Group #20241761 — subgroups

Subgroups — C₂×D₄⋊(C₄₇⋊C₈) #20241761

Order 6016.

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

normal subgroups only

This group has 344 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	C₂×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄⋊(C₄₇⋊C₈)	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₇⋊C₈	—	2	1	no	—
6	C₂²×C₄₇⋊C₈	—	2	1	no	—
7	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
8	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
9	C₄×C₄₇⋊C₈	—	2	1	no	—
10	C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
11	C₂²×D₄×C₄₇	C₄	1	1	yes	characteristic
12	C₂³×C₄×C₄₇	—	2	1	no	—
13	C₄×D₄×C₄₇	—	2	1	no	—
14	C₄×D₄×C₄₇	—	2	1	no	—
15	C₄×D₄×C₄₇	C₄	1	2	yes	—
16	C₄×D₄×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
19	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄₇	—	2	1	no	—
21	C₂×D₄×C₄₇	—	2	1	no	—
22	C₂×D₄×C₄₇	—	2	2	no	—
23	C₂×D₄×C₄₇	C₈	1	4	yes	complemented
24	C₂×D₄×C₄₇	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₄₇	—	2	1	no	—
26	C₂²×C₄×C₄₇	—	2	2	no	—
27	C₂²×C₄×C₄₇	—	2	2	no	—
28	C₂²×C₄×C₄₇	—	4	2	no	—
29	C₂²×C₄×C₄₇	—	4	2	no	—
30	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
32	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
33	C₄⋊C₄×C₄₇	—	2	1	no	—
34	C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
35	C₂²⋊C₄×C₄₇	—	2	2	no	—
36	C₂²⋊C₄×C₄₇	—	2	2	no	—
37	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₄²×C₄₇	D₄	1	1	yes	characteristic
39	C₄²×C₄₇	D₄	1	1	yes	characteristic
40	C₄²×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×C₄₇⋊C₈	—	2	4	no	—
42	C₂×C₄₇⋊C₈	—	2	2	no	—
43	C₂×C₄₇⋊C₈	—	2	2	no	—
44	C₂×C₄₇⋊C₈	—	4	2	no	—
45	C₂³×C₄₇	—	2	4	no	—
46	C₂³×C₄₇	—	2	2	no	—
47	C₂³×C₄₇	—	4	2	no	—
48	C₂³×C₄₇	—	4	2	no	—
49	C₂³×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
50	D₄×C₄₇	—	2	4	no	—
51	D₄×C₄₇	—	2	2	no	—
52	D₄×C₄₇	C₂×C₈	1	4	yes	complemented
53	C₂×C₄×C₄₇	—	2	2	no	—
54	C₂×C₄×C₄₇	—	2	2	no	—
55	C₂×C₄×C₄₇	—	4	2	no	—
56	C₂×C₄×C₄₇	—	4	4	no	—
57	C₂×C₄×C₄₇	—	4	2	no	—
58	C₂×C₄×C₄₇	—	4	2	no	—
59	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
63	C₂×C₄×C₄₇	M₁₆	1	2	yes	—
64	C₂×C₄×C₄₇	D₈	1	2	yes	—
65	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
66	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₄₇⋊C₈	—	2	4	no	—
70	C₄₇⋊C₈	—	4	2	no	—
71	C₂²×C₄₇	—	2	4	no	—
72	C₂²×C₄₇	—	4	8	no	—
73	C₂²×C₄₇	—	4	2	no	—
74	C₂²×C₄₇	—	4	2	no	—
75	C₂²×C₄₇	C₂²⋊C₈	1	2	yes	—
76	C₂²×C₄₇	#102	1	2	yes	—
77	C₂²×C₄₇	#104	1	2	yes	—
78	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₄×C₄₇	—	2	1	no	—
80	C₄×C₄₇	—	2	1	no	—
81	C₄×C₄₇	—	4	2	no	—
82	C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
83	C₄×C₄₇	#102	1	2	yes	—
84	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
85	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
86	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
87	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
88	C₂×D₄⋊C₈	—	47	1	no	maximal, Sylow
89	C₂×C₄₇	—	4	4	no	—
90	C₂×C₄₇	D₄⋊C₈	1	4	yes	complemented
91	C₂×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
92	C₂×C₄₇	C₂×#102	1	1	yes	characteristic
93	C₂×C₄₇	C₂×#104	1	1	yes	characteristic
94	C₂×C₄×D₄	D₄₇	1	1	yes	characteristic
95	C₂×C₄⋊C₈	—	47	1	no	—
96	C₂×C₄×C₈	—	47	1	no	—
97	D₄⋊C₈	—	47	4	no	—
98	C₄₇	C₂×D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
99	C₂²×D₄	Dic₄₇	1	1	yes	characteristic
100	C₂³×C₄	—	2	1	no	—
101	C₂²×C₈	—	94	1	no	—
102	C₂²×C₈	—	94	1	no	—
103	C₄×D₄	—	2	1	no	—
104	C₄×D₄	—	2	1	no	—
105	C₄×D₄	Dic₄₇	1	2	yes	—
106	C₄×D₄	C₂×D₄₇	1	2	yes	—
107	C₂×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
108	C₂×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
110	C₄⋊C₈	—	47	2	no	—
111	C₄⋊C₈	—	94	1	no	—
112	C₄×C₈	—	47	2	no	—
113	C₄×C₈	—	94	1	no	—
114	C₂⁴	—	2	1	no	—
115	C₂×D₄	—	2	2	no	—
116	C₂×D₄	—	2	1	no	—
117	C₂×D₄	C₄₇⋊C₈	1	4	yes	complemented
118	C₂×D₄	C₂×Dic₄₇	1	2	yes	—
119	C₂²×C₄	—	2	1	no	—
120	C₂²×C₄	—	2	2	no	—
121	C₂²×C₄	—	2	2	no	—
122	C₂²×C₄	—	4	2	no	—
123	C₂²×C₄	—	4	2	no	—
124	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
125	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
126	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
127	C₂×C₈	—	94	4	no	—
128	C₂×C₈	—	94	2	no	—
129	C₂×C₈	—	94	2	no	—
130	C₂×C₈	—	188	2	no	—
131	C₄⋊C₄	—	2	1	no	—
132	C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
133	C₂²⋊C₄	—	2	2	no	—
134	C₂²⋊C₄	—	2	2	no	—
135	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
136	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
137	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
138	C₄²	C₂²×D₄₇	1	1	yes	characteristic
139	C₂³	—	2	4	no	—
140	C₂³	—	2	2	no	—
141	C₂³	—	4	2	no	—
142	C₂³	—	4	2	no	—
143	C₂³	C₂²⋊Dic₄₇	1	1	yes	characteristic
144	D₄	—	2	4	no	—
145	D₄	—	2	2	no	—
146	D₄	C₂×C₄₇⋊C₈	1	4	yes	complemented
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	4	2	no	—
150	C₂×C₄	—	4	4	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	4	2	no	—
153	C₂×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
154	C₂×C₄	#10625329	1	2	yes	—
155	C₂×C₄	#10625334	1	2	yes	—
156	C₂×C₄	#10625335	1	2	yes	—
157	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
158	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
159	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
160	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
161	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
162	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
163	C₈	—	94	4	no	—
164	C₈	—	188	2	no	—
165	C₂²	—	2	4	no	—
166	C₂²	—	4	8	no	—
167	C₂²	—	4	2	no	—
168	C₂²	—	4	2	no	—
169	C₂²	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
170	C₂²	#13093945	1	2	yes	—
171	C₂²	#13093951	1	2	yes	—
172	C₂²	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	—	4	2	no	—
176	C₄	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
177	C₄	#13093945	1	2	yes	—
178	C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
179	C₄	C₂×#10625329	1	1	yes	characteristic
180	C₄	C₂×#10625334	1	1	yes	characteristic
181	C₄	C₂×#10625335	1	1	yes	characteristic
182	C₂	—	4	4	no	—
183	C₂	D₄⋊(C₄₇⋊C₈)	1	4	yes	direct product factor
184	C₂	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
185	C₂	C₂×#13093945	1	1	yes	characteristic
186	C₂	C₂×#13093951	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₄₇⋊C₈)

C₂

yes

maximal, characteristic, complemented

C₂×C₄×C₄₇⋊C₈

C₂

yes

maximal, characteristic, complemented

D₄⋊(C₄₇⋊C₈)

C₂

yes

maximal, direct product factor

C₂×C₄×D₄×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

complemented

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

C₂²

yes

complemented

C₂²×D₄×C₄₇

C₄

yes

characteristic

C₂³×C₄×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

C₄

yes

—

C₄×D₄×C₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₈

yes

complemented

C₂×D₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₄

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

C₂×C₈

yes

complemented

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

M₁₆

yes

—

C₂×C₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

SD₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊C₈

yes

—

C₂²×C₄₇

#102

yes

—

C₂²×C₄₇

#104

yes

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊C₈

yes

—

C₄×C₄₇

#102

yes

—

C₄×C₄₇

C₂²×C₈

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×D₄⋊C₈

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

D₄⋊C₈

yes

complemented

C₂×C₄₇

C₂×C₂²⋊C₈

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄×D₄

D₄₇

yes

characteristic

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

D₄⋊C₈

—

C₄₇

C₂×D₄⋊C₈

yes

characteristic, complemented, Sylow

C₂²×D₄

Dic₄₇

yes

characteristic

100

C₂³×C₄

—

101

C₂²×C₈

—

102

C₂²×C₈

—

103

C₄×D₄

—

104

C₄×D₄

—

105

C₄×D₄

Dic₄₇

yes

—

106

C₄×D₄

C₂×D₄₇

yes

—

107

C₂×C₄⋊C₄

Dic₄₇

yes

characteristic

108

C₂×C₂²⋊C₄

—

109

C₂×C₄²

C₂×D₄₇

yes

characteristic

110

C₄⋊C₈

—

111

C₄⋊C₈

—

112

C₄×C₈

—

113

C₄×C₈

—

114

C₂⁴

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

C₄₇⋊C₈

yes

complemented

118

C₂×D₄

C₂×Dic₄₇

yes

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

125

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

126

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

188

—

131

C₄⋊C₄

—

132

C₄⋊C₄

C₂×Dic₄₇

yes

—

133

C₂²⋊C₄

—

134

C₂²⋊C₄

—

135

C₄²

C₂×Dic₄₇

yes

characteristic

136

C₄²

C₂²⋊D₄₇

yes

characteristic

137

C₄²

C₂²⋊D₄₇

yes

characteristic

138

C₄²

C₂²×D₄₇

yes

characteristic

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

—

143

C₂³

C₂²⋊Dic₄₇

yes

characteristic

144

D₄

—

145

D₄

—

146

D₄

C₂×C₄₇⋊C₈

yes

complemented

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

C₂×C₄₇⋊C₈

yes

—

154

C₂×C₄

#10625329

yes

—

155

C₂×C₄

#10625334

yes

—

156

C₂×C₄

#10625335

yes

—

157

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

158

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

159

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

160

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

161

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

162

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

163

C₈

—

164

C₈

—

188

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

C₂²⋊(C₄₇⋊C₈)

yes

—

170

C₂²

#13093945

yes

—

171

C₂²

#13093951

yes

—

172

C₂²

C₂×C₂²⋊Dic₄₇

yes

characteristic

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

C₂²⋊(C₄₇⋊C₈)

yes

—

177

C₄

#13093945

yes

—

178

C₄

C₂²×C₄₇⋊C₈

yes

characteristic

179

C₄

C₂×#10625329

yes

characteristic

180

C₄

C₂×#10625334

yes

characteristic

181

C₄

C₂×#10625335

yes

characteristic

182

C₂

—

183

C₂

D₄⋊(C₄₇⋊C₈)

yes

direct product factor

184

C₂

C₂×C₂²⋊(C₄₇⋊C₈)

yes

characteristic

185

C₂

C₂×#13093945

yes

characteristic

186

C₂

C₂×#13093951

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂²×C₈
Frattini	C₄²	C₂²×D₄₇
Fitting	C₂×C₄×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂²⋊C₄
hypercenter	C₂×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂×D₄⋊C₈
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₄

subgroup

G/H

center

C₂²×C₄

C₂²⋊D₄₇

commutator

C₄×C₄₇

C₂²×C₈

Frattini

C₄²

C₂²×D₄₇

Fitting

C₂×C₄×D₄×C₄₇

C₂

socle

C₂³×C₄₇

C₂²⋊C₄

hypercenter

C₂×C₄×D₄

D₄₇

hypocenter

C₄₇

C₂×D₄⋊C₈

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₄

N	H ≅ G/N	type
1. C₂×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
2. C₂×C₄×C₄₇⋊C₈	C₂	semidirect
3. D₄⋊(C₄₇⋊C₈)	C₂	direct (N × H)
8. C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
10. C₄×C₄₇⋊C₈	C₂²	semidirect
23. C₂×D₄×C₄₇	C₈	semidirect
52. D₄×C₄₇	C₂×C₈	semidirect
90. C₂×C₄₇	D₄⋊C₈	semidirect
98. C₄₇	C₂×D₄⋊C₈	semidirect
117. C₂×D₄	C₄₇⋊C₈	semidirect
146. D₄	C₂×C₄₇⋊C₈	semidirect
183. C₂	D₄⋊(C₄₇⋊C₈)	direct (N × H)

H ≅ G/N

type

1. C₂×C₄⋊(C₄₇⋊C₈)

C₂

semidirect

2. C₂×C₄×C₄₇⋊C₈

C₂

semidirect

3. D₄⋊(C₄₇⋊C₈)

C₂

direct (N × H)

8. C₄⋊(C₄₇⋊C₈)

C₂²

semidirect

10. C₄×C₄₇⋊C₈

C₂²

semidirect

23. C₂×D₄×C₄₇

C₈

semidirect

52. D₄×C₄₇

C₂×C₈

semidirect

90. C₂×C₄₇

D₄⋊C₈

semidirect

98. C₄₇

C₂×D₄⋊C₈

semidirect

117. C₂×D₄

C₄₇⋊C₈

semidirect

146. D₄

C₂×C₄₇⋊C₈

semidirect

183. C₂

D₄⋊(C₄₇⋊C₈)

direct (N × H)

Subgroups — C₂×D₄⋊(C₄₇⋊C₈) #20241761

Conjugacy classes of subgroups

Complements

Subgroups — C2×D4⋊(C47⋊C8) #20241761

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₄⋊(C₄₇⋊C₈) #20241761