Group #16791166 — subgroups

Subgroups — #16791166

Order 3328.

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×#11718249	C₂	1	2	yes	maximal, complemented
2	#13129950	C₂	1	4	yes	maximal, complemented
3	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
5	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
6	C₂²×#6090	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×D₁₃	—	2	4	no	—
8	C₂×C₁₆×D₁₃	C₄	1	2	yes	—
9	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
10	#11718249	—	2	4	no	—
11	C₂×#88036	C₂²	1	4	yes	complemented
12	C₂²×C₄×D₁₃	C₈	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×#1055	C₈	1	1	yes	characteristic
15	C₂×C₈×D₁₃	—	2	2	no	—
16	C₂×C₈×D₁₃	—	2	2	no	—
17	C₂×C₈×D₁₃	C₈	1	2	yes	—
18	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	—	2	2	no	—
20	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
21	C₂×#6090	C₂×C₄	1	1	yes	characteristic
22	C₂×#6090	D₄	1	4	yes	—
23	C₂×#6090	C₂³	1	1	yes	characteristic
24	C₁₆×D₁₃	—	2	4	no	—
25	C₁₆×D₁₃	—	2	4	no	—
26	#88036	—	2	4	no	—
27	#13553	—	13	1	no	maximal, Sylow
28	C₂³×D₁₃	C₁₆	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
30	C₂²×Dic₁₃	C₁₆	1	1	yes	characteristic
31	C₂×C₄×D₁₃	—	2	2	no	—
32	C₂×C₄×D₁₃	—	2	2	no	—
33	C₂×C₄×D₁₃	C₁₆	1	2	yes	—
34	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
35	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
36	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
38	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×#1055	—	2	2	no	—
40	C₂×#1055	C₂×C₈	1	2	yes	—
41	C₈×D₁₃	—	2	4	no	—
42	C₈×D₁₃	—	2	2	no	—
43	C₈×D₁₃	—	2	2	no	—
44	C₁₃×C₁₆	—	2	2	no	—
45	#6090	C₂²⋊C₄	1	2	yes	—
46	#6090	C₂×D₄	1	2	yes	—
47	C₂³×C₁₆	—	13	1	no	—
48	C₂×M₆₄	—	13	2	no	—
49	C₂²⋊C₃₂	—	13	4	no	—
50	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
51	C₂²×D₁₃	—	2	2	no	—
52	C₂²×D₁₃	—	2	4	no	—
53	C₂²×D₁₃	C₂×C₁₆	1	2	yes	—
54	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
55	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
56	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
57	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
58	C₂×Dic₁₃	—	2	2	no	—
59	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
60	C₄×D₁₃	—	2	4	no	—
61	C₄×D₁₃	—	2	2	no	—
62	C₄×D₁₃	—	2	2	no	—
63	C₈×C₁₃	C₂²⋊C₈	1	2	yes	—
64	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
66	#1055	—	2	2	no	—
67	C₂³×C₈	—	13	1	no	—
68	C₂²×C₁₆	—	13	1	no	—
69	C₂²×C₁₆	—	13	2	no	—
70	C₂²×C₁₆	—	13	2	no	—
71	C₂²×C₁₆	—	26	4	no	—
72	C₂²×C₁₆	#261	1	1	yes	characteristic
73	M₆₄	—	26	4	no	—
74	C₂×C₃₂	—	13	4	no	—
75	C₂²×C₁₃	—	2	2	no	—
76	C₂²×C₁₃	C₂²⋊C₁₆	1	2	yes	—
77	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
78	C₂×D₁₃	—	2	8	no	—
79	C₂×D₁₃	—	2	2	no	—
80	C₂×D₁₃	—	2	2	no	—
81	C₂×D₁₃	M₆₄	1	4	yes	complemented
82	C₄×C₁₃	C₂²⋊C₁₆	1	2	yes	—
83	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
84	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
85	Dic₁₃	—	2	2	no	—
86	C₂³×C₄	—	13	1	no	—
87	C₂²×C₈	—	13	1	no	—
88	C₂²×C₈	—	13	2	no	—
89	C₂²×C₈	—	13	2	no	—
90	C₂²×C₈	—	26	2	no	—
91	C₂²×C₈	—	26	2	no	—
92	C₂²×C₈	C₂×#261	1	1	yes	characteristic
93	C₂×C₁₆	—	2	2	no	—
94	C₂×C₁₆	—	13	4	no	—
95	C₂×C₁₆	—	13	1	no	—
96	C₂×C₁₆	—	13	1	no	—
97	C₂×C₁₆	—	26	4	no	—
98	C₂×C₁₆	—	26	4	no	—
99	C₂×C₁₆	C₂×#261	1	2	yes	—
100	C₃₂	—	26	4	no	—
101	C₂×C₁₃	—	2	2	no	—
102	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
103	C₂×C₁₃	C₂×M₆₄	1	2	yes	—
104	D₁₃	—	2	4	no	—
105	C₂⁴	—	13	1	no	—
106	C₂²×C₄	—	13	1	no	—
107	C₂²×C₄	—	13	2	no	—
108	C₂²×C₄	—	13	2	no	—
109	C₂²×C₄	—	26	2	no	—
110	C₂²×C₄	—	26	2	no	—
111	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
112	C₂×C₈	—	13	2	no	—
113	C₂×C₈	—	26	2	no	—
114	C₂×C₈	—	26	4	no	—
115	C₂×C₈	—	26	2	no	—
116	C₂×C₈	—	26	2	no	—
117	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
118	C₂×C₈	#6118	1	2	yes	—
119	C₂×C₈	C₂²⋊#261	1	2	yes	—
120	C₂×C₈	C₂²×#261	1	1	yes	characteristic
121	C₁₆	—	2	2	no	—
122	C₁₆	—	13	2	no	—
123	C₁₆	—	13	2	no	—
124	C₁₃	#13553	1	1	yes	characteristic, complemented, Sylow
125	C₂³	—	13	2	no	—
126	C₂³	—	26	4	no	—
127	C₂³	—	26	2	no	—
128	C₂³	D₁₃⋊C₁₆	1	1	yes	characteristic
129	C₂×C₄	—	13	2	no	—
130	C₂×C₄	—	26	2	no	—
131	C₂×C₄	—	26	4	no	—
132	C₂×C₄	—	26	2	no	—
133	C₂×C₄	—	26	2	no	—
134	C₂×C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
135	C₂×C₄	#88098	1	2	yes	—
136	C₂×C₄	#88111	1	2	yes	—
137	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
138	C₈	—	26	2	no	—
139	C₈	#88111	1	2	yes	—
140	C₈	C₂×#6118	1	1	yes	characteristic
141	C₈	C₂×C₂²⋊#261	1	1	yes	characteristic
142	C₂²	—	2	2	no	—
143	C₂²	—	13	4	no	—
144	C₂²	—	26	8	no	—
145	C₂²	—	26	2	no	—
146	C₂²	—	26	2	no	—
147	C₂²	#11718259	1	2	yes	—
148	C₂²	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
149	C₄	—	26	2	no	—
150	C₄	#11718259	1	2	yes	—
151	C₄	C₂×#88098	1	1	yes	characteristic
152	C₄	C₂×#88111	1	1	yes	characteristic
153	C₂	—	2	2	no	—
154	C₂	—	26	4	no	—
155	C₂	C₂×#11718259	1	1	yes	characteristic
156	C₂	D₁₃⋊M₆₄	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718249

C₂

yes

maximal, complemented

#13129950

C₂

yes

maximal, complemented

C₂²×C₁₆×D₁₃

C₂

yes

maximal, characteristic

C₂²×C₈×D₁₃

C₄

yes

characteristic

C₂²×C₁₃×C₁₆

C₄

yes

characteristic

C₂²×#6090

C₂²

yes

characteristic

C₂×C₁₆×D₁₃

—

C₂×C₁₆×D₁₃

C₄

yes

—

C₂×C₁₆×D₁₃

C₂²

yes

—

#11718249

—

C₂×#88036

C₂²

yes

complemented

C₂²×C₄×D₁₃

C₈

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×#1055

C₈

yes

characteristic

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

C₈

yes

—

C₂×C₈×D₁₃

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₂×#6090

C₂×C₄

yes

characteristic

C₂×#6090

D₄

yes

—

C₂×#6090

C₂³

yes

characteristic

C₁₆×D₁₃

—

C₁₆×D₁₃

—

#88036

—

#13553

—

maximal, Sylow

C₂³×D₁₃

C₁₆

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂²×Dic₁₃

C₁₆

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₁₆

yes

—

C₂×C₄×D₁₃

C₂×C₈

yes

—

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

C₂×#1055

—

C₂×#1055

C₂×C₈

yes

—

C₈×D₁₃

—

C₈×D₁₃

—

C₈×D₁₃

—

C₁₃×C₁₆

—

#6090

C₂²⋊C₄

yes

—

#6090

C₂×D₄

yes

—

C₂³×C₁₆

—

C₂×M₆₄

—

C₂²⋊C₃₂

—

C₂³×C₁₃

C₂×C₁₆

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

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

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×C₁₆

yes

—

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

—

C₈×C₁₃

C₂²⋊C₈

yes

—

C₈×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₁₃

C₂×M₁₆

yes

characteristic

#1055

—

C₂³×C₈

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂²×C₁₆

#261

yes

characteristic

M₆₄

—

C₂×C₃₂

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂²⋊C₁₆

yes

—

C₂²×C₁₃

C₂²×C₁₆

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

M₆₄

yes

complemented

C₄×C₁₃

C₂²⋊C₁₆

yes

—

C₄×C₁₃

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₁₃

C₂×M₃₂

yes

characteristic

Dic₁₃

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×#261

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#261

yes

—

100

C₃₂

—

101

C₂×C₁₃

—

102

C₂×C₁₃

C₂×C₂²⋊C₁₆

yes

characteristic

103

C₂×C₁₃

C₂×M₆₄

yes

—

104

D₁₃

—

105

C₂⁴

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

D₁₃⋊C₈

yes

characteristic

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

D₁₃⋊C₈

yes

characteristic

118

C₂×C₈

#6118

yes

—

119

C₂×C₈

C₂²⋊#261

yes

—

120

C₂×C₈

C₂²×#261

yes

characteristic

121

C₁₆

—

122

C₁₆

—

123

C₁₆

—

124

C₁₃

#13553

yes

characteristic, complemented, Sylow

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

D₁₃⋊C₁₆

yes

characteristic

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

D₁₃⋊C₁₆

yes

characteristic

135

C₂×C₄

#88098

yes

—

136

C₂×C₄

#88111

yes

—

137

C₂×C₄

C₂×D₁₃⋊C₈

yes

characteristic

138

C₈

—

139

C₈

#88111

yes

—

140

C₈

C₂×#6118

yes

characteristic

141

C₈

C₂×C₂²⋊#261

yes

characteristic

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

#11718259

yes

—

148

C₂²

C₂×D₁₃⋊C₁₆

yes

characteristic

149

C₄

—

150

C₄

#11718259

yes

—

151

C₄

C₂×#88098

yes

characteristic

152

C₄

C₂×#88111

yes

characteristic

153

C₂

—

154

C₂

—

155

C₂

C₂×#11718259

yes

characteristic

156

C₂

D₁₃⋊M₆₄

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₂²×C₁₃×C₁₆	C₄
prime radical	C₂³×D₁₃	C₁₆
cosocle	C₂×#6090	C₂³
hypercenter	C₂²×C₁₆	#261
hypocenter	C₁₃	#13553
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#261

commutator, socle

C₂²×C₁₃

C₂²×C₁₆

Fitting

C₂²×C₁₃×C₁₆

C₄

prime radical

C₂³×D₁₃

C₁₆

C₂³

C₂²×C₁₆

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
1. C₂×#11718249	C₂	semidirect
2. #13129950	C₂	semidirect
11. C₂×#88036	C₂²	semidirect
81. C₂×D₁₃	M₆₄	semidirect
124. C₁₃	#13553	semidirect

H ≅ G/N

type

1. C₂×#11718249

C₂

semidirect

2. #13129950

C₂

semidirect

11. C₂×#88036

C₂²

semidirect

81. C₂×D₁₃

M₆₄

semidirect

124. C₁₃

#13553

semidirect

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

subgroup	index
C₂×#11718249	2
#13129950	2
C₂²×C₁₆×D₁₃	2
#13553	13

subgroup

index

C₂×#11718249

#13129950

C₂²×C₁₆×D₁₃

#13553

Subgroups — #16791166

Conjugacy classes of subgroups

Complements

Maximal subgroups