Group #20246221 — subgroups

Subgroups — Q₈×(C₂×D₄₇)⋊C₄ #20246221

Order 6016.

820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 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×Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689029	C₂	1	3	yes	maximal, complemented
4	#15689028	C₂	1	3	yes	maximal, complemented
5	#15688980	C₂	1	3	yes	maximal
6	C₄×(C₂×D₄₇)⋊C₄	C₂	1	3	yes	maximal
7	C₂×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₉₄	C₂²	1	3	yes	—
9	C₂×Q₈×D₄₇	—	2	4	no	—
10	C₂×Q₈×D₄₇	—	2	4	no	—
11	C₂×Q₈×D₄₇	C₄	1	8	yes	complemented
12	C₂²×C₄×D₄₇	C₂²	1	3	yes	—
13	Q₈×Dic₄₇	—	2	4	no	—
14	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
15	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
16	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
18	C₄₇⋊#95	C₂²	1	3	yes	—
19	C₄₇⋊#95	C₂²	1	3	yes	—
20	C₄₇⋊#95	C₂²	1	6	yes	—
21	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₄×Q₈×C₄₇	—	2	4	no	—
23	C₂×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
24	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
25	C₂³×D₄₇	C₂³	1	1	yes	characteristic
26	C₂×Q₈×C₄₇	C₂×C₄	1	4	yes	—
27	C₂×Q₈×C₄₇	D₄	1	4	yes	—
28	C₂×Q₈×C₄₇	D₄	1	4	yes	—
29	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
30	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
32	C₂²×Dic₄₇	C₂³	1	3	yes	—
33	C₂²×Dic₄₇	C₂³	1	3	yes	—
34	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
35	Q₈×D₄₇	—	2	32	no	—
36	C₂×C₄×D₄₇	—	2	6	no	—
37	C₂×C₄×D₄₇	—	2	6	no	—
38	C₂×C₄×D₄₇	C₂×C₄	1	12	yes	—
39	C₂×Dic₉₄	—	2	6	no	—
40	C₂×Dic₉₄	—	2	6	no	—
41	C₂×Dic₉₄	C₂×C₄	1	12	yes	—
42	C₄⋊C₄×C₄₇	—	2	6	no	—
43	C₄²×C₄₇	—	2	6	no	—
44	(C₂×D₄₇)⋊C₄	—	2	6	no	—
45	(C₂×D₄₇)⋊C₄	Q₈	1	4	yes	direct product factor
46	C₄⋊Dic₄₇	—	2	6	no	—
47	C₄×Dic₄₇	—	2	6	no	—
48	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
49	C₂²×D₄₇	—	2	1	no	—
50	C₂²×D₄₇	—	2	1	no	—
51	C₂²×D₄₇	—	2	1	no	—
52	C₂²×D₄₇	—	2	1	no	—
53	C₂²×D₄₇	C₂²×C₄	1	2	yes	—
54	C₂²×D₄₇	C₂×Q₈	1	2	yes	—
55	C₂²×D₄₇	#41	1	2	yes	—
56	Q₈×C₄₇	C₂²⋊C₄	1	16	yes	complemented
57	C₂×C₄×C₄₇	—	2	1	no	—
58	C₂×C₄×C₄₇	—	2	1	no	—
59	C₂×C₄×C₄₇	—	2	3	no	—
60	C₂×C₄×C₄₇	—	2	3	no	—
61	C₂×C₄×C₄₇	—	2	3	no	—
62	C₂×C₄×C₄₇	C₂²×C₄	1	6	yes	—
63	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
64	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
65	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	complemented
66	C₂×Dic₄₇	—	2	1	no	—
67	C₂×Dic₄₇	—	2	3	no	—
68	C₂×Dic₄₇	—	2	3	no	—
69	C₂×Dic₄₇	—	2	1	no	—
70	C₂×Dic₄₇	—	2	3	no	—
71	C₂×Dic₄₇	—	2	3	no	—
72	C₂×Dic₄₇	—	2	3	no	—
73	C₂×Dic₄₇	C₂²×C₄	1	6	yes	—
74	C₂×Dic₄₇	C₂×Q₈	1	2	yes	complemented
75	C₄×D₄₇	—	2	24	no	—
76	Dic₉₄	—	2	24	no	—
77	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
78	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
79	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
80	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
81	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
82	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
83	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
84	C₂×D₄₇	—	2	2	no	—
85	C₂×D₄₇	—	2	2	no	—
86	C₂×D₄₇	—	2	2	no	—
87	C₂×D₄₇	—	2	2	no	—
88	C₂×D₄₇	—	2	2	no	—
89	C₂×D₄₇	—	2	2	no	—
90	C₂×D₄₇	C₄×Q₈	1	4	yes	complemented
91	C₄×C₄₇	—	2	2	no	—
92	C₄×C₄₇	—	4	3	no	—
93	C₄×C₄₇	C₂×C₂²⋊C₄	1	12	yes	—
94	Dic₄₇	—	2	6	no	—
95	Dic₄₇	—	2	2	no	—
96	Dic₄₇	—	4	3	no	—
97	Q₈×C₂²⋊C₄	—	47	1	no	maximal, Sylow
98	C₂×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
100	C₂×C₄₇	#519	1	1	yes	characteristic
101	C₂×C₄₇	#548	1	1	yes	characteristic
102	C₂×C₄₇	#548	1	1	yes	characteristic
103	C₂×C₄₇	D₄×Q₈	1	1	yes	characteristic
104	C₂×C₄₇	D₄×Q₈	1	1	yes	characteristic
105	D₄₇	—	2	4	no	—
106	C₂³×Q₈	—	47	1	no	—
107	C₂×C₄×Q₈	—	47	1	no	—
108	C₂×C₄×Q₈	D₄₇	1	1	yes	characteristic, complemented
109	#391	—	47	3	no	—
110	#391	—	47	3	no	—
111	#380	—	47	3	no	—
112	C₄×C₂²⋊C₄	—	47	3	no	—
113	C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
114	C₂²×Q₈	—	47	8	no	—
115	C₂²×Q₈	—	47	3	no	—
116	C₂²×Q₈	—	94	4	no	—
117	C₂²×Q₈	—	94	4	no	—
118	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
119	C₂³×C₄	—	47	3	no	—
120	C₄×Q₈	—	2	4	no	—
121	C₄×Q₈	—	94	4	no	—
122	C₂×C₄⋊C₄	—	47	3	no	—
123	C₂×C₄⋊C₄	C₂×D₄₇	1	3	yes	—
124	C₂×C₂²⋊C₄	—	47	1	no	—
125	C₂×C₂²⋊C₄	—	47	3	no	—
126	C₂×C₄²	—	47	3	no	—
127	C₂×C₄²	C₂×D₄₇	1	3	yes	—
128	#95	—	47	3	no	—
129	#95	—	47	3	no	—
130	#95	—	47	6	no	—
131	C₂⁴	—	47	1	no	—
132	C₂×Q₈	—	47	12	no	—
133	C₂×Q₈	—	94	32	no	—
134	C₂×Q₈	—	94	6	no	—
135	C₂×Q₈	—	94	6	no	—
136	C₂×Q₈	C₄×D₄₇	1	4	yes	—
137	C₂×Q₈	D₁₈₈	1	4	yes	—
138	C₂×Q₈	C₂²⋊D₄₇	1	4	yes	—
139	C₂²×C₄	—	47	3	no	—
140	C₂²×C₄	—	47	1	no	—
141	C₂²×C₄	—	47	12	no	—
142	C₂²×C₄	—	47	3	no	—
143	C₂²×C₄	—	94	6	no	—
144	C₂²×C₄	—	94	6	no	—
145	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
146	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
147	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
148	C₄⋊C₄	—	2	6	no	—
149	C₄⋊C₄	—	94	6	no	—
150	C₂²⋊C₄	—	47	4	no	—
151	C₂²⋊C₄	—	94	6	no	—
152	C₄²	—	2	6	no	—
153	C₄²	—	94	6	no	—
154	C₂³	—	47	2	no	—
155	C₂³	—	47	2	no	—
156	C₂³	—	47	2	no	—
157	C₂³	—	94	1	no	—
158	C₂³	—	94	1	no	—
159	C₂³	—	94	1	no	—
160	C₂³	—	94	1	no	—
161	C₂³	C₂³×D₄₇	1	1	yes	characteristic
162	Q₈	—	94	24	no	—
163	Q₈	(C₂×D₄₇)⋊C₄	1	16	yes	direct product factor
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	3	no	—
167	C₂×C₄	—	2	3	no	—
168	C₂×C₄	—	2	3	no	—
169	C₂×C₄	—	47	6	no	—
170	C₂×C₄	—	47	2	no	—
171	C₂×C₄	—	94	3	no	—
172	C₂×C₄	—	94	1	no	—
173	C₂×C₄	—	94	3	no	—
174	C₂×C₄	—	94	1	no	—
175	C₂×C₄	—	94	24	no	—
176	C₂×C₄	—	94	3	no	—
177	C₂×C₄	—	94	3	no	—
178	C₂×C₄	—	94	3	no	—
179	C₂×C₄	C₂×C₄×D₄₇	1	6	yes	—
180	C₂×C₄	C₂×D₁₈₈	1	6	yes	—
181	C₂×C₄	Q₈×D₄₇	1	2	yes	complemented
182	C₂×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
183	C₂²	—	47	4	no	—
184	C₂²	—	94	2	no	—
185	C₂²	—	94	2	no	—
186	C₂²	—	94	2	no	—
187	C₂²	—	94	2	no	—
188	C₂²	—	94	2	no	—
189	C₂²	—	94	2	no	—
190	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
191	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
192	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
193	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
194	C₂²	#41×D₄₇	1	1	yes	characteristic
195	C₂²	#13094071	1	1	yes	characteristic
196	C₂²	#13094072	1	1	yes	characteristic
197	C₄	—	2	2	no	—
198	C₄	—	4	3	no	—
199	C₄	—	94	2	no	—
200	C₄	—	94	6	no	—
201	C₄	—	188	3	no	—
202	C₄	C₂×(C₂×D₄₇)⋊C₄	1	12	yes	—
203	C₂	—	94	4	no	—
204	C₂	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
205	C₂	C₄×Q₈×D₄₇	1	1	yes	characteristic
206	C₂	#15689599	1	1	yes	characteristic
207	C₂	#15689780	1	1	yes	characteristic
208	C₂	#15689785	1	1	yes	characteristic
209	C₂	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
210	C₂	Q₈×D₁₈₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Q₈×D₄₇

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₄₇

C₂

yes

maximal, characteristic, complemented

#15689029

C₂

yes

maximal, complemented

#15689028

C₂

yes

maximal, complemented

#15688980

C₂

yes

maximal

C₄×(C₂×D₄₇)⋊C₄

C₂

yes

maximal

C₂×C₄×Q₈×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₉₄

C₂²

yes

—

C₂×Q₈×D₄₇

—

C₂×Q₈×D₄₇

—

C₂×Q₈×D₄₇

C₄

yes

complemented

C₂²×C₄×D₄₇

C₂²

yes

—

Q₈×Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

C₂³×D₄₇

C₂³

yes

characteristic

C₂×Q₈×C₄₇

C₂×C₄

yes

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

Q₈×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂×C₄

yes

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

Q₈

yes

direct product factor

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂²×C₄

yes

—

C₂²×D₄₇

C₂×Q₈

yes

—

C₂²×D₄₇

#41

yes

—

Q₈×C₄₇

C₂²⋊C₄

yes

complemented

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

complemented

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

C₂×Q₈

yes

complemented

C₄×D₄₇

—

Dic₉₄

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

C₄×Q₈

yes

complemented

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Q₈×C₂²⋊C₄

—

maximal, Sylow

C₂×C₄₇

C₂²×C₂²⋊C₄

yes

characteristic

C₂×C₄₇

C₂×C₄×Q₈

yes

characteristic

100

C₂×C₄₇

#519

yes

characteristic

101

C₂×C₄₇

#548

yes

characteristic

102

C₂×C₄₇

#548

yes

characteristic

103

C₂×C₄₇

D₄×Q₈

yes

characteristic

104

C₂×C₄₇

D₄×Q₈

yes

characteristic

105

D₄₇

—

106

C₂³×Q₈

—

107

C₂×C₄×Q₈

—

108

C₂×C₄×Q₈

D₄₇

yes

characteristic, complemented

109

#391

—

110

#391

—

111

#380

—

112

C₄×C₂²⋊C₄

—

113

C₄₇

Q₈×C₂²⋊C₄

yes

characteristic, complemented, Sylow

114

C₂²×Q₈

—

115

C₂²×Q₈

—

116

C₂²×Q₈

—

117

C₂²×Q₈

—

118

C₂²×Q₈

C₂×D₄₇

yes

characteristic

119

C₂³×C₄

—

120

C₄×Q₈

—

121

C₄×Q₈

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

124

C₂×C₂²⋊C₄

—

125

C₂×C₂²⋊C₄

—

126

C₂×C₄²

—

127

C₂×C₄²

C₂×D₄₇

yes

—

128

#95

—

129

#95

—

130

#95

—

131

C₂⁴

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

C₄×D₄₇

yes

—

137

C₂×Q₈

D₁₈₈

yes

—

138

C₂×Q₈

C₂²⋊D₄₇

yes

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

C₂²×D₄₇

yes

—

146

C₂²×C₄

C₂²×D₄₇

yes

characteristic

147

C₂²×C₄

C₂²×D₄₇

yes

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₂²⋊C₄

—

151

C₂²⋊C₄

—

152

C₄²

—

153

C₄²

—

154

C₂³

—

155

C₂³

—

156

C₂³

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

C₂³×D₄₇

yes

characteristic

162

Q₈

—

163

Q₈

(C₂×D₄₇)⋊C₄

yes

direct product factor

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

C₂×C₄×D₄₇

yes

—

180

C₂×C₄

C₂×D₁₈₈

yes

—

181

C₂×C₄

Q₈×D₄₇

yes

complemented

182

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

C₂²×C₄×D₄₇

yes

characteristic

191

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

192

C₂²

C₂²×D₁₈₈

yes

characteristic

193

C₂²

C₂×Q₈×D₄₇

yes

characteristic

194

C₂²

#41×D₄₇

yes

characteristic

195

C₂²

#13094071

yes

characteristic

196

C₂²

#13094072

yes

characteristic

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

188

—

202

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

—

203

C₂

—

204

C₂

C₂²×(C₂×D₄₇)⋊C₄

yes

characteristic

205

C₂

C₄×Q₈×D₄₇

yes

characteristic

206

C₂

#15689599

yes

characteristic

207

C₂

#15689780

yes

characteristic

208

C₂

#15689785

yes

characteristic

209

C₂

Q₈×C₂²⋊D₄₇

yes

characteristic

210

C₂

Q₈×D₁₈₈

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₂×C₄×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×C₄×Q₈	D₄₇
hypocenter	C₄₇	Q₈×C₂²⋊C₄
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Fitting

C₂×C₄×Q₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂⁴

hypercenter

C₂×C₄×Q₈

D₄₇

hypocenter

C₄₇

Q₈×C₂²⋊C₄

LCS

G ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
2. C₂×Q₈×Dic₄₇	C₂	semidirect
3. #15689029	C₂	semidirect
4. #15689028	C₂	semidirect
7. C₂×C₄×Q₈×C₄₇	C₂	semidirect
11. C₂×Q₈×D₄₇	C₄	semidirect
45. (C₂×D₄₇)⋊C₄	Q₈	direct (N × H)
56. Q₈×C₄₇	C₂²⋊C₄	semidirect
65. C₂×C₄×C₄₇	C₂×Q₈	semidirect
74. C₂×Dic₄₇	C₂×Q₈	semidirect
90. C₂×D₄₇	C₄×Q₈	semidirect
108. C₂×C₄×Q₈	D₄₇	semidirect
113. C₄₇	Q₈×C₂²⋊C₄	semidirect
163. Q₈	(C₂×D₄₇)⋊C₄	direct (N × H)
181. C₂×C₄	Q₈×D₄₇	semidirect

H ≅ G/N

type

2. C₂×Q₈×Dic₄₇

C₂

semidirect

3. #15689029

C₂

semidirect

4. #15689028

C₂

semidirect

7. C₂×C₄×Q₈×C₄₇

C₂

semidirect

11. C₂×Q₈×D₄₇

C₄

semidirect

45. (C₂×D₄₇)⋊C₄

Q₈

direct (N × H)

56. Q₈×C₄₇

C₂²⋊C₄

semidirect

65. C₂×C₄×C₄₇

C₂×Q₈

semidirect

74. C₂×Dic₄₇

C₂×Q₈

semidirect

90. C₂×D₄₇

C₄×Q₈

semidirect

108. C₂×C₄×Q₈

D₄₇

semidirect

113. C₄₇

Q₈×C₂²⋊C₄

semidirect

163. Q₈

(C₂×D₄₇)⋊C₄

direct (N × H)

181. C₂×C₄

Q₈×D₄₇

semidirect

Subgroups — Q₈×(C₂×D₄₇)⋊C₄ #20246221

Conjugacy classes of subgroups

Complements

Subgroups — Q8×(C2×D47)⋊C4 #20246221

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×(C₂×D₄₇)⋊C₄ #20246221