Group #14673918 — subgroups

Subgroups — #14673918

Order 2816.

252 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 95 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	#13068780	C₂	1	1	yes	maximal, characteristic
2	#13066721	C₂	1	2	yes	maximal
3	#13066716	C₂	1	2	yes	maximal
4	#13066698	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1945	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
7	C₁₁×#427	C₂²	1	1	yes	characteristic
8	C₁₁×#424	—	2	1	no	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×#66882	—	2	1	no	—
11	C₂×#66881	C₂²	1	2	yes	—
12	C₂×#66876	C₂²	1	2	yes	—
13	#10622549	—	2	1	no	—
14	C₁₁×#339	—	2	1	no	—
15	C₂×C₁₁×M₁₆	—	2	1	no	—
16	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
18	C₁₁×#117	—	2	1	no	—
19	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₁	—	2	2	no	—
21	C₁₁×#108	—	2	2	no	—
22	C₁₁×#107	Q₈	1	2	yes	—
23	C₁₁×#106	—	2	1	no	—
24	C₁₁×C₄⋊C₈	—	4	2	no	—
25	C₄×C₈×C₁₁	—	2	2	no	—
26	C₁₁⋊#95	—	4	2	no	—
27	#66882	—	4	2	no	—
28	#66881	—	2	4	no	—
29	#66876	—	2	2	no	—
30	#66876	—	2	2	no	—
31	C₂×C₁₁⋊C₁₆	—	2	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	C₁₁×M₁₆	—	4	1	no	—
37	C₁₁×M₁₆	—	4	1	no	—
38	C₂×C₈×C₁₁	—	2	1	no	—
39	C₂×C₈×C₁₁	—	2	1	no	—
40	C₂×C₈×C₁₁	—	4	1	no	—
41	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
42	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
44	C₂×C₈×C₁₁	#41	1	2	yes	—
45	C₂×C₈×C₁₁	#41	1	2	yes	—
46	C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₁₁×C₂²⋊C₄	—	4	1	no	—
48	C₄²×C₁₁	—	2	1	no	—
49	C₄²×C₁₁	—	4	1	no	—
50	C₄²×C₁₁	Q₁₆	1	2	yes	—
51	C₄⋊Dic₁₁	—	4	2	no	—
52	C₄⋊Dic₁₁	—	4	2	no	—
53	C₁₁⋊C₁₆	—	4	2	no	—
54	#1945	D₁₁	1	1	yes	characteristic
55	#1846	—	11	1	no	—
56	#1386	—	11	2	no	—
57	#1383	—	11	2	no	—
58	#1376	—	11	1	no	—
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	—	4	2	no	—
63	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
64	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
65	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
68	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
69	C₂×Dic₁₁	—	8	4	no	—
70	C₂×Dic₁₁	—	8	2	no	—
71	C₈×C₁₁	—	2	2	no	—
72	C₈×C₁₁	—	8	1	no	—
73	C₈×C₁₁	#125	1	2	yes	—
74	C₈×C₁₁	#126	1	2	yes	—
75	C₂×M₃₂	—	11	2	no	—
76	C₂×#108	C₂×D₁₁	1	1	yes	characteristic
77	#427	C₂×D₁₁	1	1	yes	characteristic
78	C₂×#107	—	22	1	no	—
79	C₂×#106	—	11	2	no	—
80	#424	—	2	1	no	—
81	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
82	#382	—	22	1	no	—
83	#339	—	2	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	—	8	2	no	—
90	C₄×C₁₁	#400	1	1	yes	characteristic
91	C₄×C₁₁	#477	1	1	yes	characteristic
92	C₄×C₁₁	#481	1	1	yes	characteristic
93	C₄×C₁₁	#487	1	1	yes	characteristic
94	Dic₁₁	—	16	2	no	—
95	C₂×M₁₆	—	2	1	no	—
96	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
97	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
98	#117	—	2	1	no	—
99	C₂×C₄⋊C₄	—	22	2	no	—
100	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
101	M₃₂	—	22	2	no	—
102	M₃₂	—	22	2	no	—
103	C₂×C₁₆	—	22	2	no	—
104	#108	—	2	2	no	—
105	#107	—	44	2	no	—
106	#107	Dic₂₂	1	2	yes	—
107	#106	—	2	1	no	—
108	#106	—	22	4	no	—
109	C₄⋊C₈	—	4	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×C₂²⋊D₁₁	1	1	yes	characteristic
119	M₁₆	—	4	1	no	—
120	M₁₆	—	4	1	no	—
121	C₂×C₈	—	2	1	no	—
122	C₂×C₈	—	2	1	no	—
123	C₂×C₈	—	4	1	no	—
124	C₂×C₈	#4324	1	2	yes	—
125	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
126	C₂×C₈	#4339	1	1	yes	characteristic
127	C₂×C₈	#4341	1	2	yes	—
128	C₂×C₈	#4343	1	2	yes	—
129	C₄⋊C₄	—	2	2	no	—
130	C₄⋊C₄	—	44	2	no	—
131	C₄⋊C₄	—	44	2	no	—
132	C₂²⋊C₄	—	4	1	no	—
133	C₄²	—	2	1	no	—
134	C₄²	—	4	1	no	—
135	C₄²	#4326	1	2	yes	—
136	C₁₆	—	44	2	no	—
137	C₁₁	#13542	1	1	yes	characteristic, complemented, Sylow
138	C₂³	#67002	1	1	yes	characteristic
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	4	2	no	—
142	C₂×C₄	—	88	4	no	—
143	C₂×C₄	—	88	2	no	—
144	C₂×C₄	#66977	1	1	yes	characteristic
145	C₂×C₄	C₂×#4324	1	1	yes	characteristic
146	C₂×C₄	#66988	1	1	yes	characteristic
147	C₂×C₄	C₂×#4326	1	1	yes	characteristic
148	C₂×C₄	#67000	1	1	yes	characteristic
149	C₂×C₄	#67002	1	1	yes	characteristic
150	C₈	—	2	2	no	—
151	C₈	—	8	1	no	—
152	C₈	#66943	1	2	yes	—
153	C₈	#66951	1	2	yes	—
154	C₂²	—	2	2	no	—
155	C₂²	#10622621	1	1	yes	characteristic
156	C₂²	#10622657	1	1	yes	characteristic
157	C₂²	#10622680	1	1	yes	characteristic
158	C₄	—	4	2	no	—
159	C₄	—	8	2	no	—
160	C₄	—	176	2	no	—
161	C₄	#10622599	1	1	yes	characteristic
162	C₄	#10622634	1	1	yes	characteristic
163	C₄	#10622647	1	1	yes	characteristic
164	C₄	#10622706	1	1	yes	characteristic
165	C₂	—	2	1	no	—
166	C₂	—	2	1	no	—
167	C₂	#13070179	1	1	yes	characteristic
168	C₂	#13070792	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068780

C₂

yes

maximal, characteristic

#13066721

C₂

yes

maximal

#13066716

C₂

yes

maximal

#13066698

C₂

yes

maximal, characteristic

C₁₁×#1945

C₂

yes

maximal, characteristic

C₂×C₁₁×#108

C₂²

yes

characteristic

C₁₁×#427

C₂²

yes

characteristic

C₁₁×#424

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66882

—

C₂×#66881

C₂²

yes

—

C₂×#66876

C₂²

yes

—

#10622549

—

C₁₁×#339

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₁₁×#117

—

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₁₁×#108

—

C₁₁×#107

Q₈

yes

—

C₁₁×#106

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

—

C₁₁⋊#95

—

—

—

—

—

C₂×C₁₁⋊C₁₆

—

#13542

—

maximal, Sylow

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×Dic₁₁

—

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

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

—

C₁₁×C₄⋊C₄

—

C₁₁×C₂²⋊C₄

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

Q₁₆

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₁₁⋊C₁₆

—

#1945

D₁₁

yes

—

—

—

—

C₂³×C₁₁

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₁₁

—

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

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#125

yes

—

C₈×C₁₁

#126

yes

—

C₂×M₃₂

—

C₂×#108

C₂×D₁₁

yes

characteristic

#427

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

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

Dic₁₁

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₁

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

100

C₂×C₄²

C₂²⋊D₁₁

yes

characteristic

101

M₃₂

—

102

M₃₂

—

103

C₂×C₁₆

—

104

#108

—

105

#107

—

106

#107

Dic₂₂

yes

—

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×C₂²⋊D₁₁

yes

characteristic

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

#4324

yes

—

125

C₂×C₈

C₂×Dic₂₂

yes

characteristic

126

C₂×C₈

#4339

yes

characteristic

127

C₂×C₈

#4341

yes

—

128

C₂×C₈

#4343

yes

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₂²⋊C₄

—

133

C₄²

—

134

C₄²

—

135

C₄²

#4326

yes

—

136

C₁₆

—

137

C₁₁

#13542

yes

characteristic, complemented, Sylow

138

C₂³

#67002

yes

characteristic

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

#66977

yes

characteristic

145

C₂×C₄

C₂×#4324

yes

characteristic

146

C₂×C₄

#66988

yes

characteristic

147

C₂×C₄

C₂×#4326

yes

characteristic

148

C₂×C₄

#67000

yes

characteristic

149

C₂×C₄

#67002

yes

characteristic

150

C₈

—

151

C₈

—

152

C₈

#66943

yes

—

153

C₈

#66951

yes

—

154

C₂²

—

155

C₂²

#10622621

yes

characteristic

156

C₂²

#10622657

yes

characteristic

157

C₂²

#10622680

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

176

—

161

C₄

#10622599

yes

characteristic

162

C₄

#10622634

yes

characteristic

163

C₄

#10622647

yes

characteristic

164

C₄

#10622706

yes

characteristic

165

C₂

—

166

C₂

—

167

C₂

#13070179

yes

characteristic

168

C₂

#13070792

yes

—

	subgroup	G/H
center	C₂²	#10622621
commutator, cosocle	C₂²×C₈×C₁₁	C₂³
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1945	C₂
socle	C₂²×C₁₁	#476
prime radical	C₂³×C₁₁	AGL(1,ℤ/8)
hypercenter	#1945	D₁₁
hypocenter	C₁₁	#13542
LCS	G ▷ C₂²×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1945

subgroup

G/H

center

C₂²

#10622621

commutator, cosocle

C₂²×C₈×C₁₁

C₂³

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#1945

C₂

C₂²×C₁₁

C₂³×C₁₁

D₁₁

C₁₁

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

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1945

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
#13068780	2
#13066721	2
#13066716	2
#13066698	2
C₁₁×#1945	2
#13542	11

subgroup

index

C₁₁×#1945

Subgroups — #14673918

Conjugacy classes of subgroups

Complements

Maximal subgroups