Group #20244251 — subgroups

Subgroups — #20244251

Order 6016.

384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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×#10625334	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13093946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689026	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689024	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#102×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#10625334	—	2	2	no	—
10	C₂×#10625334	—	2	2	no	—
11	C₂×#10625334	C₄	1	4	yes	complemented
12	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
15	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
16	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
17	#13093957	—	2	2	no	—
18	#13093946	—	2	2	no	—
19	C₈×Dic₄₇	—	2	2	no	—
20	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
23	#102×C₄₇	—	2	2	no	—
24	C₂⁴×C₄₇	—	2	1	no	—
25	C₂³×D₄₇	—	2	1	no	—
26	C₂×D₄×C₄₇	—	2	1	no	—
27	C₂×D₄×C₄₇	—	2	1	no	—
28	C₂×D₄×C₄₇	—	2	1	no	—
29	C₂×D₄×C₄₇	—	2	1	no	—
30	C₂×D₄×C₄₇	—	2	1	no	—
31	C₂×D₄×C₄₇	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₄₇	—	2	1	no	—
33	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
34	C₂²×Dic₄₇	—	2	1	no	—
35	C₂²×Dic₄₇	D₄	1	2	yes	—
36	C₂×D₁₈₈	—	2	1	no	—
37	C₂×D₁₈₈	—	2	1	no	—
38	C₂×D₁₈₈	—	2	1	no	—
39	C₂×D₁₈₈	—	2	1	no	—
40	C₂×D₁₈₈	—	2	1	no	—
41	C₂×D₁₈₈	C₂×C₄	1	2	yes	—
42	C₂×C₈×C₄₇	—	2	1	no	—
43	C₂×C₈×C₄₇	—	2	1	no	—
44	C₂×C₈×C₄₇	D₄	1	2	yes	—
45	C₄⋊C₄×C₄₇	—	2	1	no	—
46	C₄⋊C₄×C₄₇	—	2	1	no	—
47	C₂²⋊Dic₄₇	—	4	4	no	—
48	#10625334	—	2	8	no	—
49	(C₂×D₄₇)⋊C₄	—	4	4	no	—
50	C₄⋊Dic₄₇	—	2	1	no	—
51	C₄⋊Dic₄₇	—	2	1	no	—
52	C₄×Dic₄₇	—	2	1	no	—
53	C₄×Dic₄₇	—	2	1	no	—
54	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
55	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
56	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
57	C₂³×C₄₇	—	2	2	no	—
58	C₂³×C₄₇	—	4	1	no	—
59	C₂³×C₄₇	—	4	1	no	—
60	C₂³×C₄₇	—	4	2	no	—
61	C₂³×C₄₇	—	4	2	no	—
62	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
63	C₂²×D₄₇	—	2	2	no	—
64	C₂²×D₄₇	—	4	1	no	—
65	C₂²×D₄₇	—	4	1	no	—
66	C₂²×D₄₇	—	4	2	no	—
67	C₂²×D₄₇	—	4	2	no	—
68	D₄×C₄₇	—	2	2	no	—
69	D₄×C₄₇	—	2	2	no	—
70	D₄×C₄₇	—	4	1	no	—
71	D₄×C₄₇	—	4	1	no	—
72	C₂×C₄×C₄₇	—	4	1	no	—
73	C₂×C₄×C₄₇	—	4	2	no	—
74	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
79	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
80	C₂×Dic₄₇	—	2	2	no	—
81	C₂×Dic₄₇	—	2	2	no	—
82	C₂×Dic₄₇	—	4	1	no	—
83	C₂×Dic₄₇	—	4	2	no	—
84	C₂×Dic₄₇	D₈	1	4	yes	complemented
85	D₁₈₈	—	2	2	no	—
86	D₁₈₈	—	2	2	no	—
87	D₁₈₈	—	4	1	no	—
88	D₁₈₈	—	4	1	no	—
89	C₈×C₄₇	—	2	2	no	—
90	C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	complemented
91	C₂²×C₄₇	—	4	2	no	—
92	C₂²×C₄₇	—	4	4	no	—
93	C₂²×C₄₇	—	8	2	no	—
94	C₂²×C₄₇	—	8	1	no	—
95	C₂²×C₄₇	—	8	1	no	—
96	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
97	C₂²×C₄₇	#121	1	1	yes	characteristic
98	C₂²×C₄₇	#127	1	1	yes	characteristic
99	C₂²×C₄₇	C₂×D₈	1	2	yes	—
100	C₂²×C₄₇	#135	1	2	yes	—
101	C₂×D₄₇	—	4	2	no	—
102	C₂×D₄₇	—	4	4	no	—
103	C₂×D₄₇	—	8	2	no	—
104	C₂×D₄₇	—	8	1	no	—
105	C₂×D₄₇	—	8	1	no	—
106	C₄×C₄₇	—	8	1	no	—
107	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
109	C₄×C₄₇	#121	1	1	yes	characteristic
110	C₄×C₄₇	#124	1	1	yes	characteristic
111	Dic₄₇	—	2	4	no	—
112	Dic₄₇	—	8	1	no	—
113	#1970	—	47	1	no	maximal, Sylow
114	C₂×C₄₇	—	8	2	no	—
115	C₂×C₄₇	#390	1	1	yes	characteristic
116	C₂×C₄₇	C₄×D₈	1	2	yes	—
117	C₂×C₄₇	#466	1	2	yes	—
118	C₂×C₄₇	#493	1	1	yes	characteristic
119	C₂×C₄₇	#495	1	1	yes	characteristic
120	D₄₇	—	8	2	no	—
121	C₂²×D₈	—	47	1	no	—
122	C₂×#107	—	47	1	no	—
123	C₂×#102	—	47	1	no	—
124	C₂×#102	D₄₇	1	1	yes	characteristic, complemented
125	C₂×C₄×C₈	—	47	1	no	—
126	#390	—	47	1	no	—
127	#390	—	47	1	no	—
128	C₄₇	#1970	1	1	yes	characteristic, complemented, Sylow
129	C₂²×D₄	—	47	1	no	—
130	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
131	C₂×D₈	—	47	4	no	—
132	C₂×D₈	—	94	2	no	—
133	C₂×D₈	—	94	2	no	—
134	C₂²×C₈	—	47	1	no	—
135	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
136	C₂×C₄⋊C₄	—	47	1	no	—
137	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
138	C₂×C₂²⋊C₄	—	94	2	no	—
139	C₂×C₂²⋊C₄	—	94	2	no	—
140	C₂×C₄²	—	47	1	no	—
141	#107	—	94	2	no	—
142	#102	—	2	2	no	—
143	#102	—	94	2	no	—
144	C₄×C₈	—	94	2	no	—
145	C₂⁴	—	2	1	no	—
146	C₂⁴	—	94	1	no	—
147	C₂×D₄	—	2	1	no	—
148	C₂×D₄	—	2	1	no	—
149	C₂×D₄	—	2	1	no	—
150	C₂×D₄	—	2	1	no	—
151	C₂×D₄	—	2	1	no	—
152	C₂×D₄	—	47	2	no	—
153	C₂×D₄	—	94	1	no	—
154	C₂×D₄	—	94	1	no	—
155	C₂×D₄	—	94	1	no	—
156	C₂×D₄	—	94	1	no	—
157	C₂×D₄	—	94	1	no	—
158	C₂×D₄	C₄×D₄₇	1	2	yes	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	47	2	no	—
161	C₂²×C₄	—	94	1	no	—
162	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
163	D₈	—	94	8	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	47	2	no	—
167	C₂×C₈	—	47	2	no	—
168	C₂×C₈	—	47	2	no	—
169	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	1	no	—
172	C₄⋊C₄	—	94	1	no	—
173	C₄⋊C₄	—	94	1	no	—
174	C₂²⋊C₄	—	188	4	no	—
175	C₂²⋊C₄	—	188	4	no	—
176	C₄²	—	94	1	no	—
177	C₄²	—	94	1	no	—
178	C₂³	—	2	2	no	—
179	C₂³	—	4	1	no	—
180	C₂³	—	4	1	no	—
181	C₂³	—	4	2	no	—
182	C₂³	—	4	2	no	—
183	C₂³	—	94	2	no	—
184	C₂³	—	188	1	no	—
185	C₂³	—	188	1	no	—
186	C₂³	—	188	2	no	—
187	C₂³	—	188	2	no	—
188	C₂³	D₄×D₄₇	1	1	yes	characteristic
189	D₄	—	2	2	no	—
190	D₄	—	2	2	no	—
191	D₄	—	4	1	no	—
192	D₄	—	4	1	no	—
193	D₄	—	94	2	no	—
194	D₄	—	94	2	no	—
195	D₄	—	188	1	no	—
196	D₄	—	188	1	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	47	4	no	—
200	C₂×C₄	—	94	2	no	—
201	C₂×C₄	—	94	2	no	—
202	C₂×C₄	—	188	1	no	—
203	C₂×C₄	—	188	2	no	—
204	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
205	C₂×C₄	#10625350	1	1	yes	characteristic
206	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
207	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
208	C₂×C₄	#10625352	1	1	yes	characteristic
209	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
210	C₈	—	2	2	no	—
211	C₈	—	47	4	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	4	4	no	—
214	C₂²	—	8	1	no	—
215	C₂²	—	8	1	no	—
216	C₂²	—	8	2	no	—
217	C₂²	—	376	1	no	—
218	C₂²	—	376	1	no	—
219	C₂²	—	376	2	no	—
220	C₂²	—	188	2	no	—
221	C₂²	—	188	4	no	—
222	C₂²	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
223	C₂²	#13093997	1	1	yes	characteristic
224	C₂²	#13094020	1	1	yes	characteristic
225	C₂²	D₈×D₄₇	1	2	yes	—
226	C₂²	#13094045	1	2	yes	—
227	C₄	—	8	1	no	—
228	C₄	—	94	4	no	—
229	C₄	—	376	1	no	—
230	C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
231	C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
232	C₄	#13093996	1	1	yes	characteristic
233	C₄	#13094010	1	1	yes	characteristic
234	C₂	—	8	2	no	—
235	C₂	—	376	2	no	—
236	C₂	#15689023	1	1	yes	characteristic
237	C₂	#15689203	1	2	yes	—
238	C₂	#15689358	1	2	yes	—
239	C₂	#15689498	1	1	yes	characteristic
240	C₂	#15689504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10625334

C₂

yes

maximal, characteristic

C₂×#13093957

C₂

yes

maximal, characteristic, complemented

C₂×#13093946

C₂

yes

maximal, characteristic, complemented

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic, complemented

#15689026

C₂

yes

maximal, characteristic, complemented

#15689024

C₂

yes

maximal, characteristic, complemented

C₂×#102×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

—

—

C₄

yes

complemented

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×C₂²⋊Dic₄₇

—

C₂×(C₂×D₄₇)⋊C₄

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093957

—

#13093946

—

C₈×Dic₄₇

—

C₂²×D₄×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

#102×C₄₇

—

C₂⁴×C₄₇

—

C₂³×D₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

#10625334

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

complemented

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

—

C₄₇⋊C₈

C₂²⋊C₄

yes

complemented

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄×D₄

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

C₂×D₈

yes

—

100

C₂²×C₄₇

#135

yes

—

101

C₂×D₄₇

—

102

C₂×D₄₇

—

103

C₂×D₄₇

—

104

C₂×D₄₇

—

105

C₂×D₄₇

—

106

C₄×C₄₇

—

107

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

108

C₄×C₄₇

C₄×D₄

yes

characteristic

109

C₄×C₄₇

#121

yes

characteristic

110

C₄×C₄₇

#124

yes

characteristic

111

Dic₄₇

—

112

Dic₄₇

—

113

#1970

—

maximal, Sylow

114

C₂×C₄₇

—

115

C₂×C₄₇

#390

yes

characteristic

116

C₂×C₄₇

C₄×D₈

yes

—

117

C₂×C₄₇

#466

yes

—

118

C₂×C₄₇

#493

yes

characteristic

119

C₂×C₄₇

#495

yes

characteristic

120

D₄₇

—

121

C₂²×D₈

—

122

C₂×#107

—

123

C₂×#102

—

124

C₂×#102

D₄₇

yes

characteristic, complemented

125

C₂×C₄×C₈

—

126

#390

—

127

#390

—

128

C₄₇

#1970

yes

characteristic, complemented, Sylow

129

C₂²×D₄

—

130

C₂²×D₄

C₂×D₄₇

yes

characteristic

131

C₂×D₈

—

132

C₂×D₈

—

133

C₂×D₈

—

134

C₂²×C₈

—

135

C₂²×C₈

C₂×D₄₇

yes

characteristic

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

138

C₂×C₂²⋊C₄

—

139

C₂×C₂²⋊C₄

—

140

C₂×C₄²

—

141

#107

—

142

#102

—

143

#102

—

144

C₄×C₈

—

145

C₂⁴

—

146

C₂⁴

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

C₄×D₄₇

yes

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₂²×D₄₇

yes

characteristic

163

D₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

C₂²⋊D₄₇

yes

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₂²⋊C₄

—

188

—

175

C₂²⋊C₄

—

188

—

176

C₄²

—

177

C₄²

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

188

—

185

C₂³

—

188

—

186

C₂³

—

188

—

187

C₂³

—

188

—

188

C₂³

D₄×D₄₇

yes

characteristic

189

D₄

—

190

D₄

—

191

D₄

—

192

D₄

—

193

D₄

—

194

D₄

—

195

D₄

—

188

—

196

D₄

—

188

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

188

—

203

C₂×C₄

—

188

—

204

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

205

C₂×C₄

#10625350

yes

characteristic

206

C₂×C₄

D₄×D₄₇

yes

characteristic

207

C₂×C₄

D₄×D₄₇

yes

characteristic

208

C₂×C₄

#10625352

yes

characteristic

209

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

210

C₈

—

211

C₈

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

376

—

218

C₂²

—

376

—

219

C₂²

—

376

—

220

C₂²

—

188

—

221

C₂²

—

188

—

222

C₂²

(C₂²⋊D₄₇)⋊C₄

yes

characteristic

223

C₂²

#13093997

yes

characteristic

224

C₂²

#13094020

yes

characteristic

225

C₂²

D₈×D₄₇

yes

—

226

C₂²

#13094045

yes

—

227

C₄

—

228

C₄

—

229

C₄

—

376

—

230

C₄

C₂²⋊C₄×D₄₇

yes

characteristic

231

C₄

C₄×C₂²⋊D₄₇

yes

characteristic

232

C₄

#13093996

yes

characteristic

233

C₄

#13094010

yes

characteristic

234

C₂

—

235

C₂

—

376

—

236

C₂

#15689023

yes

characteristic

237

C₂

#15689203

yes

—

238

C₂

#15689358

yes

—

239

C₂

#15689498

yes

characteristic

240

C₂

#15689504

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#102×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×#102	D₄₇
hypocenter	C₄₇	#1970
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

subgroup

G/H

center

C₂³

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#102×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

N	H ≅ G/N	type
2. C₂×#13093957	C₂	semidirect
3. C₂×#13093946	C₂	semidirect
4. C₂×C₈×Dic₄₇	C₂	semidirect
5. #15689026	C₂	semidirect
6. #15689024	C₂	semidirect
7. C₂×#102×C₄₇	C₂	semidirect
11. C₂×#10625334	C₄	semidirect
84. C₂×Dic₄₇	D₈	semidirect
90. C₄₇⋊C₈	C₂²⋊C₄	semidirect
124. C₂×#102	D₄₇	semidirect
128. C₄₇	#1970	semidirect

H ≅ G/N

type

2. C₂×#13093957

C₂

semidirect

3. C₂×#13093946

C₂

semidirect

4. C₂×C₈×Dic₄₇

C₂

semidirect

5. #15689026

C₂

semidirect

6. #15689024

C₂

semidirect

7. C₂×#102×C₄₇

C₂

semidirect

11. C₂×#10625334

C₄

semidirect

84. C₂×Dic₄₇

D₈

semidirect

90. C₄₇⋊C₈

C₂²⋊C₄

semidirect

124. C₂×#102

D₄₇

semidirect

128. C₄₇

#1970

semidirect

Subgroups — #20244251

Conjugacy classes of subgroups

Complements