Group #14670196 — subgroups

Subgroups — #14670196

Order 2816.

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

normal subgroups only

This group has 278 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	#13070381	C₂	1	2	yes	maximal
2	#13070376	C₂	1	2	yes	maximal
3	#13070375	C₂	1	1	yes	maximal, characteristic
4	#13068371	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#2153	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
7	C₁₁×#405	C₂²	1	1	yes	characteristic
8	#10622714	C₂²	1	2	yes	—
9	C₂×#66876	C₂²	1	1	yes	characteristic
10	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₁₁×#364	—	2	2	no	—
12	C₁₁⋊#338	C₄	1	1	yes	characteristic
13	#10622195	C₄	1	1	yes	characteristic
14	#10622169	C₄	1	2	yes	—
15	#10622149	—	2	4	no	—
16	Dic₁₁⋊C₁₆	—	2	4	no	—
17	C₄⋊(C₁₁⋊C₁₆)	—	2	2	no	—
18	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
20	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
21	#66979	C₂×C₄	1	2	yes	—
22	C₂×#4318	C₂×C₄	1	2	yes	—
23	C₁₁×M₃₂	—	2	2	no	—
24	C₁₁×M₃₂	—	2	2	no	—
25	C₂×C₁₁×C₁₆	—	2	2	no	—
26	C₁₁×#97	Q₈	1	2	yes	—
27	C₄×C₈×C₁₁	D₄	1	2	yes	—
28	#66879	Q₈	1	4	yes	—
29	C₈×Dic₁₁	D₄	1	4	yes	—
30	#66876	—	2	2	no	—
31	C₂×C₁₁⋊C₁₆	—	2	1	no	—
32	C₂×C₁₁⋊C₁₆	—	2	1	no	—
33	C₂×C₁₁⋊C₁₆	—	2	2	no	—
34	#12902	—	11	1	no	maximal, Sylow
35	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
36	C₁₁×M₁₆	—	2	2	no	—
37	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
38	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
39	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
42	C₁₁×C₄⋊C₄	—	2	1	no	—
43	C₁₁×C₂²⋊C₄	—	2	1	no	—
44	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
45	C₂²⋊Dic₁₁	—	2	2	no	—
46	C₄⋊Dic₁₁	—	2	2	no	—
47	C₄×Dic₁₁	C₄⋊C₄	1	4	yes	—
48	#4318	—	2	2	no	—
49	#4318	—	2	2	no	—
50	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
51	C₁₁×C₁₆	—	4	2	no	—
52	C₁₁⋊C₁₆	—	4	1	no	—
53	C₁₁⋊C₁₆	—	4	1	no	—
54	#2153	—	11	2	no	—
55	#2153	D₁₁	1	1	yes	characteristic
56	#2151	—	11	2	no	—
57	#2151	—	11	1	no	—
58	#1747	—	11	1	no	—
59	C₂³×C₁₁	#131	1	1	yes	characteristic
60	C₂×C₄×C₁₁	—	2	2	no	—
61	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
62	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₁	#131	1	2	yes	—
64	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
65	C₂×Dic₁₁	—	2	4	no	—
66	C₈×C₁₁	—	2	2	no	—
67	C₈×C₁₁	#127	1	1	yes	characteristic
68	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
69	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
70	C₁₁⋊C₈	—	2	4	no	—
71	C₂×M₃₂	—	11	1	no	—
72	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
73	C₂²×C₁₆	—	11	1	no	—
74	#405	—	11	2	no	—
75	#405	C₂×D₁₁	1	1	yes	characteristic
76	#364	—	2	2	no	—
77	#364	—	22	4	no	—
78	C₄⋊C₁₆	—	22	4	no	—
79	C₄⋊C₁₆	—	22	2	no	—
80	#338	—	11	1	no	—
81	H(3,ℤ/4)	—	11	1	no	—
82	H(3,ℤ/4)	—	11	2	no	—
83	C₂²×C₁₁	—	4	1	no	—
84	C₂²×C₁₁	#424	1	1	yes	characteristic
85	C₂²×C₁₁	#424	1	2	yes	—
86	C₄×C₁₁	—	4	2	no	—
87	C₄×C₁₁	#384	1	1	yes	characteristic
88	C₄×C₁₁	#424	1	2	yes	—
89	C₄×C₁₁	#424	1	1	yes	characteristic
90	Dic₁₁	—	4	4	no	—
91	C₂×M₁₆	—	11	2	no	—
92	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
93	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
94	#117	—	11	2	no	—
95	#117	C₄×D₁₁	1	1	yes	characteristic
96	M₃₂	—	2	2	no	—
97	M₃₂	—	2	2	no	—
98	M₃₂	—	22	2	no	—
99	C₂×C₁₆	—	2	2	no	—
100	C₂×C₁₆	—	22	2	no	—
101	C₂×C₁₆	—	22	1	no	—
102	C₂×C₁₆	—	22	1	no	—
103	#97	—	11	4	no	—
104	#97	Dic₂₂	1	2	yes	—
105	C₄×C₈	—	11	4	no	—
106	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
107	C₂×C₁₁	—	2	2	no	—
108	C₂×C₁₁	—	2	1	no	—
109	C₂×C₁₁	#1843	1	1	yes	characteristic
110	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
111	M₁₆	—	2	2	no	—
112	M₁₆	—	22	2	no	—
113	M₁₆	—	22	2	no	—
114	C₂×C₈	—	11	4	no	—
115	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
116	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
117	C₂×C₈	D₄×D₁₁	1	2	yes	—
118	C₂×C₈	Q₈×D₁₁	1	2	yes	—
119	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
120	C₄⋊C₄	—	2	1	no	—
121	C₄⋊C₄	—	22	2	no	—
122	C₂²⋊C₄	—	2	1	no	—
123	C₂²⋊C₄	—	22	2	no	—
124	C₄²	—	11	4	no	—
125	C₄²	Dic₁₁⋊C₄	1	2	yes	—
126	C₁₆	—	4	2	no	—
127	C₁₆	—	44	1	no	—
128	C₁₆	—	44	1	no	—
129	C₁₁	#12902	1	1	yes	characteristic, complemented, Sylow
130	C₂³	#66960	1	1	yes	characteristic
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	22	4	no	—
133	C₂×C₄	C₄⋊C₄×D₁₁	1	2	yes	—
134	C₂×C₄	#66954	1	2	yes	—
135	C₂×C₄	#66960	1	1	yes	characteristic
136	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
137	C₈	—	2	2	no	—
138	C₈	—	22	4	no	—
139	C₈	#66941	1	2	yes	—
140	C₈	#66993	1	1	yes	characteristic
141	C₈	#66997	1	1	yes	characteristic
142	C₂²	—	4	1	no	—
143	C₂²	#10622452	1	2	yes	—
144	C₂²	#10622732	1	1	yes	characteristic
145	C₄	—	4	2	no	—
146	C₄	—	44	4	no	—
147	C₄	#10622452	1	2	yes	—
148	C₄	#10622589	1	1	yes	characteristic
149	C₄	#10622715	1	1	yes	characteristic
150	C₂	—	2	1	no	—
151	C₂	—	2	2	no	—
152	C₂	#13068769	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13070381

C₂

yes

maximal

#13070376

C₂

yes

maximal

#13070375

C₂

yes

maximal, characteristic

#13068371

C₂

yes

maximal, characteristic

C₁₁×#2153

C₂

yes

maximal, characteristic

C₂×C₁₁×M₃₂

C₂²

yes

—

C₁₁×#405

C₂²

yes

characteristic

#10622714

C₂²

yes

—

C₂×#66876

C₂²

yes

characteristic

C₂²×C₁₁⋊C₁₆

C₂²

yes

characteristic

C₁₁×#364

—

C₁₁⋊#338

C₄

yes

characteristic

#10622195

C₄

yes

characteristic

#10622169

C₄

yes

—

#10622149

—

Dic₁₁⋊C₁₆

—

C₄⋊(C₁₁⋊C₁₆)

—

C₂×C₁₁×M₁₆

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₁₁×#117

C₂×C₄

yes

characteristic

#66979

C₂×C₄

yes

—

C₂×#4318

C₂×C₄

yes

—

C₁₁×M₃₂

—

C₁₁×M₃₂

—

C₂×C₁₁×C₁₆

—

C₁₁×#97

Q₈

yes

—

C₄×C₈×C₁₁

D₄

yes

—

#66879

Q₈

yes

—

C₈×Dic₁₁

D₄

yes

—

#66876

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

—

#12902

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₁₁×M₁₆

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₂²⋊C₄

—

C₄²×C₁₁

C₄⋊C₄

yes

—

C₂²⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄×Dic₁₁

C₄⋊C₄

yes

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

C₁₁×C₁₆

—

C₁₁⋊C₁₆

—

C₁₁⋊C₁₆

—

#2153

—

#2153

D₁₁

yes

—

—

—

C₂³×C₁₁

#131

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#131

yes

—

C₂×C₄×C₁₁

#131

yes

characteristic

C₂×Dic₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#127

yes

characteristic

C₈×C₁₁

C₄⋊Q₈

yes

—

C₈×C₁₁

C₄⋊Q₈

yes

characteristic

C₁₁⋊C₈

—

C₂×M₃₂

—

C₂×M₃₂

C₂×D₁₁

yes

—

C₂²×C₁₆

—

#405

—

#405

C₂×D₁₁

yes

characteristic

#364

—

#364

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#338

—

H(3,ℤ/4)

—

H(3,ℤ/4)

—

C₂²×C₁₁

—

C₂²×C₁₁

#424

yes

characteristic

C₂²×C₁₁

#424

yes

—

C₄×C₁₁

—

C₄×C₁₁

#384

yes

characteristic

C₄×C₁₁

#424

yes

—

C₄×C₁₁

#424

yes

characteristic

Dic₁₁

—

C₂×M₁₆

—

C₂×M₁₆

C₄×D₁₁

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

#117

—

#117

C₄×D₁₁

yes

characteristic

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

#97

—

104

#97

Dic₂₂

yes

—

105

C₄×C₈

—

106

C₄×C₈

C₂²⋊D₁₁

yes

—

107

C₂×C₁₁

—

108

C₂×C₁₁

—

109

C₂×C₁₁

#1843

yes

characteristic

110

C₂²×C₄

C₂×C₄×D₁₁

yes

characteristic

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

C₂×C₈

—

115

C₂×C₈

Dic₁₁⋊C₄

yes

—

116

C₂×C₈

C₂×Dic₂₂

yes

characteristic

117

C₂×C₈

D₄×D₁₁

yes

—

118

C₂×C₈

Q₈×D₁₁

yes

—

119

C₂×C₈

C₂×C₂²⋊D₁₁

yes

characteristic

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₂²⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₄²

Dic₁₁⋊C₄

yes

—

126

C₁₆

—

127

C₁₆

—

128

C₁₆

—

129

C₁₁

#12902

yes

characteristic, complemented, Sylow

130

C₂³

#66960

yes

characteristic

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₄⋊C₄×D₁₁

yes

—

134

C₂×C₄

#66954

yes

—

135

C₂×C₄

#66960

yes

characteristic

136

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

#66941

yes

—

140

C₈

#66993

yes

characteristic

141

C₈

#66997

yes

characteristic

142

C₂²

—

143

C₂²

#10622452

yes

—

144

C₂²

#10622732

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

#10622452

yes

—

148

C₄

#10622589

yes

characteristic

149

C₄

#10622715

yes

characteristic

150

C₂

—

151

C₂

—

152

C₂

#13068769

yes

characteristic

	subgroup	G/H
center	C₈	#66993
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#2153	C₂
socle	C₂×C₁₁	#1843
prime radical	C₂³×C₁₁	#131
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#2153	D₁₁
hypocenter	C₁₁	#12902
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2153

subgroup

G/H

center

C₈

#66993

commutator

C₂²×C₄×C₁₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#2153

C₂

C₂×C₁₁

C₂³×C₁₁

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2153

N	H ≅ G/N	type
129. C₁₁	#12902	semidirect

H ≅ G/N

type

129. C₁₁

#12902

semidirect

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

subgroup	index
#13070381	2
#13070376	2
#13070375	2
#13068371	2
C₁₁×#2153	2
#12902	11

subgroup

index

C₁₁×#2153

Subgroups — #14670196

Conjugacy classes of subgroups

Complements

Maximal subgroups