Group #14668052 — subgroups

Subgroups — #14668052

Order 2816.

212 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 71 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	#13070869	C₂	1	1	yes	maximal, characteristic
2	#13067986	C₂	1	2	yes	maximal
3	#13066690	C₂	1	1	yes	maximal, characteristic
4	#13066666	C₂	1	2	yes	maximal
5	C₁₁×#2183	C₂	1	1	yes	maximal, characteristic
6	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic
7	#10622633	—	2	2	no	—
8	C₂×Dic₈₈	—	2	1	no	—
9	C₂×Dic₈₈	—	2	1	no	—
10	#10622312	C₂²	1	2	yes	—
11	C₁₁×C₄⋊C₁₆	—	2	1	no	—
12	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₁₁×#346	—	2	1	no	—
14	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
15	#10622120	—	2	2	no	—
16	#10622096	C₂²	1	2	yes	—
17	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
18	C₂×Dic₄₄	—	2	2	no	—
19	C₂×Dic₄₄	—	2	2	no	—
20	#66922	—	2	2	no	—
21	C₂×C₁₁×C₁₆	—	2	1	no	—
22	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
23	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
24	C₁₁×C₄⋊C₈	—	2	1	no	—
25	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₁	—	2	1	no	—
27	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
28	#66899	—	4	2	no	—
29	#66872	—	4	2	no	—
30	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
31	Dic₈₈	—	4	2	no	—
32	Dic₈₈	—	4	2	no	—
33	#12443	—	11	1	no	maximal, Sylow
34	C₂×Q₈×C₁₁	D₈	1	1	yes	characteristic
35	C₂×Dic₂₂	—	4	2	no	—
36	C₂×C₈×C₁₁	—	2	1	no	—
37	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
39	C₁₁×C₄⋊C₄	—	2	1	no	—
40	C₁₁×C₄⋊C₄	D₈	1	1	yes	characteristic
41	C₄²×C₁₁	—	2	1	no	—
42	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
43	C₄⋊Dic₁₁	—	4	2	no	—
44	C₄⋊Dic₁₁	—	4	2	no	—
45	C₂×C₁₁⋊C₈	—	4	2	no	—
46	Dic₄₄	—	4	2	no	—
47	Dic₄₄	—	4	2	no	—
48	Dic₄₄	—	8	2	no	—
49	C₁₁×C₁₆	—	2	1	no	—
50	C₁₁×C₁₆	—	4	1	no	—
51	C₁₁×C₁₆	SD₁₆	1	2	yes	—
52	#2247	—	11	1	no	—
53	#2183	D₁₁	1	1	yes	characteristic
54	#1670	—	11	2	no	—
55	#1372	—	11	1	no	—
56	#1362	—	11	2	no	—
57	Q₈×C₁₁	—	2	2	no	—
58	C₂×C₄×C₁₁	—	2	1	no	—
59	C₂×C₄×C₁₁	—	2	1	no	—
60	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
61	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
62	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
63	C₂×Dic₁₁	—	8	2	no	—
64	Dic₂₂	—	8	2	no	—
65	Dic₂₂	—	8	2	no	—
66	C₈×C₁₁	—	2	1	no	—
67	C₈×C₁₁	—	4	1	no	—
68	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
69	C₈×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
70	C₁₁⋊C₈	—	8	2	no	—
71	C₂×Q₃₂	—	22	1	no	—
72	C₂×Q₃₂	—	22	1	no	—
73	#494	—	11	2	no	—
74	#475	—	22	2	no	—
75	C₈×Q₈	C₂×D₁₁	1	1	yes	characteristic
76	C₄⋊C₁₆	—	2	1	no	—
77	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
78	#346	—	2	1	no	—
79	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
80	#335	—	11	2	no	—
81	#332	—	22	2	no	—
82	C₂²×C₁₁	#466	1	1	yes	characteristic
83	C₄×C₁₁	—	2	1	no	—
84	C₄×C₁₁	—	4	1	no	—
85	C₄×C₁₁	—	4	1	no	—
86	C₄×C₁₁	#460	1	1	yes	characteristic
87	C₄×C₁₁	#472	1	1	yes	characteristic
88	C₄×C₁₁	#510	1	2	yes	—
89	Dic₁₁	—	16	2	no	—
90	C₂×Q₁₆	—	22	2	no	—
91	C₂×Q₁₆	—	22	2	no	—
92	C₄⋊Q₈	—	22	2	no	—
93	C₄×Q₈	D₄₄	1	1	yes	characteristic
94	Q₃₂	—	44	2	no	—
95	Q₃₂	—	44	2	no	—
96	C₂×C₁₆	—	2	1	no	—
97	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
98	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
99	#106	—	44	2	no	—
100	C₄⋊C₈	—	2	1	no	—
101	C₄⋊C₈	—	22	2	no	—
102	C₄⋊C₈	D₄₄	1	1	yes	characteristic
103	#103	—	44	2	no	—
104	C₄×C₈	—	2	1	no	—
105	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
106	C₂×C₁₁	#1668	1	1	yes	characteristic
107	C₂×C₁₁	#2219	1	1	yes	characteristic
108	C₂×C₁₁	#2222	1	1	yes	characteristic
109	C₂×Q₈	—	44	2	no	—
110	C₂×Q₈	D₈₈	1	1	yes	characteristic
111	Q₁₆	—	44	2	no	—
112	Q₁₆	—	44	2	no	—
113	Q₁₆	—	88	2	no	—
114	C₂×C₈	—	2	1	no	—
115	C₂×C₈	—	44	2	no	—
116	C₂×C₈	#4339	1	1	yes	characteristic
117	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
118	C₄⋊C₄	—	2	1	no	—
119	C₄⋊C₄	—	44	2	no	—
120	C₄⋊C₄	—	44	2	no	—
121	C₄⋊C₄	D₈₈	1	1	yes	characteristic
122	C₄²	—	2	1	no	—
123	C₄²	C₂×D₄₄	1	1	yes	characteristic
124	C₁₆	—	2	1	no	—
125	C₁₆	—	4	1	no	—
126	C₁₆	#4325	1	2	yes	—
127	C₁₁	#12443	1	1	yes	characteristic, complemented, Sylow
128	Q₈	—	2	2	no	—
129	Q₈	—	88	2	no	—
130	Q₈	—	88	2	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	88	2	no	—
134	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
135	C₂×C₄	#66957	1	1	yes	characteristic
136	C₂×C₄	#66983	1	1	yes	characteristic
137	C₈	—	2	1	no	—
138	C₈	—	4	1	no	—
139	C₈	—	88	2	no	—
140	C₈	C₂×#4325	1	1	yes	characteristic
141	C₈	#67002	1	1	yes	characteristic
142	C₂²	#10622728	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	4	1	no	—
145	C₄	—	4	1	no	—
146	C₄	—	176	2	no	—
147	C₄	#10622522	1	2	yes	—
148	C₄	#10622640	1	1	yes	characteristic
149	C₄	#10622755	1	1	yes	characteristic
150	C₂	#13067976	1	1	yes	characteristic
151	C₂	#13070724	1	1	yes	characteristic
152	C₂	#13070741	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13070869

C₂

yes

maximal, characteristic

#13067986

C₂

yes

maximal

#13066690

C₂

yes

maximal, characteristic

#13066666

C₂

yes

maximal

C₁₁×#2183

C₂

yes

maximal, characteristic

C₈×Q₈×C₁₁

C₂²

yes

characteristic

#10622633

—

C₂×Dic₈₈

—

C₂×Dic₈₈

—

#10622312

C₂²

yes

—

C₁₁×C₄⋊C₁₆

—

C₁₁×C₄⋊C₁₆

C₂²

yes

characteristic

C₁₁×#346

—

C₄×C₁₁×C₁₆

C₂²

yes

characteristic

#10622120

—

#10622096

C₂²

yes

—

C₄×Q₈×C₁₁

D₄

yes

characteristic

C₂×Dic₄₄

—

C₂×Dic₄₄

—

#66922

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

D₄

yes

characteristic

C₂×C₁₁×C₁₆

D₄

yes

characteristic

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

D₄

yes

characteristic

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

C₂³

yes

characteristic

#66899

—

#66872

—

C₄⋊(C₁₁⋊C₈)

—

Dic₈₈

—

Dic₈₈

—

#12443

—

maximal, Sylow

C₂×Q₈×C₁₁

D₈

yes

characteristic

C₂×Dic₂₂

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

#41

yes

characteristic

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

D₈

yes

characteristic

C₄²×C₁₁

—

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₂×C₁₁⋊C₈

—

Dic₄₄

—

Dic₄₄

—

Dic₄₄

—

C₁₁×C₁₆

—

C₁₁×C₁₆

—

C₁₁×C₁₆

SD₁₆

yes

—

#2247

—

#2183

D₁₁

yes

—

—

—

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#121

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

#135

yes

characteristic

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

C₂×SD₁₆

yes

characteristic

C₈×C₁₁

AGL(1,ℤ/8)

yes

characteristic

C₁₁⋊C₈

—

C₂×Q₃₂

—

C₂×Q₃₂

—

#494

—

#475

—

C₈×Q₈

C₂×D₁₁

yes

characteristic

C₄⋊C₁₆

—

C₄⋊C₁₆

C₂×D₁₁

yes

characteristic

#346

—

C₄×C₁₆

C₂×D₁₁

yes

characteristic

#335

—

#332

—

C₂²×C₁₁

#466

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

Dic₁₁

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

D₄₄

yes

characteristic

Q₃₂

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₁₁

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₁

yes

characteristic

#106

—

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₄⋊C₈

D₄₄

yes

characteristic

103

#103

—

104

C₄×C₈

—

105

C₄×C₈

C₂²×D₁₁

yes

characteristic

106

C₂×C₁₁

#1668

yes

characteristic

107

C₂×C₁₁

#2219

yes

characteristic

108

C₂×C₁₁

#2222

yes

characteristic

109

C₂×Q₈

—

110

C₂×Q₈

D₈₈

yes

characteristic

111

Q₁₆

—

112

Q₁₆

—

113

Q₁₆

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

#4339

yes

characteristic

117

C₂×C₈

C₂×C₂²⋊D₁₁

yes

characteristic

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

D₈₈

yes

characteristic

122

C₄²

—

123

C₄²

C₂×D₄₄

yes

characteristic

124

C₁₆

—

125

C₁₆

—

126

C₁₆

#4325

yes

—

127

C₁₁

#12443

yes

characteristic, complemented, Sylow

128

Q₈

—

129

Q₈

—

130

Q₈

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

C₂×D₈₈

yes

characteristic

135

C₂×C₄

#66957

yes

characteristic

136

C₂×C₄

#66983

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

C₂×#4325

yes

characteristic

141

C₈

#67002

yes

characteristic

142

C₂²

#10622728

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

176

—

147

C₄

#10622522

yes

—

148

C₄

#10622640

yes

characteristic

149

C₄

#10622755

yes

characteristic

150

C₂

#13067976

yes

characteristic

151

C₂

#13070724

yes

characteristic

152

C₂

#13070741

yes

characteristic

	subgroup	G/H
center	C₂²	#10622728
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#2183	C₂
socle, prime radical	C₂²×C₁₁	#466
hypercenter	#2183	D₁₁
hypocenter	C₁₁	#12443
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈ ◁ #2183

subgroup

G/H

center

C₂²

#10622728

commutator, cosocle

C₄×C₈×C₁₁

C₂³

Frattini

C₄×C₈

C₂²×D₁₁

Fitting

C₁₁×#2183

C₂

C₂²×C₁₁

D₁₁

C₁₁

G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈ ◁ #2183

N	H ≅ G/N	type
127. C₁₁	#12443	semidirect

H ≅ G/N

type

127. C₁₁

#12443

semidirect

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

subgroup	index
#13070869	2
#13067986	2
#13066690	2
#13066666	2
C₁₁×#2183	2
#12443	11

subgroup

index

C₁₁×#2183

Subgroups — #14668052

Conjugacy classes of subgroups

Complements

Maximal subgroups