Group #14646769 — subgroups

Subgroups — #14646769

Order 2816.

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

normal subgroups only

This group has 320 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	#13067379	C₂	1	2	yes	maximal
2	#13067254	C₂	1	2	yes	maximal
3	#13066527	C₂	1	2	yes	maximal
4	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#533	C₂²	1	1	yes	characteristic
6	C₁₁×#446	—	2	2	no	—
7	C₈×Q₈×C₁₁	—	2	2	no	—
8	C₁₁×#424	C₄	1	2	yes	—
9	C₁₁×#423	C₂²	1	1	yes	characteristic
10	C₁₁×#405	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	#10622539	C₂²	1	4	yes	—
13	#10622181	—	2	4	no	—
14	#10622096	—	2	2	no	—
15	#10622095	—	2	2	no	—
16	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₁₁×C₄⋊Q₈	Q₈	1	2	yes	—
20	C₁₁×#125	D₄	1	2	yes	—
21	C₁₁×C₂²⋊Q₈	—	2	2	no	—
22	C₄×Q₈×C₁₁	—	2	2	no	—
23	C₁₁×#117	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
25	C₁₁×C₄⋊C₈	—	2	4	no	—
26	C₁₁×C₄⋊C₈	—	2	2	no	—
27	C₁₁×#97	—	2	2	no	—
28	C₄×C₈×C₁₁	—	2	2	no	—
29	C₄×C₈×C₁₁	D₄	1	2	yes	—
30	C₄×C₈×C₁₁	D₄	1	2	yes	—
31	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
32	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
33	#66867	—	2	4	no	—
34	#8631	—	11	1	no	maximal, Sylow
35	C₂×Q₈×C₁₁	—	2	2	no	—
36	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	#41	1	2	yes	—
38	C₁₁×M₁₆	—	4	2	no	—
39	C₂×C₈×C₁₁	—	2	2	no	—
40	C₂×C₈×C₁₁	—	2	2	no	—
41	C₂×C₈×C₁₁	—	4	1	no	—
42	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
45	C₁₁×C₄⋊C₄	—	2	4	no	—
46	C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₁₁×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
48	C₁₁×C₂²⋊C₄	—	2	2	no	—
49	C₄²×C₁₁	—	2	2	no	—
50	C₄²×C₁₁	C₂×D₄	1	2	yes	—
51	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
52	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₁₁⋊C₈	—	4	4	no	—
54	#2960	D₁₁	1	1	yes	characteristic
55	#1568	—	11	2	no	—
56	#1537	—	11	2	no	—
57	#1307	—	11	2	no	—
58	C₂³×C₁₁	#117	1	1	yes	characteristic
59	Q₈×C₁₁	—	4	4	no	—
60	C₂×C₄×C₁₁	—	2	1	no	—
61	C₂×C₄×C₁₁	—	2	1	no	—
62	C₂×C₄×C₁₁	—	2	4	no	—
63	C₂×C₄×C₁₁	—	4	2	no	—
64	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₁	#121	1	2	yes	—
67	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
68	C₈×C₁₁	—	2	1	no	—
69	C₈×C₁₁	—	2	2	no	—
70	C₈×C₁₁	—	4	2	no	—
71	C₈×C₁₁	#101	1	2	yes	—
72	C₁₁⋊C₈	—	8	4	no	—
73	#533	C₂×D₁₁	1	1	yes	characteristic
74	#446	—	2	2	no	—
75	C₈×Q₈	—	2	2	no	—
76	#432	—	11	4	no	—
77	#424	Dic₁₁	1	2	yes	—
78	#423	C₂×D₁₁	1	1	yes	characteristic
79	#405	Dic₁₁	1	2	yes	—
80	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
81	#335	—	22	2	no	—
82	#334	—	22	2	no	—
83	#330	—	22	4	no	—
84	C₂²×C₁₁	—	2	1	no	—
85	C₂²×C₁₁	—	2	2	no	—
86	C₂²×C₁₁	#380	1	1	yes	characteristic
87	C₄×C₁₁	—	2	1	no	—
88	C₄×C₁₁	—	2	2	no	—
89	C₄×C₁₁	—	2	2	no	—
90	C₄×C₁₁	—	4	4	no	—
91	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
92	C₄×C₁₁	#413	1	1	yes	characteristic
93	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
94	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
95	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
96	C₄⋊Q₈	Dic₂₂	1	2	yes	—
97	#125	D₄₄	1	2	yes	—
98	C₂²⋊Q₈	—	2	2	no	—
99	C₄×Q₈	—	2	2	no	—
100	#117	C₂×Dic₁₁	1	2	yes	—
101	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
102	C₄⋊C₈	—	2	4	no	—
103	C₄⋊C₈	—	2	2	no	—
104	C₄⋊C₈	—	22	4	no	—
105	C₂²⋊C₈	—	22	4	no	—
106	#97	—	2	2	no	—
107	#97	—	22	4	no	—
108	C₄×C₈	—	2	2	no	—
109	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
110	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
111	C₂×C₁₁	—	4	1	no	—
112	C₂×C₁₁	#1801	1	1	yes	characteristic
113	C₂×C₁₁	#1814	1	2	yes	—
114	C₂×Q₈	—	2	2	no	—
115	C₂²×C₄	#4339	1	2	yes	—
116	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
117	M₁₆	—	4	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	4	1	no	—
121	C₂×C₈	—	44	4	no	—
122	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
123	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
124	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
125	C₄⋊C₄	—	2	2	no	—
126	C₄⋊C₄	—	2	4	no	—
127	C₄⋊C₄	C₄⋊Dic₁₁	1	4	yes	—
128	C₂²⋊C₄	—	2	2	no	—
129	C₄²	—	2	2	no	—
130	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
131	C₄²	C₂×D₄₄	1	1	yes	characteristic
132	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
133	C₁₁	#8631	1	1	yes	characteristic, complemented, Sylow
134	C₂³	#66979	1	1	yes	characteristic
135	Q₈	—	4	4	no	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	2	1	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	4	2	no	—
140	C₂×C₄	#66977	1	2	yes	—
141	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
142	C₂×C₄	#66983	1	2	yes	—
143	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
144	C₈	—	2	1	no	—
145	C₈	—	2	2	no	—
146	C₈	—	4	2	no	—
147	C₈	—	88	4	no	—
148	C₈	#66900	1	2	yes	—
149	C₂²	—	2	1	no	—
150	C₂²	—	2	2	no	—
151	C₂²	#10622825	1	1	yes	characteristic
152	C₄	—	2	1	no	—
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	4	4	no	—
156	C₄	C₂×#66900	1	1	yes	characteristic
157	C₄	#10622850	1	1	yes	characteristic
158	C₂	—	4	1	no	—
159	C₂	#13068612	1	1	yes	characteristic
160	C₂	#13068670	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13067379

C₂

yes

maximal

#13067254

C₂

yes

maximal

#13066527

C₂

yes

maximal

C₁₁×#2960

C₂

yes

maximal, characteristic

C₁₁×#533

C₂²

yes

characteristic

C₁₁×#446

—

C₈×Q₈×C₁₁

—

C₁₁×#424

C₄

yes

—

C₁₁×#423

C₂²

yes

characteristic

C₁₁×#405

C₄

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622539

C₂²

yes

—

#10622181

—

#10622096

—

#10622095

—

C₂×C₁₁×M₁₆

C₂×C₄

yes

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₁₁×C₄⋊Q₈

Q₈

yes

—

C₁₁×#125

D₄

yes

—

C₁₁×C₂²⋊Q₈

—

C₄×Q₈×C₁₁

—

C₁₁×#117

C₂×C₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₁₁×#97

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#66867

—

#8631

—

maximal, Sylow

C₂×Q₈×C₁₁

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

characteristic

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

C₄⋊C₄

yes

—

C₁₁×C₂²⋊C₄

—

C₄²×C₁₁

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₁₁⋊C₈

—

#2960

D₁₁

yes

—

—

—

C₂³×C₁₁

#117

yes

characteristic

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#121

yes

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#101

yes

—

C₁₁⋊C₈

—

#533

C₂×D₁₁

yes

characteristic

#446

—

C₈×Q₈

—

#432

—

#424

Dic₁₁

yes

—

#423

C₂×D₁₁

yes

characteristic

#405

Dic₁₁

yes

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#380

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂×M₁₆

C₂×Dic₁₁

yes

—

C₂²×C₈

C₂×Dic₁₁

yes

characteristic

C₂²×C₈

C₂×Dic₁₁

yes

characteristic

C₄⋊Q₈

Dic₂₂

yes

—

#125

D₄₄

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

100

#117

C₂×Dic₁₁

yes

—

101

C₂×C₄²

C₂²×D₁₁

yes

characteristic

102

C₄⋊C₈

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₂²⋊C₈

—

106

#97

—

107

#97

—

108

C₄×C₈

—

109

C₄×C₈

C₂²⋊D₁₁

yes

—

110

C₄×C₈

C₂²⋊D₁₁

yes

—

111

C₂×C₁₁

—

112

C₂×C₁₁

#1801

yes

characteristic

113

C₂×C₁₁

#1814

yes

—

114

C₂×Q₈

—

115

C₂²×C₄

#4339

yes

—

116

C₂²×C₄

C₂²×Dic₁₁

yes

characteristic

117

M₁₆

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

C₂²⋊Dic₁₁

yes

characteristic

123

C₂×C₈

C₂²⋊Dic₁₁

yes

—

124

C₂×C₈

C₂²⋊Dic₁₁

yes

characteristic

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄⋊C₄

C₄⋊Dic₁₁

yes

—

128

C₂²⋊C₄

—

129

C₄²

—

130

C₄²

C₂×Dic₂₂

yes

characteristic

131

C₄²

C₂×D₄₄

yes

characteristic

132

C₄²

C₂×C₂²⋊D₁₁

yes

—

133

C₁₁

#8631

yes

characteristic, complemented, Sylow

134

C₂³

#66979

yes

characteristic

135

Q₈

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

#66977

yes

—

141

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

142

C₂×C₄

#66983

yes

—

143

C₂×C₄

C₂×C₂²⋊Dic₁₁

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

—

148

C₈

#66900

yes

—

149

C₂²

—

150

C₂²

—

151

C₂²

#10622825

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

C₂×#66900

yes

characteristic

157

C₄

#10622850

yes

characteristic

158

C₂

—

159

C₂

#13068612

yes

characteristic

160

C₂

#13068670

yes

—

	subgroup	G/H
center	C₂²	#10622825
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2960	C₂
socle	C₂²×C₁₁	#380
prime radical	C₂³×C₁₁	#117
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2960	D₁₁
hypocenter	C₁₁	#8631
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

subgroup

G/H

center

C₂²

#10622825

commutator

C₂²×C₄×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#2960

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

N	H ≅ G/N	type
133. C₁₁	#8631	semidirect

H ≅ G/N

type

133. C₁₁

#8631

semidirect

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

subgroup	index
#13067379	2
#13067254	2
#13066527	2
C₁₁×#2960	2
#8631	11

subgroup

index

C₁₁×#2960

Subgroups — #14646769

Conjugacy classes of subgroups

Complements

Maximal subgroups