Group #16791175 — subgroups

Subgroups — #16791175

Order 3328.

290 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 108 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×#11718249	C₂	1	2	yes	maximal, complemented
2	#13129952	C₂	1	4	yes	maximal, complemented
3	C₂×#11718568	C₂	1	1	yes	maximal, characteristic
4	C₂×#88155	C₄	1	1	yes	characteristic
5	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic
6	C₂²×#6090	C₂²	1	1	yes	characteristic
7	#11718568	—	2	2	no	—
8	#11718568	—	2	2	no	—
9	C₂×#88038	C₂²	1	2	yes	—
10	C₂×C₁₆×D₁₃	C₄	1	2	yes	—
11	#11718249	—	2	2	no	—
12	#11718249	C₂²	1	4	yes	—
13	C₂×#88036	—	2	2	no	—
14	C₂×#6127	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×#6099	C₈	1	1	yes	characteristic
17	#88155	—	2	2	no	—
18	#88155	—	2	2	no	—
19	C₂×#6094	C₈	1	2	yes	—
20	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
21	C₁₃×M₃₂	—	2	2	no	—
22	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
23	C₂×#6090	C₂×C₄	1	1	yes	characteristic
24	C₂×#6090	D₄	1	2	yes	—
25	C₂×#6090	D₄	1	2	yes	—
26	C₂×#6090	C₂³	1	1	yes	characteristic
27	#88038	—	2	4	no	—
28	C₁₆×D₁₃	—	2	2	no	—
29	C₁₆×D₁₃	—	2	2	no	—
30	#88036	—	2	4	no	—
31	#13556	—	13	1	no	maximal, Sylow
32	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₂²⋊D₁₃	C₁₆	1	2	yes	—
34	#6127	—	2	2	no	—
35	#6127	—	2	2	no	—
36	C₂×D₅₂	C₁₆	1	1	yes	characteristic
37	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
38	C₂×Dic₂₆	C₁₆	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
40	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
42	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	#6099	—	2	2	no	—
44	C₂×#1055	C₂×C₈	1	2	yes	—
45	#6094	—	2	4	no	—
46	C₈×D₁₃	—	2	2	no	—
47	C₈×D₁₃	—	2	2	no	—
48	C₁₃×C₁₆	—	2	2	no	—
49	#6090	C₂²⋊C₄	1	1	yes	characteristic
50	#6090	C₂²⋊C₄	1	1	yes	characteristic
51	#6090	C₂×D₄	1	2	yes	—
52	C₂×#504	—	13	1	no	—
53	C₂×M₆₄	—	13	2	no	—
54	#1400	—	13	4	no	—
55	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
56	C₂²×D₁₃	C₂×C₁₆	1	2	yes	—
57	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
58	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
59	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
60	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
61	C₂²⋊D₁₃	—	2	4	no	—
62	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
63	D₅₂	—	2	2	no	—
64	C₄×D₁₃	—	2	2	no	—
65	C₄×D₁₃	—	2	2	no	—
66	Dic₂₆	—	2	2	no	—
67	C₈×C₁₃	C₂²⋊C₈	1	2	yes	—
68	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
70	#1055	—	2	2	no	—
71	C₂×#131	—	13	1	no	—
72	#504	—	26	2	no	—
73	#504	—	26	2	no	—
74	C₂×M₃₂	—	13	2	no	—
75	C₂×M₃₂	#261	1	1	yes	characteristic
76	C₂²×C₁₆	—	13	1	no	—
77	C₂²×C₁₆	—	13	2	no	—
78	M₆₄	—	13	4	no	—
79	M₆₄	—	26	2	no	—
80	C₂×C₃₂	—	26	2	no	—
81	C₂²×C₁₃	—	4	1	no	—
82	C₂²×C₁₃	C₂²⋊C₁₆	1	2	yes	—
83	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
84	C₂×D₁₃	—	2	2	no	—
85	C₂×D₁₃	—	4	2	no	—
86	C₄×C₁₃	C₂²⋊C₁₆	1	2	yes	—
87	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
88	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
89	Dic₁₃	—	2	2	no	—
90	C₂×#41	—	13	1	no	—
91	#131	—	26	2	no	—
92	#131	—	26	2	no	—
93	C₂×M₁₆	—	13	1	no	—
94	C₂×M₁₆	—	13	2	no	—
95	C₂²×C₈	—	13	2	no	—
96	C₂²×C₈	C₂×#261	1	1	yes	characteristic
97	M₃₂	—	2	2	no	—
98	M₃₂	—	26	4	no	—
99	C₂×C₁₆	—	13	2	no	—
100	C₂×C₁₆	—	13	2	no	—
101	C₂×C₁₆	—	13	1	no	—
102	C₂×C₁₆	—	13	1	no	—
103	C₂×C₁₆	—	26	2	no	—
104	C₂×C₁₆	—	26	2	no	—
105	C₂×C₁₆	C₂×#261	1	2	yes	—
106	C₃₂	—	26	4	no	—
107	C₂×C₁₃	—	2	1	no	—
108	C₂×C₁₃	—	2	2	no	—
109	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
110	D₁₃	—	4	2	no	—
111	#41	—	26	2	no	—
112	#41	—	26	2	no	—
113	C₂×Q₈	—	13	1	no	—
114	C₂×D₄	—	13	2	no	—
115	C₂×D₄	—	13	1	no	—
116	C₂²×C₄	—	13	2	no	—
117	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
118	M₁₆	—	26	2	no	—
119	M₁₆	—	26	4	no	—
120	C₂×C₈	—	13	2	no	—
121	C₂×C₈	—	26	2	no	—
122	C₂×C₈	—	26	2	no	—
123	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
124	C₂×C₈	#6118	1	2	yes	—
125	C₂×C₈	C₂²⋊#261	1	2	yes	—
126	C₂×C₈	C₂²×#261	1	1	yes	characteristic
127	C₁₆	—	2	2	no	—
128	C₁₆	—	13	2	no	—
129	C₁₆	—	13	1	no	—
130	C₁₆	—	13	1	no	—
131	C₁₃	#13556	1	1	yes	characteristic, complemented, Sylow
132	C₂³	—	13	2	no	—
133	C₂³	D₁₃⋊C₁₆	1	1	yes	characteristic
134	Q₈	—	26	2	no	—
135	D₄	—	26	4	no	—
136	D₄	—	26	2	no	—
137	C₂×C₄	—	13	2	no	—
138	C₂×C₄	—	26	2	no	—
139	C₂×C₄	—	26	2	no	—
140	C₂×C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
141	C₂×C₄	#88098	1	2	yes	—
142	C₂×C₄	#88111	1	2	yes	—
143	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
144	C₈	—	26	2	no	—
145	C₈	#88111	1	2	yes	—
146	C₈	C₂×#6118	1	1	yes	characteristic
147	C₈	C₂×C₂²⋊#261	1	1	yes	characteristic
148	C₂²	—	4	1	no	—
149	C₂²	—	26	2	no	—
150	C₂²	—	52	2	no	—
151	C₂²	#11718259	1	2	yes	—
152	C₂²	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
153	C₄	—	26	2	no	—
154	C₄	#11718259	1	2	yes	—
155	C₄	C₂×#88098	1	1	yes	characteristic
156	C₄	C₂×#88111	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	2	no	—
159	C₂	—	52	2	no	—
160	C₂	C₂×#11718259	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718249

C₂

yes

maximal, complemented

#13129952

C₂

yes

maximal, complemented

C₂×#11718568

C₂

yes

maximal, characteristic

C₂×#88155

C₄

yes

characteristic

C₂×C₁₃×M₃₂

C₄

yes

characteristic

C₂²×#6090

C₂²

yes

—

—

C₂²

yes

—

C₂×C₁₆×D₁₃

C₄

yes

—

#11718249

—

#11718249

C₂²

yes

—

C₂×#88036

—

C₂×#6127

C₈

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×#6099

C₈

yes

—

—

C₈

yes

—

C₂×C₈×D₁₃

C₂×C₄

yes

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₂×#6090

C₂×C₄

yes

characteristic

C₂×#6090

D₄

yes

—

C₂×#6090

D₄

yes

—

C₂×#6090

C₂³

yes

characteristic

#88038

—

C₁₆×D₁₃

—

C₁₆×D₁₃

—

#88036

—

#13556

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂×C₂²⋊D₁₃

C₁₆

yes

—

#6127

—

#6127

—

C₂×D₅₂

C₁₆

yes

characteristic

C₂×C₄×D₁₃

C₂×C₈

yes

—

C₂×Dic₂₆

C₁₆

yes

characteristic

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

#6099

—

C₂×#1055

C₂×C₈

yes

—

#6094

—

C₈×D₁₃

—

C₈×D₁₃

—

C₁₃×C₁₆

—

#6090

C₂²⋊C₄

yes

characteristic

#6090

C₂²⋊C₄

yes

characteristic

#6090

C₂×D₄

yes

—

C₂×#504

—

C₂×M₆₄

—

#1400

—

C₂³×C₁₃

C₂×C₁₆

yes

characteristic

C₂²×D₁₃

C₂×C₁₆

yes

—

C₂×C₄×C₁₃

C₂²⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

M₃₂

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂²⋊D₁₃

—

C₂×Dic₁₃

C₂×C₁₆

yes

—

D₅₂

—

C₄×D₁₃

—

C₄×D₁₃

—

Dic₂₆

—

C₈×C₁₃

C₂²⋊C₈

yes

—

C₈×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₁₃

C₂×M₁₆

yes

—

—

—

—

C₂×M₃₂

—

C₂×M₃₂

#261

yes

characteristic

C₂²×C₁₆

—

C₂²×C₁₆

—

M₆₄

—

M₆₄

—

C₂×C₃₂

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂²⋊C₁₆

yes

—

C₂²×C₁₃

C₂²×C₁₆

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

C₂²⋊C₁₆

yes

—

C₄×C₁₃

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₁₃

C₂×M₃₂

yes

characteristic

Dic₁₃

—

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×#261

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₂×C₁₆

—

104

C₂×C₁₆

—

105

C₂×C₁₆

C₂×#261

yes

—

106

C₃₂

—

107

C₂×C₁₃

—

108

C₂×C₁₃

—

109

C₂×C₁₃

C₂×C₂²⋊C₁₆

yes

characteristic

110

D₁₃

—

111

#41

—

112

#41

—

113

C₂×Q₈

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂²×C₄

—

117

C₂²×C₄

D₁₃⋊C₈

yes

characteristic

118

M₁₆

—

119

M₁₆

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

D₁₃⋊C₈

yes

characteristic

124

C₂×C₈

#6118

yes

—

125

C₂×C₈

C₂²⋊#261

yes

—

126

C₂×C₈

C₂²×#261

yes

characteristic

127

C₁₆

—

128

C₁₆

—

129

C₁₆

—

130

C₁₆

—

131

C₁₃

#13556

yes

characteristic, complemented, Sylow

132

C₂³

—

133

C₂³

D₁₃⋊C₁₆

yes

characteristic

134

Q₈

—

135

D₄

—

136

D₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

D₁₃⋊C₁₆

yes

characteristic

141

C₂×C₄

#88098

yes

—

142

C₂×C₄

#88111

yes

—

143

C₂×C₄

C₂×D₁₃⋊C₈

yes

characteristic

144

C₈

—

145

C₈

#88111

yes

—

146

C₈

C₂×#6118

yes

characteristic

147

C₈

C₂×C₂²⋊#261

yes

characteristic

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

#11718259

yes

—

152

C₂²

C₂×D₁₃⋊C₁₆

yes

characteristic

153

C₄

—

154

C₄

#11718259

yes

—

155

C₄

C₂×#88098

yes

characteristic

156

C₄

C₂×#88111

yes

characteristic

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

C₂×#11718259

yes

characteristic

	subgroup	G/H
center	C₈	C₂×C₂²⋊#261
commutator	C₂²×C₁₃	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂×C₁₃×M₃₂	C₄
socle	C₂×C₁₃	C₂×C₂²⋊C₁₆
prime radical	C₂×#6127	C₈
cosocle	C₂×#6090	C₂³
hypercenter	C₂×M₃₂	#261
hypocenter	C₁₃	#13556
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₈

C₂×C₂²⋊#261

commutator

C₂²×C₁₃

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×#261

Fitting

C₂×C₁₃×M₃₂

C₄

socle

C₂×C₁₃

C₂×C₂²⋊C₁₆

C₈

C₂³

C₂×M₃₂

C₁₃

G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
1. C₂×#11718249	C₂	semidirect
2. #13129952	C₂	semidirect
131. C₁₃	#13556	semidirect

H ≅ G/N

type

1. C₂×#11718249

C₂

semidirect

2. #13129952

C₂

semidirect

131. C₁₃

#13556

semidirect

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

subgroup	index
C₂×#11718249	2
#13129952	2
C₂×#11718568	2
#13556	13

subgroup

index

Subgroups — #16791175

Conjugacy classes of subgroups

Complements

Maximal subgroups