Group #14658585 — subgroups

Subgroups — #14658585

Order 2816.

294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 85 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	#13069436	C₂	1	1	yes	maximal, characteristic
2	#13068757	C₂	1	1	yes	maximal, characteristic
3	#13067287	C₂	1	2	yes	maximal
4	#13066475	C₂	1	2	yes	maximal
5	C₁₁×#1281	C₂	1	1	yes	maximal, characteristic
6	C₂×#66922	C₂²	1	1	yes	characteristic
7	C₁₁×#431	C₂²	1	2	yes	—
8	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
9	C₂×#66880	—	2	2	no	—
10	#10622549	C₂²	1	1	yes	characteristic
11	#10622537	C₂²	1	2	yes	—
12	#10622190	—	2	2	no	—
13	#10622124	—	2	4	no	—
14	C₂²×Dic₂₂	—	2	1	no	—
15	C₂²×C₈×C₁₁	D₄	1	2	yes	—
16	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₁	—	2	2	no	—
18	C₂×C₄⋊Dic₁₁	—	2	1	no	—
19	C₂×#4318	—	2	2	no	—
20	#66922	—	2	2	no	—
21	#66922	—	2	1	no	—
22	#66922	D₄	1	2	yes	—
23	C₁₁×C₄⋊C₈	—	2	2	no	—
24	C₁₁×C₂²⋊C₈	—	2	2	no	—
25	C₁₁×#97	—	2	2	no	—
26	C₄×C₈×C₁₁	—	2	2	no	—
27	C₁₁⋊#95	—	2	2	no	—
28	#66880	—	4	4	no	—
29	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
31	#10635	—	11	1	no	maximal, Sylow
32	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₁	#41	1	2	yes	—
34	C₂²×Dic₁₁	—	4	1	no	—
35	C₂²×Dic₁₁	—	4	1	no	—
36	C₂×Dic₂₂	—	2	2	no	—
37	C₂×Dic₂₂	—	4	1	no	—
38	C₂×Dic₂₂	—	4	2	no	—
39	C₂×Dic₂₂	—	4	2	no	—
40	C₂×C₈×C₁₁	—	2	2	no	—
41	C₂×C₈×C₁₁	—	2	2	no	—
42	C₂×C₈×C₁₁	—	2	2	no	—
43	C₂×C₈×C₁₁	—	4	2	no	—
44	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
45	C₄²×C₁₁	#41	1	1	yes	characteristic
46	C₄²×C₁₁	#41	1	2	yes	—
47	C₄⋊Dic₁₁	—	2	4	no	—
48	C₄⋊Dic₁₁	—	4	2	no	—
49	C₄⋊Dic₁₁	—	4	2	no	—
50	#4318	—	4	2	no	—
51	#4318	—	4	2	no	—
52	C₂×C₁₁⋊C₈	—	4	2	no	—
53	#1960	—	11	1	no	—
54	#1838	—	11	1	no	—
55	#1546	—	11	2	no	—
56	#1286	—	11	2	no	—
57	#1281	D₁₁	1	1	yes	characteristic
58	C₂³×C₁₁	#124	1	1	yes	characteristic
59	C₂×C₄×C₁₁	—	4	2	no	—
60	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
61	C₂×C₄×C₁₁	#123	1	2	yes	—
62	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
63	C₂×C₄×C₁₁	#126	1	2	yes	—
64	C₂×C₄×C₁₁	#135	1	2	yes	—
65	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
66	C₂×Dic₁₁	—	4	2	no	—
67	C₂×Dic₁₁	—	8	1	no	—
68	C₂×Dic₁₁	—	8	1	no	—
69	C₂×Dic₁₁	—	8	2	no	—
70	C₂×Dic₁₁	—	8	1	no	—
71	Dic₂₂	—	4	4	no	—
72	Dic₂₂	—	8	2	no	—
73	C₈×C₁₁	—	4	2	no	—
74	C₈×C₁₁	—	8	2	no	—
75	C₁₁⋊C₈	—	8	2	no	—
76	C₂×C₄⋊Q₈	—	11	1	no	—
77	#431	C₂×D₁₁	1	2	yes	—
78	#423	—	11	2	no	—
79	C₂×#103	—	22	2	no	—
80	C₂×#97	C₂×D₁₁	1	1	yes	characteristic
81	#382	—	11	1	no	—
82	#341	—	22	2	no	—
83	#332	—	22	4	no	—
84	C₂²×C₁₁	—	2	2	no	—
85	C₂²×C₁₁	#397	1	1	yes	characteristic
86	C₂²×C₁₁	#488	1	1	yes	characteristic
87	C₂²×C₁₁	#490	1	1	yes	characteristic
88	C₄×C₁₁	—	2	2	no	—
89	C₄×C₁₁	—	2	2	no	—
90	C₄×C₁₁	#463	1	2	yes	—
91	C₄×C₁₁	#482	1	2	yes	—
92	Dic₁₁	—	8	2	no	—
93	Dic₁₁	—	16	1	no	—
94	C₂²×Q₈	—	22	1	no	—
95	C₂×M₁₆	—	22	2	no	—
96	C₂²×C₈	D₄₄	1	2	yes	—
97	C₄⋊Q₈	—	11	2	no	—
98	C₄⋊Q₈	—	22	2	no	—
99	C₄⋊Q₈	—	22	1	no	—
100	C₂×C₄⋊C₄	—	22	2	no	—
101	C₂×C₄⋊C₄	—	22	1	no	—
102	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
103	C₄⋊C₈	—	2	2	no	—
104	C₄⋊C₈	—	22	2	no	—
105	C₄⋊C₈	—	22	2	no	—
106	#103	—	44	4	no	—
107	C₂²⋊C₈	—	2	2	no	—
108	#97	—	2	2	no	—
109	C₄×C₈	—	2	2	no	—
110	#95	—	22	2	no	—
111	C₂×C₁₁	—	2	1	no	—
112	C₂×C₁₁	—	2	1	no	—
113	C₂×C₁₁	#2073	1	1	yes	characteristic
114	C₂×C₁₁	#2082	1	2	yes	—
115	C₂×Q₈	—	22	2	no	—
116	C₂×Q₈	—	44	1	no	—
117	C₂×Q₈	—	44	2	no	—
118	C₂×Q₈	—	44	2	no	—
119	C₂²×C₄	—	44	1	no	—
120	C₂²×C₄	—	44	1	no	—
121	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
122	C₂²×C₄	#4339	1	2	yes	—
123	M₁₆	—	44	2	no	—
124	M₁₆	—	44	2	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	2	2	no	—
127	C₂×C₈	—	2	2	no	—
128	C₂×C₈	—	4	2	no	—
129	C₂×C₈	—	44	2	no	—
130	C₄⋊C₄	—	22	4	no	—
131	C₄⋊C₄	—	44	2	no	—
132	C₄⋊C₄	—	44	2	no	—
133	C₄²	D₄×D₁₁	1	1	yes	characteristic
134	C₄²	#4341	1	2	yes	—
135	C₄²	#4343	1	1	yes	characteristic
136	C₁₁	#10635	1	1	yes	characteristic, complemented, Sylow
137	C₂³	#66928	1	1	yes	characteristic
138	Q₈	—	44	4	no	—
139	Q₈	—	88	2	no	—
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	44	2	no	—
142	C₂×C₄	—	88	1	no	—
143	C₂×C₄	—	88	1	no	—
144	C₂×C₄	—	88	2	no	—
145	C₂×C₄	—	88	1	no	—
146	C₂×C₄	#66936	1	2	yes	—
147	C₂×C₄	#66939	1	1	yes	characteristic
148	C₂×C₄	#66948	1	1	yes	characteristic
149	C₂×C₄	#66951	1	2	yes	—
150	C₂×C₄	#66957	1	2	yes	—
151	C₂×C₄	#66961	1	2	yes	—
152	C₈	—	4	2	no	—
153	C₈	—	8	2	no	—
154	C₈	—	88	2	no	—
155	C₂²	—	2	2	no	—
156	C₂²	#10622287	1	1	yes	characteristic
157	C₂²	#10622310	1	1	yes	characteristic
158	C₂²	#10622326	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	2	2	no	—
161	C₄	—	88	2	no	—
162	C₄	—	176	1	no	—
163	C₄	#10622350	1	2	yes	—
164	C₄	#10622457	1	2	yes	—
165	C₂	—	2	1	no	—
166	C₂	—	2	1	no	—
167	C₂	#13070031	1	1	yes	characteristic
168	C₂	#13070082	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13069436

C₂

yes

maximal, characteristic

#13068757

C₂

yes

maximal, characteristic

#13067287

C₂

yes

maximal

#13066475

C₂

yes

maximal

C₁₁×#1281

C₂

yes

maximal, characteristic

C₂×#66922

C₂²

yes

characteristic

C₁₁×#431

C₂²

yes

—

C₂×C₁₁×#97

C₂²

yes

characteristic

C₂×#66880

—

#10622549

C₂²

yes

characteristic

#10622537

C₂²

yes

—

#10622190

—

#10622124

—

C₂²×Dic₂₂

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

—

—

—

D₄

yes

—

C₁₁×C₄⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₁₁×#97

—

C₄×C₈×C₁₁

—

C₁₁⋊#95

—

#66880

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#10635

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₄²×C₁₁

C₂×D₄

yes

C₄²×C₁₁

yes

C₄²×C₁₁

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

#124

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#121

yes

characteristic

C₂×C₄×C₁₁

#123

yes

—

C₂×C₄×C₁₁

#123

yes

characteristic

C₂×C₄×C₁₁

#126

yes

—

C₂×C₄×C₁₁

#135

yes

—

C₂×C₄×C₁₁

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×C₄⋊Q₈

—

#431

C₂×D₁₁

yes

—

#423

—

C₂×#103

—

C₂×#97

C₂×D₁₁

yes

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#463

yes

—

C₄×C₁₁

#482

yes

—

Dic₁₁

—

Dic₁₁

—

C₂²×Q₈

—

C₂×M₁₆

—

C₂²×C₈

D₄₄

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄²

C₂²×D₁₁

yes

characteristic

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₄⋊C₈

—

106

#103

—

107

C₂²⋊C₈

—

108

#97

—

109

C₄×C₈

—

110

#95

—

111

C₂×C₁₁

—

112

C₂×C₁₁

—

113

C₂×C₁₁

#2073

yes

characteristic

114

C₂×C₁₁

#2082

yes

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

C₂×D₄₄

yes

characteristic

122

C₂²×C₄

#4339

yes

—

123

M₁₆

—

124

M₁₆

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄²

D₄×D₁₁

yes

characteristic

134

C₄²

#4341

yes

—

135

C₄²

#4343

yes

characteristic

136

C₁₁

#10635

yes

characteristic, complemented, Sylow

137

C₂³

#66928

yes

characteristic

138

Q₈

—

139

Q₈

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

#66936

yes

—

147

C₂×C₄

#66939

yes

characteristic

148

C₂×C₄

#66948

yes

characteristic

149

C₂×C₄

#66951

yes

—

150

C₂×C₄

#66957

yes

—

151

C₂×C₄

#66961

yes

—

152

C₈

—

153

C₈

—

154

C₈

—

155

C₂²

—

156

C₂²

#10622287

yes

characteristic

157

C₂²

#10622310

yes

characteristic

158

C₂²

#10622326

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

176

—

163

C₄

#10622350

yes

—

164

C₄

#10622457

yes

—

165

C₂

—

166

C₂

—

167

C₂

#13070031

yes

characteristic

168

C₂

#13070082

yes

—

	subgroup	G/H
center	C₂²	#10622287
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1281	C₂
socle	C₂²×C₁₁	#397
prime radical	C₂³×C₁₁	#124
hypercenter	#1281	D₁₁
hypocenter	C₁₁	#10635
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂²

#10622287

commutator, cosocle

C₂×C₄²×C₁₁

C₂³

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1281

C₂

C₂²×C₁₁

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
136. C₁₁	#10635	semidirect

H ≅ G/N

type

136. C₁₁

#10635

semidirect

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

subgroup	index
#13069436	2
#13068757	2
#13067287	2
#13066475	2
C₁₁×#1281	2
#10635	11

subgroup

index

C₁₁×#1281

Subgroups — #14658585

Conjugacy classes of subgroups

Complements

Maximal subgroups