Group #19133287 — subgroups

Subgroups — #19133287

Order 5504.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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	#14583447	C₂	1	1	yes	maximal, characteristic
2	#14582955	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582647	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582647	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582643	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621900	C₄	1	2	yes	—
9	C₂×C₈×D₄₃	—	2	1	no	—
10	#13063325	C₂²	1	1	yes	characteristic
11	#13063312	C₄	1	2	yes	—
12	#13063296	—	2	1	no	—
13	#13063296	—	2	1	no	—
14	D₄×Dic₄₃	—	2	1	no	—
15	D₄×Dic₄₃	—	2	1	no	—
16	C₄²×D₄₃	C₂²	1	1	yes	characteristic
17	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
18	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
19	Dic₄₃⋊C₈	—	2	1	no	—
20	(C₂×D₄₃)⋊C₈	—	2	1	no	—
21	#13063235	—	2	1	no	—
22	#127×C₄₃	C₂²	1	1	yes	characteristic
23	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×D₄×C₄₃	—	2	1	no	—
26	C₂×D₄×C₄₃	—	2	1	no	—
27	C₂×D₄×C₄₃	C₂×C₄	1	2	yes	—
28	C₂×C₂²⋊D₄₃	—	2	2	no	—
29	C₂²×Dic₄₃	—	2	2	no	—
30	#10621900	—	4	4	no	—
31	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
33	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
34	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
35	C₂×C₈×C₄₃	—	2	1	no	—
36	C₂×C₈×C₄₃	—	2	1	no	—
37	C₄²×C₄₃	C₂³	1	1	yes	characteristic
38	C₂²⋊Dic₄₃	—	2	2	no	—
39	C₂²⋊Dic₄₃	—	2	2	no	—
40	C₄⋊Dic₄₃	—	2	1	no	—
41	C₄⋊Dic₄₃	—	2	1	no	—
42	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
43	C₄×Dic₄₃	D₄	1	1	yes	characteristic
44	C₄×Dic₄₃	D₄	1	1	yes	characteristic
45	C₂×C₄₃⋊C₈	—	2	1	no	—
46	C₂×C₄₃⋊C₈	—	2	1	no	—
47	C₈×D₄₃	—	4	2	no	—
48	C₂³×C₄₃	—	2	2	no	—
49	C₂²×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
50	D₄×C₄₃	—	4	2	no	—
51	D₄×C₄₃	—	4	1	no	—
52	D₄×C₄₃	—	4	1	no	—
53	D₄×C₄₃	—	4	1	no	—
54	D₄×C₄₃	—	4	1	no	—
55	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₂²⋊D₄₃	—	4	4	no	—
59	C₂×Dic₄₃	—	2	2	no	—
60	C₂×Dic₄₃	—	4	4	no	—
61	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
64	C₄×D₄₃	—	2	2	no	—
65	C₄×D₄₃	—	2	1	no	—
66	C₄×D₄₃	—	2	1	no	—
67	C₄×D₄₃	—	2	1	no	—
68	C₄×D₄₃	—	2	1	no	—
69	Dic₈₆	—	4	2	no	—
70	C₈×C₄₃	—	4	1	no	—
71	C₈×C₄₃	—	4	1	no	—
72	C₄₃⋊C₈	—	4	1	no	—
73	C₄₃⋊C₈	—	4	1	no	—
74	C₂²×C₄₃	—	4	2	no	—
75	C₂²×C₄₃	—	4	2	no	—
76	C₂²×C₄₃	—	4	2	no	—
77	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×D₄₃	—	2	1	no	—
79	C₂×D₄₃	—	2	1	no	—
80	C₂×D₄₃	#100	1	2	yes	—
81	C₄×C₄₃	—	2	1	no	—
82	C₄×C₄₃	#135	1	1	yes	characteristic
83	C₄×C₄₃	#135	1	1	yes	characteristic
84	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
85	C₄×C₄₃	#137	1	1	yes	characteristic
86	Dic₄₃	—	2	1	no	—
87	Dic₄₃	—	2	1	no	—
88	Dic₄₃	—	2	1	no	—
89	Dic₄₃	—	4	2	no	—
90	#1551	—	43	1	no	maximal, Sylow
91	C₂×C₄₃	—	8	2	no	—
92	C₂×C₄₃	C₂×#100	1	1	yes	characteristic
93	C₂×C₄₃	#416	1	1	yes	characteristic
94	C₂×C₄₃	#417	1	1	yes	characteristic
95	D₄₃	—	2	2	no	—
96	#532	—	43	1	no	—
97	#432	—	43	1	no	—
98	C₂×C₄⋊C₈	—	43	1	no	—
99	#333	—	43	1	no	—
100	#333	—	43	1	no	—
101	#331	—	43	1	no	—
102	#331	D₄₃	1	1	yes	characteristic, complemented
103	C₄₃	#1551	1	1	yes	characteristic, complemented, Sylow
104	C₂×#41	—	43	2	no	—
105	C₂²×C₈	—	86	1	no	—
106	C₄⋊Q₈	—	43	1	no	—
107	#127	C₂×D₄₃	1	1	yes	characteristic
108	#124	—	43	2	no	—
109	#121	—	86	1	no	—
110	#121	—	86	1	no	—
111	C₄×D₄	—	86	1	no	—
112	C₄×D₄	—	86	1	no	—
113	C₂×C₄²	—	43	1	no	—
114	C₄⋊C₈	—	43	1	no	—
115	C₄⋊C₈	—	43	1	no	—
116	C₄⋊C₈	—	86	1	no	—
117	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
118	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
119	C₂²⋊C₈	—	86	1	no	—
120	#97	—	86	1	no	—
121	#41	—	172	4	no	—
122	C₂×Q₈	—	43	2	no	—
123	C₂×D₄	—	2	1	no	—
124	C₂×D₄	—	2	1	no	—
125	C₂×D₄	—	86	2	no	—
126	C₂×D₄	C₄×D₄₃	1	2	yes	—
127	C₂²×C₄	—	43	1	no	—
128	C₂²×C₄	—	43	1	no	—
129	C₂²×C₄	—	43	1	no	—
130	C₂²×C₄	—	86	2	no	—
131	C₂×C₈	—	2	1	no	—
132	C₂×C₈	—	2	1	no	—
133	C₂×C₈	—	86	1	no	—
134	C₂×C₈	—	86	1	no	—
135	C₂×C₈	—	172	2	no	—
136	C₄⋊C₄	—	86	1	no	—
137	C₄⋊C₄	—	86	1	no	—
138	C₂²⋊C₄	—	86	2	no	—
139	C₂²⋊C₄	—	86	2	no	—
140	C₄²	—	43	1	no	—
141	C₄²	—	43	1	no	—
142	C₄²	—	43	1	no	—
143	C₄²	C₂²×D₄₃	1	1	yes	characteristic
144	C₂³	—	2	2	no	—
145	C₂³	—	43	1	no	—
146	Q₈	—	172	2	no	—
147	D₄	—	4	2	no	—
148	D₄	—	4	1	no	—
149	D₄	—	4	1	no	—
150	D₄	—	4	1	no	—
151	D₄	—	4	1	no	—
152	D₄	—	172	4	no	—
153	C₂×C₄	—	43	1	no	—
154	C₂×C₄	—	43	1	no	—
155	C₂×C₄	—	43	1	no	—
156	C₂×C₄	—	86	2	no	—
157	C₂×C₄	—	86	1	no	—
158	C₂×C₄	—	86	1	no	—
159	C₂×C₄	—	86	1	no	—
160	C₂×C₄	—	86	1	no	—
161	C₂×C₄	—	86	2	no	—
162	C₂×C₄	—	172	4	no	—
163	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
164	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
165	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
166	C₈	—	4	1	no	—
167	C₈	—	4	1	no	—
168	C₈	—	172	1	no	—
169	C₈	—	172	1	no	—
170	C₂²	—	4	2	no	—
171	C₂²	—	4	2	no	—
172	C₂²	—	4	2	no	—
173	C₂²	—	43	2	no	—
174	C₂²	—	86	1	no	—
175	C₂²	—	86	1	no	—
176	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
177	C₄	—	2	1	no	—
178	C₄	—	86	1	no	—
179	C₄	—	86	1	no	—
180	C₄	—	86	1	no	—
181	C₄	—	172	2	no	—
182	C₄	#13063344	1	1	yes	characteristic
183	C₄	#13063346	1	1	yes	characteristic
184	C₄	#13063349	1	1	yes	characteristic
185	C₄	#13063354	1	1	yes	characteristic
186	C₂	—	8	2	no	—
187	C₂	—	86	2	no	—
188	C₂	#100×D₄₃	1	1	yes	characteristic
189	C₂	#14582892	1	1	yes	characteristic
190	C₂	#14582897	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583447

C₂

yes

maximal, characteristic

#14582955

C₂

yes

maximal, characteristic, complemented

C₄⋊C₈×D₄₃

C₂

yes

maximal, characteristic, complemented

#14582647

C₂

yes

maximal, characteristic, complemented

#14582647

C₂

yes

maximal, characteristic, complemented

#14582643

C₂

yes

maximal, characteristic, complemented

C₄₃×#331

C₂

yes

maximal, characteristic, complemented

C₂×#10621900

C₄

yes

—

C₂×C₈×D₄₃

—

#13063325

C₂²

yes

characteristic

#13063312

C₄

yes

—

#13063296

—

#13063296

—

D₄×Dic₄₃

—

D₄×Dic₄₃

—

C₄²×D₄₃

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

(C₂×D₄₃)⋊C₈

—

#13063235

—

#127×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

C₂×C₄

yes

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

—

#10621900

—

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₈×D₄₃

—

C₂³×C₄₃

—

C₂²×D₄₃

C₂²⋊C₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

#100

yes

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#1551

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#532

—

#432

—

C₂×C₄⋊C₈

—

#333

—

100

#333

—

101

#331

—

102

#331

D₄₃

yes

characteristic, complemented

103

C₄₃

#1551

yes

characteristic, complemented, Sylow

104

C₂×#41

—

105

C₂²×C₈

—

106

C₄⋊Q₈

—

107

#127

C₂×D₄₃

yes

characteristic

108

#124

—

109

#121

—

110

#121

—

111

C₄×D₄

—

112

C₄×D₄

—

113

C₂×C₄²

—

114

C₄⋊C₈

—

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

C₄⋊C₈

C₂×D₄₃

yes

characteristic

118

C₄⋊C₈

C₂×D₄₃

yes

characteristic

119

C₂²⋊C₈

—

120

#97

—

121

#41

—

172

—

122

C₂×Q₈

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

C₄×D₄₃

yes

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

172

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₂²⋊C₄

—

139

C₂²⋊C₄

—

140

C₄²

—

141

C₄²

—

142

C₄²

—

143

C₄²

C₂²×D₄₃

yes

characteristic

144

C₂³

—

145

C₂³

—

146

Q₈

—

172

—

147

D₄

—

148

D₄

—

149

D₄

—

150

D₄

—

151

D₄

—

152

D₄

—

172

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

172

—

163

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

164

C₂×C₄

D₄×D₄₃

yes

characteristic

165

C₂×C₄

D₄×D₄₃

yes

characteristic

166

C₈

—

167

C₈

—

168

C₈

—

172

—

169

C₈

—

172

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

—

176

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

172

—

182

C₄

#13063344

yes

characteristic

183

C₄

#13063346

yes

characteristic

184

C₄

#13063349

yes

characteristic

185

C₄

#13063354

yes

characteristic

186

C₂

—

187

C₂

—

188

C₂

#100×D₄₃

yes

characteristic

189

C₂

#14582892

yes

characteristic

190

C₂

#14582897

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#331	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#331	D₄₃
hypocenter	C₄₃	#1551
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #331

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#331

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #331

N	H ≅ G/N	type
2. #14582955	C₂	semidirect
3. C₄⋊C₈×D₄₃	C₂	semidirect
4. #14582647	C₂	semidirect
5. #14582647	C₂	semidirect
6. #14582643	C₂	semidirect
7. C₄₃×#331	C₂	semidirect
102. #331	D₄₃	semidirect
103. C₄₃	#1551	semidirect

H ≅ G/N

type

2. #14582955

C₂

semidirect

3. C₄⋊C₈×D₄₃

C₂

semidirect

4. #14582647

C₂

semidirect

5. #14582647

C₂

semidirect

6. #14582643

C₂

semidirect

7. C₄₃×#331

C₂

semidirect

102. #331

D₄₃

semidirect

103. C₄₃

#1551

semidirect

Subgroups — #19133287

Conjugacy classes of subgroups

Complements