Group #20246591 — subgroups

Subgroups — C₂×#15689037 #20246591

Order 6016.

1252 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 269 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×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
4	#15689037	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₄₇	C₂²	1	2	yes	—
8	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₄₇⋊C₄	—	2	4	no	—
11	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	complemented
12	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
13	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
14	C₂×C₂²⋊Dic₄₇	C₂²	1	8	yes	complemented
15	C₂×C₂²⋊Dic₄₇	C₂²	1	8	yes	complemented
16	C₄₇⋊#95	C₂²	1	4	yes	complemented
17	C₂⁵×C₄₇	C₂²	1	2	yes	—
18	C₂²×D₄×C₄₇	—	2	8	no	—
19	C₂²×D₄×C₄₇	—	2	4	no	—
20	C₂²×D₄×C₄₇	C₂²	1	4	yes	—
21	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄₇	—	2	4	no	—
23	C₂⁴×C₄₇	—	2	4	no	—
24	C₂⁴×C₄₇	—	2	4	no	—
25	C₂⁴×C₄₇	—	2	4	no	—
26	C₂⁴×C₄₇	—	2	4	no	—
27	C₂⁴×C₄₇	—	2	4	no	—
28	C₂⁴×C₄₇	D₄	1	8	yes	—
29	C₂⁴×C₄₇	C₂³	1	4	yes	—
30	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
31	C₂×D₄×C₄₇	—	2	32	no	—
32	C₂×D₄×C₄₇	—	2	16	no	—
33	C₂×D₄×C₄₇	—	2	8	no	—
34	C₂²×C₄×C₄₇	—	2	4	no	—
35	C₂²×C₄×C₄₇	D₄	1	4	yes	—
36	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
37	C₂²×Dic₄₇	—	2	2	no	—
38	C₂²×Dic₄₇	—	2	2	no	—
39	C₂²×Dic₄₇	—	2	4	no	—
40	C₂²×Dic₄₇	—	2	4	no	—
41	C₂²×Dic₄₇	—	2	4	no	—
42	C₂²×Dic₄₇	—	2	2	no	—
43	C₂²×Dic₄₇	—	2	4	no	—
44	C₂²×Dic₄₇	D₄	1	4	yes	complemented
45	C₂²×Dic₄₇	C₂³	1	4	yes	—
46	C₂²×Dic₄₇	C₂³	1	2	yes	—
47	C₂²×Dic₄₇	C₂³	1	2	yes	—
48	C₂²⋊Dic₄₇	—	2	16	no	—
49	C₂²⋊Dic₄₇	—	2	16	no	—
50	Dic₄₇⋊C₄	—	2	8	no	—
51	C₂³×C₄₇	—	2	16	no	—
52	C₂³×C₄₇	—	2	16	no	—
53	C₂³×C₄₇	—	2	16	no	—
54	C₂³×C₄₇	—	2	4	no	—
55	C₂³×C₄₇	—	2	4	no	—
56	C₂³×C₄₇	—	2	4	no	—
57	C₂³×C₄₇	—	2	4	no	—
58	C₂³×C₄₇	—	2	4	no	—
59	C₂³×C₄₇	—	2	4	no	—
60	C₂³×C₄₇	—	4	8	no	—
61	C₂³×C₄₇	—	4	8	no	—
62	C₂³×C₄₇	—	4	8	no	—
63	C₂³×C₄₇	—	4	8	no	—
64	C₂³×C₄₇	C₂×D₄	1	2	yes	—
65	C₂³×C₄₇	C₂×D₄	1	8	yes	—
66	C₂³×C₄₇	C₂×D₄	1	4	yes	—
67	C₂³×C₄₇	C₂×D₄	1	2	yes	—
68	C₂³×C₄₇	#41	1	2	yes	—
69	C₂³×C₄₇	#41	1	4	yes	—
70	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
71	D₄×C₄₇	—	2	32	no	—
72	C₂×C₄×C₄₇	—	2	8	no	—
73	C₂×C₄×C₄₇	—	2	4	no	—
74	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
75	C₂×Dic₄₇	—	2	8	no	—
76	C₂×Dic₄₇	—	2	2	no	—
77	C₂×Dic₄₇	—	2	2	no	—
78	C₂×Dic₄₇	—	2	2	no	—
79	C₂×Dic₄₇	—	2	4	no	—
80	C₂×Dic₄₇	—	2	4	no	—
81	C₂×Dic₄₇	—	2	4	no	—
82	C₂×Dic₄₇	—	2	4	no	—
83	C₂×Dic₄₇	—	4	4	no	—
84	C₂×Dic₄₇	—	4	8	no	—
85	C₂×Dic₄₇	C₂×D₄	1	4	yes	complemented
86	C₂²×C₄₇	—	2	8	no	—
87	C₂²×C₄₇	—	2	8	no	—
88	C₂²×C₄₇	—	2	8	no	—
89	C₂²×C₄₇	—	4	4	no	—
90	C₂²×C₄₇	—	4	4	no	—
91	C₂²×C₄₇	—	4	4	no	—
92	C₂²×C₄₇	—	4	4	no	—
93	C₂²×C₄₇	—	4	32	no	—
94	C₂²×C₄₇	#120	1	4	yes	—
95	C₂²×C₄₇	#121	1	4	yes	—
96	C₂²×C₄₇	#121	1	8	yes	—
97	C₂²×C₄₇	#123	1	8	yes	—
98	C₂²×C₄₇	#124	1	4	yes	—
99	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
100	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
101	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
102	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
103	C₂²×C₄₇	C₂×#41	1	2	yes	—
104	C₄×C₄₇	—	2	4	no	—
105	Dic₄₇	—	2	4	no	—
106	Dic₄₇	—	4	2	no	—
107	Dic₄₇	—	4	4	no	—
108	C₂×#394	—	47	1	no	maximal, Sylow
109	C₂×C₄₇	—	4	8	no	—
110	C₂×C₄₇	#394	1	8	yes	complemented
111	C₂×C₄₇	C₂×#120	1	1	yes	characteristic
112	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
113	C₂×C₄₇	C₂×#121	1	2	yes	—
114	C₂×C₄₇	C₂×#123	1	2	yes	—
115	C₂×C₄₇	C₂×#124	1	1	yes	characteristic
116	C₂³×D₄	D₄₇	1	1	yes	characteristic
117	C₂²×C₄⋊C₄	—	47	1	no	—
118	C₂²×C₂²⋊C₄	—	47	2	no	—
119	C₂²×C₂²⋊C₄	—	47	2	no	—
120	#394	—	47	8	no	—
121	C₂×#95	—	47	1	no	—
122	C₄₇	C₂×#394	1	1	yes	characteristic, complemented, Sylow
123	C₂⁵	C₂×D₄₇	1	2	yes	—
124	C₂²×D₄	—	2	8	no	—
125	C₂²×D₄	—	2	4	no	—
126	C₂²×D₄	C₂×D₄₇	1	4	yes	—
127	C₂³×C₄	—	47	1	no	—
128	C₂³×C₄	—	47	1	no	—
129	C₂³×C₄	—	47	2	no	—
130	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
131	C₂×C₄⋊C₄	—	47	4	no	—
132	C₂×C₄⋊C₄	—	94	4	no	—
133	C₂×C₂²⋊C₄	—	47	8	no	—
134	C₂×C₂²⋊C₄	—	47	8	no	—
135	C₂×C₂²⋊C₄	—	94	8	no	—
136	C₂×C₂²⋊C₄	—	94	8	no	—
137	#95	—	47	4	no	—
138	C₂⁴	—	2	4	no	—
139	C₂⁴	—	2	4	no	—
140	C₂⁴	—	2	4	no	—
141	C₂⁴	—	2	4	no	—
142	C₂⁴	—	2	4	no	—
143	C₂⁴	—	2	4	no	—
144	C₂⁴	C₂²⋊D₄₇	1	8	yes	—
145	C₂⁴	C₂²×D₄₇	1	4	yes	—
146	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
147	C₂×D₄	—	2	32	no	—
148	C₂×D₄	—	2	16	no	—
149	C₂×D₄	—	2	8	no	—
150	C₂²×C₄	—	2	4	no	—
151	C₂²×C₄	—	47	4	no	—
152	C₂²×C₄	—	47	2	no	—
153	C₂²×C₄	—	47	4	no	—
154	C₂²×C₄	—	47	2	no	—
155	C₂²×C₄	—	94	2	no	—
156	C₂²×C₄	—	94	2	no	—
157	C₂²×C₄	—	94	4	no	—
158	C₂²×C₄	—	94	4	no	—
159	C₂²×C₄	—	94	4	no	—
160	C₂²×C₄	—	94	4	no	—
161	C₂²×C₄	—	94	2	no	—
162	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
163	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
164	C₄⋊C₄	—	94	8	no	—
165	C₂²⋊C₄	—	94	16	no	—
166	C₂²⋊C₄	—	94	16	no	—
167	C₂³	—	2	16	no	—
168	C₂³	—	2	16	no	—
169	C₂³	—	2	16	no	—
170	C₂³	—	2	4	no	—
171	C₂³	—	2	4	no	—
172	C₂³	—	2	4	no	—
173	C₂³	—	2	4	no	—
174	C₂³	—	2	4	no	—
175	C₂³	—	2	4	no	—
176	C₂³	—	4	8	no	—
177	C₂³	—	4	8	no	—
178	C₂³	—	4	8	no	—
179	C₂³	—	4	8	no	—
180	C₂³	D₄×D₄₇	1	2	yes	—
181	C₂³	#10625352	1	2	yes	—
182	C₂³	#10625352	1	4	yes	—
183	C₂³	C₂×C₂²⋊D₄₇	1	8	yes	—
184	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
185	C₂³	C₂×C₂²⋊D₄₇	1	4	yes	—
186	C₂³	C₂³×D₄₇	1	1	yes	characteristic
187	D₄	—	2	32	no	—
188	C₂×C₄	—	2	8	no	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	47	4	no	—
191	C₂×C₄	—	94	8	no	—
192	C₂×C₄	—	94	2	no	—
193	C₂×C₄	—	94	2	no	—
194	C₂×C₄	—	94	4	no	—
195	C₂×C₄	—	94	4	no	—
196	C₂×C₄	—	94	4	no	—
197	C₂×C₄	—	94	2	no	—
198	C₂×C₄	—	94	4	no	—
199	C₂×C₄	—	188	4	no	—
200	C₂×C₄	—	188	8	no	—
201	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
202	C₂²	—	2	8	no	—
203	C₂²	—	2	8	no	—
204	C₂²	—	2	8	no	—
205	C₂²	—	4	32	no	—
206	C₂²	—	4	4	no	—
207	C₂²	—	4	4	no	—
208	C₂²	—	4	4	no	—
209	C₂²	—	4	4	no	—
210	C₂²	#13093993	1	4	yes	—
211	C₂²	#13093995	1	4	yes	—
212	C₂²	#13093996	1	8	yes	—
213	C₂²	#13094005	1	8	yes	—
214	C₂²	#13094011	1	4	yes	—
215	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
216	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
217	C₂²	C₂²×C₂²⋊D₄₇	1	2	yes	—
218	C₂²	C₂×#10625352	1	1	yes	characteristic
219	C₂²	C₂×#10625352	1	2	yes	—
220	C₄	—	2	4	no	—
221	C₄	—	94	4	no	—
222	C₄	—	188	2	no	—
223	C₄	—	188	4	no	—
224	C₂	—	4	8	no	—
225	C₂	#15689037	1	8	yes	direct product factor
226	C₂	C₂×#13093993	1	1	yes	characteristic
227	C₂	C₂×#13093995	1	1	yes	characteristic
228	C₂	C₂×#13093996	1	2	yes	—
229	C₂	C₂×#13094005	1	2	yes	—
230	C₂	C₂×#13094011	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₄₇⋊C₄

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊Dic₄₇

C₂

yes

maximal, complemented

C₂²×C₂²⋊Dic₄₇

C₂

yes

maximal, complemented

#15689037

C₂

yes

maximal, direct product factor

C₂×C₄₇⋊#95

C₂

yes

maximal, characteristic, complemented

C₂³×D₄×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₂×Dic₄₇⋊C₄

C₂²

yes

complemented

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

complemented

C₂×C₂²⋊Dic₄₇

C₂²

yes

complemented

C₄₇⋊#95

C₂²

yes

complemented

C₂⁵×C₄₇

C₂²

yes

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

D₄

yes

—

C₂⁴×C₄₇

C₂³

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

complemented

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

complemented

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#120

yes

—

C₂²×C₄₇

#121

yes

—

C₂²×C₄₇

#121

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

#124

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

100

C₂²×C₄₇

C₂²×D₄

yes

—

101

C₂²×C₄₇

C₂²×D₄

yes

characteristic

102

C₂²×C₄₇

C₂×#41

yes

characteristic

103

C₂²×C₄₇

C₂×#41

yes

—

104

C₄×C₄₇

—

105

Dic₄₇

—

106

Dic₄₇

—

107

Dic₄₇

—

108

C₂×#394

—

maximal, Sylow

109

C₂×C₄₇

—

110

C₂×C₄₇

#394

yes

complemented

111

C₂×C₄₇

C₂×#120

yes

characteristic

112

C₂×C₄₇

C₂×#121

yes

characteristic

113

C₂×C₄₇

C₂×#121

yes

—

114

C₂×C₄₇

C₂×#123

yes

—

115

C₂×C₄₇

C₂×#124

yes

characteristic

116

C₂³×D₄

D₄₇

yes

characteristic

117

C₂²×C₄⋊C₄

—

118

C₂²×C₂²⋊C₄

—

119

C₂²×C₂²⋊C₄

—

120

#394

—

121

C₂×#95

—

122

C₄₇

C₂×#394

yes

characteristic, complemented, Sylow

123

C₂⁵

C₂×D₄₇

yes

—

124

C₂²×D₄

—

125

C₂²×D₄

—

126

C₂²×D₄

C₂×D₄₇

yes

—

127

C₂³×C₄

—

128

C₂³×C₄

—

129

C₂³×C₄

—

130

C₂³×C₄

C₂×D₄₇

yes

characteristic

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₂²⋊C₄

—

134

C₂×C₂²⋊C₄

—

135

C₂×C₂²⋊C₄

—

136

C₂×C₂²⋊C₄

—

137

#95

—

138

C₂⁴

—

139

C₂⁴

—

140

C₂⁴

—

141

C₂⁴

—

142

C₂⁴

—

143

C₂⁴

—

144

C₂⁴

C₂²⋊D₄₇

yes

—

145

C₂⁴

C₂²×D₄₇

yes

—

146

C₂⁴

C₂²×D₄₇

yes

characteristic

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₂²⋊D₄₇

yes

—

163

C₂²×C₄

C₂²×D₄₇

yes

—

164

C₄⋊C₄

—

165

C₂²⋊C₄

—

166

C₂²⋊C₄

—

167

C₂³

—

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

174

C₂³

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

D₄×D₄₇

yes

—

181

C₂³

#10625352

yes

—

182

C₂³

#10625352

yes

—

183

C₂³

C₂×C₂²⋊D₄₇

yes

—

184

C₂³

C₂×C₂²⋊D₄₇

yes

—

185

C₂³

C₂×C₂²⋊D₄₇

yes

—

186

C₂³

C₂³×D₄₇

yes

characteristic

187

D₄

—

188

C₂×C₄

—

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

—

188

—

200

C₂×C₄

—

188

—

201

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

#13093993

yes

—

211

C₂²

#13093995

yes

—

212

C₂²

#13093996

yes

—

213

C₂²

#13094005

yes

—

214

C₂²

#13094011

yes

—

215

C₂²

C₂×D₄×D₄₇

yes

characteristic

216

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

217

C₂²

C₂²×C₂²⋊D₄₇

yes

—

218

C₂²

C₂×#10625352

yes

characteristic

219

C₂²

C₂×#10625352

yes

—

220

C₄

—

221

C₄

—

222

C₄

—

188

—

223

C₄

—

188

—

224

C₂

—

225

C₂

#15689037

yes

direct product factor

226

C₂

C₂×#13093993

yes

characteristic

227

C₂

C₂×#13093995

yes

characteristic

228

C₂

C₂×#13093996

yes

—

229

C₂

C₂×#13094005

yes

—

230

C₂

C₂×#13094011

yes

characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂⁴
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂³×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂³×D₄	D₄₇
hypocenter	C₄₇	C₂×#394
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×D₄

subgroup

G/H

center

C₂⁴

C₂²×D₄₇

commutator

C₂³×C₄₇

C₂⁴

Frattini

C₂³

C₂³×D₄₇

Fitting

C₂³×D₄×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂³×D₄

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂³×D₄

N	H ≅ G/N	type
1. C₂²×Dic₄₇⋊C₄	C₂	semidirect
2. C₂²×C₂²⋊Dic₄₇	C₂	semidirect
3. C₂²×C₂²⋊Dic₄₇	C₂	semidirect
4. #15689037	C₂	direct (N × H)
5. C₂×C₄₇⋊#95	C₂	semidirect
11. C₂×Dic₄₇⋊C₄	C₂²	semidirect
14. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
15. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
16. C₄₇⋊#95	C₂²	semidirect
44. C₂²×Dic₄₇	D₄	semidirect
85. C₂×Dic₄₇	C₂×D₄	semidirect
110. C₂×C₄₇	#394	semidirect
122. C₄₇	C₂×#394	semidirect
225. C₂	#15689037	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₄₇⋊C₄

C₂

semidirect

2. C₂²×C₂²⋊Dic₄₇

C₂

semidirect

3. C₂²×C₂²⋊Dic₄₇

C₂

semidirect

4. #15689037

C₂

direct (N × H)

5. C₂×C₄₇⋊#95

C₂

semidirect

11. C₂×Dic₄₇⋊C₄

C₂²

semidirect

14. C₂×C₂²⋊Dic₄₇

C₂²

semidirect

15. C₂×C₂²⋊Dic₄₇

C₂²

semidirect

16. C₄₇⋊#95

C₂²

semidirect

44. C₂²×Dic₄₇

D₄

semidirect

85. C₂×Dic₄₇

C₂×D₄

semidirect

110. C₂×C₄₇

#394

semidirect

122. C₄₇

C₂×#394

semidirect

225. C₂

#15689037

direct (N × H)

Subgroups — C₂×#15689037 #20246591

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689037 #20246591

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689037 #20246591