Group #14647586 — subgroups

Subgroups — #14647586

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	#13067375	C₂	1	1	yes	maximal, characteristic
3	#13067374	C₂	1	2	yes	maximal
4	C₂×#10622092	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1567	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×#335	—	2	2	no	—
13	#10622117	—	2	4	no	—
14	#10622096	—	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	#8826	—	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	D₈	1	4	yes	—
51	C₂×C₁₁⋊C₈	Q₁₆	1	4	yes	—
52	#1848	—	11	2	no	—
53	#1567	—	11	2	no	—
54	#1567	—	11	1	no	—
55	#1567	D₁₁	1	1	yes	characteristic
56	C₂×#322	—	11	1	no	—
57	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
58	C₂×C₄×C₁₁	—	2	2	no	—
59	C₂×C₄×C₁₁	—	2	2	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
64	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
65	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
67	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
68	C₈×C₁₁	—	2	4	no	—
69	C₈×C₁₁	—	8	2	no	—
70	C₁₁⋊C₈	—	2	4	no	—
71	C₁₁⋊C₈	—	8	2	no	—
72	C₁₁⋊C₈	#107	1	8	yes	—
73	C₂×#108	—	22	4	no	—
74	#423	—	11	2	no	—
75	#423	C₂×D₁₁	1	2	yes	—
76	C₂×C₄×C₈	—	11	1	no	—
77	C₂×C₄×C₈	—	11	1	no	—
78	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
79	#335	—	2	2	no	—
80	#335	—	22	4	no	—
81	#335	—	22	2	no	—
82	#322	—	11	4	no	—
83	C₂²×C₁₁	—	2	1	no	—
84	C₂²×C₁₁	—	2	1	no	—
85	C₂²×C₁₁	#384	1	1	yes	characteristic
86	C₂²×C₁₁	#500	1	2	yes	—
87	C₄×C₁₁	—	2	1	no	—
88	C₄×C₁₁	—	2	1	no	—
89	C₄×C₁₁	C₂×#107	1	2	yes	—
90	C₄×C₁₁	#430	1	2	yes	—
91	C₄×C₁₁	#430	1	2	yes	—
92	C₄×C₁₁	#493	1	1	yes	characteristic
93	C₄×C₁₁	#494	1	1	yes	characteristic
94	C₂×M₁₆	—	2	2	no	—
95	C₂×M₁₆	—	22	2	no	—
96	C₂²×C₈	—	11	2	no	—
97	C₂²×C₈	—	11	2	no	—
98	C₂²×C₈	Dic₂₂	1	2	yes	—
99	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
100	#108	—	44	8	no	—
101	C₄⋊C₈	—	2	2	no	—
102	C₄⋊C₈	—	2	2	no	—
103	C₄⋊C₈	—	22	2	no	—
104	C₄⋊C₈	—	22	2	no	—
105	C₄×C₈	—	11	2	no	—
106	C₄×C₈	—	11	2	no	—
107	C₄×C₈	—	11	2	no	—
108	C₄×C₈	—	11	2	no	—
109	C₄×C₈	C₄×D₁₁	1	2	yes	—
110	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
111	C₂×C₁₁	—	2	2	no	—
112	C₂×C₁₁	#1845	1	1	yes	characteristic
113	C₂×C₁₁	#1849	1	1	yes	characteristic
114	C₂×C₁₁	#1849	1	1	yes	characteristic
115	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
116	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
117	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
118	M₁₆	—	4	4	no	—
119	M₁₆	—	44	4	no	—
120	C₂×C₈	—	4	2	no	—
121	C₂×C₈	—	4	2	no	—
122	C₂×C₈	—	11	4	no	—
123	C₂×C₈	—	11	4	no	—
124	C₂×C₈	—	11	4	no	—
125	C₂×C₈	—	11	4	no	—
126	C₂×C₈	—	44	2	no	—
127	C₂×C₈	—	44	2	no	—
128	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
129	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
130	C₄²	D₄×D₁₁	1	1	yes	characteristic
131	C₄²	Q₈×D₁₁	1	1	yes	characteristic
132	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
133	C₁₁	#8826	1	1	yes	characteristic, complemented, Sylow
134	C₂³	#66941	1	1	yes	characteristic
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	#66941	1	1	yes	characteristic
138	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
139	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
140	C₂×C₄	D₈×D₁₁	1	2	yes	—
141	C₂×C₄	Q₁₆×D₁₁	1	2	yes	—
142	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
143	C₂×C₄	#66993	1	1	yes	characteristic
144	C₂×C₄	#66997	1	1	yes	characteristic
145	C₈	—	2	4	no	—
146	C₈	—	8	2	no	—
147	C₈	—	11	8	no	—
148	C₈	—	22	4	no	—
149	C₈	—	88	2	no	—
150	C₂²	—	2	1	no	—
151	C₂²	—	2	1	no	—
152	C₂²	#10622487	1	2	yes	—
153	C₂²	#10622589	1	1	yes	characteristic
154	C₄	—	2	1	no	—
155	C₄	—	2	1	no	—
156	C₄	D₁₁×#107	1	2	yes	—
157	C₄	#10622506	1	2	yes	—
158	C₄	#10622737	1	2	yes	—
159	C₄	#10622764	1	1	yes	characteristic
160	C₄	#10622794	1	1	yes	characteristic
161	C₂	—	2	2	no	—
162	C₂	#13068774	1	1	yes	characteristic
163	C₂	#13068789	1	1	yes	characteristic
164	C₂	#13068790	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068787

C₂

yes

maximal

#13067375

C₂

yes

maximal, characteristic

#13067374

C₂

yes

maximal

C₂×#10622092

C₂

yes

maximal, characteristic

C₁₁×#1567

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×#335

—

#10622117

—

#10622096

—

#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

—

#8826

—

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

D₈

yes

—

C₂×C₁₁⋊C₈

Q₁₆

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×D₈

yes

—

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

#107

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

#500

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#107

yes

—

C₄×C₁₁

#430

yes

—

C₄×C₁₁

#430

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

Dic₂₂

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

100

#108

—

101

C₄⋊C₈

—

102

C₄⋊C₈

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₄×C₈

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₄×C₈

C₄×D₁₁

yes

—

110

C₄×C₈

C₂²⋊D₁₁

yes

—

111

C₂×C₁₁

—

112

C₂×C₁₁

#1845

yes

characteristic

113

C₂×C₁₁

#1849

yes

characteristic

114

C₂×C₁₁

#1849

yes

characteristic

115

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

116

C₂²×C₄

D₄×D₁₁

yes

characteristic

117

C₂²×C₄

Q₈×D₁₁

yes

characteristic

118

M₁₆

—

119

M₁₆

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

Dic₁₁⋊C₄

yes

—

129

C₄²

C₂×C₄×D₁₁

yes

characteristic

130

C₄²

D₄×D₁₁

yes

characteristic

131

C₄²

Q₈×D₁₁

yes

characteristic

132

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

133

C₁₁

#8826

yes

characteristic, complemented, Sylow

134

C₂³

#66941

yes

characteristic

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

#66941

yes

characteristic

138

C₂×C₄

C₄⋊C₄×D₁₁

yes

characteristic

139

C₂×C₄

C₄⋊C₄×D₁₁

yes

characteristic

140

C₂×C₄

D₈×D₁₁

yes

—

141

C₂×C₄

Q₁₆×D₁₁

yes

—

142

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

143

C₂×C₄

#66993

yes

characteristic

144

C₂×C₄

#66997

yes

characteristic

145

C₈

—

146

C₈

—

147

C₈

—

148

C₈

—

149

C₈

—

150

C₂²

—

151

C₂²

—

152

C₂²

#10622487

yes

—

153

C₂²

#10622589

yes

characteristic

154

C₄

—

155

C₄

—

156

C₄

D₁₁×#107

yes

—

157

C₄

#10622506

yes

—

158

C₄

#10622737

yes

—

159

C₄

#10622764

yes

characteristic

160

C₄

#10622794

yes

characteristic

161

C₂

—

162

C₂

#13068774

yes

characteristic

163

C₂

#13068789

yes

characteristic

164

C₂

#13068790

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#66993
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1567	C₂
socle	C₂²×C₁₁	#384
prime radical	C₂³×C₁₁	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1567	D₁₁
hypocenter	C₁₁	#8826
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

subgroup

G/H

center

C₂×C₄

#66993

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1567

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 ◁ #1567

N	H ≅ G/N	type
133. C₁₁	#8826	semidirect

H ≅ G/N

type

133. C₁₁

#8826

semidirect

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

subgroup	index
#13068787	2
#13067375	2
#13067374	2
C₂×#10622092	2
C₁₁×#1567	2
#8826	11

subgroup

index

C₁₁×#1567

Subgroups — #14647586

Conjugacy classes of subgroups

Complements

Maximal subgroups