Group #14640643 — subgroups

Subgroups — #14640643

Order 2816.

242 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 151 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×#10622096	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₁×C₁₆	C₄	1	2	yes	—
4	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
6	C₄×C₁₁×C₁₆	—	2	2	no	—
7	#10622096	—	2	2	no	—
8	#10622096	C₄	1	4	yes	—
9	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
11	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
12	C₂²×C₁₁⋊C₈	—	4	2	no	—
13	C₂×C₁₁×C₁₆	—	2	2	no	—
14	C₂×C₁₁×C₁₆	—	2	2	no	—
15	C₂×C₁₁×C₁₆	C₈	1	4	yes	complemented
16	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₁	D₄	1	2	yes	—
18	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
19	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
20	#7154	—	11	1	no	maximal, Sylow
21	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
23	C₂²×C₄×C₁₁	Q₁₆	1	1	yes	characteristic
24	C₂×C₈×C₁₁	—	2	2	no	—
25	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
26	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
29	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
30	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
31	C₄²×C₁₁	SD₁₆	1	2	yes	—
32	C₂×C₁₁⋊C₈	—	4	4	no	—
33	C₂×C₁₁⋊C₈	—	8	2	no	—
34	C₂×C₁₁⋊C₈	—	8	2	no	—
35	C₁₁×C₁₆	—	2	4	no	—
36	C₂×C₄×C₁₆	D₁₁	1	1	yes	characteristic
37	C₂×#335	—	11	2	no	—
38	C₂³×C₁₁	#107	1	1	yes	characteristic
39	C₂×C₄×C₁₁	—	2	2	no	—
40	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
41	C₂×C₄×C₁₁	#102	1	2	yes	—
42	C₂×C₄×C₁₁	#103	1	2	yes	—
43	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
44	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
45	C₂×C₄×C₁₁	#108	1	2	yes	—
46	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
48	C₂×C₄×C₁₁	Q₃₂	1	1	yes	characteristic
49	C₈×C₁₁	—	2	2	no	—
50	C₈×C₁₁	C₄×C₈	1	1	yes	characteristic
51	C₈×C₁₁	#97	1	1	yes	characteristic
52	C₈×C₁₁	C₂²⋊C₈	1	2	yes	—
53	C₁₁⋊C₈	—	8	4	no	—
54	C₂²×C₁₆	Dic₁₁	1	2	yes	—
55	C₂×C₄⋊C₈	—	22	2	no	—
56	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
57	C₄×C₁₆	—	2	2	no	—
58	#335	—	11	4	no	—
59	#335	—	22	2	no	—
60	C₂²×C₁₁	#335	1	2	yes	—
61	C₂²×C₁₁	#340	1	1	yes	characteristic
62	C₂²×C₁₁	#366	1	1	yes	characteristic
63	C₂²×C₁₁	#367	1	1	yes	characteristic
64	C₂²×C₁₁	#368	1	2	yes	—
65	C₄×C₁₁	—	2	2	no	—
66	C₄×C₁₁	#334	1	2	yes	—
67	C₄×C₁₁	#336	1	1	yes	characteristic
68	C₄×C₁₁	#341	1	1	yes	characteristic
69	C₄×C₁₁	#357	1	2	yes	—
70	C₄×C₁₁	#358	1	2	yes	—
71	C₂²×C₈	—	44	2	no	—
72	C₂²×C₈	Dic₂₂	1	1	yes	characteristic
73	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
74	C₂×C₄²	D₄₄	1	1	yes	characteristic
75	C₂×C₁₆	—	2	2	no	—
76	C₂×C₁₆	—	2	2	no	—
77	C₂×C₁₆	C₁₁⋊C₈	1	4	yes	complemented
78	C₄⋊C₈	—	22	4	no	—
79	C₄⋊C₈	—	44	2	no	—
80	C₄×C₈	C₄×D₁₁	1	2	yes	—
81	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
82	C₂×C₁₁	#1277	1	1	yes	characteristic
83	C₂×C₁₁	#1371	1	2	yes	—
84	C₂×C₁₁	#1372	1	2	yes	—
85	C₂×C₁₁	#1380	1	1	yes	characteristic
86	C₂×C₁₁	#1381	1	1	yes	characteristic
87	C₂²×C₄	D₈₈	1	1	yes	characteristic
88	C₂²×C₄	Dic₄₄	1	1	yes	characteristic
89	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	44	4	no	—
92	C₂×C₈	—	88	2	no	—
93	C₂×C₈	—	88	2	no	—
94	C₂×C₈	C₂×C₁₁⋊C₈	1	2	yes	—
95	C₂×C₈	#4318	1	2	yes	—
96	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
97	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
98	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
99	C₄²	#4314	1	2	yes	—
100	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
101	C₁₆	—	2	4	no	—
102	C₁₁	#7154	1	1	yes	characteristic, complemented, Sylow
103	C₂³	#66882	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	D₁₇₆	1	1	yes	characteristic
106	C₂×C₄	#66864	1	2	yes	—
107	C₂×C₄	Dic₈₈	1	1	yes	characteristic
108	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	2	yes	—
109	C₂×C₄	#66880	1	2	yes	—
110	C₂×C₄	#66881	1	1	yes	characteristic
111	C₂×C₄	#66883	1	2	yes	—
112	C₂×C₄	#66885	1	2	yes	—
113	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	88	4	no	—
116	C₈	C₄×C₁₁⋊C₈	1	1	yes	characteristic
117	C₈	#66867	1	1	yes	characteristic
118	C₈	C₂²⋊(C₁₁⋊C₈)	1	2	yes	—
119	C₂²	#10622096	1	2	yes	—
120	C₂²	#10622142	1	1	yes	characteristic
121	C₂²	#10622143	1	1	yes	characteristic
122	C₂²	#10622144	1	2	yes	—
123	C₂²	#10622189	1	1	yes	characteristic
124	C₄	—	2	2	no	—
125	C₄	#10622095	1	2	yes	—
126	C₄	#10622141	1	2	yes	—
127	C₄	#10622147	1	2	yes	—
128	C₄	#10622162	1	1	yes	characteristic
129	C₄	#10622190	1	1	yes	characteristic
130	C₂	#13066451	1	1	yes	characteristic
131	C₂	#13066688	1	2	yes	—
132	C₂	#13066690	1	2	yes	—
133	C₂	#13066708	1	1	yes	characteristic
134	C₂	#13066710	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622096

C₂

yes

maximal

C₂×C₄×C₁₁×C₁₆

C₂

yes

maximal, characteristic

C₂²×C₁₁×C₁₆

C₄

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊(C₁₁⋊C₈)

—

C₄×C₁₁×C₁₆

—

#10622096

—

#10622096

C₄

yes

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

Q₈

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂²×C₁₁⋊C₈

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

C₈

yes

complemented

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#7154

—

maximal, Sylow

C₂²×C₄×C₁₁

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₁

D₈

yes

characteristic

C₂²×C₄×C₁₁

Q₁₆

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄²

yes

characteristic

C₂×C₈×C₁₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₂×C₈

yes

—

C₂×C₈×C₁₁

M₁₆

yes

—

C₄²×C₁₁

C₂²⋊C₄

yes

—

C₄²×C₁₁

SD₁₆

yes

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

—

C₂×C₄×C₁₆

D₁₁

yes

characteristic

C₂×#335

—

C₂³×C₁₁

#107

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#95

yes

characteristic

C₂×C₄×C₁₁

#102

yes

—

C₂×C₄×C₁₁

#103

yes

—

C₂×C₄×C₁₁

C₄⋊C₈

yes

—

C₂×C₄×C₁₁

#106

yes

characteristic

C₂×C₄×C₁₁

#108

yes

—

C₂×C₄×C₁₁

D₁₆

yes

characteristic

C₂×C₄×C₁₁

SD₃₂

yes

—

C₂×C₄×C₁₁

Q₃₂

yes

characteristic

C₈×C₁₁

—

C₈×C₁₁

C₄×C₈

yes

characteristic

C₈×C₁₁

#97

yes

characteristic

C₈×C₁₁

C₂²⋊C₈

yes

—

C₁₁⋊C₈

—

C₂²×C₁₆

Dic₁₁

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₄×C₁₆

—

#335

—

#335

—

C₂²×C₁₁

#335

yes

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

—

C₄×C₁₁

—

C₄×C₁₁

#334

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

C₄×C₁₁

#358

yes

—

C₂²×C₈

—

C₂²×C₈

Dic₂₂

yes

characteristic

C₂²×C₈

C₂×Dic₁₁

yes

characteristic

C₂×C₄²

D₄₄

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₁₁⋊C₈

yes

complemented

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

C₄×D₁₁

yes

—

C₄×C₈

C₂²⋊D₁₁

yes

—

C₂×C₁₁

#1277

yes

characteristic

C₂×C₁₁

#1371

yes

—

C₂×C₁₁

#1372

yes

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂²×C₄

D₈₈

yes

characteristic

C₂²×C₄

Dic₄₄

yes

characteristic

C₂²×C₄

C₄⋊Dic₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₁₁⋊C₈

yes

—

C₂×C₈

#4318

yes

—

C₂×C₈

C₄×Dic₁₁

yes

characteristic

C₂×C₈

Dic₁₁⋊C₄

yes

—

C₂×C₈

C₂²⋊Dic₁₁

yes

characteristic

C₄²

#4314

yes

—

100

C₄²

(C₂×D₁₁)⋊C₄

yes

—

101

C₁₆

—

102

C₁₁

#7154

yes

characteristic, complemented, Sylow

103

C₂³

#66882

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

D₁₇₆

yes

characteristic

106

C₂×C₄

#66864

yes

—

107

C₂×C₄

Dic₈₈

yes

characteristic

108

C₂×C₄

C₄⋊(C₁₁⋊C₈)

yes

—

109

C₂×C₄

#66880

yes

—

110

C₂×C₄

#66881

yes

characteristic

111

C₂×C₄

#66883

yes

—

112

C₂×C₄

#66885

yes

—

113

C₂×C₄

C₁₁⋊#95

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

C₄×C₁₁⋊C₈

yes

characteristic

117

C₈

#66867

yes

characteristic

118

C₈

C₂²⋊(C₁₁⋊C₈)

yes

—

119

C₂²

#10622096

yes

—

120

C₂²

#10622142

yes

characteristic

121

C₂²

#10622143

yes

characteristic

122

C₂²

#10622144

yes

—

123

C₂²

#10622189

yes

characteristic

124

C₄

—

125

C₄

#10622095

yes

—

126

C₄

#10622141

yes

—

127

C₄

#10622147

yes

—

128

C₄

#10622162

yes

characteristic

129

C₄

#10622190

yes

characteristic

130

C₂

#13066451

yes

characteristic

131

C₂

#13066688

yes

—

132

C₂

#13066690

yes

—

133

C₂

#13066708

yes

characteristic

134

C₂

#13066710

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₈₈
commutator	C₈×C₁₁	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₂×C₄×C₁₁×C₁₆	C₂
socle, prime radical	C₂³×C₁₁	#107
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	C₂×C₄×C₁₆	D₁₁
hypocenter	C₁₁	#7154
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

subgroup

G/H

center

C₂²×C₄

D₈₈

commutator

C₈×C₁₁

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₁

Fitting

C₂×C₄×C₁₁×C₁₆

C₂

socle, prime radical

C₂³×C₁₁

#107

cosocle

C₂×C₄×C₈×C₁₁

C₂²

hypercenter

C₂×C₄×C₁₆

D₁₁

hypocenter

C₁₁

#7154

LCS

G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

N	H ≅ G/N	type
15. C₂×C₁₁×C₁₆	C₈	semidirect
77. C₂×C₁₆	C₁₁⋊C₈	semidirect
102. C₁₁	#7154	semidirect

H ≅ G/N

type

15. C₂×C₁₁×C₁₆

C₈

semidirect

77. C₂×C₁₆

C₁₁⋊C₈

semidirect

102. C₁₁

#7154

semidirect

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

subgroup	index
C₂×#10622096	2
C₂×C₄×C₁₁×C₁₆	2
#7154	11

subgroup

index

C₂×#10622096

C₂×C₄×C₁₁×C₁₆

#7154

Subgroups — #14640643

Conjugacy classes of subgroups

Complements

Maximal subgroups