Group #26102808 — subgroups

Subgroups — #26102808

Order 12032.

474 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 175 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	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal
2	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	4	yes	—
4	C₂×C₄×C₄₇⋊C₈	—	2	2	no	—
5	#15688878	—	2	2	no	—
6	C₂³×C₈×C₄₇	C₄	1	2	yes	—
7	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
8	C₄₇×#336	—	2	2	no	—
9	C₂²×C₄₇⋊C₈	—	2	4	no	—
10	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
11	C₂²⋊(C₄₇⋊C₈)	C₈	1	8	yes	complemented
12	C₄×C₄₇⋊C₈	—	4	4	no	—
13	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
15	C₂²×C₈×C₄₇	—	2	2	no	—
16	C₂²×C₈×C₄₇	—	2	2	no	—
17	C₂²×C₈×C₄₇	—	4	2	no	—
18	C₂²×C₈×C₄₇	—	4	2	no	—
19	C₂²×C₈×C₄₇	C₈	1	4	yes	complemented
20	C₂×C₄²×C₄₇	—	4	2	no	—
21	C₂×C₄²×C₄₇	D₄	1	2	yes	—
22	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
24	C₂⁴×C₄₇	C₄²	1	1	yes	characteristic
25	C₂²×C₄×C₄₇	—	2	2	no	—
26	C₂²×C₄×C₄₇	—	2	1	no	—
27	C₂²×C₄×C₄₇	—	2	1	no	—
28	C₂²×C₄×C₄₇	—	4	2	no	—
29	C₂²×C₄×C₄₇	—	4	2	no	—
30	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
31	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
33	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
35	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
36	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
37	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
38	C₂×C₈×C₄₇	—	2	4	no	—
39	C₂×C₈×C₄₇	—	4	4	no	—
40	C₂×C₈×C₄₇	—	4	2	no	—
41	C₂×C₈×C₄₇	—	4	2	no	—
42	C₂×C₈×C₄₇	—	4	4	no	—
43	C₄²×C₄₇	—	2	4	no	—
44	C₄²×C₄₇	—	4	1	no	—
45	C₄²×C₄₇	—	4	1	no	—
46	C₂×C₄₇⋊C₈	—	2	8	no	—
47	C₂×C₄₇⋊C₈	—	4	4	no	—
48	C₂×C₄₇⋊C₈	—	4	4	no	—
49	C₂³×C₄₇	—	2	1	no	—
50	C₂³×C₄₇	—	2	1	no	—
51	C₂³×C₄₇	—	2	2	no	—
52	C₂³×C₄₇	#95	1	1	yes	characteristic
53	C₂³×C₄₇	C₄×C₈	1	2	yes	—
54	C₂³×C₄₇	C₄×C₈	1	1	yes	characteristic
55	C₂³×C₄₇	#97	1	2	yes	—
56	C₂³×C₄₇	#97	1	1	yes	characteristic
57	C₂×C₄×C₄₇	—	2	2	no	—
58	C₂×C₄×C₄₇	—	2	2	no	—
59	C₂×C₄×C₄₇	—	2	1	no	—
60	C₂×C₄×C₄₇	—	2	1	no	—
61	C₂×C₄×C₄₇	—	2	2	no	—
62	C₂×C₄×C₄₇	—	2	2	no	—
63	C₂×C₄×C₄₇	—	2	2	no	—
64	C₂×C₄×C₄₇	—	2	2	no	—
65	C₂×C₄×C₄₇	—	2	2	no	—
66	C₂×C₄×C₄₇	—	2	2	no	—
67	C₂×C₄×C₄₇	—	4	4	no	—
68	C₂×C₄×C₄₇	—	4	4	no	—
69	C₂×C₄×C₄₇	C₂²⋊C₈	1	4	yes	—
70	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
71	C₂×C₄×C₄₇	#99	1	2	yes	—
72	C₂×C₄×C₄₇	#100	1	1	yes	characteristic
73	C₂×C₄×C₄₇	#101	1	1	yes	characteristic
74	C₂×C₄×C₄₇	C₄⋊C₈	1	4	yes	—
75	C₂×C₄×C₄₇	C₄⋊C₈	1	2	yes	—
76	C₈×C₄₇	—	4	4	no	—
77	C₄₇⋊C₈	—	4	8	no	—
78	#7016	—	47	1	no	maximal, Sylow
79	C₂²×C₄₇	—	2	1	no	—
80	C₂²×C₄₇	—	2	1	no	—
81	C₂²×C₄₇	—	2	1	no	—
82	C₂²×C₄₇	—	2	1	no	—
83	C₂²×C₄₇	—	2	2	no	—
84	C₂²×C₄₇	—	2	2	no	—
85	C₂²×C₄₇	—	2	2	no	—
86	C₂²×C₄₇	—	2	2	no	—
87	C₂²×C₄₇	C₈²	1	1	yes	characteristic
88	C₂²×C₄₇	#322	1	1	yes	characteristic
89	C₂²×C₄₇	#322	1	2	yes	—
90	C₂²×C₄₇	#336	1	2	yes	—
91	C₂²×C₄₇	#336	1	1	yes	characteristic
92	C₂²×C₄₇	#342	1	1	yes	characteristic
93	C₂²×C₄₇	#343	1	1	yes	characteristic
94	C₂²×C₄₇	#344	1	2	yes	—
95	C₄×C₄₇	—	2	2	no	—
96	C₄×C₄₇	—	2	4	no	—
97	C₄×C₄₇	—	2	4	no	—
98	C₄×C₄₇	#323	1	2	yes	—
99	C₄×C₄₇	#324	1	2	yes	—
100	C₄×C₂²⋊C₈	—	47	2	no	—
101	C₂×#336	D₄₇	1	1	yes	characteristic
102	C₂×C₄₇	—	2	1	no	—
103	C₂×C₄₇	—	2	1	no	—
104	C₂×C₄₇	—	2	2	no	—
105	C₂×C₄₇	#1273	1	1	yes	characteristic
106	C₂×C₄₇	#1280	1	1	yes	characteristic
107	C₂×C₄₇	#1281	1	1	yes	characteristic
108	C₂×C₄₇	#1282	1	2	yes	—
109	C₂×C₄₇	#1283	1	2	yes	—
110	C₂³×C₈	Dic₄₇	1	2	yes	—
111	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
112	C₂×C₂²⋊C₈	—	47	4	no	—
113	C₂×C₄×C₈	—	94	2	no	—
114	#336	—	2	2	no	—
115	#336	—	94	2	no	—
116	C₄₇	#7016	1	1	yes	characteristic, complemented, Sylow
117	C₂³×C₄	C₄×D₄₇	1	2	yes	—
118	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
119	C₂²×C₈	—	2	2	no	—
120	C₂²×C₈	—	2	2	no	—
121	C₂²×C₈	—	4	2	no	—
122	C₂²×C₈	—	4	2	no	—
123	C₂²×C₈	—	94	4	no	—
124	C₂²×C₈	C₄₇⋊C₈	1	4	yes	complemented
125	C₂×C₄²	—	4	2	no	—
126	C₂×C₄²	Dic₉₄	1	1	yes	characteristic
127	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
128	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
129	C₂²⋊C₈	—	47	8	no	—
130	C₂²⋊C₈	—	94	4	no	—
131	C₄×C₈	—	188	4	no	—
132	C₂⁴	C₄×Dic₄₇	1	1	yes	characteristic
133	C₂²×C₄	—	2	2	no	—
134	C₂²×C₄	—	2	1	no	—
135	C₂²×C₄	—	2	1	no	—
136	C₂²×C₄	—	4	2	no	—
137	C₂²×C₄	—	4	2	no	—
138	C₂²×C₄	C₈×D₄₇	1	4	yes	—
139	C₂²×C₄	#10625324	1	4	yes	—
140	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
141	C₂²×C₄	#10625329	1	2	yes	—
142	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
143	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
144	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
145	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	—	4	4	no	—
148	C₂×C₈	—	4	2	no	—
149	C₂×C₈	—	4	2	no	—
150	C₂×C₈	—	4	4	no	—
151	C₂×C₈	—	94	8	no	—
152	C₂×C₈	—	188	4	no	—
153	C₂×C₈	—	188	4	no	—
154	C₄²	—	2	4	no	—
155	C₄²	—	4	1	no	—
156	C₄²	—	4	1	no	—
157	C₂³	—	2	1	no	—
158	C₂³	—	2	1	no	—
159	C₂³	—	2	2	no	—
160	C₂³	C₄₇⋊#95	1	1	yes	characteristic
161	C₂³	C₈×Dic₄₇	1	2	yes	—
162	C₂³	C₄×C₄₇⋊C₈	1	1	yes	characteristic
163	C₂³	#13093934	1	2	yes	—
164	C₂³	#13093935	1	1	yes	characteristic
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	(C₂×D₄₇)⋊C₈	1	4	yes	—
178	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
179	C₂×C₄	#13093939	1	2	yes	—
180	C₂×C₄	#13093941	1	1	yes	characteristic
181	C₂×C₄	#13093943	1	1	yes	characteristic
182	C₂×C₄	Dic₄₇⋊C₈	1	4	yes	—
183	C₂×C₄	C₄⋊(C₄₇⋊C₈)	1	2	yes	—
184	C₈	—	4	4	no	—
185	C₈	—	188	8	no	—
186	C₂²	—	2	1	no	—
187	C₂²	—	2	1	no	—
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	2	2	no	—
192	C₂²	—	2	2	no	—
193	C₂²	—	2	2	no	—
194	C₂²	C₈×C₄₇⋊C₈	1	1	yes	characteristic
195	C₂²	#15688844	1	1	yes	characteristic
196	C₂²	#15688845	1	2	yes	—
197	C₂²	#15688877	1	2	yes	—
198	C₂²	#15688878	1	1	yes	characteristic
199	C₂²	#15688890	1	1	yes	characteristic
200	C₂²	#15688892	1	1	yes	characteristic
201	C₂²	#15688894	1	2	yes	—
202	C₄	—	2	2	no	—
203	C₄	—	2	4	no	—
204	C₄	—	2	4	no	—
205	C₄	#15688847	1	2	yes	—
206	C₄	#15688849	1	2	yes	—
207	C₂	—	2	1	no	—
208	C₂	—	2	1	no	—
209	C₂	—	2	2	no	—
210	C₂	C₄₇⋊#1273	1	1	yes	characteristic
211	C₂	#20241231	1	1	yes	characteristic
212	C₂	#20241233	1	1	yes	characteristic
213	C₂	#20241235	1	2	yes	—
214	C₂	#20241238	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₂²⋊(C₄₇⋊C₈)

C₂

yes

maximal

C₂×C₄₇×#336

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₄₇⋊C₈)

C₄

yes

—

C₂×C₄×C₄₇⋊C₈

—

#15688878

—

C₂³×C₈×C₄₇

C₄

yes

—

C₂²×C₄²×C₄₇

C₂²

yes

characteristic

C₄₇×#336

—

C₂²×C₄₇⋊C₈

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

C₈

yes

complemented

C₄×C₄₇⋊C₈

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₈

yes

complemented

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

Q₈

yes

characteristic

C₂⁴×C₄₇

C₄²

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₈

yes

—

C₂²×C₄×C₄₇

C₂×C₈

yes

—

C₂²×C₄×C₄₇

M₁₆

yes

—

C₂²×C₄×C₄₇

M₁₆

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#95

yes

characteristic

C₂³×C₄₇

C₄×C₈

yes

—

C₂³×C₄₇

C₄×C₈

yes

characteristic

C₂³×C₄₇

#97

yes

—

C₂³×C₄₇

#97

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

C₂×C₄×C₄₇

#99

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₄⋊C₈

yes

—

C₂×C₄×C₄₇

C₄⋊C₈

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

#7016

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₈²

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#336

yes

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#323

yes

—

C₄×C₄₇

#324

yes

—

100

C₄×C₂²⋊C₈

—

101

C₂×#336

D₄₇

yes

characteristic

102

C₂×C₄₇

—

103

C₂×C₄₇

—

104

C₂×C₄₇

—

105

C₂×C₄₇

#1273

yes

characteristic

106

C₂×C₄₇

#1280

yes

characteristic

107

C₂×C₄₇

#1281

yes

characteristic

108

C₂×C₄₇

#1282

yes

—

109

C₂×C₄₇

#1283

yes

—

110

C₂³×C₈

Dic₄₇

yes

—

111

C₂²×C₄²

C₂×D₄₇

yes

characteristic

112

C₂×C₂²⋊C₈

—

113

C₂×C₄×C₈

—

114

#336

—

115

#336

—

116

C₄₇

#7016

yes

characteristic, complemented, Sylow

117

C₂³×C₄

C₄×D₄₇

yes

—

118

C₂³×C₄

C₂×Dic₄₇

yes

characteristic

119

C₂²×C₈

—

120

C₂²×C₈

—

121

C₂²×C₈

—

122

C₂²×C₈

—

123

C₂²×C₈

—

124

C₂²×C₈

C₄₇⋊C₈

yes

complemented

125

C₂×C₄²

—

126

C₂×C₄²

Dic₉₄

yes

characteristic

127

C₂×C₄²

D₁₈₈

yes

characteristic

128

C₂×C₄²

C₂²⋊D₄₇

yes

—

129

C₂²⋊C₈

—

130

C₂²⋊C₈

—

131

C₄×C₈

—

188

—

132

C₂⁴

C₄×Dic₄₇

yes

characteristic

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

C₈×D₄₇

yes

—

139

C₂²×C₄

#10625324

yes

—

140

C₂²×C₄

C₂×C₄₇⋊C₈

yes

—

141

C₂²×C₄

#10625329

yes

—

142

C₂²×C₄

Dic₄₇⋊C₄

yes

—

143

C₂²×C₄

C₄⋊Dic₄₇

yes

characteristic

144

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

145

C₂²×C₄

C₂²⋊Dic₄₇

yes

characteristic

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

188

—

153

C₂×C₈

—

188

—

154

C₄²

—

155

C₄²

—

156

C₄²

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

C₄₇⋊#95

yes

characteristic

161

C₂³

C₈×Dic₄₇

yes

—

162

C₂³

C₄×C₄₇⋊C₈

yes

characteristic

163

C₂³

#13093934

yes

—

164

C₂³

#13093935

yes

characteristic

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

(C₂×D₄₇)⋊C₈

yes

—

178

C₂×C₄

C₂²⋊(C₄₇⋊C₈)

yes

—

179

C₂×C₄

#13093939

yes

—

180

C₂×C₄

#13093941

yes

characteristic

181

C₂×C₄

#13093943

yes

characteristic

182

C₂×C₄

Dic₄₇⋊C₈

yes

—

183

C₂×C₄

C₄⋊(C₄₇⋊C₈)

yes

—

184

C₈

—

185

C₈

—

188

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

C₈×C₄₇⋊C₈

yes

characteristic

195

C₂²

#15688844

yes

characteristic

196

C₂²

#15688845

yes

—

197

C₂²

#15688877

yes

—

198

C₂²

#15688878

yes

characteristic

199

C₂²

#15688890

yes

characteristic

200

C₂²

#15688892

yes

characteristic

201

C₂²

#15688894

yes

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

#15688847

yes

—

206

C₄

#15688849

yes

—

207

C₂

—

208

C₂

—

209

C₂

—

210

C₂

C₄₇⋊#1273

yes

characteristic

211

C₂

#20241231

yes

characteristic

212

C₂

#20241233

yes

characteristic

213

C₂

#20241235

yes

—

214

C₂

#20241238

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₄₇
commutator	C₂²×C₄₇	C₈²
Frattini	C₂²×C₄²	C₂×D₄₇
Fitting	C₂×C₄₇×#336	C₂
socle	C₂³×C₄₇	#95
prime radical	C₂⁴×C₄₇	C₄²
cosocle	C₂²×C₄²×C₄₇	C₂²
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	#7016
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#336

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₄₇

commutator

C₂²×C₄₇

C₈²

Frattini

C₂²×C₄²

C₂×D₄₇

Fitting

C₂×C₄₇×#336

C₂

socle

C₂³×C₄₇

#95

prime radical

C₂⁴×C₄₇

C₄²

cosocle

C₂²×C₄²×C₄₇

C₂²

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#336

N	H ≅ G/N	type
11. C₂²⋊(C₄₇⋊C₈)	C₈	semidirect
19. C₂²×C₈×C₄₇	C₈	semidirect
116. C₄₇	#7016	semidirect
124. C₂²×C₈	C₄₇⋊C₈	semidirect

H ≅ G/N

type

11. C₂²⋊(C₄₇⋊C₈)

C₈

semidirect

19. C₂²×C₈×C₄₇

C₈

semidirect

116. C₄₇

#7016

semidirect

124. C₂²×C₈

C₄₇⋊C₈

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₂×C₄₇×#336	2
#7016	47

subgroup

index

C₄×C₂²⋊(C₄₇⋊C₈)

C₂×C₄₇×#336

#7016

Subgroups — #26102808

Conjugacy classes of subgroups

Complements

Maximal subgroups