Group #14640849 — subgroups

Subgroups — #14640849

Order 2816.

270 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 87 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	#13068654	C₂	1	2	yes	maximal
2	C₂×C₁₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
4	C₂²×C₁₁×C₁₆	C₄	1	2	yes	—
5	#10622820	—	2	2	no	—
6	C₂×#66883	—	2	2	no	—
7	C₁₁×C₂²⋊C₁₆	—	2	2	no	—
8	#10622190	C₄	1	4	yes	—
9	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₁	—	4	2	no	—
11	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
12	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₁	D₄	1	2	yes	—
14	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
15	C₂×#4318	—	2	4	no	—
16	C₂×C₁₁×C₁₆	—	2	2	no	—
17	C₂×C₁₁×C₁₆	—	4	2	no	—
18	C₂²⋊(C₁₁⋊C₈)	—	4	2	no	—
19	C₂²⋊(C₁₁⋊C₈)	—	4	2	no	—
20	#66883	—	4	4	no	—
21	#7231	—	11	1	no	maximal, Sylow
22	C₂⁴×C₁₁	Q₁₆	1	1	yes	characteristic
23	C₂²×C₄×C₁₁	—	4	1	no	—
24	C₂²×C₄×C₁₁	—	4	1	no	—
25	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
26	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
28	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
29	C₂×C₈×C₁₁	—	2	4	no	—
30	C₂×C₈×C₁₁	—	2	2	no	—
31	C₂×C₈×C₁₁	—	4	2	no	—
32	C₂×C₈×C₁₁	—	4	1	no	—
33	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
36	#4318	—	4	4	no	—
37	#4318	—	4	4	no	—
38	C₂×C₁₁⋊C₈	—	4	4	no	—
39	C₁₁×C₁₆	—	4	2	no	—
40	C₂×C₂²⋊C₁₆	D₁₁	1	1	yes	characteristic
41	#1810	—	11	2	no	—
42	C₂³×C₁₁	—	2	2	no	—
43	C₂³×C₁₁	—	4	1	no	—
44	C₂³×C₁₁	—	4	1	no	—
45	C₂³×C₁₁	#103	1	2	yes	—
46	C₂³×C₁₁	#107	1	1	yes	characteristic
47	C₂×C₄×C₁₁	—	2	2	no	—
48	C₂×C₄×C₁₁	—	2	1	no	—
49	C₂×C₄×C₁₁	—	2	2	no	—
50	C₂×C₄×C₁₁	—	2	1	no	—
51	C₂×C₄×C₁₁	—	4	1	no	—
52	C₂×C₄×C₁₁	—	4	2	no	—
53	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
54	C₂×C₄×C₁₁	#102	1	2	yes	—
55	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
56	C₈×C₁₁	—	2	1	no	—
57	C₈×C₁₁	—	2	2	no	—
58	C₈×C₁₁	#99	1	2	yes	—
59	C₁₁⋊C₈	—	8	4	no	—
60	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
61	C₂²×C₁₆	Dic₁₁	1	2	yes	—
62	C₂×#108	—	22	2	no	—
63	#407	—	22	2	no	—
64	C₂²⋊C₁₆	—	2	2	no	—
65	#341	—	11	4	no	—
66	C₂²×C₁₁	—	2	1	no	—
67	C₂²×C₁₁	—	2	1	no	—
68	C₂²×C₁₁	—	2	2	no	—
69	C₂²×C₁₁	—	2	2	no	—
70	C₂²×C₁₁	—	2	2	no	—
71	C₂²×C₁₁	—	4	4	no	—
72	C₂²×C₁₁	#340	1	1	yes	characteristic
73	C₂²×C₁₁	#368	1	2	yes	—
74	C₄×C₁₁	—	2	2	no	—
75	C₄×C₁₁	—	2	1	no	—
76	C₄×C₁₁	H(3,ℤ/4)	1	1	yes	characteristic
77	C₄×C₁₁	#342	1	1	yes	characteristic
78	C₂³×C₄	D₄₄	1	1	yes	characteristic
79	C₂×M₁₆	—	22	4	no	—
80	C₂²×C₈	—	4	2	no	—
81	C₂²×C₈	Dic₂₂	1	1	yes	characteristic
82	C₂²×C₈	C₄×D₁₁	1	2	yes	—
83	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
84	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
85	C₂×C₁₆	—	2	2	no	—
86	C₂×C₁₆	—	4	2	no	—
87	#108	—	44	4	no	—
88	C₂²⋊C₈	—	44	2	no	—
89	C₂²⋊C₈	—	44	2	no	—
90	C₂×C₁₁	—	2	2	no	—
91	C₂×C₁₁	—	4	2	no	—
92	C₂×C₁₁	#1289	1	1	yes	characteristic
93	C₂×C₁₁	#1381	1	1	yes	characteristic
94	C₂×C₁₁	#1385	1	1	yes	characteristic
95	C₂⁴	Dic₄₄	1	1	yes	characteristic
96	C₂²×C₄	—	4	1	no	—
97	C₂²×C₄	—	4	1	no	—
98	C₂²×C₄	#4314	1	2	yes	—
99	C₂²×C₄	D₈₈	1	1	yes	characteristic
100	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
101	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
102	M₁₆	—	44	4	no	—
103	M₁₆	—	44	4	no	—
104	C₂×C₈	—	2	4	no	—
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	4	1	no	—
107	C₂×C₈	—	4	2	no	—
108	C₂×C₈	—	44	4	no	—
109	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
110	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
111	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
112	C₁₆	—	4	2	no	—
113	C₁₁	#7231	1	1	yes	characteristic, complemented, Sylow
114	C₂³	—	2	2	no	—
115	C₂³	—	4	1	no	—
116	C₂³	—	4	1	no	—
117	C₂³	#66880	1	2	yes	—
118	C₂³	#66882	1	1	yes	characteristic
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	4	2	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	#66881	1	1	yes	characteristic
126	C₂×C₄	#66885	1	2	yes	—
127	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
128	C₈	—	2	1	no	—
129	C₈	—	2	2	no	—
130	C₈	—	88	4	no	—
131	C₈	#66898	1	2	yes	—
132	C₂²	—	2	1	no	—
133	C₂²	—	2	1	no	—
134	C₂²	—	2	2	no	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	2	no	—
137	C₂²	—	4	4	no	—
138	C₂²	#10622144	1	2	yes	—
139	C₂²	#10622189	1	1	yes	characteristic
140	C₄	—	2	2	no	—
141	C₄	—	2	1	no	—
142	C₄	#10622164	1	1	yes	characteristic
143	C₄	#10622195	1	1	yes	characteristic
144	C₂	—	2	2	no	—
145	C₂	—	4	2	no	—
146	C₂	#13066484	1	1	yes	characteristic
147	C₂	#13066710	1	1	yes	characteristic
148	C₂	#13066720	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068654

C₂

yes

maximal

C₂×C₁₁×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂³×C₈×C₁₁

C₂²

yes

characteristic

C₂²×C₁₁×C₁₆

C₄

yes

—

#10622820

—

C₂×#66883

—

C₁₁×C₂²⋊C₁₆

—

#10622190

C₄

yes

—

C₂³×C₄×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

—

C₂²×C₈×C₁₁

C₂×C₄

yes

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

D₄

yes

—

C₂²×C₈×C₁₁

Q₈

yes

characteristic

C₂×#4318

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

—

C₂²⋊(C₁₁⋊C₈)

—

C₂²⋊(C₁₁⋊C₈)

—

#66883

—

#7231

—

maximal, Sylow

C₂⁴×C₁₁

Q₁₆

yes

characteristic

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₁

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₁

D₈

yes

characteristic

C₂²×C₄×C₁₁

SD₁₆

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄²

yes

characteristic

C₂×C₈×C₁₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

—

C₂×C₂²⋊C₁₆

D₁₁

yes

characteristic

#1810

—

C₂³×C₁₁

—

C₂³×C₁₁

—

C₂³×C₁₁

—

C₂³×C₁₁

#103

yes

—

C₂³×C₁₁

#107

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#95

yes

characteristic

C₂×C₄×C₁₁

#102

yes

—

C₂×C₄×C₁₁

#106

yes

characteristic

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#99

yes

—

C₁₁⋊C₈

—

C₂³×C₈

C₂×D₁₁

yes

characteristic

C₂²×C₁₆

Dic₁₁

yes

—

C₂×#108

—

#407

—

C₂²⋊C₁₆

—

#341

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#340

yes

characteristic

C₂²×C₁₁

#368

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂³×C₄

D₄₄

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

Dic₂₂

yes

characteristic

C₂²×C₈

C₄×D₁₁

yes

—

C₂²×C₈

C₂×Dic₁₁

yes

characteristic

C₂²×C₈

C₂²⋊D₁₁

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂×C₁₁

—

C₂×C₁₁

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂⁴

Dic₄₄

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#4314

yes

—

C₂²×C₄

D₈₈

yes

characteristic

100

C₂²×C₄

C₄⋊Dic₁₁

yes

characteristic

101

C₂²×C₄

(C₂×D₁₁)⋊C₄

yes

—

102

M₁₆

—

103

M₁₆

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₄×Dic₁₁

yes

characteristic

110

C₂×C₈

Dic₁₁⋊C₄

yes

—

111

C₂×C₈

C₂²⋊Dic₁₁

yes

characteristic

112

C₁₆

—

113

C₁₁

#7231

yes

characteristic, complemented, Sylow

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

#66880

yes

—

118

C₂³

#66882

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

#66881

yes

characteristic

126

C₂×C₄

#66885

yes

—

127

C₂×C₄

C₁₁⋊#95

yes

characteristic

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

#66898

yes

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

#10622144

yes

—

139

C₂²

#10622189

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

#10622164

yes

characteristic

143

C₄

#10622195

yes

characteristic

144

C₂

—

145

C₂

—

146

C₂

#13066484

yes

characteristic

147

C₂

#13066710

yes

characteristic

148

C₂

#13066720

yes

characteristic

	subgroup	G/H
center	C₂²	#10622189
commutator	C₂×C₈×C₁₁	C₄²
Frattini	C₂³×C₈	C₂×D₁₁
Fitting	C₂×C₁₁×C₂²⋊C₁₆	C₂
socle	C₂²×C₁₁	#340
prime radical	C₂⁴×C₁₁	Q₁₆
cosocle	C₂³×C₈×C₁₁	C₂²
hypercenter	C₂×C₂²⋊C₁₆	D₁₁
hypocenter	C₁₁	#7231
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×C₂²⋊C₁₆

subgroup

G/H

center

C₂²

#10622189

commutator

C₂×C₈×C₁₁

C₄²

Frattini

C₂³×C₈

C₂×D₁₁

Fitting

C₂×C₁₁×C₂²⋊C₁₆

C₂

socle

C₂²×C₁₁

#340

prime radical

C₂⁴×C₁₁

Q₁₆

cosocle

C₂³×C₈×C₁₁

C₂²

hypercenter

C₂×C₂²⋊C₁₆

D₁₁

hypocenter

C₁₁

#7231

LCS

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×C₂²⋊C₁₆

N	H ≅ G/N	type
113. C₁₁	#7231	semidirect

H ≅ G/N

type

113. C₁₁

#7231

semidirect

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

subgroup	index
#13068654	2
C₂×C₁₁×C₂²⋊C₁₆	2
#7231	11

subgroup

index

#13068654

C₂×C₁₁×C₂²⋊C₁₆

#7231

Subgroups — #14640849

Conjugacy classes of subgroups

Complements

Maximal subgroups