Group #14672366 — subgroups

Subgroups — #14672366

Order 2816.

334 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10622296	C₂	1	1	yes	maximal, characteristic
2	#13070372	C₂	1	1	yes	maximal, characteristic
3	#13066726	C₂	1	4	yes	maximal
4	C₄×C₁₁×#108	C₂	1	1	yes	maximal, characteristic
5	C₂×#66923	—	2	1	no	—
6	C₂×C₁₁×#108	C₂²	1	2	yes	—
7	C₄×C₁₁×M₁₆	—	2	1	no	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×#66882	C₂²	1	2	yes	—
10	C₂×#66881	—	2	1	no	—
11	C₂×#66876	C₂²	1	2	yes	—
12	#10622296	—	2	2	no	—
13	#10622296	C₄	1	4	yes	—
14	C₁₁×#341	—	2	1	no	—
15	C₄⋊(C₁₁⋊C₁₆)	—	2	2	no	—
16	C₂×C₁₁×M₁₆	—	2	2	no	—
17	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₁	—	2	2	no	—
21	C₂×Dic₁₁⋊C₄	—	4	2	no	—
22	#66923	—	2	4	no	—
23	#66923	—	4	1	no	—
24	#66923	—	4	1	no	—
25	C₁₁×#108	—	2	2	no	—
26	C₁₁×#108	Q₈	1	4	yes	—
27	C₁₁×#97	—	4	1	no	—
28	C₄×C₈×C₁₁	—	4	1	no	—
29	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₁	D₄	1	2	yes	—
31	#66882	—	2	2	no	—
32	#66882	C₂×C₄	1	4	yes	—
33	#66881	—	2	4	no	—
34	#66876	—	2	4	no	—
35	C₂×C₁₁⋊C₁₆	—	2	2	no	—
36	#13280	—	11	1	no	maximal, Sylow
37	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
38	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂²×Dic₁₁	—	4	2	no	—
40	C₁₁×M₁₆	—	2	4	no	—
41	C₁₁×M₁₆	—	4	2	no	—
42	C₂×C₈×C₁₁	—	2	2	no	—
43	C₂×C₈×C₁₁	—	4	2	no	—
44	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
45	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
48	C₂×C₈×C₁₁	#41	1	2	yes	—
49	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
50	C₄²×C₁₁	D₈	1	1	yes	characteristic
51	C₄²×C₁₁	D₈	1	1	yes	characteristic
52	C₄⋊Dic₁₁	—	2	4	no	—
53	C₄⋊Dic₁₁	—	4	2	no	—
54	Dic₁₁⋊C₄	—	4	4	no	—
55	Dic₁₁⋊C₄	—	4	4	no	—
56	C₁₁⋊C₁₆	—	4	2	no	—
57	C₂×#499	—	11	1	no	—
58	#2150	—	11	1	no	—
59	C₄×#108	D₁₁	1	1	yes	characteristic
60	#1387	—	11	4	no	—
61	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
62	C₂×C₄×C₁₁	—	4	2	no	—
63	C₂×C₄×C₁₁	#102	1	2	yes	—
64	C₂×C₄×C₁₁	#102	1	2	yes	—
65	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
67	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₁₁	#137	1	2	yes	—
69	C₂×Dic₁₁	—	4	4	no	—
70	C₂×Dic₁₁	—	8	4	no	—
71	C₈×C₁₁	—	2	2	no	—
72	C₈×C₁₁	—	4	4	no	—
73	C₈×C₁₁	C₄×Q₈	1	2	yes	—
74	C₈×C₁₁	#124	1	1	yes	characteristic
75	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
76	C₂×#125	—	22	1	no	—
77	C₂×M₃₂	—	11	2	no	—
78	#499	—	11	4	no	—
79	#499	—	22	2	no	—
80	C₂×#108	C₂×D₁₁	1	2	yes	—
81	C₂×#107	—	11	2	no	—
82	C₂×#106	—	22	1	no	—
83	C₄×M₁₆	—	2	1	no	—
84	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
85	C₄⋊C₁₆	—	22	2	no	—
86	#341	—	2	1	no	—
87	C₂²×C₁₁	—	2	2	no	—
88	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
89	C₂²×C₁₁	#475	1	2	yes	—
90	C₄×C₁₁	—	2	2	no	—
91	C₄×C₁₁	—	2	2	no	—
92	C₄×C₁₁	#391	1	1	yes	characteristic
93	C₄×C₁₁	#419	1	1	yes	characteristic
94	C₄×C₁₁	#474	1	2	yes	—
95	Dic₁₁	—	8	4	no	—
96	C₂×M₁₆	—	2	2	no	—
97	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
98	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
99	#125	—	22	4	no	—
100	#125	—	44	1	no	—
101	#125	—	44	1	no	—
102	C₂×C₄⋊C₄	—	22	2	no	—
103	C₂×C₄⋊C₄	—	44	2	no	—
104	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
105	M₃₂	—	22	4	no	—
106	C₂×C₁₆	—	22	2	no	—
107	#108	—	2	2	no	—
108	#108	Dic₂₂	1	4	yes	—
109	#107	—	11	4	no	—
110	#107	—	22	2	no	—
111	#106	—	22	4	no	—
112	#97	—	4	1	no	—
113	C₄×C₈	—	4	1	no	—
114	C₄×C₈	C₄×D₁₁	1	2	yes	—
115	C₄×C₈	D₄₄	1	2	yes	—
116	C₂×C₁₁	—	2	2	no	—
117	C₂×C₁₁	#1988	1	1	yes	characteristic
118	C₂×C₁₁	#2148	1	2	yes	—
119	C₂²×C₄	—	44	2	no	—
120	C₂²×C₄	#4325	1	2	yes	—
121	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
122	M₁₆	—	2	4	no	—
123	M₁₆	—	4	2	no	—
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	4	2	no	—
126	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
127	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
128	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
129	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
130	C₂×C₈	#4339	1	2	yes	—
131	C₄⋊C₄	—	22	4	no	—
132	C₄⋊C₄	—	44	4	no	—
133	C₄⋊C₄	—	44	4	no	—
134	C₄⋊C₄	—	44	2	no	—
135	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
136	C₄²	#4323	1	1	yes	characteristic
137	C₄²	#4323	1	1	yes	characteristic
138	C₁₆	—	44	2	no	—
139	C₁₁	#13280	1	1	yes	characteristic, complemented, Sylow
140	C₂³	C₂×#4325	1	1	yes	characteristic
141	C₂×C₄	—	4	2	no	—
142	C₂×C₄	—	44	4	no	—
143	C₂×C₄	—	88	4	no	—
144	C₂×C₄	#66873	1	2	yes	—
145	C₂×C₄	#66873	1	2	yes	—
146	C₂×C₄	#66977	1	2	yes	—
147	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
148	C₂×C₄	C₂×#4323	1	1	yes	characteristic
149	C₂×C₄	#67004	1	2	yes	—
150	C₈	—	2	2	no	—
151	C₈	—	4	4	no	—
152	C₈	C₄×Dic₂₂	1	2	yes	—
153	C₈	#66922	1	1	yes	characteristic
154	C₈	#66928	1	1	yes	characteristic
155	C₂²	—	2	2	no	—
156	C₂²	C₂×#66873	1	1	yes	characteristic
157	C₂²	#10622633	1	2	yes	—
158	C₄	—	2	2	no	—
159	C₄	—	2	2	no	—
160	C₄	—	88	4	no	—
161	C₄	#10622542	1	1	yes	characteristic
162	C₄	#10622617	1	1	yes	characteristic
163	C₄	#10622620	1	2	yes	—
164	C₂	—	2	2	no	—
165	C₂	#13069568	1	1	yes	characteristic
166	C₂	#13070363	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622296

C₂

yes

maximal, characteristic

#13070372

C₂

yes

maximal, characteristic

#13066726

C₂

yes

maximal

C₄×C₁₁×#108

C₂

yes

maximal, characteristic

C₂×#66923

—

C₂×C₁₁×#108

C₂²

yes

—

C₄×C₁₁×M₁₆

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66882

C₂²

yes

—

C₂×#66881

—

C₂×#66876

C₂²

yes

—

#10622296

—

#10622296

C₄

yes

—

C₁₁×#341

—

C₄⋊(C₁₁⋊C₁₆)

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×Dic₁₁⋊C₄

—

#66923

—

#66923

—

#66923

—

C₁₁×#108

—

C₁₁×#108

Q₈

yes

—

C₁₁×#97

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

#66882

—

#66882

C₂×C₄

yes

—

#66881

—

#66876

—

C₂×C₁₁⋊C₁₆

—

#13280

—

maximal, Sylow

C₂²×C₄×C₁₁

SD₁₆

yes

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×Dic₁₁

—

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

—

C₂×C₈×C₁₁

#41

yes

—

C₄²×C₁₁

C₂²⋊C₄

yes

—

C₄²×C₁₁

D₈

yes

characteristic

C₄²×C₁₁

D₈

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

Dic₁₁⋊C₄

—

C₁₁⋊C₁₆

—

C₂×#499

—

#2150

—

C₄×#108

D₁₁

yes

characteristic

#1387

—

C₂³×C₁₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#102

yes

—

C₂×C₄×C₁₁

#102

yes

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

C₄×Q₈

yes

—

C₈×C₁₁

#124

yes

characteristic

C₈×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×#125

—

C₂×M₃₂

—

#499

—

#499

—

C₂×#108

C₂×D₁₁

yes

—

C₂×#107

—

C₂×#106

—

C₄×M₁₆

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₄⋊C₁₆

—

#341

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂×#102

yes

characteristic

C₂²×C₁₁

#475

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

Dic₁₁

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₁

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

#125

—

100

#125

—

101

#125

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄²

C₂²⋊D₁₁

yes

characteristic

105

M₃₂

—

106

C₂×C₁₆

—

107

#108

—

108

#108

Dic₂₂

yes

—

109

#107

—

110

#107

—

111

#106

—

112

#97

—

113

C₄×C₈

—

114

C₄×C₈

C₄×D₁₁

yes

—

115

C₄×C₈

D₄₄

yes

—

116

C₂×C₁₁

—

117

C₂×C₁₁

#1988

yes

characteristic

118

C₂×C₁₁

#2148

yes

—

119

C₂²×C₄

—

120

C₂²×C₄

#4325

yes

—

121

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

122

M₁₆

—

123

M₁₆

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

127

C₂×C₈

C₂×Dic₂₂

yes

—

128

C₂×C₈

C₂×C₄×D₁₁

yes

characteristic

129

C₂×C₈

C₂×D₄₄

yes

characteristic

130

C₂×C₈

#4339

yes

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄²

(C₂×D₁₁)⋊C₄

yes

—

136

C₄²

#4323

yes

characteristic

137

C₄²

#4323

yes

characteristic

138

C₁₆

—

139

C₁₁

#13280

yes

characteristic, complemented, Sylow

140

C₂³

C₂×#4325

yes

characteristic

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

#66873

yes

—

145

C₂×C₄

#66873

yes

—

146

C₂×C₄

#66977

yes

—

147

C₂×C₄

C₂×(C₂×D₁₁)⋊C₄

yes

characteristic

148

C₂×C₄

C₂×#4323

yes

characteristic

149

C₂×C₄

#67004

yes

—

150

C₈

—

151

C₈

—

152

C₈

C₄×Dic₂₂

yes

—

153

C₈

#66922

yes

characteristic

154

C₈

#66928

yes

characteristic

155

C₂²

—

156

C₂²

C₂×#66873

yes

characteristic

157

C₂²

#10622633

yes

—

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

#10622542

yes

characteristic

162

C₄

#10622617

yes

characteristic

163

C₄

#10622620

yes

—

164

C₂

—

165

C₂

#13069568

yes

characteristic

166

C₂

#13070363

yes

—

	subgroup	G/H
center	C₂²	C₂×#66873
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₄×C₁₁×#108	C₂
socle	C₂²×C₁₁	C₂×#102
prime radical	C₂³×C₁₁	C₂×SD₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₄×#108	D₁₁
hypocenter	C₁₁	#13280
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#108

subgroup

G/H

center

C₂²

C₂×#66873

commutator

C₂×C₈×C₁₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₄×C₁₁×#108

C₂

socle

C₂²×C₁₁

C₂×#102

prime radical

C₂³×C₁₁

C₂×SD₁₆

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#108

N	H ≅ G/N	type
139. C₁₁	#13280	semidirect

H ≅ G/N

type

139. C₁₁

#13280

semidirect

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

subgroup	index
C₂×#10622296	2
#13070372	2
#13066726	2
C₄×C₁₁×#108	2
#13280	11

subgroup

index

C₄×C₁₁×#108

Subgroups — #14672366

Conjugacy classes of subgroups

Complements

Maximal subgroups