Group #14647488 — subgroups

Subgroups — #14647488

Order 2816.

220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 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	1	yes	maximal, characteristic
2	#13066908	C₂	1	1	yes	maximal, characteristic
3	#13066479	C₂	1	2	yes	maximal
4	#13066477	C₂	1	2	yes	maximal
5	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#432	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	#10622539	C₂²	1	2	yes	—
9	#10622538	C₂²	1	1	yes	characteristic
10	#10622538	C₂²	1	1	yes	characteristic
11	C₁₁×#335	—	2	1	no	—
12	C₁₁×#334	—	2	1	no	—
13	#10622096	—	2	1	no	—
14	#10622095	—	2	1	no	—
15	#10622092	C₄	1	4	yes	—
16	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
17	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
18	C₁₁×C₄⋊C₈	—	2	2	no	—
19	C₁₁×C₂²⋊C₈	—	2	2	no	—
20	C₁₁×#97	—	2	2	no	—
21	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
24	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
25	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
26	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
27	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
28	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
29	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
30	#66867	—	2	2	no	—
31	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
32	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
33	#8799	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
37	C₂×C₈×C₁₁	—	4	2	no	—
38	C₂×C₈×C₁₁	—	4	2	no	—
39	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
40	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
41	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
43	C₄²×C₁₁	#41	1	1	yes	characteristic
44	C₄²×C₁₁	#41	1	1	yes	characteristic
45	C₂×C₁₁⋊C₈	—	2	2	no	—
46	C₂×C₁₁⋊C₈	—	2	2	no	—
47	C₂×C₁₁⋊C₈	—	4	2	no	—
48	#1568	—	11	1	no	—
49	#1568	D₁₁	1	1	yes	characteristic
50	#1452	—	11	1	no	—
51	#1287	—	11	2	no	—
52	#1287	—	11	2	no	—
53	C₂³×C₁₁	#125	1	1	yes	characteristic
54	C₂×C₄×C₁₁	—	2	2	no	—
55	C₂×C₄×C₁₁	—	4	1	no	—
56	C₂×C₄×C₁₁	—	4	1	no	—
57	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
59	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
60	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
61	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
62	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
63	C₈×C₁₁	—	2	2	no	—
64	C₈×C₁₁	—	2	2	no	—
65	C₈×C₁₁	—	8	2	no	—
66	C₁₁⋊C₈	—	4	2	no	—
67	C₁₁⋊C₈	—	4	2	no	—
68	C₁₁⋊C₈	—	8	2	no	—
69	#432	—	11	2	no	—
70	#432	C₂×D₁₁	1	2	yes	—
71	#431	—	11	1	no	—
72	#431	—	11	1	no	—
73	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
74	#335	—	2	1	no	—
75	#335	—	22	1	no	—
76	#334	—	2	1	no	—
77	#334	—	22	1	no	—
78	#322	—	11	4	no	—
79	C₂²×C₁₁	—	2	1	no	—
80	C₂²×C₁₁	—	2	1	no	—
81	C₂²×C₁₁	—	2	1	no	—
82	C₂²×C₁₁	#382	1	1	yes	characteristic
83	C₄×C₁₁	—	2	1	no	—
84	C₄×C₁₁	—	2	1	no	—
85	C₄×C₁₁	—	2	1	no	—
86	C₄×C₁₁	—	2	1	no	—
87	C₄×C₁₁	—	2	1	no	—
88	C₄×C₁₁	#430	1	2	yes	—
89	C₂²×C₈	Dic₂₂	1	2	yes	—
90	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
91	C₄⋊C₈	—	2	2	no	—
92	C₄⋊C₈	—	22	1	no	—
93	C₄⋊C₈	—	22	1	no	—
94	C₄⋊C₈	—	22	2	no	—
95	C₂²⋊C₈	—	2	2	no	—
96	C₂²⋊C₈	—	22	1	no	—
97	C₂²⋊C₈	—	22	1	no	—
98	C₂²⋊C₈	—	22	2	no	—
99	#97	—	2	2	no	—
100	#97	—	22	2	no	—
101	C₄×C₈	—	11	2	no	—
102	C₄×C₈	—	11	2	no	—
103	C₄×C₈	C₄×D₁₁	1	2	yes	—
104	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
105	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
106	C₂×C₁₁	—	4	1	no	—
107	C₂×C₁₁	#1833	1	1	yes	characteristic
108	C₂×C₁₁	#1833	1	1	yes	characteristic
109	C₂×C₁₁	#1838	1	1	yes	characteristic
110	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
111	C₂²×C₄	#4341	1	1	yes	characteristic
112	C₂²×C₄	#4343	1	1	yes	characteristic
113	C₂×C₈	—	4	2	no	—
114	C₂×C₈	—	4	2	no	—
115	C₂×C₈	—	22	2	no	—
116	C₂×C₈	—	22	2	no	—
117	C₂×C₈	—	44	2	no	—
118	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
119	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
120	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
121	C₄²	#4341	1	1	yes	characteristic
122	C₄²	#4343	1	1	yes	characteristic
123	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
124	C₁₁	#8799	1	1	yes	characteristic, complemented, Sylow
125	C₂³	#66943	1	1	yes	characteristic
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	#66943	1	1	yes	characteristic
130	C₂×C₄	#66945	1	1	yes	characteristic
131	C₂×C₄	#66945	1	1	yes	characteristic
132	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
133	C₂×C₄	#66989	1	1	yes	characteristic
134	C₂×C₄	#67000	1	1	yes	characteristic
135	C₈	—	2	2	no	—
136	C₈	—	2	2	no	—
137	C₈	—	8	2	no	—
138	C₈	—	44	2	no	—
139	C₈	—	44	2	no	—
140	C₈	—	88	2	no	—
141	C₂²	—	2	1	no	—
142	C₂²	—	2	1	no	—
143	C₂²	—	2	1	no	—
144	C₂²	#10622590	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	—	2	1	no	—
148	C₄	—	2	1	no	—
149	C₄	—	2	1	no	—
150	C₄	#10622737	1	2	yes	—
151	C₂	—	4	1	no	—
152	C₂	#13068739	1	1	yes	characteristic
153	C₂	#13068741	1	1	yes	characteristic
154	C₂	#13068756	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13067379

C₂

yes

maximal, characteristic

#13066908

C₂

yes

maximal, characteristic

#13066479

C₂

yes

maximal

#13066477

C₂

yes

maximal

C₁₁×#1568

C₂

yes

maximal, characteristic

C₁₁×#432

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622539

C₂²

yes

—

#10622538

C₂²

yes

characteristic

#10622538

C₂²

yes

characteristic

C₁₁×#335

—

C₁₁×#334

—

#10622096

—

#10622095

—

#10622092

C₄

yes

—

C₂²×C₈×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₁₁×C₄⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₁₁×#97

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

characteristic

C₂²⋊(C₁₁⋊C₈)

—

C₂²⋊(C₁₁⋊C₈)

—

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#66867

—

C₄×C₁₁⋊C₈

C₂×C₄

yes

—

C₄×C₁₁⋊C₈

C₂×C₄

yes

—

#8799

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×Q₈

yes

C₂²×C₄×C₁₁

yes

C₂²×C₄×C₁₁

yes

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

C₄²×C₁₁

yes

C₄²×C₁₁

yes

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#1568

—

#1568

D₁₁

yes

—

—

—

C₂³×C₁₁

#125

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

#432

—

#432

C₂×D₁₁

yes

—

#431

—

#431

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#382

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#430

yes

—

C₂²×C₈

Dic₂₂

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

100

#97

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₄×C₈

C₄×D₁₁

yes

—

104

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

105

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

106

C₂×C₁₁

—

107

C₂×C₁₁

#1833

yes

characteristic

108

C₂×C₁₁

#1833

yes

characteristic

109

C₂×C₁₁

#1838

yes

characteristic

110

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

111

C₂²×C₄

#4341

yes

characteristic

112

C₂²×C₄

#4343

yes

characteristic

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

Dic₁₁⋊C₄

yes

—

119

C₂×C₈

Dic₁₁⋊C₄

yes

—

120

C₄²

C₂×C₄×D₁₁

yes

characteristic

121

C₄²

#4341

yes

characteristic

122

C₄²

#4343

yes

characteristic

123

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

124

C₁₁

#8799

yes

characteristic, complemented, Sylow

125

C₂³

#66943

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

#66943

yes

characteristic

130

C₂×C₄

#66945

yes

characteristic

131

C₂×C₄

#66945

yes

characteristic

132

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

133

C₂×C₄

#66989

yes

characteristic

134

C₂×C₄

#67000

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

#10622590

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

#10622737

yes

—

151

C₂

—

152

C₂

#13068739

yes

characteristic

153

C₂

#13068741

yes

characteristic

154

C₂

#13068756

yes

characteristic

	subgroup	G/H
center	C₂²	#10622590
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1568	C₂
socle	C₂²×C₁₁	#382
prime radical	C₂³×C₁₁	#125
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1568	D₁₁
hypocenter	C₁₁	#8799
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#10622590

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1568

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
124. C₁₁	#8799	semidirect

H ≅ G/N

type

124. C₁₁

#8799

semidirect

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

subgroup	index
#13067379	2
#13066908	2
#13066479	2
#13066477	2
C₁₁×#1568	2
#8799	11

subgroup

index

C₁₁×#1568

Subgroups — #14647488

Conjugacy classes of subgroups

Complements

Maximal subgroups