Group #14641003 — subgroups

Subgroups — #14641003

Order 2816.

194 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 91 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	#13067379	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622095	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	#10622539	—	2	1	no	—
6	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
7	C₁₁×C₄⋊C₁₆	—	2	1	no	—
8	C₁₁×C₂²⋊C₁₆	C₄	1	2	yes	—
9	C₄×C₁₁×C₁₆	—	2	1	no	—
10	#10622096	C₄	1	2	yes	—
11	#10622095	—	2	1	no	—
12	#10622095	—	2	1	no	—
13	#10622095	C₄	1	2	yes	—
14	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
16	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
17	C₂²×C₁₁⋊C₈	—	4	1	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	D₄	1	1	yes	characteristic
23	C₂²⋊(C₁₁⋊C₈)	—	4	1	no	—
24	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
25	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
26	C₄⋊(C₁₁⋊C₈)	—	4	1	no	—
27	#66867	—	4	1	no	—
28	#7290	—	11	1	no	maximal, Sylow
29	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₁	Q₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₁	—	2	2	no	—
33	C₂×C₈×C₁₁	—	4	1	no	—
34	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
38	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
39	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
40	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
41	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
42	C₂×C₁₁⋊C₈	—	4	2	no	—
43	C₂×C₁₁⋊C₈	—	4	2	no	—
44	C₂×C₁₁⋊C₈	—	8	2	no	—
45	C₁₁×C₁₆	—	4	2	no	—
46	#2162	D₁₁	1	1	yes	characteristic
47	#1568	—	11	1	no	—
48	C₂×#334	—	11	1	no	—
49	C₂³×C₁₁	#107	1	1	yes	characteristic
50	C₂×C₄×C₁₁	—	2	2	no	—
51	C₂×C₄×C₁₁	—	2	1	no	—
52	C₂×C₄×C₁₁	—	2	1	no	—
53	C₂×C₄×C₁₁	—	2	2	no	—
54	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
55	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
56	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
57	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
58	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
59	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
60	C₈×C₁₁	—	2	1	no	—
61	C₈×C₁₁	—	2	1	no	—
62	C₈×C₁₁	—	2	1	no	—
63	C₈×C₁₁	#108	1	2	yes	—
64	C₁₁⋊C₈	—	8	2	no	—
65	C₁₁⋊C₈	—	8	2	no	—
66	#432	—	22	1	no	—
67	C₂×C₄⋊C₈	—	22	1	no	—
68	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
69	C₄⋊C₁₆	—	2	1	no	—
70	C₂²⋊C₁₆	Dic₁₁	1	2	yes	—
71	C₄×C₁₆	—	2	1	no	—
72	#335	—	11	2	no	—
73	#334	—	11	2	no	—
74	#334	—	22	1	no	—
75	#334	—	22	1	no	—
76	C₂²×C₁₁	—	2	1	no	—
77	C₂²×C₁₁	—	2	1	no	—
78	C₂²×C₁₁	#340	1	1	yes	characteristic
79	C₂²×C₁₁	#368	1	2	yes	—
80	C₄×C₁₁	—	2	1	no	—
81	C₄×C₁₁	—	2	1	no	—
82	C₄×C₁₁	—	2	1	no	—
83	C₄×C₁₁	—	2	1	no	—
84	C₄×C₁₁	#341	1	1	yes	characteristic
85	C₄×C₁₁	#344	1	1	yes	characteristic
86	C₄×C₁₁	#360	1	2	yes	—
87	C₂²×C₈	—	44	1	no	—
88	C₂²×C₈	Dic₂₂	1	1	yes	characteristic
89	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
90	C₂×C₄²	D₄₄	1	1	yes	characteristic
91	C₂×C₁₆	—	2	2	no	—
92	C₄⋊C₈	—	22	2	no	—
93	C₄⋊C₈	—	22	2	no	—
94	C₄⋊C₈	—	44	1	no	—
95	C₂²⋊C₈	—	44	1	no	—
96	#97	—	44	1	no	—
97	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
98	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
99	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
100	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
101	C₂×C₁₁	—	2	2	no	—
102	C₂×C₁₁	#1301	1	1	yes	characteristic
103	C₂×C₁₁	#1381	1	1	yes	characteristic
104	C₂×C₁₁	#1386	1	1	yes	characteristic
105	C₂²×C₄	D₈₈	1	1	yes	characteristic
106	C₂²×C₄	Dic₄₄	1	1	yes	characteristic
107	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	4	1	no	—
110	C₂×C₈	—	44	2	no	—
111	C₂×C₈	—	44	2	no	—
112	C₂×C₈	—	88	2	no	—
113	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
114	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
115	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
116	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
117	C₄²	#4314	1	1	yes	characteristic
118	C₄²	#4314	1	1	yes	characteristic
119	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
120	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
121	C₁₆	—	4	2	no	—
122	C₁₁	#7290	1	1	yes	characteristic, complemented, Sylow
123	C₂³	#66882	1	1	yes	characteristic
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	#66880	1	1	yes	characteristic
129	C₂×C₄	#66880	1	1	yes	characteristic
130	C₂×C₄	#66881	1	1	yes	characteristic
131	C₂×C₄	#66885	1	1	yes	characteristic
132	C₂×C₄	#66885	1	1	yes	characteristic
133	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
134	C₈	—	2	1	no	—
135	C₈	—	2	1	no	—
136	C₈	—	2	1	no	—
137	C₈	—	88	2	no	—
138	C₈	—	88	2	no	—
139	C₈	#66886	1	2	yes	—
140	C₂²	—	2	1	no	—
141	C₂²	—	2	1	no	—
142	C₂²	#10622144	1	2	yes	—
143	C₂²	#10622189	1	1	yes	characteristic
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	—	2	1	no	—
148	C₄	#10622156	1	2	yes	—
149	C₄	#10622171	1	1	yes	characteristic
150	C₄	#10622196	1	1	yes	characteristic
151	C₂	—	2	2	no	—
152	C₂	#13066512	1	1	yes	characteristic
153	C₂	#13066710	1	1	yes	characteristic
154	C₂	#13066722	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13067379

C₂

yes

maximal, characteristic

C₂×#10622095

C₂

yes

maximal, characteristic

C₁₁×#2162

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622539

—

C₂×C₄⋊(C₁₁⋊C₈)

—

C₁₁×C₄⋊C₁₆

—

C₁₁×C₂²⋊C₁₆

C₄

yes

—

C₄×C₁₁×C₁₆

—

#10622096

C₄

yes

—

#10622095

—

#10622095

—

#10622095

C₄

yes

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

Q₈

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂²×C₁₁⋊C₈

—

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

D₄

yes

characteristic

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#66867

—

#7290

—

maximal, Sylow

C₂²×C₄×C₁₁

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₁

D₈

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

C₂²⋊C₄

yes

characteristic

C₄²×C₁₁

SD₁₆

yes

characteristic

C₄²×C₁₁

SD₁₆

yes

characteristic

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

—

#2162

D₁₁

yes

characteristic

#1568

—

C₂×#334

—

C₂³×C₁₁

#107

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

#108

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

#432

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

Dic₁₁

yes

—

C₄×C₁₆

—

—

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#340

yes

characteristic

C₂²×C₁₁

#368

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

C₂²×C₈

—

C₂²×C₈

Dic₂₂

yes

characteristic

C₂²×C₈

C₂×Dic₁₁

yes

characteristic

C₂×C₄²

D₄₄

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

C₄×D₁₁

yes

characteristic

C₄×C₈

C₄×D₁₁

yes

characteristic

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

100

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

101

C₂×C₁₁

—

102

C₂×C₁₁

#1301

yes

characteristic

103

C₂×C₁₁

#1381

yes

characteristic

104

C₂×C₁₁

#1386

yes

characteristic

105

C₂²×C₄

D₈₈

yes

characteristic

106

C₂²×C₄

Dic₄₄

yes

characteristic

107

C₂²×C₄

C₄⋊Dic₁₁

yes

characteristic

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₄×Dic₁₁

yes

characteristic

114

C₂×C₈

Dic₁₁⋊C₄

yes

characteristic

115

C₂×C₈

Dic₁₁⋊C₄

yes

characteristic

116

C₂×C₈

C₂²⋊Dic₁₁

yes

characteristic

117

C₄²

#4314

yes

characteristic

118

C₄²

#4314

yes

characteristic

119

C₄²

(C₂×D₁₁)⋊C₄

yes

characteristic

120

C₄²

(C₂×D₁₁)⋊C₄

yes

characteristic

121

C₁₆

—

122

C₁₁

#7290

yes

characteristic, complemented, Sylow

123

C₂³

#66882

yes

characteristic

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

#66880

yes

characteristic

129

C₂×C₄

#66880

yes

characteristic

130

C₂×C₄

#66881

yes

characteristic

131

C₂×C₄

#66885

yes

characteristic

132

C₂×C₄

#66885

yes

characteristic

133

C₂×C₄

C₁₁⋊#95

yes

characteristic

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

#66886

yes

—

140

C₂²

—

141

C₂²

—

142

C₂²

#10622144

yes

—

143

C₂²

#10622189

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

#10622156

yes

—

149

C₄

#10622171

yes

characteristic

150

C₄

#10622196

yes

characteristic

151

C₂

—

152

C₂

#13066512

yes

characteristic

153

C₂

#13066710

yes

characteristic

154

C₂

#13066722

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	#107
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	#2162	D₁₁
hypocenter	C₁₁	#7290
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
122. C₁₁	#7290	semidirect

H ≅ G/N

type

122. C₁₁

#7290

semidirect

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

subgroup	index
#13067379	2
C₂×#10622095	2
C₁₁×#2162	2
#7290	11

subgroup

index

#13067379

C₂×#10622095

C₁₁×#2162

#7290

Subgroups — #14641003

Conjugacy classes of subgroups

Complements

Maximal subgroups