Group #19134937 — subgroups

Subgroups — #19134937

Order 5504.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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
2	C₂×#13063290	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063248	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063248	C₂	1	1	yes	maximal, characteristic
5	#14582804	C₂	1	1	yes	maximal, characteristic
6	#14582653	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#340	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
9	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₇₂	—	2	2	no	—
11	C₂×Dic₁₇₂	—	2	2	no	—
12	C₂×Dic₁₇₂	C₄	1	4	yes	complemented
13	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#13063290	—	2	2	no	—
15	#13063290	—	2	2	no	—
16	C₂×Dic₄₃⋊C₄	—	2	1	no	—
17	C₂×C₄×Dic₄₃	—	2	1	no	—
18	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
19	#13063248	—	2	2	no	—
20	#13063248	—	2	2	no	—
21	C₄₃⋊#95	—	2	1	no	—
22	C₄₃⋊#95	—	2	1	no	—
23	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	—	2	1	no	—
27	C₂²×C₄×C₄₃	—	2	1	no	—
28	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
29	C₂²×Dic₄₃	—	2	1	no	—
30	C₂²×Dic₄₃	—	2	1	no	—
31	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
32	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
33	C₂×Dic₈₆	—	2	1	no	—
34	C₂×Dic₈₆	—	2	1	no	—
35	C₂×Dic₈₆	—	2	1	no	—
36	C₂×Dic₈₆	—	2	1	no	—
37	C₂×Dic₈₆	—	2	1	no	—
38	C₂×Dic₈₆	—	2	1	no	—
39	C₂×Dic₈₆	—	2	1	no	—
40	C₂×Dic₈₆	—	2	1	no	—
41	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
42	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
43	C₂×Dic₈₆	D₄	1	2	yes	—
44	C₂×Dic₈₆	D₄	1	2	yes	—
45	C₂×C₈×C₄₃	—	2	1	no	—
46	C₂×C₈×C₄₃	—	2	1	no	—
47	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
48	C₄⋊C₄×C₄₃	—	2	1	no	—
49	C₄⋊C₄×C₄₃	—	2	1	no	—
50	C₄⋊C₄×C₄₃	—	2	1	no	—
51	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
52	Dic₄₃⋊C₄	—	2	4	no	—
53	C₄×Dic₄₃	—	2	4	no	—
54	C₄×Dic₄₃	—	2	1	no	—
55	C₄×Dic₄₃	—	2	1	no	—
56	C₂×C₄₃⋊C₈	—	2	1	no	—
57	C₂×C₄₃⋊C₈	—	2	1	no	—
58	C₂×C₄₃⋊C₈	—	2	1	no	—
59	Dic₁₇₂	—	2	8	no	—
60	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	—	4	1	no	—
63	C₂×C₄×C₄₃	—	4	1	no	—
64	C₂×C₄×C₄₃	—	4	1	no	—
65	C₂×C₄×C₄₃	—	4	1	no	—
66	C₂×C₄×C₄₃	—	4	1	no	—
67	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
72	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
73	C₂×Dic₄₃	—	2	2	no	—
74	C₂×Dic₄₃	—	2	1	no	—
75	C₂×Dic₄₃	—	2	2	no	—
76	C₂×Dic₄₃	—	2	2	no	—
77	C₂×Dic₄₃	—	2	1	no	—
78	C₂×Dic₄₃	—	2	2	no	—
79	C₂×Dic₄₃	—	2	1	no	—
80	C₂×Dic₄₃	—	2	1	no	—
81	C₂×Dic₄₃	—	2	1	no	—
82	C₂×Dic₄₃	—	4	1	no	—
83	C₂×Dic₄₃	—	4	1	no	—
84	C₂×Dic₄₃	Q₁₆	1	2	yes	complemented
85	Dic₈₆	—	2	2	no	—
86	Dic₈₆	—	2	2	no	—
87	Dic₈₆	—	2	2	no	—
88	Dic₈₆	—	2	2	no	—
89	Dic₈₆	—	2	2	no	—
90	Dic₈₆	—	4	1	no	—
91	Dic₈₆	—	4	1	no	—
92	Dic₈₆	C₂²⋊C₄	1	4	yes	—
93	C₈×C₄₃	—	2	2	no	—
94	C₄₃⋊C₈	—	4	1	no	—
95	C₂²×C₄₃	C₄×D₄	1	1	yes	characteristic
96	C₂²×C₄₃	#120	1	1	yes	characteristic
97	C₂²×C₄₃	#121	1	1	yes	characteristic
98	C₂²×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
99	C₂²×C₄₃	#135	1	1	yes	characteristic
100	C₂²×C₄₃	#137	1	1	yes	characteristic
101	C₂²×C₄₃	#137	1	1	yes	characteristic
102	C₄×C₄₃	—	4	2	no	—
103	C₄×C₄₃	—	8	1	no	—
104	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
106	C₄×C₄₃	#121	1	1	yes	characteristic
107	C₄×C₄₃	#123	1	1	yes	characteristic
108	Dic₄₃	—	2	4	no	—
109	Dic₄₃	—	2	2	no	—
110	Dic₄₃	—	4	2	no	—
111	Dic₄₃	—	4	1	no	—
112	#1878	—	43	1	no	maximal, Sylow
113	C₂×C₄₃	#386	1	1	yes	characteristic
114	C₂×C₄₃	C₄×Q₁₆	1	1	yes	characteristic
115	C₂×C₄₃	#441	1	1	yes	characteristic
116	C₂×C₄₃	#451	1	1	yes	characteristic
117	C₂×C₄₃	#452	1	1	yes	characteristic
118	C₂×C₄₃	#462	1	1	yes	characteristic
119	C₂×C₄₃	#464	1	1	yes	characteristic
120	C₂²×Q₁₆	—	43	1	no	—
121	C₂×C₄×Q₈	—	43	1	no	—
122	C₂×#103	—	43	1	no	—
123	C₂×#103	—	43	1	no	—
124	#391	—	43	1	no	—
125	#340	D₄₃	1	1	yes	characteristic
126	#336	—	43	1	no	—
127	C₄₃	#1878	1	1	yes	characteristic, complemented, Sylow
128	C₂²×Q₈	—	43	1	no	—
129	C₂²×Q₈	—	43	1	no	—
130	C₂×Q₁₆	—	43	4	no	—
131	C₂×Q₁₆	—	86	2	no	—
132	C₂×Q₁₆	—	86	2	no	—
133	C₂²×C₈	—	43	1	no	—
134	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
135	C₄×Q₈	—	86	2	no	—
136	C₄×Q₈	—	86	2	no	—
137	C₂×C₄⋊C₄	—	86	1	no	—
138	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
139	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
140	C₂×C₄²	—	43	1	no	—
141	C₂×C₄²	—	86	1	no	—
142	#103	—	86	2	no	—
143	#103	—	86	2	no	—
144	#95	—	86	1	no	—
145	#95	—	86	1	no	—
146	C₂×Q₈	—	43	2	no	—
147	C₂×Q₈	—	43	2	no	—
148	C₂×Q₈	—	43	2	no	—
149	C₂×Q₈	—	43	2	no	—
150	C₂×Q₈	—	86	1	no	—
151	C₂×Q₈	—	86	1	no	—
152	C₂×Q₈	—	86	1	no	—
153	C₂×Q₈	—	86	1	no	—
154	C₂×Q₈	—	86	1	no	—
155	C₂×Q₈	—	86	1	no	—
156	C₂×Q₈	—	86	1	no	—
157	C₂×Q₈	—	86	1	no	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	43	1	no	—
161	C₂²×C₄	—	43	1	no	—
162	C₂²×C₄	—	86	1	no	—
163	C₂²×C₄	—	86	1	no	—
164	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
165	Q₁₆	—	86	8	no	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	2	1	no	—
168	C₂×C₈	—	86	1	no	—
169	C₂×C₈	—	86	1	no	—
170	C₂×C₈	—	86	1	no	—
171	C₂×C₈	C₄×D₄₃	1	2	yes	—
172	C₄⋊C₄	—	2	1	no	—
173	C₄⋊C₄	—	2	1	no	—
174	C₄⋊C₄	—	2	1	no	—
175	C₄⋊C₄	—	86	4	no	—
176	C₄⋊C₄	D₁₇₂	1	2	yes	—
177	C₄²	—	86	4	no	—
178	C₄²	—	86	1	no	—
179	C₄²	—	86	1	no	—
180	C₂³	D₄×D₄₃	1	1	yes	characteristic
181	Q₈	—	43	4	no	—
182	Q₈	—	86	2	no	—
183	Q₈	—	86	2	no	—
184	Q₈	—	86	2	no	—
185	Q₈	—	86	2	no	—
186	Q₈	—	86	2	no	—
187	Q₈	—	172	1	no	—
188	Q₈	—	172	1	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	43	2	no	—
196	C₂×C₄	—	86	2	no	—
197	C₂×C₄	—	86	1	no	—
198	C₂×C₄	—	86	2	no	—
199	C₂×C₄	—	86	2	no	—
200	C₂×C₄	—	86	1	no	—
201	C₂×C₄	—	86	2	no	—
202	C₂×C₄	—	86	1	no	—
203	C₂×C₄	—	86	1	no	—
204	C₂×C₄	—	86	1	no	—
205	C₂×C₄	—	172	1	no	—
206	C₂×C₄	—	172	1	no	—
207	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
208	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
209	C₂×C₄	#10621898	1	1	yes	characteristic
210	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
211	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
212	C₂×C₄	#10621902	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	—	172	1	no	—
215	C₂²	#13063287	1	1	yes	characteristic
216	C₂²	#13063295	1	1	yes	characteristic
217	C₂²	#13063298	1	1	yes	characteristic
218	C₂²	Q₁₆×D₄₃	1	1	yes	characteristic
219	C₂²	#13063344	1	1	yes	characteristic
220	C₂²	#13063354	1	1	yes	characteristic
221	C₂²	#13063354	1	1	yes	characteristic
222	C₄	—	4	2	no	—
223	C₄	—	8	1	no	—
224	C₄	—	86	2	no	—
225	C₄	—	86	4	no	—
226	C₄	—	172	1	no	—
227	C₄	—	172	2	no	—
228	C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
229	C₄	C₄×D₁₇₂	1	1	yes	characteristic
230	C₄	#13063300	1	1	yes	characteristic
231	C₄	#13063310	1	1	yes	characteristic
232	C₂	#14582777	1	1	yes	characteristic
233	C₂	#14582993	1	1	yes	characteristic
234	C₂	#14583005	1	1	yes	characteristic
235	C₂	#14583056	1	1	yes	characteristic
236	C₂	#14583062	1	1	yes	characteristic
237	C₂	#14583108	1	1	yes	characteristic
238	C₂	#14583120	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₇₂

C₂

yes

maximal, characteristic

C₂×#13063290

C₂

yes

maximal, characteristic

C₂×#13063248

C₂

yes

maximal, characteristic

C₂×#13063248

C₂

yes

maximal, characteristic

#14582804

C₂

yes

maximal, characteristic

#14582653

C₂

yes

maximal, characteristic

C₄₃×#340

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₄

yes

complemented

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

#13063290

—

#13063290

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063248

—

#13063248

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×Dic₈₆

D₄

yes

—

C₂×Dic₈₆

D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×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×C₄×C₄₃

C₂×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

Q₁₆

yes

complemented

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

C₂²⋊C₄

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₄×D₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×Q₁₆

yes

characteristic

C₂²×C₄₃

#135

yes

characteristic

100

C₂²×C₄₃

#137

yes

characteristic

101

C₂²×C₄₃

#137

yes

characteristic

102

C₄×C₄₃

—

103

C₄×C₄₃

—

104

C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

105

C₄×C₄₃

C₄×D₄

yes

characteristic

106

C₄×C₄₃

#121

yes

characteristic

107

C₄×C₄₃

#123

yes

characteristic

108

Dic₄₃

—

109

Dic₄₃

—

110

Dic₄₃

—

111

Dic₄₃

—

112

#1878

—

maximal, Sylow

113

C₂×C₄₃

#386

yes

characteristic

114

C₂×C₄₃

C₄×Q₁₆

yes

characteristic

115

C₂×C₄₃

#441

yes

characteristic

116

C₂×C₄₃

#451

yes

characteristic

117

C₂×C₄₃

#452

yes

characteristic

118

C₂×C₄₃

#462

yes

characteristic

119

C₂×C₄₃

#464

yes

characteristic

120

C₂²×Q₁₆

—

121

C₂×C₄×Q₈

—

122

C₂×#103

—

123

C₂×#103

—

124

#391

—

125

#340

D₄₃

yes

characteristic

126

#336

—

127

C₄₃

#1878

yes

characteristic, complemented, Sylow

128

C₂²×Q₈

—

129

C₂²×Q₈

—

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂²×C₈

—

134

C₂²×C₈

C₂×D₄₃

yes

characteristic

135

C₄×Q₈

—

136

C₄×Q₈

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

139

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

140

C₂×C₄²

—

141

C₂×C₄²

—

142

#103

—

143

#103

—

144

#95

—

145

#95

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂²×D₄₃

yes

characteristic

165

Q₁₆

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

C₄×D₄₃

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

D₁₇₂

yes

—

177

C₄²

—

178

C₄²

—

179

C₄²

—

180

C₂³

D₄×D₄₃

yes

characteristic

181

Q₈

—

182

Q₈

—

183

Q₈

—

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

172

—

188

Q₈

—

172

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

172

—

206

C₂×C₄

—

172

—

207

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

208

C₂×C₄

C₂×D₁₇₂

yes

characteristic

209

C₂×C₄

#10621898

yes

characteristic

210

C₂×C₄

D₄×D₄₃

yes

characteristic

211

C₂×C₄

D₄×D₄₃

yes

characteristic

212

C₂×C₄

#10621902

yes

characteristic

213

C₈

—

214

C₈

—

172

—

215

C₂²

#13063287

yes

characteristic

216

C₂²

#13063295

yes

characteristic

217

C₂²

#13063298

yes

characteristic

218

C₂²

Q₁₆×D₄₃

yes

characteristic

219

C₂²

#13063344

yes

characteristic

220

C₂²

#13063354

yes

characteristic

221

C₂²

#13063354

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

172

—

227

C₄

—

172

—

228

C₄

C₂²⋊C₄×D₄₃

yes

characteristic

229

C₄

C₄×D₁₇₂

yes

characteristic

230

C₄

#13063300

yes

characteristic

231

C₄

#13063310

yes

characteristic

232

C₂

#14582777

yes

characteristic

233

C₂

#14582993

yes

characteristic

234

C₂

#14583005

yes

characteristic

235

C₂

#14583056

yes

characteristic

236

C₂

#14583062

yes

characteristic

237

C₂

#14583108

yes

characteristic

238

C₂

#14583120

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#340	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#340	D₄₃
hypocenter	C₄₃	#1878
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#340

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
12. C₂×Dic₁₇₂	C₄	semidirect
84. C₂×Dic₄₃	Q₁₆	semidirect
127. C₄₃	#1878	semidirect

H ≅ G/N

type

12. C₂×Dic₁₇₂

C₄

semidirect

84. C₂×Dic₄₃

Q₁₆

semidirect

127. C₄₃

#1878

semidirect

Subgroups — #19134937

Conjugacy classes of subgroups

Complements