Group #14647583 — subgroups

Subgroups — #14647583

Order 2816.

338 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 147 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	#13068787	C₂	1	2	yes	maximal
2	#13067372	C₂	1	1	yes	maximal, characteristic
3	#13067371	C₂	1	2	yes	maximal
4	C₂×#10622092	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1566	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#423	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66886	—	2	4	no	—
9	#10622537	C₂²	1	2	yes	—
10	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
12	C₁₁×#334	—	2	2	no	—
13	#10622118	—	2	4	no	—
14	#10622095	—	2	2	no	—
15	#10622092	C₄	1	4	yes	—
16	C₂×C₁₁×M₁₆	—	2	2	no	—
17	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
18	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×#4318	—	2	2	no	—
20	C₂²×C₁₁⋊C₈	D₄	1	2	yes	—
21	C₂²×C₁₁⋊C₈	Q₈	1	2	yes	—
22	C₁₁×C₄⋊C₈	—	2	2	no	—
23	C₁₁×C₄⋊C₈	—	2	2	no	—
24	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₁₁	D₄	1	2	yes	—
26	#66886	—	4	8	no	—
27	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
28	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
29	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
30	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
31	C₄×C₁₁⋊C₈	D₄	1	2	yes	—
32	C₄×C₁₁⋊C₈	Q₈	1	2	yes	—
33	#8825	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
37	C₁₁×M₁₆	—	4	4	no	—
38	C₂×C₈×C₁₁	—	4	2	no	—
39	C₂×C₈×C₁₁	—	4	2	no	—
40	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
41	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
43	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
44	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
45	#4318	—	4	4	no	—
46	C₂×C₁₁⋊C₈	—	4	2	no	—
47	C₂×C₁₁⋊C₈	—	4	2	no	—
48	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
49	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
50	C₂×C₁₁⋊C₈	SD₁₆	1	8	yes	—
51	#1848	—	11	2	no	—
52	#1566	—	11	2	no	—
53	#1566	—	11	1	no	—
54	#1566	D₁₁	1	1	yes	characteristic
55	C₂×#322	—	11	1	no	—
56	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
57	C₂×C₄×C₁₁	—	2	2	no	—
58	C₂×C₄×C₁₁	—	2	2	no	—
59	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
63	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
64	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
65	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
66	C₈×C₁₁	—	2	4	no	—
67	C₈×C₁₁	—	8	2	no	—
68	C₁₁⋊C₈	—	2	4	no	—
69	C₁₁⋊C₈	—	8	2	no	—
70	C₁₁⋊C₈	#106	1	8	yes	—
71	C₂×#108	—	22	4	no	—
72	#423	—	11	2	no	—
73	#423	C₂×D₁₁	1	2	yes	—
74	C₂×C₄×C₈	—	11	1	no	—
75	C₂×C₄×C₈	—	11	1	no	—
76	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
77	#334	—	2	2	no	—
78	#334	—	22	4	no	—
79	#334	—	22	2	no	—
80	#322	—	11	4	no	—
81	C₂²×C₁₁	—	2	1	no	—
82	C₂²×C₁₁	—	2	1	no	—
83	C₂²×C₁₁	#384	1	1	yes	characteristic
84	C₂²×C₁₁	#498	1	2	yes	—
85	C₄×C₁₁	—	2	1	no	—
86	C₄×C₁₁	—	2	1	no	—
87	C₄×C₁₁	C₂×#106	1	2	yes	—
88	C₄×C₁₁	#430	1	2	yes	—
89	C₄×C₁₁	#430	1	2	yes	—
90	C₄×C₁₁	#492	1	2	yes	—
91	C₂×M₁₆	—	2	2	no	—
92	C₂×M₁₆	—	22	2	no	—
93	C₂²×C₈	—	11	2	no	—
94	C₂²×C₈	—	11	2	no	—
95	C₂²×C₈	Dic₂₂	1	2	yes	—
96	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
97	#108	—	44	8	no	—
98	C₄⋊C₈	—	2	2	no	—
99	C₄⋊C₈	—	2	2	no	—
100	C₄⋊C₈	—	22	2	no	—
101	C₄⋊C₈	—	22	2	no	—
102	C₄×C₈	—	11	2	no	—
103	C₄×C₈	—	11	2	no	—
104	C₄×C₈	—	11	2	no	—
105	C₄×C₈	—	11	2	no	—
106	C₄×C₈	C₄×D₁₁	1	2	yes	—
107	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
108	C₂×C₁₁	—	2	2	no	—
109	C₂×C₁₁	#1844	1	1	yes	characteristic
110	C₂×C₁₁	#1849	1	1	yes	characteristic
111	C₂×C₁₁	#1849	1	1	yes	characteristic
112	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
113	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
114	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
115	M₁₆	—	4	4	no	—
116	M₁₆	—	44	4	no	—
117	C₂×C₈	—	4	2	no	—
118	C₂×C₈	—	4	2	no	—
119	C₂×C₈	—	11	4	no	—
120	C₂×C₈	—	11	8	no	—
121	C₂×C₈	—	11	4	no	—
122	C₂×C₈	—	44	2	no	—
123	C₂×C₈	—	44	2	no	—
124	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
125	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
126	C₄²	D₄×D₁₁	1	1	yes	characteristic
127	C₄²	Q₈×D₁₁	1	1	yes	characteristic
128	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
129	C₁₁	#8825	1	1	yes	characteristic, complemented, Sylow
130	C₂³	#66941	1	1	yes	characteristic
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	#66941	1	1	yes	characteristic
134	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
135	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
136	C₂×C₄	SD₁₆×D₁₁	1	4	yes	—
137	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
138	C₂×C₄	#66993	1	1	yes	characteristic
139	C₂×C₄	#66997	1	1	yes	characteristic
140	C₈	—	2	4	no	—
141	C₈	—	8	2	no	—
142	C₈	—	11	8	no	—
143	C₈	—	22	4	no	—
144	C₈	—	88	2	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	#10622468	1	2	yes	—
148	C₂²	#10622589	1	1	yes	characteristic
149	C₄	—	2	1	no	—
150	C₄	—	2	1	no	—
151	C₄	D₁₁×#106	1	2	yes	—
152	C₄	#10622506	1	2	yes	—
153	C₄	#10622737	1	2	yes	—
154	C₄	#10622788	1	2	yes	—
155	C₂	—	2	2	no	—
156	C₂	#13068771	1	1	yes	characteristic
157	C₂	#13068789	1	1	yes	characteristic
158	C₂	#13068790	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068787

C₂

yes

maximal

#13067372

C₂

yes

maximal, characteristic

#13067371

C₂

yes

maximal

C₂×#10622092

C₂

yes

maximal, characteristic

C₁₁×#1566

C₂

yes

maximal, characteristic

C₁₁×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66886

—

#10622537

C₂²

yes

—

C₂×C₄×C₁₁⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₁₁⋊C₈

C₂²

yes

characteristic

C₁₁×#334

—

#10622118

—

#10622095

—

#10622092

C₄

yes

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₂²×C₁₁⋊C₈

D₄

yes

—

C₂²×C₁₁⋊C₈

Q₈

yes

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

#66886

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄×C₁₁⋊C₈

C₂×C₄

yes

—

C₄×C₁₁⋊C₈

C₂×C₄

yes

—

C₄×C₁₁⋊C₈

D₄

yes

—

C₄×C₁₁⋊C₈

Q₈

yes

—

#8825

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×Q₈

yes

characteristic

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₁⋊C₈

SD₁₆

yes

—

—

—

—

D₁₁

yes

characteristic

C₂×#322

—

C₂³×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

#106

yes

—

C₂×#108

—

#423

—

#423

C₂×D₁₁

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#498

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#106

yes

—

C₄×C₁₁

#430

yes

—

C₄×C₁₁

#430

yes

—

C₄×C₁₁

#492

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

Dic₂₂

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

C₄×D₁₁

yes

—

107

C₄×C₈

C₂²⋊D₁₁

yes

—

108

C₂×C₁₁

—

109

C₂×C₁₁

#1844

yes

characteristic

110

C₂×C₁₁

#1849

yes

characteristic

111

C₂×C₁₁

#1849

yes

characteristic

112

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

113

C₂²×C₄

D₄×D₁₁

yes

characteristic

114

C₂²×C₄

Q₈×D₁₁

yes

characteristic

115

M₁₆

—

116

M₁₆

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

Dic₁₁⋊C₄

yes

—

125

C₄²

C₂×C₄×D₁₁

yes

characteristic

126

C₄²

D₄×D₁₁

yes

characteristic

127

C₄²

Q₈×D₁₁

yes

characteristic

128

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

129

C₁₁

#8825

yes

characteristic, complemented, Sylow

130

C₂³

#66941

yes

characteristic

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

#66941

yes

characteristic

134

C₂×C₄

C₄⋊C₄×D₁₁

yes

characteristic

135

C₂×C₄

C₄⋊C₄×D₁₁

yes

characteristic

136

C₂×C₄

SD₁₆×D₁₁

yes

—

137

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

138

C₂×C₄

#66993

yes

characteristic

139

C₂×C₄

#66997

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

—

143

C₈

—

144

C₈

—

145

C₂²

—

146

C₂²

—

147

C₂²

#10622468

yes

—

148

C₂²

#10622589

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

D₁₁×#106

yes

—

152

C₄

#10622506

yes

—

153

C₄

#10622737

yes

—

154

C₄

#10622788

yes

—

155

C₂

—

156

C₂

#13068771

yes

characteristic

157

C₂

#13068789

yes

characteristic

158

C₂

#13068790

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#66993
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1566	C₂
socle	C₂²×C₁₁	#384
prime radical	C₂³×C₁₁	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1566	D₁₁
hypocenter	C₁₁	#8825
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂×C₄

#66993

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1566

C₂

socle

C₂²×C₁₁

#384

prime radical

C₂³×C₁₁

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
129. C₁₁	#8825	semidirect

H ≅ G/N

type

129. C₁₁

#8825

semidirect

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

subgroup	index
#13068787	2
#13067372	2
#13067371	2
C₂×#10622092	2
C₁₁×#1566	2
#8825	11

subgroup

index

C₁₁×#1566

Subgroups — #14647583

Conjugacy classes of subgroups

Complements

Maximal subgroups