgroup	G/H
center	C₈	D₄×#595
commutator	C₄×C₁₇	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×#595
Fitting	C₁₇×#364	C₄
socle	C₂×C₁₇	D₄×C₁₆
prime radical	#10587590	C₈
cosocle	C₂×#63214	C₂³
hypercenter	#364	#595
hypocenter	C₁₇	#13647
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×#595

commutator

C₄×C₁₇

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×#595

Fitting

C₁₇×#364

C₄

socle

C₂×C₁₇

D₄×C₁₆

C₈

C₂³

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
1. #14545208	C₂	semidirect
2. #14543943	C₂	semidirect
3. #14543902	C₂	semidirect
4. C₄×#10587467	C₂	semidirect
94. C₁₇	#13647	semidirect

H ≅ G/N

type

1. #14545208

C₂

semidirect

2. #14543943

C₂

semidirect

3. #14543902

C₂

semidirect

4. C₄×#10587467

C₂

semidirect

94. C₁₇

#13647

semidirect

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

subgroup	index
#14545208	2
#14543943	2
#14543902	2
C₄×#10587467	2
#14530620	2
#13647	17

subgroup

index

Subgroups — #17962871

Conjugacy classes of subgroups

Complements

Maximal subgroups