Group #14673967 — subgroups

Subgroups — #14673967

Order 2816.

330 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 155 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×#10622137	C₂	1	2	yes	maximal, complemented
2	C₂²⋊(C₁₁⋊C₃₂)	C₂	1	4	yes	maximal, complemented
3	C₂³×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₁	C₄	1	1	yes	characteristic
5	C₂²×C₁₁×C₁₆	—	2	4	no	—
6	C₂²×C₁₁×C₁₆	C₄	1	1	yes	characteristic
7	C₂²×C₁₁×C₁₆	C₄	1	2	yes	—
8	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
9	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	#10622137	—	2	4	no	—
11	C₂×C₁₁⋊C₃₂	C₂²	1	4	yes	complemented
12	C₂³×C₄×C₁₁	C₈	1	1	yes	characteristic
13	C₂²×C₈×C₁₁	—	2	2	no	—
14	C₂²×C₈×C₁₁	—	2	2	no	—
15	C₂²×C₈×C₁₁	C₈	1	2	yes	—
16	C₂²×C₈×C₁₁	C₈	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₁×C₁₆	—	2	2	no	—
20	C₂×C₁₁×C₁₆	—	2	4	no	—
21	C₂×C₁₁×C₁₆	—	2	4	no	—
22	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
23	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
24	C₂×C₁₁×C₁₆	D₄	1	4	yes	—
25	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
26	C₁₁⋊C₃₂	—	2	4	no	—
27	#13553	—	11	1	no	maximal, Sylow
28	C₂⁴×C₁₁	C₁₆	1	1	yes	characteristic
29	C₂²×C₄×C₁₁	—	2	2	no	—
30	C₂²×C₄×C₁₁	—	2	2	no	—
31	C₂²×C₄×C₁₁	C₁₆	1	1	yes	characteristic
32	C₂²×C₄×C₁₁	C₁₆	1	2	yes	—
33	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
34	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₁	—	2	4	no	—
36	C₂×C₈×C₁₁	—	2	2	no	—
37	C₂×C₈×C₁₁	—	2	2	no	—
38	C₂×C₈×C₁₁	—	2	2	no	—
39	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
40	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
43	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₁₁×C₁₆	—	2	2	no	—
45	C₁₁×C₁₆	C₂²⋊C₄	1	2	yes	—
46	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
47	C₂³×C₁₆	D₁₁	1	1	yes	characteristic
48	C₂×M₆₄	—	11	2	no	—
49	C₂²⋊C₃₂	—	11	4	no	—
50	C₂³×C₁₁	—	2	2	no	—
51	C₂³×C₁₁	—	2	4	no	—
52	C₂³×C₁₁	C₂×C₁₆	1	1	yes	characteristic
53	C₂³×C₁₁	C₂×C₁₆	1	2	yes	—
54	C₂×C₄×C₁₁	—	2	2	no	—
55	C₂×C₄×C₁₁	—	2	4	no	—
56	C₂×C₄×C₁₁	—	2	2	no	—
57	C₂×C₄×C₁₁	—	2	2	no	—
58	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
59	C₂×C₄×C₁₁	C₂×C₁₆	1	2	yes	—
60	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
61	C₂×C₄×C₁₁	M₃₂	1	2	yes	—
62	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
63	C₈×C₁₁	—	2	2	no	—
64	C₈×C₁₁	C₂²⋊C₈	1	2	yes	—
65	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₈×C₁₁	C₂×M₁₆	1	1	yes	characteristic
67	C₂³×C₈	Dic₁₁	1	1	yes	characteristic
68	C₂²×C₁₆	—	2	4	no	—
69	C₂²×C₁₆	Dic₁₁	1	1	yes	characteristic
70	C₂²×C₁₆	Dic₁₁	1	2	yes	—
71	C₂²×C₁₆	C₂×D₁₁	1	2	yes	—
72	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
73	M₆₄	—	22	4	no	—
74	C₂×C₃₂	—	11	4	no	—
75	C₂²×C₁₁	—	2	8	no	—
76	C₂²×C₁₁	—	2	2	no	—
77	C₂²×C₁₁	—	2	2	no	—
78	C₂²×C₁₁	—	2	2	no	—
79	C₂²×C₁₁	C₂²⋊C₁₆	1	2	yes	—
80	C₂²×C₁₁	M₆₄	1	4	yes	complemented
81	C₂²×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
82	C₄×C₁₁	—	2	2	no	—
83	C₄×C₁₁	C₂²⋊C₁₆	1	2	yes	—
84	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
85	C₄×C₁₁	C₂×M₃₂	1	1	yes	characteristic
86	C₂³×C₄	C₁₁⋊C₈	1	1	yes	characteristic
87	C₂²×C₈	—	2	2	no	—
88	C₂²×C₈	—	2	2	no	—
89	C₂²×C₈	C₁₁⋊C₈	1	1	yes	characteristic
90	C₂²×C₈	C₁₁⋊C₈	1	2	yes	—
91	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
92	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
93	C₂×C₁₆	—	2	2	no	—
94	C₂×C₁₆	—	2	4	no	—
95	C₂×C₁₆	—	2	4	no	—
96	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
97	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
98	C₂×C₁₆	C₂²⋊D₁₁	1	4	yes	—
99	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
100	C₃₂	—	22	4	no	—
101	C₂×C₁₁	—	2	2	no	—
102	C₂×C₁₁	—	2	4	no	—
103	C₂×C₁₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
104	C₂×C₁₁	C₂×M₆₄	1	2	yes	—
105	C₂⁴	C₁₁⋊C₁₆	1	1	yes	characteristic
106	C₂²×C₄	—	2	2	no	—
107	C₂²×C₄	—	2	2	no	—
108	C₂²×C₄	C₁₁⋊C₁₆	1	1	yes	characteristic
109	C₂²×C₄	C₁₁⋊C₁₆	1	2	yes	—
110	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
111	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
112	C₂×C₈	—	2	2	no	—
113	C₂×C₈	—	2	4	no	—
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	C₂×C₁₁⋊C₈	1	2	yes	—
117	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
118	C₂×C₈	#4318	1	2	yes	—
119	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
120	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
121	C₁₆	—	2	2	no	—
122	C₁₆	C₂²⋊Dic₁₁	1	2	yes	—
123	C₁₆	C₂×C₂²⋊D₁₁	1	2	yes	—
124	C₁₁	#13553	1	1	yes	characteristic, complemented, Sylow
125	C₂³	—	2	4	no	—
126	C₂³	—	2	2	no	—
127	C₂³	C₂×C₁₁⋊C₁₆	1	2	yes	—
128	C₂³	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	C₂×C₁₁⋊C₁₆	1	2	yes	—
134	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
135	C₂×C₄	#66876	1	2	yes	—
136	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	2	yes	—
137	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
138	C₈	—	2	2	no	—
139	C₈	C₂²⋊(C₁₁⋊C₈)	1	2	yes	—
140	C₈	C₂×#4318	1	1	yes	characteristic
141	C₈	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
142	C₂²	—	2	8	no	—
143	C₂²	—	2	2	no	—
144	C₂²	—	2	2	no	—
145	C₂²	—	2	2	no	—
146	C₂²	#10622137	1	4	yes	complemented
147	C₂²	C₂²⋊(C₁₁⋊C₁₆)	1	2	yes	—
148	C₂²	C₂²×C₁₁⋊C₁₆	1	1	yes	characteristic
149	C₄	—	2	2	no	—
150	C₄	C₂²⋊(C₁₁⋊C₁₆)	1	2	yes	—
151	C₄	C₂×#66876	1	1	yes	characteristic
152	C₄	C₂×C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
153	C₂	—	2	4	no	—
154	C₂	—	2	2	no	—
155	C₂	C₂×C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
156	C₂	C₂×#10622137	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622137

C₂

yes

maximal, complemented

C₂²⋊(C₁₁⋊C₃₂)

C₂

yes

maximal, complemented

C₂³×C₁₁×C₁₆

C₂

yes

maximal, characteristic

C₂³×C₈×C₁₁

C₄

yes

characteristic

C₂²×C₁₁×C₁₆

—

C₂²×C₁₁×C₁₆

C₄

yes

characteristic

C₂²×C₁₁×C₁₆

C₄

yes

—

C₂²×C₁₁×C₁₆

C₂²

yes

—

C₂²×C₁₁×C₁₆

C₂²

yes

characteristic

#10622137

—

C₂×C₁₁⋊C₃₂

C₂²

yes

complemented

C₂³×C₄×C₁₁

C₈

yes

characteristic

C₂²×C₈×C₁₁

—

C₂²×C₈×C₁₁

—

C₂²×C₈×C₁₁

C₈

yes

—

C₂²×C₈×C₁₁

C₈

yes

characteristic

C₂²×C₈×C₁₁

C₂×C₄

yes

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₁×C₁₆

D₄

yes

—

C₂×C₁₁×C₁₆

C₂³

yes

characteristic

C₁₁⋊C₃₂

—

#13553

—

maximal, Sylow

C₂⁴×C₁₁

C₁₆

yes

characteristic

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₁₆

yes

characteristic

C₂²×C₄×C₁₁

C₁₆

yes

—

C₂²×C₄×C₁₁

C₂×C₈

yes

—

C₂²×C₄×C₁₁

C₂×C₈

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₂×C₈

yes

—

C₂×C₈×C₁₁

C₂×C₈

yes

characteristic

C₂×C₈×C₁₁

M₁₆

yes

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₁₁×C₁₆

—

C₁₁×C₁₆

C₂²⋊C₄

yes

—

C₁₁×C₁₆

C₂×D₄

yes

—

C₂³×C₁₆

D₁₁

yes

characteristic

C₂×M₆₄

—

C₂²⋊C₃₂

—

C₂³×C₁₁

—

C₂³×C₁₁

—

C₂³×C₁₁

C₂×C₁₆

yes

characteristic

C₂³×C₁₁

C₂×C₁₆

yes

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂²⋊C₈

yes

—

C₂×C₄×C₁₁

C₂×C₁₆

yes

—

C₂×C₄×C₁₁

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₁

M₃₂

yes

—

C₂×C₄×C₁₁

C₂²×C₈

yes

characteristic

C₈×C₁₁

—

C₈×C₁₁

C₂²⋊C₈

yes

—

C₈×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₁₁

C₂×M₁₆

yes

characteristic

C₂³×C₈

Dic₁₁

yes

characteristic

C₂²×C₁₆

—

C₂²×C₁₆

Dic₁₁

yes

characteristic

C₂²×C₁₆

Dic₁₁

yes

—

C₂²×C₁₆

C₂×D₁₁

yes

—

C₂²×C₁₆

C₂×D₁₁

yes

characteristic

M₆₄

—

C₂×C₃₂

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂²⋊C₁₆

yes

—

C₂²×C₁₁

M₆₄

yes

complemented

C₂²×C₁₁

C₂²×C₁₆

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

C₂²⋊C₁₆

yes

—

C₄×C₁₁

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₁₁

C₂×M₃₂

yes

characteristic

C₂³×C₄

C₁₁⋊C₈

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₁₁⋊C₈

yes

characteristic

C₂²×C₈

C₁₁⋊C₈

yes

—

C₂²×C₈

C₂×Dic₁₁

yes

—

C₂²×C₈

C₂×Dic₁₁

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₁₁

yes

—

C₂×C₁₆

C₂×Dic₁₁

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₁

yes

—

C₂×C₁₆

C₂²×D₁₁

yes

characteristic

100

C₃₂

—

101

C₂×C₁₁

—

102

C₂×C₁₁

—

103

C₂×C₁₁

C₂×C₂²⋊C₁₆

yes

characteristic

104

C₂×C₁₁

C₂×M₆₄

yes

—

105

C₂⁴

C₁₁⋊C₁₆

yes

characteristic

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₁₁⋊C₁₆

yes

characteristic

109

C₂²×C₄

C₁₁⋊C₁₆

yes

—

110

C₂²×C₄

C₂×C₁₁⋊C₈

yes

—

111

C₂²×C₄

C₂×C₁₁⋊C₈

yes

characteristic

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₂×C₁₁⋊C₈

yes

—

117

C₂×C₈

C₂×C₁₁⋊C₈

yes

characteristic

118

C₂×C₈

#4318

yes

—

119

C₂×C₈

C₂²⋊Dic₁₁

yes

—

120

C₂×C₈

C₂²×Dic₁₁

yes

characteristic

121

C₁₆

—

122

C₁₆

C₂²⋊Dic₁₁

yes

—

123

C₁₆

C₂×C₂²⋊D₁₁

yes

—

124

C₁₁

#13553

yes

characteristic, complemented, Sylow

125

C₂³

—

126

C₂³

—

127

C₂³

C₂×C₁₁⋊C₁₆

yes

—

128

C₂³

C₂×C₁₁⋊C₁₆

yes

characteristic

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂×C₁₁⋊C₁₆

yes

—

134

C₂×C₄

C₂×C₁₁⋊C₁₆

yes

characteristic

135

C₂×C₄

#66876

yes

—

136

C₂×C₄

C₂²⋊(C₁₁⋊C₈)

yes

—

137

C₂×C₄

C₂²×C₁₁⋊C₈

yes

characteristic

138

C₈

—

139

C₈

C₂²⋊(C₁₁⋊C₈)

yes

—

140

C₈

C₂×#4318

yes

characteristic

141

C₈

C₂×C₂²⋊Dic₁₁

yes

characteristic

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

#10622137

yes

complemented

147

C₂²

C₂²⋊(C₁₁⋊C₁₆)

yes

—

148

C₂²

C₂²×C₁₁⋊C₁₆

yes

characteristic

149

C₄

—

150

C₄

C₂²⋊(C₁₁⋊C₁₆)

yes

—

151

C₄

C₂×#66876

yes

characteristic

152

C₄

C₂×C₂²⋊(C₁₁⋊C₈)

yes

characteristic

153

C₂

—

154

C₂

—

155

C₂

C₂×C₂²⋊(C₁₁⋊C₁₆)

yes

characteristic

156

C₂

C₂×#10622137

yes

—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₁₁
commutator, socle	C₂²×C₁₁	C₂²×C₁₆
Fitting	C₂³×C₁₁×C₁₆	C₂
prime radical	C₂⁴×C₁₁	C₁₆
cosocle	C₂×C₁₁×C₁₆	C₂³
hypercenter	C₂³×C₁₆	D₁₁
hypocenter	C₁₁	#13553
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂³×C₁₆

subgroup

G/H

center, Frattini

C₂×C₁₆

C₂²×D₁₁

commutator, socle

C₂²×C₁₁

C₂²×C₁₆

Fitting

C₂³×C₁₁×C₁₆

C₂

prime radical

C₂⁴×C₁₁

C₁₆

cosocle

C₂×C₁₁×C₁₆

C₂³

hypercenter

C₂³×C₁₆

D₁₁

C₁₁

G ▷ C₂²×C₁₁ ▷ C₁₁

C₁ ◁ C₂×C₁₆ ◁ C₂³×C₁₆

N	H ≅ G/N	type
1. C₂×#10622137	C₂	semidirect
2. C₂²⋊(C₁₁⋊C₃₂)	C₂	semidirect
11. C₂×C₁₁⋊C₃₂	C₂²	semidirect
80. C₂²×C₁₁	M₆₄	semidirect
124. C₁₁	#13553	semidirect
146. C₂²	#10622137	semidirect

H ≅ G/N

type

1. C₂×#10622137

C₂

semidirect

2. C₂²⋊(C₁₁⋊C₃₂)

C₂

semidirect

11. C₂×C₁₁⋊C₃₂

C₂²

semidirect

80. C₂²×C₁₁

M₆₄

semidirect

124. C₁₁

#13553

semidirect

146. C₂²

#10622137

semidirect

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

subgroup	index
C₂×#10622137	2
C₂²⋊(C₁₁⋊C₃₂)	2
C₂³×C₁₁×C₁₆	2
#13553	11

subgroup

index

C₂×#10622137

C₂²⋊(C₁₁⋊C₃₂)

C₂³×C₁₁×C₁₆

#13553

Subgroups — #14673967

Conjugacy classes of subgroups

Complements

Maximal subgroups