Group #20243366 — subgroups

Subgroups — #20243366

Order 6016.

400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#15688877	C₂	1	2	yes	maximal, complemented
5	C₂×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₄₇	C₄	1	1	yes	characteristic
7	C₂³×Dic₄₇	C₄	1	1	yes	characteristic
8	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×Dic₄₇	—	2	4	no	—
10	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
14	Dic₄₇⋊C₈	—	2	4	no	—
15	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
16	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
18	C₂²⋊C₈×C₄₇	—	2	2	no	—
19	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₇	—	2	2	no	—
21	C₂²×C₄×C₄₇	—	2	2	no	—
22	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₇	D₄	1	2	yes	—
24	C₂²×C₄×C₄₇	Q₈	1	2	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₇	—	2	2	no	—
27	C₂²×Dic₄₇	—	2	2	no	—
28	C₂²×Dic₄₇	—	2	2	no	—
29	C₂²×Dic₄₇	—	2	2	no	—
30	C₂²×Dic₄₇	—	2	2	no	—
31	C₂²×Dic₄₇	C₈	1	4	yes	complemented
32	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×C₄₇	—	2	2	no	—
37	C₂×C₈×C₄₇	—	2	2	no	—
38	C₂×C₈×C₄₇	—	2	2	no	—
39	C₄×Dic₄₇	—	2	2	no	—
40	C₄×Dic₄₇	—	2	2	no	—
41	C₄×Dic₄₇	—	2	2	no	—
42	C₄×Dic₄₇	D₄	1	4	yes	—
43	C₂×C₄₇⋊C₈	—	2	2	no	—
44	C₂×C₄₇⋊C₈	—	2	2	no	—
45	C₂×C₄₇⋊C₈	—	2	2	no	—
46	C₂³×C₄₇	—	2	1	no	—
47	C₂³×C₄₇	—	2	1	no	—
48	C₂³×C₄₇	—	2	1	no	—
49	C₂³×C₄₇	—	2	1	no	—
50	C₂³×C₄₇	C₄⋊C₄	1	2	yes	—
51	C₂³×C₄₇	C₂×C₈	1	2	yes	—
52	C₂³×C₄₇	M₁₆	1	2	yes	—
53	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₄×C₄₇	—	2	1	no	—
55	C₂×C₄×C₄₇	—	2	1	no	—
56	C₂×C₄×C₄₇	—	2	4	no	—
57	C₂×C₄×C₄₇	—	2	4	no	—
58	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
59	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
62	C₂×C₄×C₄₇	#41	1	2	yes	—
63	C₂×Dic₄₇	—	2	8	no	—
64	C₂×Dic₄₇	—	2	1	no	—
65	C₂×Dic₄₇	—	2	1	no	—
66	C₂×Dic₄₇	—	2	1	no	—
67	C₂×Dic₄₇	—	2	1	no	—
68	C₂×Dic₄₇	—	2	1	no	—
69	C₂×Dic₄₇	—	2	1	no	—
70	C₂×Dic₄₇	—	2	8	no	—
71	C₂×Dic₄₇	C₂²⋊C₄	1	2	yes	—
72	C₂×Dic₄₇	C₂²⋊C₄	1	2	yes	—
73	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
74	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
75	C₂×Dic₄₇	M₁₆	1	2	yes	—
76	C₂×Dic₄₇	M₁₆	1	2	yes	—
77	C₈×C₄₇	—	4	2	no	—
78	C₄₇⋊C₈	—	4	2	no	—
79	C₂²×C₄₇	—	2	2	no	—
80	C₂²×C₄₇	—	2	2	no	—
81	C₂²×C₄₇	—	2	2	no	—
82	C₂²×C₄₇	—	2	2	no	—
83	C₂²×C₄₇	—	2	2	no	—
84	C₂²×C₄₇	—	2	2	no	—
85	C₂²×C₄₇	C₄⋊C₈	1	4	yes	complemented
86	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄₇	#117	1	1	yes	characteristic
89	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
90	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
91	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
92	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
93	C₄×C₄₇	—	2	2	no	—
94	C₄×C₄₇	#121	1	2	yes	—
95	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
96	Dic₄₇	—	2	2	no	—
97	Dic₄₇	—	2	2	no	—
98	Dic₄₇	—	2	2	no	—
99	Dic₄₇	C₂²⋊C₈	1	4	yes	complemented
100	#1797	—	47	1	no	maximal, Sylow
101	C₂×C₄₇	—	2	4	no	—
102	C₂×C₄₇	#380	1	1	yes	characteristic
103	C₂×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
104	C₂×C₄₇	#407	1	1	yes	characteristic
105	C₂×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
106	C₂×C₄₇	#423	1	1	yes	characteristic
107	C₂×C₄₇	#431	1	1	yes	characteristic
108	C₂×C₄₇	#432	1	1	yes	characteristic
109	C₂²×C₄²	—	47	1	no	—
110	C₂×C₄⋊C₈	—	47	2	no	—
111	C₂×C₂²⋊C₈	—	47	1	no	—
112	C₂×C₂²⋊C₈	D₄₇	1	1	yes	characteristic
113	#336	—	47	2	no	—
114	C₄₇	#1797	1	1	yes	characteristic, complemented, Sylow
115	C₂³×C₄	—	47	1	no	—
116	C₂³×C₄	—	47	1	no	—
117	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
118	C₂²×C₈	—	47	2	no	—
119	C₂²×C₈	C₂×D₄₇	1	2	yes	—
120	C₂×C₄²	—	47	1	no	—
121	C₂×C₄²	—	47	1	no	—
122	C₂×C₄²	—	47	1	no	—
123	C₂×C₄²	—	47	1	no	—
124	C₂×C₄²	—	94	4	no	—
125	C₄⋊C₈	—	94	4	no	—
126	C₂²⋊C₈	—	2	2	no	—
127	C₂²⋊C₈	—	94	2	no	—
128	C₂⁴	C₄×D₄₇	1	1	yes	characteristic
129	C₂²×C₄	—	2	2	no	—
130	C₂²×C₄	—	2	2	no	—
131	C₂²×C₄	—	47	1	no	—
132	C₂²×C₄	—	47	4	no	—
133	C₂²×C₄	—	47	1	no	—
134	C₂²×C₄	—	47	1	no	—
135	C₂²×C₄	—	47	1	no	—
136	C₂²×C₄	—	94	2	no	—
137	C₂²×C₄	—	94	2	no	—
138	C₂²×C₄	—	94	2	no	—
139	C₂²×C₄	—	94	2	no	—
140	C₂²×C₄	—	94	2	no	—
141	C₂²×C₄	Dic₉₄	1	2	yes	—
142	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
143	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
144	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	—	2	2	no	—
148	C₂×C₈	—	94	2	no	—
149	C₂×C₈	—	94	2	no	—
150	C₂×C₈	—	94	2	no	—
151	C₄²	—	47	4	no	—
152	C₄²	—	94	2	no	—
153	C₄²	—	94	2	no	—
154	C₄²	—	94	2	no	—
155	C₂³	—	2	1	no	—
156	C₂³	—	2	1	no	—
157	C₂³	—	2	1	no	—
158	C₂³	—	2	1	no	—
159	C₂³	C₈×D₄₇	1	2	yes	—
160	C₂³	#10625324	1	2	yes	—
161	C₂³	Dic₄₇⋊C₄	1	2	yes	—
162	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	47	2	no	—
168	C₂×C₄	—	47	2	no	—
169	C₂×C₄	—	47	2	no	—
170	C₂×C₄	—	47	2	no	—
171	C₂×C₄	—	47	2	no	—
172	C₂×C₄	—	47	2	no	—
173	C₂×C₄	—	94	8	no	—
174	C₂×C₄	—	94	8	no	—
175	C₂×C₄	—	94	1	no	—
176	C₂×C₄	—	94	1	no	—
177	C₂×C₄	—	94	1	no	—
178	C₂×C₄	—	94	1	no	—
179	C₂×C₄	—	94	1	no	—
180	C₂×C₄	—	94	1	no	—
181	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
182	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
183	C₂×C₄	D₄×D₄₇	1	2	yes	—
184	C₂×C₄	#10625352	1	2	yes	—
185	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
186	C₈	—	4	2	no	—
187	C₈	—	188	2	no	—
188	C₂²	—	2	2	no	—
189	C₂²	—	2	2	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	2	2	no	—
192	C₂²	—	2	2	no	—
193	C₂²	—	2	2	no	—
194	C₂²	Dic₄₇⋊C₈	1	4	yes	complemented
195	C₂²	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
196	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
197	C₂²	#13093980	1	1	yes	characteristic
198	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
199	C₂²	M₁₆×D₄₇	1	1	yes	characteristic
200	C₂²	M₁₆×D₄₇	1	1	yes	characteristic
201	C₂²	C₂×#10625324	1	1	yes	characteristic
202	C₄	—	2	2	no	—
203	C₄	—	47	4	no	—
204	C₄	—	94	2	no	—
205	C₄	—	94	2	no	—
206	C₄	—	94	2	no	—
207	C₄	#13093996	1	2	yes	—
208	C₄	#13094001	1	2	yes	—
209	C₂	—	2	4	no	—
210	C₂	#15688981	1	1	yes	characteristic
211	C₂	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
212	C₂	#15689085	1	1	yes	characteristic
213	C₂	C₂×Dic₄₇⋊C₈	1	1	yes	characteristic
214	C₂	#15689146	1	1	yes	characteristic
215	C₂	#15689173	1	1	yes	characteristic
216	C₂	#15689177	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×Dic₄₇

C₂

yes

maximal, characteristic

C₂×Dic₄₇⋊C₈

C₂

yes

maximal, complemented

C₂×C₂²⋊(C₄₇⋊C₈)

C₂

yes

maximal, characteristic

#15688877

C₂

yes

maximal, complemented

C₂×C₂²⋊C₈×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₄

yes

characteristic

C₂³×Dic₄₇

C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

Dic₄₇⋊C₈

—

C₂²⋊(C₄₇⋊C₈)

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

—

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₈

yes

complemented

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₄⋊C₄

yes

—

C₂³×C₄₇

C₂×C₈

yes

—

C₂³×C₄₇

M₁₆

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²⋊C₄

yes

—

C₂×Dic₄₇

C₂²⋊C₄

yes

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₂×Dic₄₇

M₁₆

yes

—

C₂×Dic₄₇

M₁₆

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄⋊C₈

yes

complemented

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

#117

yes

characteristic

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

#121

yes

—

C₄×C₄₇

C₂²⋊Q₈

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

C₂²⋊C₈

yes

complemented

100

#1797

—

maximal, Sylow

101

C₂×C₄₇

—

102

C₂×C₄₇

#380

yes

characteristic

103

C₂×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

104

C₂×C₄₇

#407

yes

characteristic

105

C₂×C₄₇

C₂×C₄⋊C₈

yes

characteristic

106

C₂×C₄₇

#423

yes

characteristic

107

C₂×C₄₇

#431

yes

characteristic

108

C₂×C₄₇

#432

yes

characteristic

109

C₂²×C₄²

—

110

C₂×C₄⋊C₈

—

111

C₂×C₂²⋊C₈

—

112

C₂×C₂²⋊C₈

D₄₇

yes

characteristic

113

#336

—

114

C₄₇

#1797

yes

characteristic, complemented, Sylow

115

C₂³×C₄

—

116

C₂³×C₄

—

117

C₂³×C₄

C₂×D₄₇

yes

characteristic

118

C₂²×C₈

—

119

C₂²×C₈

C₂×D₄₇

yes

—

120

C₂×C₄²

—

121

C₂×C₄²

—

122

C₂×C₄²

—

123

C₂×C₄²

—

124

C₂×C₄²

—

125

C₄⋊C₈

—

126

C₂²⋊C₈

—

127

C₂²⋊C₈

—

128

C₂⁴

C₄×D₄₇

yes

characteristic

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

Dic₉₄

yes

—

142

C₂²×C₄

C₄×D₄₇

yes

characteristic

143

C₂²×C₄

C₂²⋊D₄₇

yes

—

144

C₂²×C₄

C₂²×D₄₇

yes

characteristic

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₄²

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

155

C₂³

—

156

C₂³

—

157

C₂³

—

158

C₂³

—

159

C₂³

C₈×D₄₇

yes

—

160

C₂³

#10625324

yes

—

161

C₂³

Dic₄₇⋊C₄

yes

—

162

C₂³

C₂×C₄×D₄₇

yes

characteristic

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

Dic₄₇⋊C₄

yes

—

182

C₂×C₄

C₂×Dic₉₄

yes

characteristic

183

C₂×C₄

D₄×D₄₇

yes

—

184

C₂×C₄

#10625352

yes

—

185

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

186

C₈

—

187

C₈

—

188

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

Dic₄₇⋊C₈

yes

complemented

195

C₂²

C₂²⋊C₄×D₄₇

yes

characteristic

196

C₂²

C₂×Dic₄₇⋊C₄

yes

characteristic

197

C₂²

#13093980

yes

characteristic

198

C₂²

C₂×C₈×D₄₇

yes

characteristic

199

C₂²

M₁₆×D₄₇

yes

characteristic

200

C₂²

M₁₆×D₄₇

yes

characteristic

201

C₂²

C₂×#10625324

yes

characteristic

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

#13093996

yes

—

208

C₄

#13094001

yes

—

209

C₂

—

210

C₂

#15688981

yes

characteristic

211

C₂

C₂²⋊C₈×D₄₇

yes

characteristic

212

C₂

#15689085

yes

characteristic

213

C₂

C₂×Dic₄₇⋊C₈

yes

characteristic

214

C₂

#15689146

yes

characteristic

215

C₂

#15689173

yes

characteristic

216

C₂

#15689177

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₈
Fitting	C₂×C₂²⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	C₂×C₂²⋊C₈	D₄₇
hypocenter	C₄₇	#1797
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂²×C₈

Fitting

C₂×C₂²⋊C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂²×C₄

hypercenter

C₂×C₂²⋊C₈

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
2. C₂×Dic₄₇⋊C₈	C₂	semidirect
4. #15688877	C₂	semidirect
31. C₂²×Dic₄₇	C₈	semidirect
85. C₂²×C₄₇	C₄⋊C₈	semidirect
99. Dic₄₇	C₂²⋊C₈	semidirect
114. C₄₇	#1797	semidirect
194. C₂²	Dic₄₇⋊C₈	semidirect

H ≅ G/N

type

2. C₂×Dic₄₇⋊C₈

C₂

semidirect

4. #15688877

C₂

semidirect

31. C₂²×Dic₄₇

C₈

semidirect

85. C₂²×C₄₇

C₄⋊C₈

semidirect

99. Dic₄₇

C₂²⋊C₈

semidirect

114. C₄₇

#1797

semidirect

194. C₂²

Dic₄₇⋊C₈

semidirect

Subgroups — #20243366

Conjugacy classes of subgroups

Complements