Group #14641024 — subgroups

Subgroups — #14641024

Order 2816.

208 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 87 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	C₄×#66883	C₂	1	1	yes	maximal, characteristic
2	#13067379	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2162	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×#66883	—	2	1	no	—
6	#10622539	—	2	1	no	—
7	C₄×#4318	—	2	1	no	—
8	C₁₁×C₄⋊C₁₆	C₄	1	2	yes	—
9	C₁₁×C₂²⋊C₁₆	—	2	1	no	—
10	C₄×C₁₁×C₁₆	—	2	1	no	—
11	#10622190	C₄	1	2	yes	—
12	#10622096	C₄	1	2	yes	—
13	#10622095	—	2	1	no	—
14	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
17	C₂×#4318	—	2	2	no	—
18	C₂×C₁₁×C₁₆	—	2	2	no	—
19	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
22	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
23	C₂²⋊(C₁₁⋊C₈)	—	4	1	no	—
24	#66883	—	2	4	no	—
25	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
26	#66867	—	4	1	no	—
27	#66867	—	4	1	no	—
28	C₄×C₁₁⋊C₈	—	4	1	no	—
29	#7297	—	11	1	no	maximal, Sylow
30	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
32	C₂²×C₄×C₁₁	Q₁₆	1	1	yes	characteristic
33	C₂×C₈×C₁₁	—	2	2	no	—
34	C₂×C₈×C₁₁	—	4	1	no	—
35	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
39	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
40	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
41	C₄²×C₁₁	D₈	1	1	yes	characteristic
42	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
43	#4318	—	2	4	no	—
44	#4318	—	4	2	no	—
45	C₂×C₁₁⋊C₈	—	4	2	no	—
46	C₂×C₁₁⋊C₈	—	4	2	no	—
47	C₁₁×C₁₆	—	4	2	no	—
48	#2162	D₁₁	1	1	yes	characteristic
49	C₄×#108	—	11	1	no	—
50	#1568	—	11	1	no	—
51	C₂³×C₁₁	#103	1	1	yes	characteristic
52	C₂×C₄×C₁₁	—	2	1	no	—
53	C₂×C₄×C₁₁	—	2	1	no	—
54	C₂×C₄×C₁₁	—	2	2	no	—
55	C₂×C₄×C₁₁	—	4	1	no	—
56	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
57	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
58	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
59	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
60	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
61	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
62	C₈×C₁₁	—	2	1	no	—
63	C₈×C₁₁	—	2	1	no	—
64	C₈×C₁₁	—	2	1	no	—
65	C₈×C₁₁	#104	1	2	yes	—
66	C₁₁⋊C₈	—	4	4	no	—
67	C₁₁⋊C₈	—	8	2	no	—
68	#432	—	22	1	no	—
69	C₂×#108	—	22	1	no	—
70	C₄×M₁₆	—	22	1	no	—
71	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
72	C₄⋊C₁₆	Dic₁₁	1	2	yes	—
73	C₂²⋊C₁₆	—	2	1	no	—
74	C₄×C₁₆	—	2	1	no	—
75	#341	—	11	2	no	—
76	#335	—	11	2	no	—
77	#334	—	22	1	no	—
78	C₂²×C₁₁	—	2	1	no	—
79	C₂²×C₁₁	—	2	1	no	—
80	C₂²×C₁₁	—	2	1	no	—
81	C₂²×C₁₁	#340	1	1	yes	characteristic
82	C₄×C₁₁	—	2	1	no	—
83	C₄×C₁₁	—	2	1	no	—
84	C₄×C₁₁	—	2	1	no	—
85	C₄×C₁₁	—	2	1	no	—
86	C₄×C₁₁	#339	1	1	yes	characteristic
87	C₄×C₁₁	#344	1	1	yes	characteristic
88	C₄×C₁₁	#359	1	2	yes	—
89	C₂×M₁₆	—	22	2	no	—
90	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
91	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
92	C₂×C₄²	D₄₄	1	1	yes	characteristic
93	C₂×C₁₆	—	2	2	no	—
94	#108	—	22	4	no	—
95	C₄⋊C₈	—	22	2	no	—
96	C₂²⋊C₈	—	44	1	no	—
97	#97	—	44	1	no	—
98	#97	—	44	1	no	—
99	C₄×C₈	—	44	1	no	—
100	C₄×C₈	Dic₂₂	1	1	yes	characteristic
101	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
102	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
103	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
104	C₂×C₁₁	—	4	1	no	—
105	C₂×C₁₁	#1303	1	1	yes	characteristic
106	C₂×C₁₁	#1382	1	1	yes	characteristic
107	C₂×C₁₁	#1388	1	1	yes	characteristic
108	C₂²×C₄	#4314	1	1	yes	characteristic
109	C₂²×C₄	Dic₄₄	1	1	yes	characteristic
110	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
111	M₁₆	—	22	4	no	—
112	M₁₆	—	44	2	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	44	2	no	—
116	C₂×C₈	—	44	2	no	—
117	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
118	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
119	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
120	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
121	C₄²	#4314	1	1	yes	characteristic
122	C₄²	D₈₈	1	1	yes	characteristic
123	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
124	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
125	C₁₆	—	4	2	no	—
126	C₁₁	#7297	1	1	yes	characteristic, complemented, Sylow
127	C₂³	#66880	1	1	yes	characteristic
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	#66880	1	1	yes	characteristic
133	C₂×C₄	#66881	1	1	yes	characteristic
134	C₂×C₄	#66882	1	1	yes	characteristic
135	C₂×C₄	#66885	1	1	yes	characteristic
136	C₂×C₄	#66885	1	1	yes	characteristic
137	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
138	C₈	—	2	1	no	—
139	C₈	—	2	1	no	—
140	C₈	—	2	1	no	—
141	C₈	—	44	4	no	—
142	C₈	—	88	2	no	—
143	C₈	#66901	1	2	yes	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	#10622189	1	1	yes	characteristic
148	C₄	—	2	1	no	—
149	C₄	—	2	1	no	—
150	C₄	—	2	1	no	—
151	C₄	—	2	1	no	—
152	C₄	#10622148	1	2	yes	—
153	C₄	#10622170	1	1	yes	characteristic
154	C₄	#10622197	1	1	yes	characteristic
155	C₂	—	4	1	no	—
156	C₂	#13066518	1	1	yes	characteristic
157	C₂	#13066712	1	1	yes	characteristic
158	C₂	#13066728	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#66883

C₂

yes

maximal, characteristic

#13067379

C₂

yes

maximal, characteristic

C₁₁×#2162

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

—

—

C₁₁×C₄⋊C₁₆

C₄

yes

—

C₁₁×C₂²⋊C₁₆

—

C₄×C₁₁×C₁₆

—

#10622190

C₄

yes

—

#10622096

C₄

yes

—

#10622095

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×#4318

—

C₂×C₁₁×C₁₆

—

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

characteristic

C₄×C₈×C₁₁

Q₈

yes

characteristic

C₂²⋊(C₁₁⋊C₈)

—

#66883

—

C₄⋊(C₁₁⋊C₈)

—

#66867

—

#66867

—

C₄×C₁₁⋊C₈

—

#7297

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₁

SD₁₆

yes

characteristic

C₂²×C₄×C₁₁

Q₁₆

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄²

yes

characteristic

C₂×C₈×C₁₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

characteristic

C₄²×C₁₁

C₂²⋊C₄

yes

characteristic

C₄²×C₁₁

C₄⋊C₄

yes

characteristic

C₄²×C₁₁

D₈

yes

characteristic

C₄²×C₁₁

SD₁₆

yes

characteristic

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

—

#2162

D₁₁

yes

characteristic

C₄×#108

—

#1568

—

C₂³×C₁₁

#103

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#104

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

#432

—

C₂×#108

—

C₄×M₁₆

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₄⋊C₁₆

Dic₁₁

yes

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

#341

—

#335

—

#334

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#340

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

C₂×M₁₆

—

C₂²×C₈

C₄×D₁₁

yes

characteristic

C₂²×C₈

C₂²⋊D₁₁

yes

characteristic

C₂×C₄²

D₄₄

yes

characteristic

C₂×C₁₆

—

#108

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

100

C₄×C₈

Dic₂₂

yes

characteristic

101

C₄×C₈

C₄×D₁₁

yes

characteristic

102

C₄×C₈

C₂×Dic₁₁

yes

characteristic

103

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

104

C₂×C₁₁

—

105

C₂×C₁₁

#1303

yes

characteristic

106

C₂×C₁₁

#1382

yes

characteristic

107

C₂×C₁₁

#1388

yes

characteristic

108

C₂²×C₄

#4314

yes

characteristic

109

C₂²×C₄

Dic₄₄

yes

characteristic

110

C₂²×C₄

(C₂×D₁₁)⋊C₄

yes

characteristic

111

M₁₆

—

112

M₁₆

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

C₄×Dic₁₁

yes

characteristic

118

C₂×C₈

Dic₁₁⋊C₄

yes

characteristic

119

C₂×C₈

Dic₁₁⋊C₄

yes

characteristic

120

C₂×C₈

C₂²⋊Dic₁₁

yes

characteristic

121

C₄²

#4314

yes

characteristic

122

C₄²

D₈₈

yes

characteristic

123

C₄²

C₄⋊Dic₁₁

yes

characteristic

124

C₄²

(C₂×D₁₁)⋊C₄

yes

characteristic

125

C₁₆

—

126

C₁₁

#7297

yes

characteristic, complemented, Sylow

127

C₂³

#66880

yes

characteristic

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

#66880

yes

characteristic

133

C₂×C₄

#66881

yes

characteristic

134

C₂×C₄

#66882

yes

characteristic

135

C₂×C₄

#66885

yes

characteristic

136

C₂×C₄

#66885

yes

characteristic

137

C₂×C₄

C₁₁⋊#95

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

143

C₈

#66901

yes

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

#10622189

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

#10622148

yes

—

153

C₄

#10622170

yes

characteristic

154

C₄

#10622197

yes

characteristic

155

C₂

—

156

C₂

#13066518

yes

characteristic

157

C₂

#13066712

yes

characteristic

158

C₂

#13066728

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#66885
commutator	C₂×C₈×C₁₁	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₁₁×#2162	C₂
socle	C₂²×C₁₁	#340
prime radical	C₂³×C₁₁	#103
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	#2162	D₁₁
hypocenter	C₁₁	#7297
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂×C₄

#66885

commutator

C₂×C₈×C₁₁

C₄²

Frattini

C₂×C₄×C₈

C₂×D₁₁

Fitting

C₁₁×#2162

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄×C₈×C₁₁

C₂²

D₁₁

C₁₁

G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

N	H ≅ G/N	type
126. C₁₁	#7297	semidirect

H ≅ G/N

type

126. C₁₁

#7297

semidirect

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

subgroup	index
C₄×#66883	2
#13067379	2
C₁₁×#2162	2
#7297	11

subgroup

index

C₄×#66883

#13067379

C₁₁×#2162

#7297

Subgroups — #14641024

Conjugacy classes of subgroups

Complements

Maximal subgroups