Group #14640999 — subgroups

Subgroups — #14640999

Order 2816.

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

normal subgroups only

This group has 184 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	#13070415	C₂	1	1	yes	maximal, characteristic
2	#13067364	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#432	—	2	1	no	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	#10622538	—	2	1	no	—
7	C₁₁×#335	C₄	1	2	yes	—
8	C₁₁×#334	—	2	1	no	—
9	C₂²⋊(C₁₁⋊C₁₆)	C₄	1	2	yes	—
10	C₄⋊(C₁₁⋊C₁₆)	—	2	1	no	—
11	C₄×C₁₁⋊C₁₆	—	2	1	no	—
12	#10622096	—	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	C₁₁×C₄⋊C₈	—	2	2	no	—
18	C₁₁×C₂²⋊C₈	—	4	1	no	—
19	C₁₁×#97	—	4	1	no	—
20	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
24	C₂²⋊(C₁₁⋊C₈)	—	4	1	no	—
25	C₂×C₁₁⋊C₁₆	—	2	2	no	—
26	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
27	C₄×C₁₁⋊C₈	—	4	1	no	—
28	#7289	—	11	1	no	maximal, Sylow
29	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
31	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₁	—	2	2	no	—
33	C₂×C₈×C₁₁	—	4	1	no	—
34	C₂×C₈×C₁₁	—	4	2	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	C₂²⋊C₄	1	1	yes	characteristic
41	C₄²×C₁₁	D₈	1	1	yes	characteristic
42	C₄²×C₁₁	Q₁₆	1	1	yes	characteristic
43	C₂×C₁₁⋊C₈	—	4	2	no	—
44	C₁₁⋊C₁₆	—	4	2	no	—
45	#2162	—	11	1	no	—
46	#1568	D₁₁	1	1	yes	characteristic
47	#1564	—	11	1	no	—
48	C₂³×C₁₁	#106	1	1	yes	characteristic
49	C₂×C₄×C₁₁	—	2	1	no	—
50	C₂×C₄×C₁₁	—	2	1	no	—
51	C₂×C₄×C₁₁	—	2	2	no	—
52	C₂×C₄×C₁₁	—	4	1	no	—
53	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
54	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
55	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
56	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
57	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
58	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
59	C₈×C₁₁	—	2	1	no	—
60	C₈×C₁₁	—	2	1	no	—
61	C₈×C₁₁	—	2	1	no	—
62	C₈×C₁₁	—	8	2	no	—
63	C₈×C₁₁	#108	1	2	yes	—
64	C₁₁⋊C₈	—	8	2	no	—
65	#432	—	2	1	no	—
66	#431	—	22	1	no	—
67	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
68	C₄⋊C₁₆	—	22	1	no	—
69	C₂²⋊C₁₆	—	11	2	no	—
70	C₄×C₁₆	—	22	1	no	—
71	#335	—	22	1	no	—
72	#335	Dic₁₁	1	2	yes	—
73	#334	—	2	1	no	—
74	#334	—	11	2	no	—
75	C₂²×C₁₁	—	2	1	no	—
76	C₂²×C₁₁	—	2	1	no	—
77	C₂²×C₁₁	—	2	1	no	—
78	C₂²×C₁₁	#340	1	1	yes	characteristic
79	C₄×C₁₁	—	2	1	no	—
80	C₄×C₁₁	—	2	1	no	—
81	C₄×C₁₁	—	2	1	no	—
82	C₄×C₁₁	—	2	1	no	—
83	C₄×C₁₁	#341	1	1	yes	characteristic
84	C₄×C₁₁	#344	1	1	yes	characteristic
85	C₄×C₁₁	#359	1	2	yes	—
86	C₂²×C₈	Dic₂₂	1	1	yes	characteristic
87	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
88	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
89	C₂×C₁₆	—	22	2	no	—
90	C₄⋊C₈	—	2	2	no	—
91	C₄⋊C₈	—	22	2	no	—
92	C₂²⋊C₈	—	4	1	no	—
93	C₂²⋊C₈	—	44	1	no	—
94	#97	—	4	1	no	—
95	C₄×C₈	—	44	1	no	—
96	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
97	C₄×C₈	D₄₄	1	1	yes	characteristic
98	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
99	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
100	C₂×C₁₁	—	4	1	no	—
101	C₂×C₁₁	#1301	1	1	yes	characteristic
102	C₂×C₁₁	#1382	1	1	yes	characteristic
103	C₂×C₁₁	#1389	1	1	yes	characteristic
104	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
105	C₂²×C₄	#4324	1	1	yes	characteristic
106	C₂²×C₄	#4325	1	1	yes	characteristic
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	4	1	no	—
109	C₂×C₈	—	4	2	no	—
110	C₂×C₈	—	44	2	no	—
111	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
112	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
113	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
114	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
115	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
116	C₄²	#4323	1	1	yes	characteristic
117	C₄²	#4326	1	1	yes	characteristic
118	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
119	C₁₆	—	44	2	no	—
120	C₁₁	#7289	1	1	yes	characteristic, complemented, Sylow
121	C₂³	#66872	1	1	yes	characteristic
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	#66871	1	1	yes	characteristic
127	C₂×C₄	#66873	1	1	yes	characteristic
128	C₂×C₄	#66874	1	1	yes	characteristic
129	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
130	C₂×C₄	#66896	1	1	yes	characteristic
131	C₂×C₄	#66899	1	1	yes	characteristic
132	C₈	—	2	1	no	—
133	C₈	—	2	1	no	—
134	C₈	—	2	1	no	—
135	C₈	—	8	2	no	—
136	C₈	—	88	2	no	—
137	C₈	#66886	1	2	yes	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	—	2	1	no	—
141	C₂²	#10622167	1	1	yes	characteristic
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	#10622194	1	1	yes	characteristic
147	C₄	#10622196	1	1	yes	characteristic
148	C₄	#10622205	1	2	yes	—
149	C₂	—	4	1	no	—
150	C₂	#13066511	1	1	yes	characteristic
151	C₂	#13066711	1	1	yes	characteristic
152	C₂	#13066730	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13070415

C₂

yes

maximal, characteristic

#13067364

C₂

yes

maximal, characteristic

C₁₁×#1568

C₂

yes

maximal, characteristic

C₁₁×#432

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622538

—

C₁₁×#335

C₄

yes

—

C₁₁×#334

—

C₂²⋊(C₁₁⋊C₁₆)

C₄

yes

—

C₄⋊(C₁₁⋊C₁₆)

—

C₄×C₁₁⋊C₁₆

—

#10622096

—

#10622095

C₄

yes

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

Q₈

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₁₁×C₄⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₁₁×#97

—

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)

—

C₂×C₁₁⋊C₁₆

—

C₄⋊(C₁₁⋊C₈)

—

C₄×C₁₁⋊C₈

—

#7289

—

maximal, Sylow

C₂²×C₄×C₁₁

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₁

SD₁₆

yes

characteristic

C₂²×C₄×C₁₁

SD₁₆

yes

characteristic

C₂×C₈×C₁₁

—

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

D₈

yes

characteristic

C₄²×C₁₁

Q₁₆

yes

characteristic

C₂×C₁₁⋊C₈

—

C₁₁⋊C₁₆

—

#2162

—

#1568

D₁₁

yes

characteristic

#1564

—

C₂³×C₁₁

#106

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

—

C₈×C₁₁

#108

yes

—

C₁₁⋊C₈

—

#432

—

#431

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

#335

—

#335

Dic₁₁

yes

—

#334

—

#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

—

C₂²×C₈

Dic₂₂

yes

characteristic

C₂²×C₈

C₄×D₁₁

yes

characteristic

C₂×C₄²

C₂²⋊D₁₁

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

C₄×D₁₁

yes

characteristic

C₄×C₈

D₄₄

yes

characteristic

C₄×C₈

C₂×Dic₁₁

yes

characteristic

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

100

C₂×C₁₁

—

101

C₂×C₁₁

#1301

yes

characteristic

102

C₂×C₁₁

#1382

yes

characteristic

103

C₂×C₁₁

#1389

yes

characteristic

104

C₂²×C₄

Dic₁₁⋊C₄

yes

characteristic

105

C₂²×C₄

#4324

yes

characteristic

106

C₂²×C₄

#4325

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

C₄×Dic₁₁

yes

characteristic

112

C₂×C₈

Dic₁₁⋊C₄

yes

characteristic

113

C₂×C₈

C₄⋊Dic₁₁

yes

characteristic

114

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

characteristic

115

C₄²

(C₂×D₁₁)⋊C₄

yes

characteristic

116

C₄²

#4323

yes

characteristic

117

C₄²

#4326

yes

characteristic

118

C₄²

C₂²⋊Dic₁₁

yes

characteristic

119

C₁₆

—

120

C₁₁

#7289

yes

characteristic, complemented, Sylow

121

C₂³

#66872

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

#66871

yes

characteristic

127

C₂×C₄

#66873

yes

characteristic

128

C₂×C₄

#66874

yes

characteristic

129

C₂×C₄

C₁₁⋊#95

yes

characteristic

130

C₂×C₄

#66896

yes

characteristic

131

C₂×C₄

#66899

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

#66886

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

#10622167

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

#10622194

yes

characteristic

147

C₄

#10622196

yes

characteristic

148

C₄

#10622205

yes

—

149

C₂

—

150

C₂

#13066511

yes

characteristic

151

C₂

#13066711

yes

characteristic

152

C₂

#13066730

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#66896
commutator	C₂×C₈×C₁₁	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₁₁×#1568	C₂
socle	C₂²×C₁₁	#340
prime radical	C₂³×C₁₁	#106
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	#1568	D₁₁
hypocenter	C₁₁	#7289
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1568

subgroup

G/H

center

C₂×C₄

#66896

commutator

C₂×C₈×C₁₁

C₄²

Frattini

C₂×C₄×C₈

C₂×D₁₁

Fitting

C₁₁×#1568

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 ◁ #1568

N	H ≅ G/N	type
120. C₁₁	#7289	semidirect

H ≅ G/N

type

120. C₁₁

#7289

semidirect

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

subgroup	index
#13070415	2
#13067364	2
C₁₁×#1568	2
#7289	11

subgroup

index

#13070415

#13067364

C₁₁×#1568

#7289

Subgroups — #14640999

Conjugacy classes of subgroups

Complements

Maximal subgroups