Group #14658794 — subgroups

Subgroups — #14658794

Order 2816.

316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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	#13069597	C₂	1	1	yes	maximal, characteristic
2	#13068770	C₂	1	1	yes	maximal, characteristic
3	#13067391	C₂	1	2	yes	maximal
4	#13067020	C₂	1	2	yes	maximal
5	C₁₁×#1274	C₂	1	1	yes	maximal, characteristic
6	#10623001	C₂²	1	1	yes	characteristic
7	C₁₁×#431	C₂²	1	2	yes	—
8	C₁₁×#376	C₂²	1	1	yes	characteristic
9	#10622537	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
11	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
12	#10622161	—	2	2	no	—
13	#10622096	—	2	4	no	—
14	#10622094	—	2	4	no	—
15	C₂×C₄²×C₁₁	D₄	1	2	yes	—
16	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
17	#66979	—	2	1	no	—
18	#66977	—	2	2	no	—
19	C₂×#4318	—	2	1	no	—
20	C₂²×C₁₁⋊C₈	—	2	2	no	—
21	#66923	—	2	1	no	—
22	#66922	Q₈	1	2	yes	—
23	C₄×Dic₂₂	—	2	2	no	—
24	C₁₁×C₄⋊C₈	—	2	2	no	—
25	C₁₁×C₂²⋊C₈	—	2	2	no	—
26	C₄×C₈×C₁₁	D₄	1	4	yes	—
27	C₁₁×#95	—	2	2	no	—
28	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
29	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₁⋊C₈)	—	4	4	no	—
32	#10668	—	11	1	no	maximal, Sylow
33	C₂²×C₄×C₁₁	—	2	2	no	—
34	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	#41	1	2	yes	—
36	C₂×Dic₂₂	—	2	2	no	—
37	C₂×C₈×C₁₁	—	2	4	no	—
38	C₄²×C₁₁	—	2	2	no	—
39	C₄²×C₁₁	Q₁₆	1	4	yes	—
40	C₄²×C₁₁	C₂×D₄	1	2	yes	—
41	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
42	C₄²×C₁₁	#41	1	1	yes	characteristic
43	C₂²⋊Dic₁₁	—	4	1	no	—
44	C₄⋊Dic₁₁	—	2	2	no	—
45	C₄⋊Dic₁₁	—	2	2	no	—
46	Dic₁₁⋊C₄	—	4	2	no	—
47	C₄×Dic₁₁	—	4	1	no	—
48	#4318	—	4	2	no	—
49	C₂×C₁₁⋊C₈	—	4	2	no	—
50	C₂×C₁₁⋊C₈	—	4	1	no	—
51	C₂×C₁₁⋊C₈	—	4	4	no	—
52	#1995	—	11	1	no	—
53	#1843	—	11	1	no	—
54	#1571	—	11	2	no	—
55	#1481	—	11	2	no	—
56	#1274	D₁₁	1	1	yes	characteristic
57	C₂³×C₁₁	#123	1	1	yes	characteristic
58	C₂×C₄×C₁₁	—	2	4	no	—
59	C₂×C₄×C₁₁	—	4	2	no	—
60	C₂×C₄×C₁₁	—	4	4	no	—
61	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
62	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂×C₄×C₁₁	#123	1	2	yes	—
64	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
65	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
66	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
67	C₂×Dic₁₁	—	4	2	no	—
68	Dic₂₂	—	4	4	no	—
69	C₈×C₁₁	—	4	4	no	—
70	C₁₁⋊C₈	—	8	2	no	—
71	C₁₁⋊C₈	—	8	1	no	—
72	#533	—	11	1	no	—
73	#431	C₂×D₁₁	1	2	yes	—
74	#423	—	11	1	no	—
75	C₂×C₄⋊C₈	—	11	2	no	—
76	C₂×C₄⋊C₈	—	22	2	no	—
77	#376	C₂×D₁₁	1	1	yes	characteristic
78	#339	—	22	2	no	—
79	#335	—	22	4	no	—
80	Q₈⋊C₈	—	22	4	no	—
81	C₂²×C₁₁	—	2	2	no	—
82	C₂²×C₁₁	#399	1	1	yes	characteristic
83	C₂²×C₁₁	#484	1	2	yes	—
84	C₄×C₁₁	—	2	2	no	—
85	C₄×C₁₁	—	2	2	no	—
86	C₄×C₁₁	—	4	4	no	—
87	C₄×C₁₁	#477	1	2	yes	—
88	C₄×C₁₁	#494	1	1	yes	characteristic
89	C₄×C₁₁	#496	1	1	yes	characteristic
90	Dic₁₁	—	8	2	no	—
91	C₂×M₁₆	—	22	1	no	—
92	C₂²×C₈	—	22	2	no	—
93	C₄⋊Q₈	—	11	2	no	—
94	#125	—	22	1	no	—
95	C₂²⋊Q₈	—	22	2	no	—
96	C₄×Q₈	—	22	2	no	—
97	#117	—	22	1	no	—
98	C₂×C₄²	D₄₄	1	2	yes	—
99	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
100	C₄⋊C₈	—	2	2	no	—
101	C₄⋊C₈	—	22	2	no	—
102	C₄⋊C₈	—	22	2	no	—
103	C₄⋊C₈	—	22	2	no	—
104	C₄⋊C₈	—	44	4	no	—
105	C₂²⋊C₈	—	2	2	no	—
106	C₄×C₈	D₄₄	1	4	yes	—
107	#95	—	2	2	no	—
108	C₂×C₁₁	—	2	2	no	—
109	C₂×C₁₁	#2095	1	1	yes	characteristic
110	C₂×C₁₁	#2098	1	2	yes	—
111	C₂×Q₈	—	22	2	no	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
114	C₂²×C₄	#4341	1	2	yes	—
115	M₁₆	—	44	2	no	—
116	C₂×C₈	—	2	4	no	—
117	C₂×C₈	—	44	2	no	—
118	C₂×C₈	—	44	1	no	—
119	C₂×C₈	—	44	4	no	—
120	C₄⋊C₄	—	22	2	no	—
121	C₄⋊C₄	—	22	2	no	—
122	C₄⋊C₄	—	44	2	no	—
123	C₂²⋊C₄	—	44	1	no	—
124	C₄²	—	2	2	no	—
125	C₄²	—	44	1	no	—
126	C₄²	Dic₄₄	1	4	yes	—
127	C₄²	C₂×D₄₄	1	2	yes	—
128	C₄²	#4341	1	1	yes	characteristic
129	C₄²	Q₈×D₁₁	1	1	yes	characteristic
130	C₁₁	#10668	1	1	yes	characteristic, complemented, Sylow
131	C₂³	#66939	1	1	yes	characteristic
132	Q₈	—	44	4	no	—
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	—	44	2	no	—
137	C₂×C₄	#66927	1	1	yes	characteristic
138	C₂×C₄	#66939	1	2	yes	—
139	C₂×C₄	#66950	1	2	yes	—
140	C₂×C₄	#66950	1	1	yes	characteristic
141	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
142	C₂×C₄	#66961	1	2	yes	—
143	C₈	—	4	4	no	—
144	C₈	—	88	2	no	—
145	C₈	—	88	1	no	—
146	C₂²	—	2	2	no	—
147	C₂²	#10622290	1	1	yes	characteristic
148	C₂²	#10622335	1	2	yes	—
149	C₄	—	2	2	no	—
150	C₄	—	2	2	no	—
151	C₄	—	4	4	no	—
152	C₄	—	88	2	no	—
153	C₄	#10622312	1	1	yes	characteristic
154	C₄	#10622325	1	1	yes	characteristic
155	C₄	#10622463	1	2	yes	—
156	C₂	—	2	2	no	—
157	C₂	#13070153	1	1	yes	characteristic
158	C₂	#13070170	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13069597

C₂

yes

maximal, characteristic

#13068770

C₂

yes

maximal, characteristic

#13067391

C₂

yes

maximal

#13067020

C₂

yes

maximal

C₁₁×#1274

C₂

yes

maximal, characteristic

#10623001

C₂²

yes

characteristic

C₁₁×#431

C₂²

yes

—

C₁₁×#376

C₂²

yes

characteristic

#10622537

C₂²

yes

characteristic

C₂×C₄⋊(C₁₁⋊C₈)

—

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

#10622161

—

#10622096

—

#10622094

—

C₂×C₄²×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

—

—

—

C₂²×C₁₁⋊C₈

—

#66923

—

#66922

Q₈

yes

—

C₄×Dic₂₂

—

C₁₁×C₄⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₄×C₈×C₁₁

D₄

yes

—

C₁₁×#95

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#10668

—

maximal, Sylow

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

Q₁₆

yes

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

C₄²×C₁₁

#41

yes

characteristic

C₂²⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

#123

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

#123

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₂×C₄×C₁₁

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₁

—

Dic₂₂

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

#533

—

#431

C₂×D₁₁

yes

—

#423

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

#376

C₂×D₁₁

yes

characteristic

#339

—

#335

—

Q₈⋊C₈

—

C₂²×C₁₁

—

C₂²×C₁₁

#399

yes

characteristic

C₂²×C₁₁

#484

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#477

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

Dic₁₁

—

C₂×M₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

D₄₄

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₄⋊C₈

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₂²⋊C₈

—

106

C₄×C₈

D₄₄

yes

—

107

#95

—

108

C₂×C₁₁

—

109

C₂×C₁₁

#2095

yes

characteristic

110

C₂×C₁₁

#2098

yes

—

111

C₂×Q₈

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂×D₄₄

yes

characteristic

114

C₂²×C₄

#4341

yes

—

115

M₁₆

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₄²

—

126

C₄²

Dic₄₄

yes

—

127

C₄²

C₂×D₄₄

yes

—

128

C₄²

#4341

yes

characteristic

129

C₄²

Q₈×D₁₁

yes

characteristic

130

C₁₁

#10668

yes

characteristic, complemented, Sylow

131

C₂³

#66939

yes

characteristic

132

Q₈

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

#66927

yes

characteristic

138

C₂×C₄

#66939

yes

—

139

C₂×C₄

#66950

yes

—

140

C₂×C₄

#66950

yes

characteristic

141

C₂×C₄

C₂×Dic₄₄

yes

—

142

C₂×C₄

#66961

yes

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₂²

—

147

C₂²

#10622290

yes

characteristic

148

C₂²

#10622335

yes

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

#10622312

yes

characteristic

154

C₄

#10622325

yes

characteristic

155

C₄

#10622463

yes

—

156

C₂

—

157

C₂

#13070153

yes

characteristic

158

C₂

#13070170

yes

—

	subgroup	G/H
center	C₂×C₄	#66927
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1274	C₂
socle	C₂²×C₁₁	#399
prime radical	C₂³×C₁₁	#123
hypercenter	#1274	D₁₁
hypocenter	C₁₁	#10668
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

subgroup

G/H

center

C₂×C₄

#66927

commutator, cosocle

C₂×C₄²×C₁₁

C₂³

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1274

C₂

C₂²×C₁₁

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

N	H ≅ G/N	type
130. C₁₁	#10668	semidirect

H ≅ G/N

type

130. C₁₁

#10668

semidirect

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

subgroup	index
#13069597	2
#13068770	2
#13067391	2
#13067020	2
C₁₁×#1274	2
#10668	11

subgroup

index

C₁₁×#1274

Subgroups — #14658794

Conjugacy classes of subgroups

Complements

Maximal subgroups