Group #19133703 — subgroups

Subgroups — #19133703

Order 5504.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14583619	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583245	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583096	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582646	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582629	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#459	C₂	1	1	yes	maximal, characteristic
8	C₂×#10621883	—	2	1	no	—
9	#13063325	C₂²	1	1	yes	characteristic
10	#13063318	—	2	2	no	—
11	#13063312	—	2	1	no	—
12	#13063304	—	2	1	no	—
13	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
14	#13063290	—	2	1	no	—
15	#13063284	—	2	1	no	—
16	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	#13063246	—	2	1	no	—
18	#13063246	—	2	2	no	—
19	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×D₈×C₄₃	—	2	1	no	—
21	#127×C₄₃	C₂²	1	1	yes	characteristic
22	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	#102×C₄₃	—	2	1	no	—
25	C₂×D₄×C₄₃	—	2	1	no	—
26	C₂×D₄×C₄₃	—	2	1	no	—
27	C₂×D₄×C₄₃	—	2	1	no	—
28	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	—	2	1	no	—
30	C₂×Dic₈₆	—	2	1	no	—
31	C₂×Dic₈₆	D₄	1	1	yes	characteristic
32	D₈×C₄₃	—	4	2	no	—
33	C₂×C₈×C₄₃	—	2	1	no	—
34	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
35	C₂²⋊C₄×C₄₃	—	2	1	no	—
36	C₄²×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²⋊Dic₄₃	—	2	2	no	—
38	C₂²⋊Dic₄₃	—	2	2	no	—
39	#10621883	—	4	2	no	—
40	C₄⋊Dic₄₃	—	2	1	no	—
41	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
42	C₄⋊Dic₄₃	D₄	1	2	yes	—
43	Dic₄₃⋊C₄	—	2	2	no	—
44	Dic₄₃⋊C₄	—	2	1	no	—
45	C₄×Dic₄₃	—	2	2	no	—
46	C₄×Dic₄₃	—	2	1	no	—
47	C₂×C₄₃⋊C₈	—	2	1	no	—
48	C₂×C₄₃⋊C₈	—	2	1	no	—
49	C₂³×C₄₃	—	2	1	no	—
50	C₂³×C₄₃	—	4	1	no	—
51	D₄×C₄₃	—	2	1	no	—
52	D₄×C₄₃	—	2	1	no	—
53	D₄×C₄₃	—	4	2	no	—
54	D₄×C₄₃	—	4	1	no	—
55	D₄×C₄₃	—	4	1	no	—
56	D₄×C₄₃	—	4	1	no	—
57	D₄×C₄₃	—	4	1	no	—
58	C₂×C₄×C₄₃	—	2	1	no	—
59	C₂×C₄×C₄₃	—	4	1	no	—
60	C₂×C₄×C₄₃	—	4	1	no	—
61	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
64	C₂×Dic₄₃	—	2	1	no	—
65	C₂×Dic₄₃	—	2	1	no	—
66	C₂×Dic₄₃	—	2	2	no	—
67	Dic₈₆	—	2	1	no	—
68	Dic₈₆	—	2	1	no	—
69	Dic₈₆	—	4	1	no	—
70	Dic₈₆	—	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	1	no	—
75	C₂²×C₄₃	—	4	1	no	—
76	C₂²×C₄₃	—	4	1	no	—
77	C₂²×C₄₃	—	8	1	no	—
78	C₂²×C₄₃	—	8	1	no	—
79	C₂²×C₄₃	—	8	1	no	—
80	C₂²×C₄₃	#120	1	1	yes	characteristic
81	C₄×C₄₃	—	2	1	no	—
82	C₄×C₄₃	—	4	1	no	—
83	C₄×C₄₃	#135	1	1	yes	characteristic
84	C₄×C₄₃	#135	1	1	yes	characteristic
85	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
87	Dic₄₃	—	4	1	no	—
88	Dic₄₃	—	4	2	no	—
89	Dic₄₃	—	4	1	no	—
90	#1628	—	43	1	no	maximal, Sylow
91	C₂×C₄₃	—	8	1	no	—
92	C₂×C₄₃	—	16	1	no	—
93	C₂×C₄₃	#449	1	1	yes	characteristic
94	C₂×C₄₃	#449	1	1	yes	characteristic
95	C₂×C₄₃	#454	1	1	yes	characteristic
96	#556	—	43	1	no	—
97	#486	—	43	1	no	—
98	#460	—	43	1	no	—
99	#459	D₄₃	1	1	yes	characteristic
100	#332	—	43	1	no	—
101	Q₈⋊C₈	—	43	1	no	—
102	D₄⋊C₈	—	43	1	no	—
103	C₄₃	#1628	1	1	yes	characteristic, complemented, Sylow
104	C₂×SD₁₆	—	86	1	no	—
105	C₂×D₈	—	2	1	no	—
106	C₄⋊Q₈	—	43	1	no	—
107	#127	C₂×D₄₃	1	1	yes	characteristic
108	#126	—	86	2	no	—
109	#124	—	86	1	no	—
110	C₂²⋊Q₈	—	86	1	no	—
111	C₄×Q₈	—	43	1	no	—
112	C₄×Q₈	—	86	1	no	—
113	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
114	#117	—	86	1	no	—
115	C₄⋊C₈	—	43	1	no	—
116	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
117	#102	—	2	1	no	—
118	#102	—	86	1	no	—
119	#102	—	86	2	no	—
120	C₄×C₈	—	43	1	no	—
121	C₂×Q₈	—	43	1	no	—
122	C₂×Q₈	—	86	1	no	—
123	C₂×D₄	—	2	1	no	—
124	C₂×D₄	—	2	1	no	—
125	C₂×D₄	—	2	1	no	—
126	C₂×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
127	C₂²×C₄	—	2	1	no	—
128	SD₁₆	—	172	2	no	—
129	D₈	—	4	2	no	—
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	—	86	1	no	—
132	C₂×C₈	—	86	1	no	—
133	C₄⋊C₄	—	43	1	no	—
134	C₄⋊C₄	—	43	2	no	—
135	C₄⋊C₄	—	86	2	no	—
136	C₄⋊C₄	—	86	1	no	—
137	C₄⋊C₄	—	86	1	no	—
138	C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
139	C₂²⋊C₄	—	2	1	no	—
140	C₂²⋊C₄	—	86	2	no	—
141	C₂²⋊C₄	—	86	2	no	—
142	C₄²	—	86	2	no	—
143	C₄²	—	86	1	no	—
144	C₄²	C₂²×D₄₃	1	1	yes	characteristic
145	C₂³	—	2	1	no	—
146	C₂³	—	4	1	no	—
147	Q₈	—	86	1	no	—
148	Q₈	—	86	1	no	—
149	Q₈	—	172	1	no	—
150	Q₈	—	172	1	no	—
151	D₄	—	2	1	no	—
152	D₄	—	2	1	no	—
153	D₄	—	4	2	no	—
154	D₄	—	4	1	no	—
155	D₄	—	4	1	no	—
156	D₄	—	4	1	no	—
157	D₄	—	4	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	4	1	no	—
160	C₂×C₄	—	4	1	no	—
161	C₂×C₄	—	86	1	no	—
162	C₂×C₄	—	86	2	no	—
163	C₂×C₄	—	86	1	no	—
164	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
165	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
166	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
167	C₈	—	4	1	no	—
168	C₈	—	172	1	no	—
169	C₈	—	172	1	no	—
170	C₂²	—	4	1	no	—
171	C₂²	—	4	1	no	—
172	C₂²	—	4	1	no	—
173	C₂²	—	8	1	no	—
174	C₂²	—	8	1	no	—
175	C₂²	—	8	1	no	—
176	C₂²	#13063293	1	1	yes	characteristic
177	C₄	—	2	1	no	—
178	C₄	—	4	1	no	—
179	C₄	—	172	1	no	—
180	C₄	—	172	2	no	—
181	C₄	—	172	1	no	—
182	C₄	#13063344	1	1	yes	characteristic
183	C₄	#13063345	1	1	yes	characteristic
184	C₄	#13063349	1	1	yes	characteristic
185	C₄	#13063351	1	1	yes	characteristic
186	C₂	—	8	1	no	—
187	C₂	—	16	1	no	—
188	C₂	#14583041	1	1	yes	characteristic
189	C₂	#14583042	1	1	yes	characteristic
190	C₂	#14583070	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583619

C₂

yes

maximal, characteristic, complemented

#14583245

C₂

yes

maximal, characteristic, complemented

#14583096

C₂

yes

maximal, characteristic, complemented

#14582646

C₂

yes

maximal, characteristic, complemented

#14582629

C₂

yes

maximal, characteristic, complemented

D₄⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic, complemented

C₄₃×#459

C₂

yes

maximal, characteristic

C₂×#10621883

—

#13063325

C₂²

yes

—

—

—

C₄×Dic₈₆

C₂²

yes

characteristic

#13063290

—

#13063284

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

#13063246

—

#13063246

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×D₈×C₄₃

—

#127×C₄₃

C₂²

yes

characteristic

C₄×D₄×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

#102×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

characteristic

D₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

#10621883

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

C₄⋊Dic₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#120

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#1628

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

D₄₃

yes

characteristic

100

#332

—

101

Q₈⋊C₈

—

102

D₄⋊C₈

—

103

C₄₃

#1628

yes

characteristic, complemented, Sylow

104

C₂×SD₁₆

—

105

C₂×D₈

—

106

C₄⋊Q₈

—

107

#127

C₂×D₄₃

yes

characteristic

108

#126

—

109

#124

—

110

C₂²⋊Q₈

—

111

C₄×Q₈

—

112

C₄×Q₈

—

113

C₄×D₄

C₂×D₄₃

yes

characteristic

114

#117

—

115

C₄⋊C₈

—

116

C₄⋊C₈

C₂×D₄₃

yes

characteristic

117

#102

—

118

#102

—

119

#102

—

120

C₄×C₈

—

121

C₂×Q₈

—

122

C₂×Q₈

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

C₂²⋊D₄₃

yes

characteristic

127

C₂²×C₄

—

128

SD₁₆

—

172

—

129

D₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

C₂²⋊D₄₃

yes

characteristic

139

C₂²⋊C₄

—

140

C₂²⋊C₄

—

141

C₂²⋊C₄

—

142

C₄²

—

143

C₄²

—

144

C₄²

C₂²×D₄₃

yes

characteristic

145

C₂³

—

146

C₂³

—

147

Q₈

—

148

Q₈

—

149

Q₈

—

172

—

150

Q₈

—

172

—

151

D₄

—

152

D₄

—

153

D₄

—

154

D₄

—

155

D₄

—

156

D₄

—

157

D₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

D₄×D₄₃

yes

characteristic

165

C₂×C₄

D₄×D₄₃

yes

characteristic

166

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

167

C₈

—

168

C₈

—

172

—

169

C₈

—

172

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

—

176

C₂²

#13063293

yes

characteristic

177

C₄

—

178

C₄

—

179

C₄

—

172

—

180

C₄

—

172

—

181

C₄

—

172

—

182

C₄

#13063344

yes

characteristic

183

C₄

#13063345

yes

characteristic

184

C₄

#13063349

yes

characteristic

185

C₄

#13063351

yes

characteristic

186

C₂

—

187

C₂

—

188

C₂

#14583041

yes

characteristic

189

C₂

#14583042

yes

characteristic

190

C₂

#14583070

yes

characteristic

	subgroup	G/H
center	C₂²	#13063293
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#459	C₂
socle	C₂²×C₄₃	#120
hypercenter	#459	D₄₃
hypocenter	C₄₃	#1628
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #459

subgroup

G/H

center

C₂²

#13063293

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#459

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #459

N	H ≅ G/N	type
1. #14583619	C₂	semidirect
2. #14583245	C₂	semidirect
3. #14583096	C₂	semidirect
4. #14582646	C₂	semidirect
5. #14582629	C₂	semidirect
6. D₄⋊(C₄₃⋊C₈)	C₂	semidirect
103. C₄₃	#1628	semidirect

H ≅ G/N

type

1. #14583619

C₂

semidirect

2. #14583245

C₂

semidirect

3. #14583096

C₂

semidirect

4. #14582646

C₂

semidirect

5. #14582629

C₂

semidirect

6. D₄⋊(C₄₃⋊C₈)

C₂

semidirect

103. C₄₃

#1628

semidirect

Subgroups — #19133703

Conjugacy classes of subgroups

Complements