Group #17962571 — subgroups

Subgroups — #17962571

Order 4352.

330 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 116 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×#11763741	C₂	1	2	yes	maximal, complemented
2	#14543898	C₂	1	4	yes	maximal, complemented
3	C₂²×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
4	#11763741	—	2	4	no	—
5	C₂×#10587467	C₂²	1	4	yes	complemented
6	C₂²×C₈×D₁₇	C₄	1	1	yes	characteristic
7	C₂²×#63214	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×D₁₇	—	2	4	no	—
9	C₂×C₁₆×D₁₇	C₄	1	2	yes	—
10	C₂×C₁₆×D₁₇	C₂²	1	2	yes	—
11	C₂²×C₁₆×C₁₇	C₄	1	1	yes	characteristic
12	C₂²×C₄×D₁₇	C₈	1	1	yes	characteristic
13	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×#3622	C₈	1	1	yes	characteristic
15	C₂×C₈×D₁₇	—	2	2	no	—
16	C₂×C₈×D₁₇	—	2	2	no	—
17	C₂×C₈×D₁₇	C₈	1	2	yes	—
18	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
19	C₂×C₁₆×C₁₇	—	2	2	no	—
20	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
21	C₂×#63214	C₂×C₄	1	1	yes	characteristic
22	C₂×#63214	D₄	1	4	yes	—
23	C₂×#63214	C₂³	1	1	yes	characteristic
24	C₁₆×D₁₇	—	2	4	no	—
25	C₁₆×D₁₇	—	2	4	no	—
26	#10587467	—	2	4	no	—
27	C₂³×D₁₇	C₁₆	1	1	yes	characteristic
28	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
29	C₂²×Dic₁₇	C₁₆	1	1	yes	characteristic
30	C₂×C₄×D₁₇	—	2	2	no	—
31	C₂×C₄×D₁₇	—	2	2	no	—
32	C₂×C₄×D₁₇	C₁₆	1	2	yes	—
33	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
34	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
35	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
37	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
38	C₂×#3622	—	2	2	no	—
39	C₂×#3622	C₂×C₈	1	2	yes	—
40	C₈×D₁₇	—	2	4	no	—
41	C₈×D₁₇	—	2	2	no	—
42	C₈×D₁₇	—	2	2	no	—
43	C₁₆×C₁₇	—	2	2	no	—
44	#63214	C₂²⋊C₄	1	2	yes	—
45	#63214	C₂×D₄	1	2	yes	—
46	#13553	—	17	1	no	maximal, Sylow
47	C₂³×C₁₇	C₂×C₁₆	1	1	yes	characteristic
48	C₂²×D₁₇	—	2	2	no	—
49	C₂²×D₁₇	—	2	4	no	—
50	C₂²×D₁₇	C₂×C₁₆	1	2	yes	—
51	C₂×C₄×C₁₇	C₂²⋊C₈	1	2	yes	—
52	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
53	C₂×C₄×C₁₇	M₃₂	1	2	yes	—
54	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
55	C₂×Dic₁₇	—	2	2	no	—
56	C₂×Dic₁₇	C₂×C₁₆	1	2	yes	—
57	C₄×D₁₇	—	2	4	no	—
58	C₄×D₁₇	—	2	2	no	—
59	C₄×D₁₇	—	2	2	no	—
60	C₈×C₁₇	C₂²⋊C₈	1	2	yes	—
61	C₈×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
63	#3622	—	2	2	no	—
64	C₂³×C₁₆	—	17	1	no	—
65	C₂×M₆₄	—	17	2	no	—
66	C₂²⋊C₃₂	—	17	4	no	—
67	C₂²×C₁₇	—	2	2	no	—
68	C₂²×C₁₇	C₂²⋊C₁₆	1	2	yes	—
69	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
70	C₂×D₁₇	—	2	8	no	—
71	C₂×D₁₇	—	2	2	no	—
72	C₂×D₁₇	—	2	2	no	—
73	C₂×D₁₇	M₆₄	1	4	yes	complemented
74	C₄×C₁₇	C₂²⋊C₁₆	1	2	yes	—
75	C₄×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
76	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
77	Dic₁₇	—	2	2	no	—
78	C₂³×C₈	—	17	1	no	—
79	C₂²×C₁₆	—	17	1	no	—
80	C₂²×C₁₆	—	17	2	no	—
81	C₂²×C₁₆	—	17	2	no	—
82	C₂²×C₁₆	—	34	4	no	—
83	C₂²×C₁₆	#595	1	1	yes	characteristic
84	M₆₄	—	34	4	no	—
85	C₂×C₃₂	—	17	4	no	—
86	C₂×C₁₇	—	2	2	no	—
87	C₂×C₁₇	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
88	C₂×C₁₇	C₂×M₆₄	1	2	yes	—
89	D₁₇	—	2	4	no	—
90	C₂³×C₄	—	17	1	no	—
91	C₂²×C₈	—	17	1	no	—
92	C₂²×C₈	—	17	2	no	—
93	C₂²×C₈	—	17	2	no	—
94	C₂²×C₈	—	34	2	no	—
95	C₂²×C₈	—	34	2	no	—
96	C₂²×C₈	C₂×#595	1	1	yes	characteristic
97	C₂×C₁₆	—	2	2	no	—
98	C₂×C₁₆	—	17	4	no	—
99	C₂×C₁₆	—	17	1	no	—
100	C₂×C₁₆	—	17	1	no	—
101	C₂×C₁₆	—	34	4	no	—
102	C₂×C₁₆	—	34	4	no	—
103	C₂×C₁₆	C₂×#595	1	2	yes	—
104	C₃₂	—	34	4	no	—
105	C₁₇	#13553	1	1	yes	characteristic, complemented, Sylow
106	C₂⁴	—	17	1	no	—
107	C₂²×C₄	—	17	1	no	—
108	C₂²×C₄	—	17	2	no	—
109	C₂²×C₄	—	17	2	no	—
110	C₂²×C₄	—	34	2	no	—
111	C₂²×C₄	—	34	2	no	—
112	C₂²×C₄	#63242	1	1	yes	characteristic
113	C₂×C₈	—	17	2	no	—
114	C₂×C₈	—	34	2	no	—
115	C₂×C₈	—	34	2	no	—
116	C₂×C₈	—	34	2	no	—
117	C₂×C₈	—	34	4	no	—
118	C₂×C₈	#63242	1	1	yes	characteristic
119	C₂×C₈	#63243	1	2	yes	—
120	C₂×C₈	C₂²⋊#595	1	2	yes	—
121	C₂×C₈	C₂²×#595	1	1	yes	characteristic
122	C₁₆	—	2	2	no	—
123	C₁₆	—	17	2	no	—
124	C₁₆	—	17	2	no	—
125	C₂³	—	17	2	no	—
126	C₂³	—	34	4	no	—
127	C₂³	—	34	2	no	—
128	C₂³	#10587529	1	1	yes	characteristic
129	C₂×C₄	—	17	2	no	—
130	C₂×C₄	—	34	2	no	—
131	C₂×C₄	—	34	2	no	—
132	C₂×C₄	—	34	2	no	—
133	C₂×C₄	—	34	4	no	—
134	C₂×C₄	#10587529	1	1	yes	characteristic
135	C₂×C₄	#10587530	1	2	yes	—
136	C₂×C₄	#10587543	1	2	yes	—
137	C₂×C₄	C₂×#63242	1	1	yes	characteristic
138	C₈	—	34	2	no	—
139	C₈	#10587543	1	2	yes	—
140	C₈	C₂×#63243	1	1	yes	characteristic
141	C₈	C₂×C₂²⋊#595	1	1	yes	characteristic
142	C₂²	—	2	2	no	—
143	C₂²	—	17	4	no	—
144	C₂²	—	34	8	no	—
145	C₂²	—	34	2	no	—
146	C₂²	—	34	2	no	—
147	C₂²	#11763704	1	2	yes	—
148	C₂²	C₂×#10587529	1	1	yes	characteristic
149	C₄	—	34	2	no	—
150	C₄	#11763704	1	2	yes	—
151	C₄	C₂×#10587543	1	1	yes	characteristic
152	C₄	C₂×#10587530	1	1	yes	characteristic
153	C₂	—	2	2	no	—
154	C₂	—	34	4	no	—
155	C₂	C₂×#11763704	1	1	yes	characteristic
156	C₂	#14545205	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763741

C₂

yes

maximal, complemented

#14543898

C₂

yes

maximal, complemented

C₂²×C₁₆×D₁₇

C₂

yes

maximal, characteristic

#11763741

—

C₂×#10587467

C₂²

yes

complemented

C₂²×C₈×D₁₇

C₄

yes

characteristic

C₂²×#63214

C₂²

yes

characteristic

C₂×C₁₆×D₁₇

—

C₂×C₁₆×D₁₇

C₄

yes

—

C₂×C₁₆×D₁₇

C₂²

yes

—

C₂²×C₁₆×C₁₇

C₄

yes

characteristic

C₂²×C₄×D₁₇

C₈

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²×#3622

C₈

yes

characteristic

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

C₈

yes

—

C₂×C₈×D₁₇

C₂×C₄

yes

—

C₂×C₁₆×C₁₇

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₂×#63214

C₂×C₄

yes

characteristic

C₂×#63214

D₄

yes

—

C₂×#63214

C₂³

yes

characteristic

C₁₆×D₁₇

—

C₁₆×D₁₇

—

#10587467

—

C₂³×D₁₇

C₁₆

yes

characteristic

C₂²×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂²×Dic₁₇

C₁₆

yes

characteristic

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₁₆

yes

—

C₂×C₄×D₁₇

C₂×C₈

yes

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

—

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×#3622

—

C₂×#3622

C₂×C₈

yes

—

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

—

C₁₆×C₁₇

—

#63214

C₂²⋊C₄

yes

—

#63214

C₂×D₄

yes

—

#13553

—

maximal, Sylow

C₂³×C₁₇

C₂×C₁₆

yes

characteristic

C₂²×D₁₇

—

C₂²×D₁₇

—

C₂²×D₁₇

C₂×C₁₆

yes

—

C₂×C₄×C₁₇

C₂²⋊C₈

yes

—

C₂×C₄×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

M₃₂

yes

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂×C₁₆

yes

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

C₈×C₁₇

C₂²⋊C₈

yes

—

C₈×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₁₇

C₂×M₁₆

yes

characteristic

#3622

—

C₂³×C₁₆

—

C₂×M₆₄

—

C₂²⋊C₃₂

—

C₂²×C₁₇

—

C₂²×C₁₇

C₂²⋊C₁₆

yes

—

C₂²×C₁₇

C₂²×C₁₆

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

M₆₄

yes

complemented

C₄×C₁₇

C₂²⋊C₁₆

yes

—

C₄×C₁₇

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₁₇

C₂×M₃₂

yes

characteristic

Dic₁₇

—

C₂³×C₈

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂²×C₁₆

#595

yes

characteristic

M₆₄

—

C₂×C₃₂

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₂²⋊C₁₆

yes

characteristic

C₂×C₁₇

C₂×M₆₄

yes

—

D₁₇

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×#595

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₂×C₁₆

C₂×#595

yes

—

104

C₃₂

—

105

C₁₇

#13553

yes

characteristic, complemented, Sylow

106

C₂⁴

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

#63242

yes

characteristic

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

#63242

yes

characteristic

119

C₂×C₈

#63243

yes

—

120

C₂×C₈

C₂²⋊#595

yes

—

121

C₂×C₈

C₂²×#595

yes

characteristic

122

C₁₆

—

123

C₁₆

—

124

C₁₆

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

#10587529

yes

characteristic

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

#10587529

yes

characteristic

135

C₂×C₄

#10587530

yes

—

136

C₂×C₄

#10587543

yes

—

137

C₂×C₄

C₂×#63242

yes

characteristic

138

C₈

—

139

C₈

#10587543

yes

—

140

C₈

C₂×#63243

yes

characteristic

141

C₈

C₂×C₂²⋊#595

yes

characteristic

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

#11763704

yes

—

148

C₂²

C₂×#10587529

yes

characteristic

149

C₄

—

150

C₄

#11763704

yes

—

151

C₄

C₂×#10587543

yes

characteristic

152

C₄

C₂×#10587530

yes

characteristic

153

C₂

—

154

C₂

—

155

C₂

C₂×#11763704

yes

characteristic

156

C₂

#14545205

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₁₆
Fitting	C₂²×C₁₆×C₁₇	C₄
prime radical	C₂³×D₁₇	C₁₆
cosocle	C₂×#63214	C₂³
hypercenter	C₂²×C₁₆	#595
hypocenter	C₁₇	#13553
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂²×C₁₆

Fitting

C₂²×C₁₆×C₁₇

C₄

prime radical

C₂³×D₁₇

C₁₆

C₂³

C₂²×C₁₆

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
1. C₂×#11763741	C₂	semidirect
2. #14543898	C₂	semidirect
5. C₂×#10587467	C₂²	semidirect
73. C₂×D₁₇	M₆₄	semidirect
105. C₁₇	#13553	semidirect

H ≅ G/N

type

1. C₂×#11763741

C₂

semidirect

2. #14543898

C₂

semidirect

5. C₂×#10587467

C₂²

semidirect

73. C₂×D₁₇

M₆₄

semidirect

105. C₁₇

#13553

semidirect

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

subgroup	index
C₂×#11763741	2
#14543898	2
C₂²×C₁₆×D₁₇	2
#13553	17

subgroup

index

C₂×#11763741

#14543898

C₂²×C₁₆×D₁₇

#13553

Subgroups — #17962571

Conjugacy classes of subgroups

Complements

Maximal subgroups