Group #19133237 — subgroups

Subgroups — #332×D₄₃ #19133237

Order 5504.

256 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 87 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⋊Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582646	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582645	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582644	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₄₃	—	2	1	no	—
9	C₂×C₈×D₄₃	—	2	1	no	—
10	C₂×C₈×D₄₃	—	2	1	no	—
11	#13063325	C₂²	1	1	yes	characteristic
12	#13063324	—	2	1	no	—
13	#13063324	C₄	1	2	yes	—
14	#13063323	—	2	1	no	—
15	C₄⋊C₄×D₄₃	—	2	1	no	—
16	C₄⋊C₄×D₄₃	C₄	1	2	yes	—
17	C₄²×D₄₃	C₂²	1	1	yes	characteristic
18	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	Dic₄₃⋊C₈	—	2	1	no	—
21	Dic₄₃⋊C₈	—	2	1	no	—
22	C₄⋊Q₈×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×Q₈×C₄₃	—	2	1	no	—
26	Q₈×D₄₃	—	4	2	no	—
27	Q₈×D₄₃	—	4	2	no	—
28	C₂×C₄×D₄₃	—	2	2	no	—
29	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
31	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
32	C₂×Dic₈₆	—	2	1	no	—
33	C₂×Dic₈₆	—	2	2	no	—
34	C₂×C₈×C₄₃	—	2	1	no	—
35	C₂×C₈×C₄₃	—	2	1	no	—
36	C₄⋊C₄×C₄₃	—	2	1	no	—
37	C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
38	C₄²×C₄₃	C₂³	1	1	yes	characteristic
39	C₄⋊Dic₄₃	—	2	1	no	—
40	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
41	Dic₄₃⋊C₄	—	2	2	no	—
42	Dic₄₃⋊C₄	—	2	2	no	—
43	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
44	C₄×Dic₄₃	D₄	1	1	yes	characteristic
45	C₄×Dic₄₃	D₄	1	1	yes	characteristic
46	C₂×C₄₃⋊C₈	—	2	1	no	—
47	C₂×C₄₃⋊C₈	—	2	1	no	—
48	C₈×D₄₃	—	4	2	no	—
49	C₈×D₄₃	—	4	2	no	—
50	C₂²×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
51	Q₈×C₄₃	—	4	1	no	—
52	Q₈×C₄₃	—	4	1	no	—
53	C₂×C₄×C₄₃	—	2	2	no	—
54	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂×Dic₄₃	—	2	2	no	—
58	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₄×D₄₃	—	2	2	no	—
62	C₄×D₄₃	—	4	4	no	—
63	C₄×D₄₃	D₈	1	2	yes	—
64	C₄×D₄₃	SD₁₆	1	2	yes	—
65	C₄×D₄₃	SD₁₆	1	2	yes	—
66	C₄×D₄₃	Q₁₆	1	2	yes	—
67	Dic₈₆	—	4	1	no	—
68	Dic₈₆	—	4	1	no	—
69	Dic₈₆	—	4	4	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×D₄₃	#101	1	2	yes	—
76	C₂×D₄₃	#102	1	2	yes	—
77	C₂×D₄₃	#103	1	2	yes	—
78	C₄×C₄₃	—	2	1	no	—
79	C₄×C₄₃	—	4	2	no	—
80	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
81	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
82	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
83	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
84	Dic₄₃	—	2	1	no	—
85	Dic₄₃	—	4	2	no	—
86	Dic₄₃	#102	1	2	yes	—
87	Dic₄₃	#103	1	2	yes	—
88	C₂×#332	—	43	1	no	maximal, Sylow
89	C₂×C₄₃	C₂×#101	1	1	yes	characteristic
90	C₂×C₄₃	C₂×#102	1	1	yes	characteristic
91	C₂×C₄₃	C₂×#103	1	1	yes	characteristic
92	D₄₃	#332	1	4	yes	direct product factor
93	C₂×C₄⋊Q₈	—	43	1	no	—
94	C₂×C₄⋊C₈	—	43	1	no	—
95	C₂×C₄⋊C₈	—	43	1	no	—
96	#332	—	43	1	no	—
97	#332	—	43	1	no	—
98	#332	—	43	1	no	—
99	#332	D₄₃	1	1	yes	characteristic, direct product factor
100	C₄₃	C₂×#332	1	1	yes	characteristic, complemented, Sylow
101	C₂²×Q₈	—	86	1	no	—
102	C₂²×C₈	—	86	1	no	—
103	C₂²×C₈	—	86	1	no	—
104	C₄⋊Q₈	—	43	2	no	—
105	C₄⋊Q₈	—	43	1	no	—
106	C₄⋊Q₈	—	86	1	no	—
107	C₄⋊Q₈	—	86	1	no	—
108	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
109	C₂×C₄⋊C₄	—	43	2	no	—
110	C₂×C₄⋊C₄	—	86	1	no	—
111	C₂×C₄²	—	43	1	no	—
112	C₄⋊C₈	—	43	1	no	—
113	C₄⋊C₈	—	43	1	no	—
114	C₄⋊C₈	—	86	1	no	—
115	C₄⋊C₈	—	86	1	no	—
116	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
117	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
118	C₂×Q₈	—	2	1	no	—
119	C₂×Q₈	—	86	2	no	—
120	C₂×Q₈	—	86	1	no	—
121	C₂×Q₈	—	172	2	no	—
122	C₂×Q₈	—	172	2	no	—
123	C₂²×C₄	—	43	1	no	—
124	C₂²×C₄	—	43	1	no	—
125	C₂²×C₄	—	43	1	no	—
126	C₂²×C₄	—	86	2	no	—
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	2	1	no	—
129	C₂×C₈	—	86	1	no	—
130	C₂×C₈	—	86	1	no	—
131	C₂×C₈	—	172	2	no	—
132	C₂×C₈	—	172	2	no	—
133	C₄⋊C₄	—	2	1	no	—
134	C₄⋊C₄	—	43	2	no	—
135	C₄⋊C₄	—	86	2	no	—
136	C₄⋊C₄	—	86	2	no	—
137	C₄⋊C₄	—	86	1	no	—
138	C₄⋊C₄	C₄×D₄₃	1	2	yes	—
139	C₄²	—	43	1	no	—
140	C₄²	—	43	1	no	—
141	C₄²	—	43	1	no	—
142	C₄²	C₂²×D₄₃	1	1	yes	characteristic
143	C₂³	—	43	1	no	—
144	Q₈	—	4	1	no	—
145	Q₈	—	4	1	no	—
146	Q₈	—	172	4	no	—
147	Q₈	—	172	1	no	—
148	Q₈	—	172	1	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	43	1	no	—
151	C₂×C₄	—	43	1	no	—
152	C₂×C₄	—	43	2	no	—
153	C₂×C₄	—	43	2	no	—
154	C₂×C₄	—	43	2	no	—
155	C₂×C₄	—	43	2	no	—
156	C₂×C₄	—	43	1	no	—
157	C₂×C₄	—	86	2	no	—
158	C₂×C₄	—	86	2	no	—
159	C₂×C₄	—	172	4	no	—
160	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
161	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
162	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
163	C₈	—	4	1	no	—
164	C₈	—	4	1	no	—
165	C₈	—	172	1	no	—
166	C₈	—	172	1	no	—
167	C₂²	—	43	2	no	—
168	C₂²	—	43	2	no	—
169	C₂²	—	43	2	no	—
170	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
171	C₄	—	2	1	no	—
172	C₄	—	4	2	no	—
173	C₄	—	43	2	no	—
174	C₄	—	43	2	no	—
175	C₄	—	86	1	no	—
176	C₄	—	172	2	no	—
177	C₄	D₈×D₄₃	1	1	yes	characteristic
178	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
179	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
180	C₄	Q₁₆×D₄₃	1	1	yes	characteristic
181	C₂	—	43	4	no	—
182	C₂	#101×D₄₃	1	1	yes	characteristic
183	C₂	#102×D₄₃	1	1	yes	characteristic
184	C₂	#103×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₄₃

C₂

yes

maximal, characteristic

C₄⋊C₈×D₄₃

C₂

yes

maximal, characteristic

C₄⋊C₈×D₄₃

C₂

yes

maximal, characteristic

#14582646

C₂

yes

maximal, characteristic, complemented

#14582645

C₂

yes

maximal, characteristic, complemented

#14582644

C₂

yes

maximal, characteristic, complemented

C₄₃×#332

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

#13063325

C₂²

yes

characteristic

#13063324

—

#13063324

C₄

yes

—

#13063323

—

C₄⋊C₄×D₄₃

—

C₄⋊C₄×D₄₃

C₄

yes

—

C₄²×D₄₃

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

Dic₄₃⋊C₈

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

Q₈×D₄₃

—

Q₈×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₈×D₄₃

—

C₈×D₄₃

—

C₂²×D₄₃

C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

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

D₈

yes

—

C₄×D₄₃

SD₁₆

yes

—

C₄×D₄₃

SD₁₆

yes

—

C₄×D₄₃

Q₁₆

yes

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₃

#101

yes

—

C₂×D₄₃

#102

yes

—

C₂×D₄₃

#103

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#102

yes

—

Dic₄₃

#103

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

direct product factor

C₂×C₄⋊Q₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

—

—

—

D₄₃

yes

characteristic, direct product factor

100

C₄₃

C₂×#332

yes

characteristic, complemented, Sylow

101

C₂²×Q₈

—

102

C₂²×C₈

—

103

C₂²×C₈

—

104

C₄⋊Q₈

—

105

C₄⋊Q₈

—

106

C₄⋊Q₈

—

107

C₄⋊Q₈

—

108

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄²

—

112

C₄⋊C₈

—

113

C₄⋊C₈

—

114

C₄⋊C₈

—

115

C₄⋊C₈

—

116

C₄⋊C₈

C₂×D₄₃

yes

characteristic

117

C₄⋊C₈

C₂×D₄₃

yes

characteristic

118

C₂×Q₈

—

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×Q₈

—

172

—

122

C₂×Q₈

—

172

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

172

—

132

C₂×C₈

—

172

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

C₄×D₄₃

yes

—

139

C₄²

—

140

C₄²

—

141

C₄²

—

142

C₄²

C₂²×D₄₃

yes

characteristic

143

C₂³

—

144

Q₈

—

145

Q₈

—

146

Q₈

—

172

—

147

Q₈

—

172

—

148

Q₈

—

172

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

172

—

160

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

161

C₂×C₄

D₄×D₄₃

yes

characteristic

162

C₂×C₄

D₄×D₄₃

yes

characteristic

163

C₈

—

164

C₈

—

165

C₈

—

172

—

166

C₈

—

172

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

172

—

177

C₄

D₈×D₄₃

yes

characteristic

178

C₄

SD₁₆×D₄₃

yes

characteristic

179

C₄

SD₁₆×D₄₃

yes

characteristic

180

C₄

Q₁₆×D₄₃

yes

characteristic

181

C₂

—

182

C₂

#101×D₄₃

yes

characteristic

183

C₂

#102×D₄₃

yes

characteristic

184

C₂

#103×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#332	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#332	D₄₃
hypocenter	C₄₃	C₂×#332
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #332

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#332

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #332

N	H ≅ G/N	type
4. #14582646	C₂	semidirect
5. #14582645	C₂	semidirect
6. #14582644	C₂	semidirect
7. C₄₃×#332	C₂	semidirect
92. D₄₃	#332	direct (N × H)
99. #332	D₄₃	direct (N × H)
100. C₄₃	C₂×#332	semidirect

H ≅ G/N

type

4. #14582646

C₂

semidirect

5. #14582645

C₂

semidirect

6. #14582644

C₂

semidirect

7. C₄₃×#332

C₂

semidirect

92. D₄₃

#332

direct (N × H)

99. #332

D₄₃

direct (N × H)

100. C₄₃

C₂×#332

semidirect

Subgroups — #332×D₄₃ #19133237

Conjugacy classes of subgroups

Complements

Subgroups — #332×D43 #19133237

Conjugacy classes of subgroups

Complements

Subgroups — #332×D₄₃ #19133237