Group #14640693 — subgroups

Subgroups — #14640693

Order 2816.

246 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 119 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	C₄×#66876	C₂	1	1	yes	maximal, characteristic
2	C₄×#66883	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#334	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66883	C₄	1	2	yes	—
7	C₂×#66876	—	2	1	no	—
8	C₄×#4318	—	2	1	no	—
9	C₁₁×#334	—	2	1	no	—
10	C₁₁×#334	C₄	1	2	yes	—
11	#10622190	—	2	1	no	—
12	#10622099	—	2	1	no	—
13	C₄×C₁₁⋊C₁₆	C₄	1	2	yes	—
14	C₂²×C₈×C₁₁	—	4	1	no	—
15	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
18	C₂×#4318	—	2	2	no	—
19	C₁₁×C₄⋊C₈	—	2	2	no	—
20	C₁₁×C₄⋊C₈	—	4	1	no	—
21	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
25	#66883	—	2	2	no	—
26	#66883	C₈	1	4	yes	complemented
27	#66876	—	2	4	no	—
28	C₂×C₁₁⋊C₁₆	—	2	2	no	—
29	#66867	—	4	1	no	—
30	C₄×C₁₁⋊C₈	—	4	1	no	—
31	#7173	—	11	1	no	maximal, Sylow
32	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
34	C₂²×C₄×C₁₁	Q₁₆	1	1	yes	characteristic
35	C₂×C₈×C₁₁	—	2	2	no	—
36	C₂×C₈×C₁₁	—	4	2	no	—
37	C₂×C₈×C₁₁	—	8	2	no	—
38	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
43	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
44	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
45	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
46	C₄²×C₁₁	D₈	1	1	yes	characteristic
47	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
48	#4318	—	2	4	no	—
49	#4318	—	4	2	no	—
50	C₂×C₁₁⋊C₈	—	4	2	no	—
51	C₁₁⋊C₁₆	—	2	4	no	—
52	C₄×M₃₂	—	11	1	no	—
53	C₄×#108	—	11	1	no	—
54	C₂×#334	D₁₁	1	1	yes	characteristic
55	C₂³×C₁₁	#103	1	1	yes	characteristic
56	C₂×C₄×C₁₁	—	2	2	no	—
57	C₂×C₄×C₁₁	—	4	1	no	—
58	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
59	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
60	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
61	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
62	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
63	C₂×C₄×C₁₁	#104	1	2	yes	—
64	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
65	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
66	C₈×C₁₁	—	2	1	no	—
67	C₈×C₁₁	—	2	1	no	—
68	C₈×C₁₁	—	8	2	no	—
69	C₈×C₁₁	C₄×C₈	1	1	yes	characteristic
70	C₈×C₁₁	#97	1	1	yes	characteristic
71	C₈×C₁₁	C₄⋊C₈	1	2	yes	—
72	C₁₁⋊C₈	—	4	4	no	—
73	C₂×M₃₂	—	22	1	no	—
74	C₂×#108	—	11	2	no	—
75	C₂×C₄⋊C₈	—	2	1	no	—
76	C₄×M₁₆	—	22	1	no	—
77	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
78	#346	—	22	1	no	—
79	C₄×C₁₆	—	11	2	no	—
80	#341	—	22	1	no	—
81	#334	—	2	1	no	—
82	#334	Dic₁₁	1	2	yes	—
83	C₂²×C₁₁	—	2	1	no	—
84	C₂²×C₁₁	—	2	1	no	—
85	C₂²×C₁₁	Q₈⋊C₈	1	2	yes	—
86	C₂²×C₁₁	#340	1	1	yes	characteristic
87	C₄×C₁₁	—	2	1	no	—
88	C₄×C₁₁	—	2	1	no	—
89	C₄×C₁₁	—	2	1	no	—
90	C₄×C₁₁	D₄⋊C₈	1	2	yes	—
91	C₄×C₁₁	#336	1	1	yes	characteristic
92	C₄×C₁₁	#339	1	1	yes	characteristic
93	C₄×C₁₁	#365	1	2	yes	—
94	C₂×M₁₆	—	22	2	no	—
95	C₂²×C₈	—	4	1	no	—
96	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
97	C₂²×C₈	D₄₄	1	1	yes	characteristic
98	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
99	M₃₂	—	22	4	no	—
100	C₂×C₁₆	—	22	2	no	—
101	#108	—	11	4	no	—
102	#108	—	22	2	no	—
103	C₄⋊C₈	—	2	2	no	—
104	C₄⋊C₈	—	4	1	no	—
105	#97	—	44	1	no	—
106	C₄×C₈	—	44	1	no	—
107	C₄×C₈	Dic₂₂	1	1	yes	characteristic
108	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
109	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
110	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
111	C₂×C₁₁	—	2	2	no	—
112	C₂×C₁₁	#1279	1	1	yes	characteristic
113	C₂×C₁₁	#1383	1	1	yes	characteristic
114	C₂×C₁₁	#1385	1	1	yes	characteristic
115	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
116	C₂²×C₄	#4324	1	1	yes	characteristic
117	C₂²×C₄	#4326	1	1	yes	characteristic
118	M₁₆	—	22	4	no	—
119	M₁₆	—	44	2	no	—
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	—	4	2	no	—
122	C₂×C₈	—	8	2	no	—
123	C₂×C₈	—	44	2	no	—
124	C₂×C₈	C₈×D₁₁	1	2	yes	—
125	C₂×C₈	#4313	1	2	yes	—
126	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
127	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
128	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
129	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
130	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
131	C₄²	#4323	1	1	yes	characteristic
132	C₄²	#4325	1	1	yes	characteristic
133	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
134	C₁₆	—	22	4	no	—
135	C₁₁	#7173	1	1	yes	characteristic, complemented, Sylow
136	C₂³	#66874	1	1	yes	characteristic
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	4	1	no	—
139	C₂×C₄	#66871	1	1	yes	characteristic
140	C₂×C₄	#66872	1	1	yes	characteristic
141	C₂×C₄	#66873	1	1	yes	characteristic
142	C₂×C₄	(C₂×D₁₁)⋊C₈	1	2	yes	—
143	C₂×C₄	#66889	1	2	yes	—
144	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
145	C₂×C₄	#66896	1	1	yes	characteristic
146	C₂×C₄	#66899	1	1	yes	characteristic
147	C₈	—	2	1	no	—
148	C₈	—	2	1	no	—
149	C₈	—	8	2	no	—
150	C₈	—	44	4	no	—
151	C₈	C₈×Dic₁₁	1	1	yes	characteristic
152	C₈	Dic₁₁⋊C₈	1	2	yes	—
153	C₈	#66879	1	1	yes	characteristic
154	C₂²	—	2	1	no	—
155	C₂²	—	2	1	no	—
156	C₂²	#10622122	1	2	yes	—
157	C₂²	#10622167	1	1	yes	characteristic
158	C₄	—	2	1	no	—
159	C₄	—	2	1	no	—
160	C₄	—	2	1	no	—
161	C₄	#10622121	1	2	yes	—
162	C₄	#10622125	1	2	yes	—
163	C₄	#10622188	1	1	yes	characteristic
164	C₄	#10622193	1	1	yes	characteristic
165	C₂	—	2	2	no	—
166	C₂	#13066455	1	1	yes	characteristic
167	C₂	#13066714	1	1	yes	characteristic
168	C₂	#13066719	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#66876

C₂

yes

maximal, characteristic

C₄×#66883

C₂

yes

maximal, characteristic

C₂×C₁₁×#334

C₂

yes

maximal, characteristic

C₂×C₁₁×C₄⋊C₈

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

C₄

yes

—

C₂×#66876

—

C₄×#4318

—

C₁₁×#334

—

C₁₁×#334

C₄

yes

—

#10622190

—

#10622099

—

C₄×C₁₁⋊C₁₆

C₄

yes

—

C₂²×C₈×C₁₁

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×#4318

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

characteristic

C₄×C₈×C₁₁

Q₈

yes

characteristic

#66883

—

#66883

C₈

yes

complemented

#66876

—

C₂×C₁₁⋊C₁₆

—

#66867

—

C₄×C₁₁⋊C₈

—

#7173

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₁

SD₁₆

yes

characteristic

C₂²×C₄×C₁₁

Q₁₆

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄²

yes

characteristic

C₂×C₈×C₁₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₂×C₈

yes

—

C₂×C₈×C₁₁

M₁₆

yes

—

C₄²×C₁₁

C₂²⋊C₄

yes

characteristic

C₄²×C₁₁

C₄⋊C₄

yes

characteristic

C₄²×C₁₁

D₈

yes

characteristic

C₄²×C₁₁

SD₁₆

yes

characteristic

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₁₁⋊C₁₆

—

C₄×M₃₂

—

C₄×#108

—

C₂×#334

D₁₁

yes

characteristic

C₂³×C₁₁

#103

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#95

yes

characteristic

C₂×C₄×C₁₁

C₂²⋊C₈

yes

—

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

—

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

C₄×C₈

yes

characteristic

C₈×C₁₁

#97

yes

characteristic

C₈×C₁₁

C₄⋊C₈

yes

—

C₁₁⋊C₈

—

C₂×M₃₂

—

C₂×#108

—

C₂×C₄⋊C₈

—

C₄×M₁₆

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#346

—

C₄×C₁₆

—

#341

—

#334

—

#334

Dic₁₁

yes

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

Q₈⋊C₈

yes

—

C₂²×C₁₁

#340

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

D₄⋊C₈

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₁

yes

characteristic

C₂²×C₈

D₄₄

yes

characteristic

C₂×C₄²

C₂²⋊D₁₁

yes

characteristic

M₃₂

—

100

C₂×C₁₆

—

101

#108

—

102

#108

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

#97

—

106

C₄×C₈

—

107

C₄×C₈

Dic₂₂

yes

characteristic

108

C₄×C₈

C₄×D₁₁

yes

characteristic

109

C₄×C₈

C₂×Dic₁₁

yes

characteristic

110

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

111

C₂×C₁₁

—

112

C₂×C₁₁

#1279

yes

characteristic

113

C₂×C₁₁

#1383

yes

characteristic

114

C₂×C₁₁

#1385

yes

characteristic

115

C₂²×C₄

(C₂×D₁₁)⋊C₄

yes

characteristic

116

C₂²×C₄

#4324

yes

characteristic

117

C₂²×C₄

#4326

yes

characteristic

118

M₁₆

—

119

M₁₆

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

C₈×D₁₁

yes

—

125

C₂×C₈

#4313

yes

—

126

C₂×C₈

C₄×Dic₁₁

yes

characteristic

127

C₂×C₈

Dic₁₁⋊C₄

yes

characteristic

128

C₂×C₈

C₄⋊Dic₁₁

yes

characteristic

129

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

characteristic

130

C₄²

Dic₁₁⋊C₄

yes

characteristic

131

C₄²

#4323

yes

characteristic

132

C₄²

#4325

yes

characteristic

133

C₄²

C₂²⋊Dic₁₁

yes

characteristic

134

C₁₆

—

135

C₁₁

#7173

yes

characteristic, complemented, Sylow

136

C₂³

#66874

yes

characteristic

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

#66871

yes

characteristic

140

C₂×C₄

#66872

yes

characteristic

141

C₂×C₄

#66873

yes

characteristic

142

C₂×C₄

(C₂×D₁₁)⋊C₈

yes

—

143

C₂×C₄

#66889

yes

—

144

C₂×C₄

C₁₁⋊#95

yes

characteristic

145

C₂×C₄

#66896

yes

characteristic

146

C₂×C₄

#66899

yes

characteristic

147

C₈

—

148

C₈

—

149

C₈

—

150

C₈

—

151

C₈

C₈×Dic₁₁

yes

characteristic

152

C₈

Dic₁₁⋊C₈

yes

—

153

C₈

#66879

yes

characteristic

154

C₂²

—

155

C₂²

—

156

C₂²

#10622122

yes

—

157

C₂²

#10622167

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

#10622121

yes

—

162

C₄

#10622125

yes

—

163

C₄

#10622188

yes

characteristic

164

C₄

#10622193

yes

characteristic

165

C₂

—

166

C₂

#13066455

yes

characteristic

167

C₂

#13066714

yes

characteristic

168

C₂

#13066719

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#66872
commutator	C₈×C₁₁	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₂×C₁₁×#334	C₂
socle	C₂²×C₁₁	#340
prime radical	C₂³×C₁₁	#103
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	C₂×#334	D₁₁
hypocenter	C₁₁	#7173
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#334

subgroup

G/H

center

C₂×C₄

#66872

commutator

C₈×C₁₁

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₁

Fitting

C₂×C₁₁×#334

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄×C₈×C₁₁

C₂²

D₁₁

C₁₁

G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#334

N	H ≅ G/N	type
26. #66883	C₈	semidirect
135. C₁₁	#7173	semidirect

H ≅ G/N

type

26. #66883

C₈

semidirect

135. C₁₁

#7173

semidirect

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

subgroup	index
C₄×#66876	2
C₄×#66883	2
C₂×C₁₁×#334	2
#7173	11

subgroup

index

C₄×#66876

C₄×#66883

C₂×C₁₁×#334

#7173

Subgroups — #14640693

Conjugacy classes of subgroups

Complements

Maximal subgroups