Group #14670161 — subgroups

Subgroups — #14670161

Order 2816.

282 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 119 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	C₂×C₁₆×Dic₁₁	C₂	1	1	yes	maximal, characteristic
2	#13068786	C₂	1	2	yes	maximal
3	#13066710	C₂	1	1	yes	maximal, characteristic
4	#13066709	C₂	1	2	yes	maximal
5	C₁₁×#1381	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×#108	C₂²	1	2	yes	—
8	C₂×#66886	—	2	2	no	—
9	#10622731	—	2	2	no	—
10	C₂×#66883	C₂²	1	2	yes	—
11	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
12	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₁₆×Dic₁₁	C₄	1	2	yes	—
14	C₁₆×Dic₁₁	C₄	1	2	yes	—
15	C₂×C₁₁×M₁₆	—	2	2	no	—
16	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
17	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
18	C₂×#4318	—	2	2	no	—
19	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
20	C₂×C₁₁×C₁₆	—	2	2	no	—
21	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
22	C₁₁×#108	—	2	2	no	—
23	C₁₁×#108	—	2	2	no	—
24	#66886	—	4	4	no	—
25	#66883	—	2	2	no	—
26	#66883	—	2	2	no	—
27	Dic₁₁⋊C₈	—	4	4	no	—
28	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₁	Q₈	1	1	yes	characteristic
31	C₈×Dic₁₁	Q₈	1	1	yes	characteristic
32	C₂×C₁₁⋊C₁₆	—	2	2	no	—
33	C₂×C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
34	#12891	—	11	1	no	maximal, Sylow
35	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₂²×Dic₁₁	Q₁₆	1	2	yes	—
37	C₁₁×M₁₆	—	4	2	no	—
38	C₁₁×M₁₆	—	4	2	no	—
39	C₂×C₈×C₁₁	—	4	2	no	—
40	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₈×C₁₁	#41	1	2	yes	—
43	C₂×C₈×C₁₁	#41	1	2	yes	—
44	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
45	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
46	C₄×Dic₁₁	D₈	1	2	yes	—
47	#4318	—	4	2	no	—
48	#4318	—	4	2	no	—
49	C₂×C₁₁⋊C₈	—	4	2	no	—
50	C₂×C₁₁⋊C₈	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₁₁⋊C₈	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₁₁⋊C₈	SD₁₆	1	4	yes	—
53	C₁₁×C₁₆	—	2	2	no	—
54	C₁₁⋊C₁₆	—	2	2	no	—
55	C₂×C₄×C₁₆	—	11	1	no	—
56	#1848	—	11	2	no	—
57	#1381	—	11	1	no	—
58	#1381	—	11	2	no	—
59	#1381	D₁₁	1	1	yes	characteristic
60	C₂³×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
61	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₁	#124	1	2	yes	—
63	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
64	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
65	C₂×Dic₁₁	—	2	4	no	—
66	C₂×Dic₁₁	#107	1	2	yes	—
67	C₂×Dic₁₁	#107	1	2	yes	—
68	C₈×C₁₁	—	8	2	no	—
69	C₈×C₁₁	#117	1	1	yes	characteristic
70	C₈×C₁₁	#117	1	1	yes	characteristic
71	C₈×C₁₁	#125	1	2	yes	—
72	C₁₁⋊C₈	—	8	2	no	—
73	C₁₁⋊C₈	#106	1	2	yes	—
74	C₁₁⋊C₈	#106	1	2	yes	—
75	C₂²×C₁₆	—	11	1	no	—
76	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
77	C₂×#108	—	11	2	no	—
78	C₂×#108	—	22	2	no	—
79	C₂×#108	C₂×D₁₁	1	2	yes	—
80	#423	—	22	2	no	—
81	C₂×C₄×C₈	—	11	1	no	—
82	C₄×C₁₆	—	11	2	no	—
83	C₄×C₁₆	—	11	2	no	—
84	C₂²×C₁₁	—	2	2	no	—
85	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
86	C₂²×C₁₁	#487	1	2	yes	—
87	C₄×C₁₁	#382	1	1	yes	characteristic
88	C₄×C₁₁	C₂×#106	1	1	yes	characteristic
89	C₄×C₁₁	#486	1	2	yes	—
90	Dic₁₁	—	2	2	no	—
91	Dic₁₁	#368	1	4	yes	—
92	C₂×M₁₆	—	2	2	no	—
93	C₂×M₁₆	—	22	2	no	—
94	C₂²×C₈	—	11	1	no	—
95	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
96	C₂×C₄²	—	11	1	no	—
97	C₂×C₁₆	—	2	2	no	—
98	C₂×C₁₆	—	11	2	no	—
99	C₂×C₁₆	—	22	2	no	—
100	C₂×C₁₆	C₄×D₁₁	1	2	yes	—
101	#108	—	2	2	no	—
102	#108	—	2	2	no	—
103	#108	—	22	2	no	—
104	#108	—	22	2	no	—
105	#108	—	44	4	no	—
106	C₄⋊C₈	—	44	4	no	—
107	C₄×C₈	—	11	1	no	—
108	C₄×C₈	—	11	1	no	—
109	C₄×C₈	—	11	1	no	—
110	C₄×C₈	—	11	1	no	—
111	C₂×C₁₁	—	2	2	no	—
112	C₂×C₁₁	#1834	1	1	yes	characteristic
113	C₂×C₁₁	C₂×#368	1	2	yes	—
114	C₂²×C₄	—	11	2	no	—
115	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
116	M₁₆	—	4	2	no	—
117	M₁₆	—	4	2	no	—
118	M₁₆	—	44	2	no	—
119	M₁₆	—	44	2	no	—
120	C₂×C₈	—	4	2	no	—
121	C₂×C₈	—	11	1	no	—
122	C₂×C₈	—	11	1	no	—
123	C₂×C₈	—	11	4	no	—
124	C₂×C₈	—	44	2	no	—
125	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
126	C₂×C₈	#4339	1	2	yes	—
127	C₂×C₈	#4341	1	2	yes	—
128	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
129	C₄²	—	11	1	no	—
130	C₄²	—	11	1	no	—
131	C₄²	—	11	2	no	—
132	C₁₆	—	2	2	no	—
133	C₁₆	—	22	2	no	—
134	C₁₁	#12891	1	1	yes	characteristic, complemented, Sylow
135	C₂³	Q₁₆×D₁₁	1	1	yes	characteristic
136	C₂×C₄	—	11	2	no	—
137	C₂×C₄	—	11	2	no	—
138	C₂×C₄	—	22	4	no	—
139	C₂×C₄	#66938	1	2	yes	—
140	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
141	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
142	C₂×C₄	SD₁₆×D₁₁	1	2	yes	—
143	C₈	—	8	2	no	—
144	C₈	—	11	2	no	—
145	C₈	—	11	2	no	—
146	C₈	—	88	2	no	—
147	C₈	#66925	1	1	yes	characteristic
148	C₈	#66930	1	1	yes	characteristic
149	C₈	#66942	1	2	yes	—
150	C₂²	—	2	2	no	—
151	C₂²	#10622405	1	2	yes	—
152	C₂²	D₁₁×#107	1	1	yes	characteristic
153	C₄	—	11	4	no	—
154	C₄	—	22	2	no	—
155	C₄	#10622263	1	1	yes	characteristic
156	C₄	#10622373	1	2	yes	—
157	C₄	D₁₁×#106	1	1	yes	characteristic
158	C₂	—	2	2	no	—
159	C₂	#13068742	1	1	yes	characteristic
160	C₂	D₁₁×#368	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×Dic₁₁

C₂

yes

maximal, characteristic

#13068786

C₂

yes

maximal

#13066710

C₂

yes

maximal, characteristic

#13066709

C₂

yes

maximal

C₁₁×#1381

C₂

yes

maximal, characteristic

C₂²×C₁₁×C₁₆

C₂²

yes

characteristic

C₂×C₁₁×#108

C₂²

yes

—

C₂×#66886

—

#10622731

—

C₂×#66883

C₂²

yes

—

C₂×C₈×Dic₁₁

C₂²

yes

characteristic

C₂²×C₁₁⋊C₁₆

C₂²

yes

characteristic

C₁₆×Dic₁₁

C₄

yes

—

C₁₆×Dic₁₁

C₄

yes

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄×Dic₁₁

D₄

yes

characteristic

C₂×#4318

—

C₂²×C₁₁⋊C₈

D₄

yes

characteristic

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

—

C₁₁×#108

—

C₁₁×#108

—

#66886

—

#66883

—

#66883

—

Dic₁₁⋊C₈

—

C₈×Dic₁₁

C₂×C₄

yes

characteristic

C₈×Dic₁₁

C₂×C₄

yes

characteristic

C₈×Dic₁₁

Q₈

yes

characteristic

C₈×Dic₁₁

Q₈

yes

characteristic

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

C₂×C₄

yes

—

#12891

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×Dic₁₁

Q₁₆

yes

—

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

#41

yes

—

C₂×C₈×C₁₁

#41

yes

—

C₄×Dic₁₁

C₄⋊C₄

yes

characteristic

C₄×Dic₁₁

C₄⋊C₄

yes

characteristic

C₄×Dic₁₁

D₈

yes

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₁₁⋊C₈

SD₁₆

yes

—

C₁₁×C₁₆

—

C₁₁⋊C₁₆

—

C₂×C₄×C₁₆

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#124

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

#107

yes

—

C₂×Dic₁₁

#107

yes

—

C₈×C₁₁

—

C₈×C₁₁

yes

C₈×C₁₁

yes

C₈×C₁₁

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

#106

yes

—

C₁₁⋊C₈

#106

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₁₁

yes

—

—

C₂×D₁₁

yes

—

#423

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂×#107

yes

characteristic

C₂²×C₁₁

#487

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

Dic₁₁

—

Dic₁₁

#368

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

100

C₂×C₁₆

C₄×D₁₁

yes

—

101

#108

—

102

#108

—

103

#108

—

104

#108

—

105

#108

—

106

C₄⋊C₈

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₄×C₈

—

110

C₄×C₈

—

111

C₂×C₁₁

—

112

C₂×C₁₁

#1834

yes

characteristic

113

C₂×C₁₁

C₂×#368

yes

—

114

C₂²×C₄

—

115

C₂²×C₄

D₄×D₁₁

yes

characteristic

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

119

M₁₆

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₂×C₄×D₁₁

yes

characteristic

126

C₂×C₈

#4339

yes

—

127

C₂×C₈

#4341

yes

—

128

C₂×C₈

Q₈×D₁₁

yes

characteristic

129

C₄²

—

130

C₄²

—

131

C₄²

—

132

C₁₆

—

133

C₁₆

—

134

C₁₁

#12891

yes

characteristic, complemented, Sylow

135

C₂³

Q₁₆×D₁₁

yes

characteristic

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

#66938

yes

—

140

C₂×C₄

C₄⋊C₄×D₁₁

yes

characteristic

141

C₂×C₄

D₈×D₁₁

yes

characteristic

142

C₂×C₄

SD₁₆×D₁₁

yes

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

#66925

yes

characteristic

148

C₈

#66930

yes

characteristic

149

C₈

#66942

yes

—

150

C₂²

—

151

C₂²

#10622405

yes

—

152

C₂²

D₁₁×#107

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

#10622263

yes

characteristic

156

C₄

#10622373

yes

—

157

C₄

D₁₁×#106

yes

characteristic

158

C₂

—

159

C₂

#13068742

yes

characteristic

160

C₂

D₁₁×#368

yes

—

	subgroup	G/H
center	C₂×C₄	D₈×D₁₁
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1381	C₂
socle	C₂²×C₁₁	C₂×#107
prime radical	C₂³×C₁₁	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1381	D₁₁
hypocenter	C₁₁	#12891
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

subgroup

G/H

center

C₂×C₄

D₈×D₁₁

commutator

C₂×C₈×C₁₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#1381

C₂

socle

C₂²×C₁₁

C₂×#107

prime radical

C₂³×C₁₁

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

N	H ≅ G/N	type
134. C₁₁	#12891	semidirect

H ≅ G/N

type

134. C₁₁

#12891

semidirect

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

subgroup	index
C₂×C₁₆×Dic₁₁	2
#13068786	2
#13066710	2
#13066709	2
C₁₁×#1381	2
#12891	11

subgroup

index

C₂×C₁₆×Dic₁₁

C₁₁×#1381

Subgroups — #14670161

Conjugacy classes of subgroups

Complements

Maximal subgroups