Group #19135692 — subgroups

Subgroups — #19135692

Order 5504.

390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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	C₂²×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#10621873	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063313	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063250	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13063247	C₂	1	1	yes	maximal, characteristic
6	#14582805	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
9	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
10	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₇₂	—	2	2	no	—
12	C₂×Dic₁₇₂	—	2	2	no	—
13	C₂×Dic₁₇₂	—	2	2	no	—
14	C₂×#10621873	—	2	2	no	—
15	C₂×#10621873	—	2	2	no	—
16	C₂×#10621873	—	2	2	no	—
17	#13063313	—	2	2	no	—
18	#13063313	—	2	2	no	—
19	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
21	#13063250	—	2	2	no	—
22	#13063247	—	2	2	no	—
23	C₄₃⋊#95	—	2	2	no	—
24	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
27	C₂³×D₄₃	—	2	1	no	—
28	C₂²×C₄×C₄₃	D₄	1	2	yes	—
29	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
30	C₂²×Dic₄₃	—	2	1	no	—
31	C₂²×Dic₄₃	—	2	1	no	—
32	C₂²×Dic₄₃	—	2	1	no	—
33	C₂×D₁₇₂	—	2	1	no	—
34	C₂×D₁₇₂	—	2	1	no	—
35	C₂×D₁₇₂	—	2	1	no	—
36	C₂×D₁₇₂	—	2	1	no	—
37	C₂×D₁₇₂	—	2	1	no	—
38	C₂×D₁₇₂	D₄	1	2	yes	—
39	C₂×Dic₈₆	—	2	1	no	—
40	C₂×Dic₈₆	—	2	1	no	—
41	C₂×Dic₈₆	—	2	1	no	—
42	C₂×Dic₈₆	—	2	1	no	—
43	C₂×Dic₈₆	—	2	1	no	—
44	C₂×Dic₈₆	—	2	1	no	—
45	C₂×Dic₈₆	—	2	1	no	—
46	C₂×Dic₈₆	—	2	1	no	—
47	C₂×Dic₈₆	—	2	1	no	—
48	C₂×Dic₈₆	—	2	1	no	—
49	C₂×Dic₈₆	D₄	1	2	yes	—
50	C₂×Dic₈₆	D₄	1	2	yes	—
51	C₂×C₈×C₄₃	—	2	1	no	—
52	C₂×C₈×C₄₃	—	2	1	no	—
53	C₂×C₈×C₄₃	—	2	1	no	—
54	C₂×C₈×C₄₃	—	2	1	no	—
55	C₂×C₈×C₄₃	D₄	1	2	yes	—
56	C₂×C₈×C₄₃	D₄	1	2	yes	—
57	C₄²×C₄₃	—	2	1	no	—
58	C₄²×C₄₃	—	2	1	no	—
59	(C₂×D₄₃)⋊C₄	—	2	8	no	—
60	C₄⋊Dic₄₃	—	2	1	no	—
61	C₄⋊Dic₄₃	—	2	1	no	—
62	Dic₁₇₂	—	2	8	no	—
63	#10621873	—	2	8	no	—
64	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×D₄₃	—	2	2	no	—
66	C₂²×D₄₃	—	4	1	no	—
67	C₂²×D₄₃	—	4	1	no	—
68	C₂²×D₄₃	—	4	2	no	—
69	C₂²×D₄₃	—	4	2	no	—
70	C₂×C₄×C₄₃	—	2	2	no	—
71	C₂×C₄×C₄₃	—	2	2	no	—
72	C₂×C₄×C₄₃	—	2	2	no	—
73	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
79	C₂×Dic₄₃	—	2	2	no	—
80	C₂×Dic₄₃	—	2	2	no	—
81	C₂×Dic₄₃	—	4	1	no	—
82	C₂×Dic₄₃	—	4	1	no	—
83	C₂×Dic₄₃	—	4	1	no	—
84	C₂×Dic₄₃	—	4	1	no	—
85	C₂×Dic₄₃	—	4	1	no	—
86	C₂×Dic₄₃	—	4	2	no	—
87	D₁₇₂	—	2	2	no	—
88	D₁₇₂	—	2	2	no	—
89	D₁₇₂	—	4	1	no	—
90	D₁₇₂	—	4	1	no	—
91	Dic₈₆	—	2	2	no	—
92	Dic₈₆	—	2	2	no	—
93	Dic₈₆	—	2	2	no	—
94	Dic₈₆	—	2	2	no	—
95	Dic₈₆	—	4	1	no	—
96	Dic₈₆	—	4	1	no	—
97	Dic₈₆	—	4	1	no	—
98	Dic₈₆	—	4	1	no	—
99	C₈×C₄₃	—	2	2	no	—
100	C₈×C₄₃	—	2	2	no	—
101	C₂²×C₄₃	#120	1	1	yes	characteristic
102	C₂²×C₄₃	#121	1	1	yes	characteristic
103	C₂²×C₄₃	#127	1	1	yes	characteristic
104	C₂²×C₄₃	#135	1	2	yes	—
105	C₂²×C₄₃	#137	1	2	yes	—
106	C₂×D₄₃	—	4	2	no	—
107	C₂×D₄₃	—	4	4	no	—
108	C₂×D₄₃	—	8	2	no	—
109	C₂×D₄₃	—	8	1	no	—
110	C₂×D₄₃	—	8	1	no	—
111	C₄×C₄₃	—	4	2	no	—
112	C₄×C₄₃	#120	1	1	yes	characteristic
113	C₄×C₄₃	#120	1	1	yes	characteristic
114	C₄×C₄₃	#121	1	1	yes	characteristic
115	C₄×C₄₃	#121	1	1	yes	characteristic
116	Dic₄₃	—	4	2	no	—
117	Dic₄₃	—	4	2	no	—
118	Dic₄₃	—	8	1	no	—
119	#2015	—	43	1	no	maximal, Sylow
120	C₂×C₄₃	#392	1	1	yes	characteristic
121	C₂×C₄₃	#452	1	2	yes	—
122	C₂×C₄₃	#464	1	2	yes	—
123	C₂×C₄₃	#495	1	1	yes	characteristic
124	C₂×C₄₃	#497	1	1	yes	characteristic
125	D₄₃	—	8	2	no	—
126	C₂²×Q₁₆	—	43	1	no	—
127	C₂²×SD₁₆	—	43	1	no	—
128	C₂×#124	—	43	1	no	—
129	C₂×#103	—	43	1	no	—
130	C₂×#102	—	43	1	no	—
131	#391	—	43	1	no	—
132	#336	D₄₃	1	1	yes	characteristic, complemented
133	C₄₃	#2015	1	1	yes	characteristic, complemented, Sylow
134	C₂²×Q₈	—	43	1	no	—
135	C₂²×Q₈	—	43	1	no	—
136	C₂²×D₄	—	43	1	no	—
137	C₂×Q₁₆	—	86	2	no	—
138	C₂×Q₁₆	—	86	2	no	—
139	C₂×Q₁₆	—	86	2	no	—
140	C₂×SD₁₆	—	86	2	no	—
141	C₂×SD₁₆	—	86	2	no	—
142	C₂×SD₁₆	—	86	2	no	—
143	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
144	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
145	#124	—	86	2	no	—
146	#124	—	86	2	no	—
147	C₂×C₄⋊C₄	—	43	1	no	—
148	C₂×C₂²⋊C₄	—	86	2	no	—
149	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
150	#103	—	86	2	no	—
151	#102	—	86	2	no	—
152	#95	—	86	2	no	—
153	C₂⁴	—	86	1	no	—
154	C₂×Q₈	—	43	2	no	—
155	C₂×Q₈	—	43	2	no	—
156	C₂×Q₈	—	86	1	no	—
157	C₂×Q₈	—	86	1	no	—
158	C₂×Q₈	—	86	1	no	—
159	C₂×Q₈	—	86	1	no	—
160	C₂×Q₈	—	86	1	no	—
161	C₂×Q₈	—	86	1	no	—
162	C₂×Q₈	—	86	1	no	—
163	C₂×Q₈	—	86	1	no	—
164	C₂×Q₈	—	86	1	no	—
165	C₂×Q₈	—	86	1	no	—
166	C₂×D₄	—	43	2	no	—
167	C₂×D₄	—	86	1	no	—
168	C₂×D₄	—	86	1	no	—
169	C₂×D₄	—	86	1	no	—
170	C₂×D₄	—	86	1	no	—
171	C₂×D₄	—	86	1	no	—
172	C₂²×C₄	—	86	1	no	—
173	C₂²×C₄	—	86	1	no	—
174	C₂²×C₄	—	86	1	no	—
175	C₂²×C₄	D₁₇₂	1	2	yes	—
176	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
177	Q₁₆	—	86	8	no	—
178	SD₁₆	—	86	8	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	2	1	no	—
183	C₂×C₈	D₁₇₂	1	2	yes	—
184	C₂×C₈	D₁₇₂	1	2	yes	—
185	C₄⋊C₄	—	86	1	no	—
186	C₄⋊C₄	—	86	1	no	—
187	C₂²⋊C₄	—	86	8	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	2	1	no	—
190	C₂³	—	86	2	no	—
191	C₂³	—	172	1	no	—
192	C₂³	—	172	1	no	—
193	C₂³	—	172	2	no	—
194	C₂³	—	172	2	no	—
195	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
196	Q₈	—	86	2	no	—
197	Q₈	—	86	2	no	—
198	Q₈	—	86	2	no	—
199	Q₈	—	86	2	no	—
200	Q₈	—	172	1	no	—
201	Q₈	—	172	1	no	—
202	Q₈	—	172	1	no	—
203	Q₈	—	172	1	no	—
204	D₄	—	86	2	no	—
205	D₄	—	86	2	no	—
206	D₄	—	172	1	no	—
207	D₄	—	172	1	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	86	2	no	—
212	C₂×C₄	—	86	2	no	—
213	C₂×C₄	—	172	1	no	—
214	C₂×C₄	—	172	2	no	—
215	C₂×C₄	—	172	1	no	—
216	C₂×C₄	—	172	1	no	—
217	C₂×C₄	—	172	1	no	—
218	C₂×C₄	—	172	1	no	—
219	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
220	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
221	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
222	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
223	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
224	C₂×C₄	#10621902	1	1	yes	characteristic
225	C₈	—	2	2	no	—
226	C₈	—	2	2	no	—
227	C₂²	—	344	2	no	—
228	C₂²	—	344	1	no	—
229	C₂²	—	344	1	no	—
230	C₂²	—	172	4	no	—
231	C₂²	—	172	2	no	—
232	C₂²	#13063295	1	1	yes	characteristic
233	C₂²	#13063300	1	1	yes	characteristic
234	C₂²	#13063322	1	1	yes	characteristic
235	C₂²	#13063347	1	2	yes	—
236	C₂²	#13063358	1	2	yes	—
237	C₄	—	4	2	no	—
238	C₄	—	344	1	no	—
239	C₄	—	172	2	no	—
240	C₄	—	172	2	no	—
241	C₄	#13063295	1	1	yes	characteristic
242	C₄	#13063295	1	1	yes	characteristic
243	C₄	#13063300	1	1	yes	characteristic
244	C₄	#13063300	1	1	yes	characteristic
245	C₂	—	344	2	no	—
246	C₂	#14582809	1	1	yes	characteristic
247	C₂	#14583063	1	2	yes	—
248	C₂	#14583122	1	2	yes	—
249	C₂	#14583283	1	1	yes	characteristic
250	C₂	#14583293	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₇₂

C₂

yes

maximal, characteristic, complemented

C₂²×#10621873

C₂

yes

maximal, characteristic

C₂×#13063313

C₂

yes

maximal, characteristic

C₂×#13063250

C₂

yes

maximal, characteristic, complemented

C₂×#13063247

C₂

yes

maximal, characteristic

#14582805

C₂

yes

maximal, characteristic, complemented

C₄₃×#336

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×D₁₇₂

C₂²

yes

characteristic

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

—

—

—

—

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

—

#13063250

—

#13063247

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

D₄

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

—

C₂×Dic₈₆

D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

#10621873

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

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×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

100

C₈×C₄₃

—

101

C₂²×C₄₃

#120

yes

characteristic

102

C₂²×C₄₃

#121

yes

characteristic

103

C₂²×C₄₃

#127

yes

characteristic

104

C₂²×C₄₃

#135

yes

—

105

C₂²×C₄₃

#137

yes

—

106

C₂×D₄₃

—

107

C₂×D₄₃

—

108

C₂×D₄₃

—

109

C₂×D₄₃

—

110

C₂×D₄₃

—

111

C₄×C₄₃

—

112

C₄×C₄₃

#120

yes

characteristic

113

C₄×C₄₃

#120

yes

characteristic

114

C₄×C₄₃

#121

yes

characteristic

115

C₄×C₄₃

#121

yes

characteristic

116

Dic₄₃

—

117

Dic₄₃

—

118

Dic₄₃

—

119

#2015

—

maximal, Sylow

120

C₂×C₄₃

#392

yes

characteristic

121

C₂×C₄₃

#452

yes

—

122

C₂×C₄₃

#464

yes

—

123

C₂×C₄₃

#495

yes

characteristic

124

C₂×C₄₃

#497

yes

characteristic

125

D₄₃

—

126

C₂²×Q₁₆

—

127

C₂²×SD₁₆

—

128

C₂×#124

—

129

C₂×#103

—

130

C₂×#102

—

131

#391

—

132

#336

D₄₃

yes

characteristic, complemented

133

C₄₃

#2015

yes

characteristic, complemented, Sylow

134

C₂²×Q₈

—

135

C₂²×Q₈

—

136

C₂²×D₄

—

137

C₂×Q₁₆

—

138

C₂×Q₁₆

—

139

C₂×Q₁₆

—

140

C₂×SD₁₆

—

141

C₂×SD₁₆

—

142

C₂×SD₁₆

—

143

C₂²×C₈

C₂×D₄₃

yes

characteristic

144

C₂²×C₈

C₂×D₄₃

yes

characteristic

145

#124

—

146

#124

—

147

C₂×C₄⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

C₂×C₄²

C₂×D₄₃

yes

characteristic

150

#103

—

151

#102

—

152

#95

—

153

C₂⁴

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

D₁₇₂

yes

—

176

C₂²×C₄

C₂²×D₄₃

yes

characteristic

177

Q₁₆

—

178

SD₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

D₁₇₂

yes

—

184

C₂×C₈

D₁₇₂

yes

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₂³

—

191

C₂³

—

172

—

192

C₂³

—

172

—

193

C₂³

—

172

—

194

C₂³

—

172

—

195

C₂³

C₂×D₁₇₂

yes

characteristic

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

Q₈

—

172

—

201

Q₈

—

172

—

202

Q₈

—

172

—

203

Q₈

—

172

—

204

D₄

—

205

D₄

—

206

D₄

—

172

—

207

D₄

—

172

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

172

—

214

C₂×C₄

—

172

—

215

C₂×C₄

—

172

—

216

C₂×C₄

—

172

—

217

C₂×C₄

—

172

—

218

C₂×C₄

—

172

—

219

C₂×C₄

C₂×D₁₇₂

yes

characteristic

220

C₂×C₄

C₂×D₁₇₂

yes

characteristic

221

C₂×C₄

D₄×D₄₃

yes

characteristic

222

C₂×C₄

D₄×D₄₃

yes

characteristic

223

C₂×C₄

D₄×D₄₃

yes

characteristic

224

C₂×C₄

#10621902

yes

characteristic

225

C₈

—

226

C₈

—

227

C₂²

—

344

—

228

C₂²

—

344

—

229

C₂²

—

344

—

230

C₂²

—

172

—

231

C₂²

—

172

—

232

C₂²

#13063295

yes

characteristic

233

C₂²

#13063300

yes

characteristic

234

C₂²

#13063322

yes

characteristic

235

C₂²

#13063347

yes

—

236

C₂²

#13063358

yes

—

237

C₄

—

238

C₄

—

344

—

239

C₄

—

172

—

240

C₄

—

172

—

241

C₄

#13063295

yes

characteristic

242

C₄

#13063295

yes

characteristic

243

C₄

#13063300

yes

characteristic

244

C₄

#13063300

yes

characteristic

245

C₂

—

344

—

246

C₂

#14582809

yes

characteristic

247

C₂

#14583063

yes

—

248

C₂

#14583122

yes

—

249

C₂

#14583283

yes

characteristic

250

C₂

#14583293

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#336	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#336	D₄₃
hypocenter	C₄₃	#2015
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#336

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
1. C₂²×Dic₁₇₂	C₂	semidirect
4. C₂×#13063250	C₂	semidirect
6. #14582805	C₂	semidirect
7. C₄₃×#336	C₂	semidirect
132. #336	D₄₃	semidirect
133. C₄₃	#2015	semidirect

H ≅ G/N

type

1. C₂²×Dic₁₇₂

C₂

semidirect

4. C₂×#13063250

C₂

semidirect

6. #14582805

C₂

semidirect

7. C₄₃×#336

C₂

semidirect

132. #336

D₄₃

semidirect

133. C₄₃

#2015

semidirect

Subgroups — #19135692

Conjugacy classes of subgroups

Complements