Group #14673919 — subgroups

Subgroups — #14673919

Order 2816.

252 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 93 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	#13069364	C₂	1	1	yes	maximal, characteristic
2	#13068780	C₂	1	1	yes	maximal, characteristic
3	#13066722	C₂	1	2	yes	maximal
4	#13066715	C₂	1	2	yes	maximal
5	C₁₁×#1376	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66883	C₂²	1	1	yes	characteristic
9	#10622719	C₂²	1	1	yes	characteristic
10	C₂×#66882	—	2	1	no	—
11	C₂×#66881	C₂²	1	2	yes	—
12	#10622715	—	2	1	no	—
13	#10622549	—	2	1	no	—
14	#10622161	—	2	1	no	—
15	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
18	#66979	—	2	1	no	—
19	C₂×C₄⋊Dic₁₁	—	2	2	no	—
20	C₂×#4318	—	2	1	no	—
21	C₁₁×M₃₂	—	2	2	no	—
22	C₁₁×M₃₂	—	2	2	no	—
23	C₂×C₁₁×C₁₆	—	2	2	no	—
24	C₄×C₈×C₁₁	—	2	2	no	—
25	C₁₁⋊#95	—	4	2	no	—
26	#66883	—	2	2	no	—
27	#66882	—	4	2	no	—
28	#66882	Q₈	1	2	yes	—
29	#66881	—	2	1	no	—
30	#66881	—	2	4	no	—
31	Dic₁₁⋊C₈	—	4	2	no	—
32	#13542	—	11	1	no	maximal, Sylow
33	C₂²×C₄×C₁₁	—	2	1	no	—
34	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
35	C₂²×Dic₁₁	—	4	2	no	—
36	C₂×C₈×C₁₁	—	2	1	no	—
37	C₂×C₈×C₁₁	—	2	1	no	—
38	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
39	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
41	C₂×C₈×C₁₁	#41	1	2	yes	—
42	C₂×C₈×C₁₁	#41	1	2	yes	—
43	C₄²×C₁₁	—	2	1	no	—
44	C₄²×C₁₁	Q₁₆	1	2	yes	—
45	C₂²⋊Dic₁₁	—	4	1	no	—
46	C₄⋊Dic₁₁	—	2	2	no	—
47	C₄⋊Dic₁₁	—	4	2	no	—
48	C₄⋊Dic₁₁	—	4	2	no	—
49	C₄×Dic₁₁	—	4	1	no	—
50	#4318	—	4	1	no	—
51	#4318	—	4	1	no	—
52	C₂×C₁₁⋊C₈	—	4	1	no	—
53	C₁₁×C₁₆	—	4	2	no	—
54	#1945	—	11	1	no	—
55	#1846	—	11	1	no	—
56	#1386	—	11	2	no	—
57	#1383	—	11	2	no	—
58	#1376	D₁₁	1	1	yes	characteristic
59	C₂³×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
60	C₂×C₄×C₁₁	—	2	2	no	—
61	C₂×C₄×C₁₁	—	4	2	no	—
62	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
64	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
65	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
67	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
68	C₂×Dic₁₁	—	4	2	no	—
69	C₂×Dic₁₁	—	8	4	no	—
70	C₂×Dic₁₁	—	8	2	no	—
71	C₈×C₁₁	—	2	2	no	—
72	C₈×C₁₁	#125	1	2	yes	—
73	C₈×C₁₁	#126	1	2	yes	—
74	C₁₁⋊C₈	—	8	1	no	—
75	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
76	C₂×#108	—	11	1	no	—
77	#427	—	11	1	no	—
78	C₂×#107	—	22	1	no	—
79	C₂×#106	—	11	2	no	—
80	#424	—	22	1	no	—
81	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
82	#382	—	22	1	no	—
83	#339	—	22	1	no	—
84	C₂²×C₁₁	—	2	2	no	—
85	C₂²×C₁₁	#476	1	1	yes	characteristic
86	C₂²×C₁₁	#484	1	1	yes	characteristic
87	C₂²×C₁₁	#490	1	1	yes	characteristic
88	C₄×C₁₁	—	4	2	no	—
89	C₄×C₁₁	#400	1	1	yes	characteristic
90	C₄×C₁₁	#477	1	1	yes	characteristic
91	C₄×C₁₁	#481	1	1	yes	characteristic
92	C₄×C₁₁	#487	1	1	yes	characteristic
93	Dic₁₁	—	8	2	no	—
94	Dic₁₁	—	16	2	no	—
95	C₂×M₁₆	—	22	1	no	—
96	C₂²×C₈	D₄₄	1	1	yes	characteristic
97	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
98	#117	—	22	1	no	—
99	C₂×C₄⋊C₄	—	22	2	no	—
100	C₂×C₄²	D₄₄	1	1	yes	characteristic
101	M₃₂	—	2	2	no	—
102	M₃₂	—	2	2	no	—
103	C₂×C₁₆	—	2	2	no	—
104	#108	—	22	2	no	—
105	#107	—	11	2	no	—
106	#107	—	44	2	no	—
107	#106	—	22	1	no	—
108	#106	—	22	4	no	—
109	C₄⋊C₈	—	44	2	no	—
110	C₄×C₈	—	2	2	no	—
111	#95	—	44	2	no	—
112	C₂×C₁₁	—	2	1	no	—
113	C₂×C₁₁	—	2	1	no	—
114	C₂×C₁₁	#2100	1	1	yes	characteristic
115	C₂×C₁₁	#2231	1	2	yes	—
116	C₂²×C₄	—	2	1	no	—
117	C₂²×C₄	—	44	2	no	—
118	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
119	M₁₆	—	44	1	no	—
120	M₁₆	—	44	1	no	—
121	C₂×C₈	—	2	1	no	—
122	C₂×C₈	—	2	1	no	—
123	C₂×C₈	—	44	1	no	—
124	C₂×C₈	#4314	1	2	yes	—
125	C₂×C₈	#4339	1	2	yes	—
126	C₂×C₈	#4341	1	1	yes	characteristic
127	C₂×C₈	#4341	1	2	yes	—
128	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
129	C₄⋊C₄	—	22	2	no	—
130	C₄⋊C₄	—	44	2	no	—
131	C₄⋊C₄	—	44	2	no	—
132	C₂²⋊C₄	—	44	1	no	—
133	C₄²	—	2	1	no	—
134	C₄²	—	44	1	no	—
135	C₄²	Dic₄₄	1	2	yes	—
136	C₁₆	—	4	2	no	—
137	C₁₁	#13542	1	1	yes	characteristic, complemented, Sylow
138	C₂³	#66961	1	1	yes	characteristic
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	44	2	no	—
142	C₂×C₄	—	88	4	no	—
143	C₂×C₄	—	88	2	no	—
144	C₂×C₄	#66928	1	1	yes	characteristic
145	C₂×C₄	#66939	1	1	yes	characteristic
146	C₂×C₄	#66950	1	1	yes	characteristic
147	C₂×C₄	C₂×#4314	1	1	yes	characteristic
148	C₂×C₄	C₂×Dic₄₄	1	1	yes	characteristic
149	C₂×C₄	#66961	1	1	yes	characteristic
150	C₈	—	2	2	no	—
151	C₈	—	88	1	no	—
152	C₈	#66932	1	2	yes	—
153	C₈	#66942	1	2	yes	—
154	C₂²	—	2	2	no	—
155	C₂²	#10622326	1	1	yes	characteristic
156	C₂²	#10622335	1	1	yes	characteristic
157	C₂²	#10622455	1	1	yes	characteristic
158	C₄	—	4	2	no	—
159	C₄	—	88	2	no	—
160	C₄	—	176	2	no	—
161	C₄	#10622272	1	1	yes	characteristic
162	C₄	#10622294	1	1	yes	characteristic
163	C₄	#10622348	1	1	yes	characteristic
164	C₄	#10622463	1	1	yes	characteristic
165	C₂	—	2	1	no	—
166	C₂	—	2	1	no	—
167	C₂	#13070180	1	1	yes	characteristic
168	C₂	#13070793	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13069364

C₂

yes

maximal, characteristic

#13068780

C₂

yes

maximal, characteristic

#13066722

C₂

yes

maximal

#13066715

C₂

yes

maximal

C₁₁×#1376

C₂

yes

maximal, characteristic

C₂×C₁₁×M₃₂

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

C₂²

yes

characteristic

#10622719

C₂²

yes

characteristic

C₂×#66882

—

C₂×#66881

C₂²

yes

—

#10622715

—

#10622549

—

#10622161

—

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

#66979

—

C₂×C₄⋊Dic₁₁

—

C₂×#4318

—

C₁₁×M₃₂

—

C₁₁×M₃₂

—

C₂×C₁₁×C₁₆

—

C₄×C₈×C₁₁

—

C₁₁⋊#95

—

#66883

—

#66882

—

#66882

Q₈

yes

—

#66881

—

#66881

—

Dic₁₁⋊C₈

—

#13542

—

maximal, Sylow

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×Dic₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₂×C₈×C₁₁

C₂×Q₈

yes

C₂×C₈×C₁₁

yes

C₂×C₈×C₁₁

yes

—

C₂×C₈×C₁₁

#41

yes

—

C₄²×C₁₁

—

C₄²×C₁₁

Q₁₆

yes

—

C₂²⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄×Dic₁₁

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₁

AGL(1,ℤ/8)

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#125

yes

—

C₈×C₁₁

#126

yes

—

C₁₁⋊C₈

—

C₂×M₃₂

C₂×D₁₁

yes

—

—

—

—

—

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#382

—

#339

—

C₂²×C₁₁

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

Dic₁₁

—

Dic₁₁

—

C₂×M₁₆

—

C₂²×C₈

D₄₄

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

100

C₂×C₄²

D₄₄

yes

characteristic

101

M₃₂

—

102

M₃₂

—

103

C₂×C₁₆

—

104

#108

—

105

#107

—

106

#107

—

107

#106

—

108

#106

—

109

C₄⋊C₈

—

110

C₄×C₈

—

111

#95

—

112

C₂×C₁₁

—

113

C₂×C₁₁

—

114

C₂×C₁₁

#2100

yes

characteristic

115

C₂×C₁₁

#2231

yes

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

C₂×D₄₄

yes

characteristic

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

#4314

yes

—

125

C₂×C₈

#4339

yes

—

126

C₂×C₈

#4341

yes

characteristic

127

C₂×C₈

#4341

yes

—

128

C₂×C₈

Q₈×D₁₁

yes

characteristic

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₂²⋊C₄

—

133

C₄²

—

134

C₄²

—

135

C₄²

Dic₄₄

yes

—

136

C₁₆

—

137

C₁₁

#13542

yes

characteristic, complemented, Sylow

138

C₂³

#66961

yes

characteristic

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

#66928

yes

characteristic

145

C₂×C₄

#66939

yes

characteristic

146

C₂×C₄

#66950

yes

characteristic

147

C₂×C₄

C₂×#4314

yes

characteristic

148

C₂×C₄

C₂×Dic₄₄

yes

characteristic

149

C₂×C₄

#66961

yes

characteristic

150

C₈

—

151

C₈

—

152

C₈

#66932

yes

—

153

C₈

#66942

yes

—

154

C₂²

—

155

C₂²

#10622326

yes

characteristic

156

C₂²

#10622335

yes

characteristic

157

C₂²

#10622455

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

176

—

161

C₄

#10622272

yes

characteristic

162

C₄

#10622294

yes

characteristic

163

C₄

#10622348

yes

characteristic

164

C₄

#10622463

yes

characteristic

165

C₂

—

166

C₂

—

167

C₂

#13070180

yes

characteristic

168

C₂

#13070793

yes

—

	subgroup	G/H
center	C₂²	#10622455
commutator, cosocle	C₂²×C₈×C₁₁	C₂³
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1376	C₂
socle	C₂²×C₁₁	#476
prime radical	C₂³×C₁₁	AGL(1,ℤ/8)
hypercenter	#1376	D₁₁
hypocenter	C₁₁	#13542
LCS	G ▷ C₂²×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1376

subgroup

G/H

center

C₂²

#10622455

commutator, cosocle

C₂²×C₈×C₁₁

C₂³

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#1376

C₂

C₂²×C₁₁

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂²×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1376

N	H ≅ G/N	type
137. C₁₁	#13542	semidirect

H ≅ G/N

type

137. C₁₁

#13542

semidirect

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

subgroup	index
#13069364	2
#13068780	2
#13066722	2
#13066715	2
C₁₁×#1376	2
#13542	11

subgroup

index

C₁₁×#1376

Subgroups — #14673919

Conjugacy classes of subgroups

Complements

Maximal subgroups