Group #20251714 — subgroups

Subgroups — #20251714

Order 6016.

688 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 177 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	C₂×#13094005	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689026	C₂	1	2	yes	maximal, complemented
4	#15689019	C₂	1	2	yes	maximal, complemented
5	#15689011	C₂	1	4	yes	maximal, complemented
6	#15689003	C₂	1	2	yes	maximal, complemented
7	#15688983	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
11	#13094005	—	2	8	no	—
12	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
13	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
14	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
16	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
17	C₂×C₄×Dic₄₇	—	2	4	no	—
18	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
19	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
20	C₄₇⋊#95	C₂²	1	2	yes	—
21	C₄₇⋊#95	C₂²	1	4	yes	—
22	C₂²×D₄×C₄₇	C₂²	1	2	yes	—
23	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
25	#121×C₄₇	—	2	4	no	—
26	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
28	C₂⁴×C₄₇	C₂³	1	2	yes	—
29	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
30	C₂×D₄×C₄₇	—	2	4	no	—
31	C₂×D₄×C₄₇	—	2	4	no	—
32	C₂×D₄×C₄₇	—	2	4	no	—
33	C₂×D₄×C₄₇	—	2	2	no	—
34	C₂×D₄×C₄₇	—	2	4	no	—
35	C₂²×C₄×C₄₇	—	2	4	no	—
36	C₂²×C₄×C₄₇	D₄	1	4	yes	—
37	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
38	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂²×Dic₄₇	—	2	2	no	—
41	C₂²×Dic₄₇	—	2	2	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	C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂²⋊C₄×C₄₇	—	2	4	no	—
50	C₂²⋊Dic₄₇	—	2	4	no	—
51	C₂²⋊Dic₄₇	—	2	8	no	—
52	C₂²⋊Dic₄₇	—	2	8	no	—
53	C₄⋊Dic₄₇	—	2	4	no	—
54	Dic₄₇⋊C₄	—	2	8	no	—
55	C₄×Dic₄₇	—	2	4	no	—
56	C₄×Dic₄₇	—	2	4	no	—
57	C₂³×C₄₇	—	2	2	no	—
58	C₂³×C₄₇	—	2	2	no	—
59	C₂³×C₄₇	—	2	2	no	—
60	C₂³×C₄₇	—	2	2	no	—
61	C₂³×C₄₇	—	2	4	no	—
62	C₂³×C₄₇	—	2	2	no	—
63	C₂³×C₄₇	—	2	4	no	—
64	C₂³×C₄₇	C₂×D₄	1	2	yes	—
65	C₂³×C₄₇	C₂×D₄	1	2	yes	—
66	C₂³×C₄₇	#41	1	2	yes	—
67	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
68	D₄×C₄₇	—	4	8	no	—
69	D₄×C₄₇	—	4	4	no	—
70	C₂×C₄×C₄₇	—	2	2	no	—
71	C₂×C₄×C₄₇	—	2	8	no	—
72	C₂×C₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	—	2	2	no	—
74	C₂×C₄×C₄₇	—	2	2	no	—
75	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
77	C₂×C₄×C₄₇	#41	1	4	yes	—
78	C₂×Dic₄₇	—	2	8	no	—
79	C₂×Dic₄₇	—	2	8	no	—
80	C₂×Dic₄₇	—	2	2	no	—
81	C₂×Dic₄₇	—	2	2	no	—
82	C₂×Dic₄₇	—	2	2	no	—
83	C₂×Dic₄₇	—	2	2	no	—
84	C₂×Dic₄₇	—	2	4	no	—
85	C₂×Dic₄₇	—	2	4	no	—
86	C₂×Dic₄₇	—	2	4	no	—
87	C₂×Dic₄₇	C₂×D₄	1	4	yes	—
88	C₂×Dic₄₇	#41	1	4	yes	—
89	C₂²×C₄₇	—	2	2	no	—
90	C₂²×C₄₇	—	2	2	no	—
91	C₂²×C₄₇	—	2	4	no	—
92	C₂²×C₄₇	—	2	4	no	—
93	C₂²×C₄₇	—	4	2	no	—
94	C₂²×C₄₇	—	4	2	no	—
95	C₂²×C₄₇	—	4	2	no	—
96	C₂²×C₄₇	—	4	4	no	—
97	C₂²×C₄₇	—	4	4	no	—
98	C₂²×C₄₇	#121	1	4	yes	—
99	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
100	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
101	C₂²×C₄₇	C₂×#41	1	2	yes	—
102	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
103	C₂²×C₄₇	C₂×#41	1	2	yes	—
104	C₄×C₄₇	—	2	2	no	—
105	C₄×C₄₇	—	4	2	no	—
106	C₄×C₄₇	#123	1	4	yes	complemented
107	Dic₄₇	—	2	4	no	—
108	Dic₄₇	—	2	4	no	—
109	Dic₄₇	—	4	4	no	—
110	#2854	—	47	1	no	maximal, Sylow
111	C₂×C₄₇	—	2	4	no	—
112	C₂×C₄₇	—	8	2	no	—
113	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
114	C₂×C₄₇	C₂×#123	1	1	yes	characteristic
115	C₂×C₄₇	#525	1	1	yes	characteristic
116	C₂×C₄₇	#529	1	2	yes	—
117	C₂×C₄₇	#532	1	2	yes	—
118	C₂×#123	—	47	2	no	—
119	C₂×#121	D₄₇	1	1	yes	characteristic
120	C₂²×C₄²	—	47	1	no	—
121	#390	—	47	2	no	—
122	#389	—	47	2	no	—
123	#388	—	47	4	no	—
124	#386	—	47	2	no	—
125	#380	—	47	1	no	—
126	C₄₇	#2854	1	1	yes	characteristic, complemented, Sylow
127	C₂²×D₄	C₂×D₄₇	1	2	yes	—
128	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
129	C₂³×C₄	—	47	1	no	—
130	C₂³×C₄	—	47	1	no	—
131	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
132	#123	—	94	8	no	—
133	#121	—	2	4	no	—
134	C₂×C₄⋊C₄	—	47	4	no	—
135	C₂×C₄⋊C₄	—	47	2	no	—
136	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
137	C₂×C₂²⋊C₄	—	47	2	no	—
138	C₂×C₂²⋊C₄	—	47	4	no	—
139	C₂×C₂²⋊C₄	—	47	4	no	—
140	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
141	C₂×C₄²	—	47	2	no	—
142	C₂×C₄²	—	47	2	no	—
143	C₂×C₄²	—	94	4	no	—
144	#95	—	47	2	no	—
145	#95	—	47	4	no	—
146	C₂⁴	C₂²×D₄₇	1	2	yes	—
147	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
148	C₂×D₄	—	2	4	no	—
149	C₂×D₄	—	2	4	no	—
150	C₂×D₄	—	2	4	no	—
151	C₂×D₄	—	2	4	no	—
152	C₂×D₄	—	2	2	no	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	—	47	4	no	—
155	C₂²×C₄	—	47	2	no	—
156	C₂²×C₄	—	47	2	no	—
157	C₂²×C₄	—	47	4	no	—
158	C₂²×C₄	—	94	4	no	—
159	C₂²×C₄	—	94	2	no	—
160	C₂²×C₄	—	94	2	no	—
161	C₂²×C₄	—	94	2	no	—
162	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
163	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
164	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
165	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
166	C₄⋊C₄	—	2	2	no	—
167	C₄⋊C₄	—	94	8	no	—
168	C₄⋊C₄	—	94	4	no	—
169	C₂²⋊C₄	—	2	4	no	—
170	C₂²⋊C₄	—	94	8	no	—
171	C₂²⋊C₄	—	94	8	no	—
172	C₂²⋊C₄	—	94	4	no	—
173	C₄²	—	94	4	no	—
174	C₄²	—	94	4	no	—
175	C₂³	—	2	2	no	—
176	C₂³	—	2	2	no	—
177	C₂³	—	2	2	no	—
178	C₂³	—	2	2	no	—
179	C₂³	—	2	4	no	—
180	C₂³	—	2	2	no	—
181	C₂³	—	2	4	no	—
182	C₂³	D₄×D₄₇	1	2	yes	—
183	C₂³	#10625352	1	2	yes	—
184	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
185	C₂³	C₂³×D₄₇	1	1	yes	characteristic
186	D₄	—	4	8	no	—
187	D₄	—	4	4	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	8	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	47	4	no	—
194	C₂×C₄	—	47	4	no	—
195	C₂×C₄	—	94	8	no	—
196	C₂×C₄	—	94	8	no	—
197	C₂×C₄	—	94	2	no	—
198	C₂×C₄	—	94	2	no	—
199	C₂×C₄	—	94	2	no	—
200	C₂×C₄	—	94	2	no	—
201	C₂×C₄	—	94	4	no	—
202	C₂×C₄	—	94	4	no	—
203	C₂×C₄	—	94	4	no	—
204	C₂×C₄	#10625352	1	4	yes	—
205	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
206	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
207	C₂²	—	2	2	no	—
208	C₂²	—	2	2	no	—
209	C₂²	—	2	4	no	—
210	C₂²	—	2	4	no	—
211	C₂²	—	4	2	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	4	no	—
215	C₂²	—	4	4	no	—
216	C₂²	#13093995	1	4	yes	—
217	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
218	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
219	C₂²	#41×D₄₇	1	2	yes	—
220	C₂²	C₂×#10625352	1	1	yes	characteristic
221	C₂²	C₂×#10625352	1	2	yes	—
222	C₄	—	2	2	no	—
223	C₄	—	4	2	no	—
224	C₄	—	94	4	no	—
225	C₄	—	94	4	no	—
226	C₄	—	188	4	no	—
227	C₄	#13094005	1	4	yes	complemented
228	C₂	—	2	4	no	—
229	C₂	—	8	2	no	—
230	C₂	C₂×#13093995	1	1	yes	characteristic
231	C₂	C₂×#13094005	1	1	yes	characteristic
232	C₂	#15689630	1	1	yes	characteristic
233	C₂	#15689654	1	2	yes	—
234	C₂	#15689668	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094005

C₂

yes

maximal, complemented

C₂²×C₄×Dic₄₇

C₂

yes

maximal, characteristic, complemented

#15689026

C₂

yes

maximal, complemented

#15689019

C₂

yes

maximal, complemented

#15689011

C₂

yes

maximal, complemented

#15689003

C₂

yes

maximal, complemented

#15688983

C₂

yes

maximal, characteristic, complemented

C₂×#121×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

#13094005

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×D₄×C₄₇

C₂²

yes

—

C₂²×D₄×C₄₇

C₂²

yes

characteristic

C₂³×C₄×C₄₇

C₂²

yes

characteristic

#121×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

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

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

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

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#121

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

100

C₂²×C₄₇

C₂²×D₄

yes

characteristic

101

C₂²×C₄₇

C₂×#41

yes

—

102

C₂²×C₄₇

C₂×#41

yes

characteristic

103

C₂²×C₄₇

C₂×#41

yes

—

104

C₄×C₄₇

—

105

C₄×C₄₇

—

106

C₄×C₄₇

#123

yes

complemented

107

Dic₄₇

—

108

Dic₄₇

—

109

Dic₄₇

—

110

#2854

—

maximal, Sylow

111

C₂×C₄₇

—

112

C₂×C₄₇

—

113

C₂×C₄₇

C₂×#121

yes

characteristic

114

C₂×C₄₇

C₂×#123

yes

characteristic

115

C₂×C₄₇

#525

yes

characteristic

116

C₂×C₄₇

#529

yes

—

117

C₂×C₄₇

#532

yes

—

118

C₂×#123

—

119

C₂×#121

D₄₇

yes

characteristic

120

C₂²×C₄²

—

121

#390

—

122

#389

—

123

#388

—

124

#386

—

125

#380

—

126

C₄₇

#2854

yes

characteristic, complemented, Sylow

127

C₂²×D₄

C₂×D₄₇

yes

—

128

C₂²×D₄

C₂×D₄₇

yes

characteristic

129

C₂³×C₄

—

130

C₂³×C₄

—

131

C₂³×C₄

C₂×D₄₇

yes

characteristic

132

#123

—

133

#121

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

137

C₂×C₂²⋊C₄

—

138

C₂×C₂²⋊C₄

—

139

C₂×C₂²⋊C₄

—

140

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

141

C₂×C₄²

—

142

C₂×C₄²

—

143

C₂×C₄²

—

144

#95

—

145

#95

—

146

C₂⁴

C₂²×D₄₇

yes

—

147

C₂⁴

C₂²×D₄₇

yes

characteristic

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

—

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

C₂²×C₄

C₂²×D₄₇

yes

characteristic

165

C₂²×C₄

C₂²×D₄₇

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₂²⋊C₄

—

170

C₂²⋊C₄

—

171

C₂²⋊C₄

—

172

C₂²⋊C₄

—

173

C₄²

—

174

C₄²

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

D₄×D₄₇

yes

—

183

C₂³

#10625352

yes

—

184

C₂³

C₂×C₂²⋊D₄₇

yes

—

185

C₂³

C₂³×D₄₇

yes

characteristic

186

D₄

—

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

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

#10625352

yes

—

205

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

206

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

#13093995

yes

—

217

C₂²

C₂×D₄×D₄₇

yes

characteristic

218

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

219

C₂²

#41×D₄₇

yes

—

220

C₂²

C₂×#10625352

yes

characteristic

221

C₂²

C₂×#10625352

yes

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

188

—

227

C₄

#13094005

yes

complemented

228

C₂

—

229

C₂

—

230

C₂

C₂×#13093995

yes

characteristic

231

C₂

C₂×#13094005

yes

characteristic

232

C₂

#15689630

yes

characteristic

233

C₂

#15689654

yes

—

234

C₂

#15689668

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×#121×C₄₇	C₂
hypercenter	C₂×#121	D₄₇
hypocenter	C₄₇	#2854
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#121

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×#121×C₄₇

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×#121

N	H ≅ G/N	type
1. C₂×#13094005	C₂	semidirect
2. C₂²×C₄×Dic₄₇	C₂	semidirect
3. #15689026	C₂	semidirect
4. #15689019	C₂	semidirect
5. #15689011	C₂	semidirect
6. #15689003	C₂	semidirect
7. #15688983	C₂	semidirect
44. C₂²×Dic₄₇	D₄	semidirect
106. C₄×C₄₇	#123	semidirect
126. C₄₇	#2854	semidirect
227. C₄	#13094005	semidirect

H ≅ G/N

type

1. C₂×#13094005

C₂

semidirect

2. C₂²×C₄×Dic₄₇

C₂

semidirect

3. #15689026

C₂

semidirect

4. #15689019

C₂

semidirect

5. #15689011

C₂

semidirect

6. #15689003

C₂

semidirect

7. #15688983

C₂

semidirect

44. C₂²×Dic₄₇

D₄

semidirect

106. C₄×C₄₇

#123

semidirect

126. C₄₇

#2854

semidirect

227. C₄

#13094005

semidirect

Subgroups — #20251714

Conjugacy classes of subgroups

Complements