Group #26368865 — subgroups

Subgroups — #26368865

Order 12032.

910 conjugacy classes of subgroups; only the 299 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 299 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×#15689526	C₂	1	2	yes	maximal
2	C₂×#15689519	C₂	1	2	yes	maximal
3	#20251786	C₂	1	1	yes	maximal, characteristic
4	#20243557	C₂	1	8	yes	maximal
5	C₄×#13093935	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#2862	C₂	1	1	yes	maximal, characteristic
7	C₂×#13094024	—	2	2	no	—
8	C₂×#13094024	C₂²	1	2	yes	—
9	#15689526	—	2	8	no	—
10	#15689519	—	2	8	no	—
11	C₂×#13093957	C₂²	1	8	yes	—
12	C₂×#13093955	C₂²	1	8	yes	—
13	C₂×#13093935	C₂²	1	4	yes	—
14	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
15	#15688993	—	2	2	no	—
16	#15688993	C₂²	1	4	yes	—
17	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#391	—	2	2	no	—
20	C₄₇×#391	—	2	2	no	—
21	C₄₇×#382	C₂²	1	4	yes	—
22	C₄³×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×Dic₉₄	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
25	#13094024	—	2	4	no	—
26	#13094024	—	2	4	no	—
27	#13094024	—	4	8	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	8	no	—
30	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
31	#13093957	—	2	16	no	—
32	#13093955	—	2	16	no	—
33	#13093935	Q₈	1	16	yes	complemented
34	C₄×C₄₇⋊C₈	D₄	1	8	yes	—
35	C₂²×Q₈×C₄₇	—	2	1	no	—
36	C₂²×Q₈×C₄₇	—	2	1	no	—
37	C₄⋊Q₈×C₄₇	—	2	4	no	—
38	C₄⋊Q₈×C₄₇	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
41	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
42	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
43	C₂×C₄²×C₄₇	D₄	1	2	yes	—
44	C₂×C₄²×C₄₇	D₄	1	2	yes	—
45	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
47	#95×C₄₇	—	2	8	no	—
48	C₂×Q₈×C₄₇	—	4	2	no	—
49	C₂×Q₈×C₄₇	—	4	2	no	—
50	C₂×Q₈×C₄₇	—	4	4	no	—
51	C₂×Q₈×C₄₇	—	4	4	no	—
52	C₂²×C₄×C₄₇	—	2	2	no	—
53	C₂²×C₄×C₄₇	—	2	2	no	—
54	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
55	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
58	C₂²×Dic₄₇	—	2	4	no	—
59	C₂×Dic₉₄	—	4	4	no	—
60	C₂×Dic₉₄	—	4	8	no	—
61	C₄⋊C₄×C₄₇	—	2	4	no	—
62	C₄⋊C₄×C₄₇	—	2	4	no	—
63	C₄⋊C₄×C₄₇	—	4	2	no	—
64	C₄⋊C₄×C₄₇	—	4	2	no	—
65	C₄²×C₄₇	—	2	4	no	—
66	C₄²×C₄₇	—	2	4	no	—
67	C₄²×C₄₇	C₂×D₄	1	4	yes	—
68	C₄²×C₄₇	C₂×Q₈	1	8	yes	—
69	C₄⋊Dic₄₇	—	2	4	no	—
70	C₄⋊Dic₄₇	—	2	4	no	—
71	C₄⋊Dic₄₇	—	4	16	no	—
72	C₄⋊Dic₄₇	—	4	4	no	—
73	C₂×C₄₇⋊C₈	C₂×D₄	1	8	yes	—
74	C₂×C₄₇⋊C₈	C₂×Q₈	1	16	yes	—
75	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
76	Q₈×C₄₇	—	8	4	no	—
77	Q₈×C₄₇	—	8	4	no	—
78	C₂×C₄×C₄₇	—	2	4	no	—
79	C₂×C₄×C₄₇	—	2	4	no	—
80	C₂×C₄×C₄₇	—	4	2	no	—
81	C₂×C₄×C₄₇	—	4	2	no	—
82	C₂×C₄×C₄₇	—	4	4	no	—
83	C₂×C₄×C₄₇	—	4	4	no	—
84	C₂×C₄×C₄₇	#127	1	2	yes	—
85	C₂×C₄×C₄₇	#127	1	2	yes	—
86	C₂×C₄×C₄₇	C₄⋊Q₈	1	8	yes	—
87	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
88	C₂×C₄×C₄₇	#137	1	4	yes	—
89	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
90	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
91	C₂×Dic₄₇	—	4	4	no	—
92	C₂×Dic₄₇	—	4	8	no	—
93	Dic₉₄	—	8	8	no	—
94	C₄₇⋊C₈	C₄⋊Q₈	1	16	yes	complemented
95	#33314	—	47	1	no	maximal, Sylow
96	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
97	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
98	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
99	C₂²×C₄₇	C₂×#137	1	2	yes	—
100	C₄×C₄₇	—	2	8	no	—
101	C₄×C₄₇	—	8	2	no	—
102	C₄×C₄₇	—	8	2	no	—
103	C₄×C₄₇	#496	1	4	yes	—
104	C₄×C₄₇	#497	1	4	yes	—
105	C₄×C₄₇	C₂×C₄⋊Q₈	1	4	yes	—
106	Dic₄₇	—	8	4	no	—
107	C₂×#500	—	47	2	no	—
108	C₂×#498	—	47	2	no	—
109	#2868	—	47	1	no	—
110	#2862	D₄₇	1	1	yes	characteristic
111	#1847	—	47	8	no	—
112	C₄×#97	—	47	1	no	—
113	C₂×C₄₇	#2868	1	1	yes	characteristic
114	C₂×C₄₇	C₂×#496	1	1	yes	characteristic
115	C₂×C₄₇	C₂×#497	1	1	yes	characteristic
116	C₂×C₄₇	#3165	1	4	yes	—
117	C₂×C₄⋊Q₈	—	47	2	no	—
118	C₂×C₄⋊Q₈	—	94	2	no	—
119	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
120	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
121	#500	—	94	8	no	—
122	#498	—	94	8	no	—
123	C₂×#107	—	47	8	no	—
124	C₂×#106	—	47	8	no	—
125	C₂×#97	—	47	4	no	—
126	C₂×C₄×C₈	—	47	2	no	—
127	#391	—	2	2	no	—
128	#391	—	2	2	no	—
129	#384	—	47	4	no	—
130	#384	—	94	2	no	—
131	#382	C₂×D₄₇	1	4	yes	—
132	C₄³	C₂×D₄₇	1	1	yes	characteristic
133	C₄₇	#33314	1	1	yes	characteristic, complemented, Sylow
134	C₂²×Q₈	—	2	1	no	—
135	C₂²×Q₈	—	2	1	no	—
136	C₂²×Q₈	—	94	2	no	—
137	C₂²×C₈	—	47	4	no	—
138	C₄⋊Q₈	—	2	4	no	—
139	C₄⋊Q₈	—	2	4	no	—
140	C₄⋊Q₈	—	94	4	no	—
141	C₄⋊Q₈	—	94	4	no	—
142	C₄⋊Q₈	—	188	8	no	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	C₂×C₄⋊C₄	—	2	1	no	—
145	C₂×C₄⋊C₄	—	47	4	no	—
146	C₂×C₄⋊C₄	—	94	2	no	—
147	C₂×C₄⋊C₄	—	94	8	no	—
148	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
149	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
150	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
151	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
152	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
153	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
154	#107	—	94	16	no	—
155	#106	—	94	16	no	—
156	#97	—	47	16	no	—
157	C₄×C₈	—	47	8	no	—
158	#95	—	2	8	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	4	no	—
162	C₂×Q₈	—	4	4	no	—
163	C₂×Q₈	—	188	4	no	—
164	C₂×Q₈	—	188	8	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	94	4	no	—
168	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
169	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
170	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
171	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
172	C₂×C₈	—	47	8	no	—
173	C₂×C₈	—	47	16	no	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	94	4	no	—
179	C₄⋊C₄	—	94	4	no	—
180	C₄⋊C₄	—	188	16	no	—
181	C₄⋊C₄	—	188	4	no	—
182	C₄²	—	2	4	no	—
183	C₄²	—	2	4	no	—
184	C₄²	D₄×D₄₇	1	4	yes	—
185	C₄²	Q₈×D₄₇	1	8	yes	—
186	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
187	Q₈	—	8	4	no	—
188	Q₈	—	8	4	no	—
189	Q₈	—	376	8	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	—	4	4	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	188	8	no	—
197	C₂×C₄	—	188	4	no	—
198	C₂×C₄	#13094020	1	2	yes	—
199	C₂×C₄	#13094020	1	2	yes	—
200	C₂×C₄	#13094022	1	8	yes	—
201	C₂×C₄	#13094049	1	4	yes	—
202	C₂×C₄	#13094054	1	4	yes	—
203	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
204	C₂×C₄	C₂×Q₈×D₄₇	1	4	yes	—
205	C₈	—	47	16	no	—
206	C₂²	C₂×#13094020	1	1	yes	characteristic
207	C₂²	C₂×#13094022	1	2	yes	—
208	C₂²	C₂×#13094049	1	2	yes	—
209	C₂²	C₂×#13094054	1	2	yes	—
210	C₄	—	2	8	no	—
211	C₄	—	8	2	no	—
212	C₄	—	8	2	no	—
213	C₄	—	376	4	no	—
214	C₄	#15689513	1	4	yes	—
215	C₄	#15689518	1	4	yes	—
216	C₄	C₄⋊Q₈×D₄₇	1	4	yes	—
217	C₂	#20251784	1	1	yes	characteristic
218	C₂	C₂×#15689513	1	1	yes	characteristic
219	C₂	C₂×#15689518	1	1	yes	characteristic
220	C₂	#20253935	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689526

C₂

yes

maximal

C₂×#15689519

C₂

yes

maximal

#20251786

C₂

yes

maximal, characteristic

#20243557

C₂

yes

maximal

C₄×#13093935

C₂

yes

maximal, characteristic

C₄₇×#2862

C₂

yes

maximal, characteristic

C₂×#13094024

—

C₂×#13094024

C₂²

yes

—

#15689526

—

#15689519

—

C₂×#13093957

C₂²

yes

—

C₂×#13093955

C₂²

yes

—

C₂×#13093935

C₂²

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

#15688993

—

#15688993

C₂²

yes

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄₇×#391

—

C₄₇×#391

—

C₄₇×#382

C₂²

yes

—

C₄³×C₄₇

C₂²

yes

characteristic

C₂²×Dic₉₄

—

C₂²×C₄₇⋊C₈

C₂³

yes

—

#13094024

—

#13094024

—

#13094024

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂³

yes

—

#13093957

—

#13093955

—

#13093935

Q₈

yes

complemented

C₄×C₄₇⋊C₈

D₄

yes

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂³

yes

—

C₂×C₄⋊C₄×C₄₇

C₂³

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₂×C₄²×C₄₇

C₂³

yes

—

#95×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂⁴

yes

characteristic

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

C₂×Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

C₂×D₄

yes

—

C₂×C₄₇⋊C₈

C₂×Q₈

yes

—

C₂³×C₄₇

C₂²×D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#127

yes

—

C₂×C₄×C₄₇

#127

yes

—

C₂×C₄×C₄₇

C₄⋊Q₈

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

C₂²×D₄

yes

—

C₂×C₄×C₄₇

C₂²×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

C₄₇⋊C₈

C₄⋊Q₈

yes

—

C₂²×C₄₇

yes

C₂²×C₄₇

C₂×C₄⋊Q₈

yes

—

C₂²×C₄₇

C₂×AGL(1,ℤ/8)

yes

—

C₂²×C₄₇

C₂×#137

yes

—

100

C₄×C₄₇

—

101

C₄×C₄₇

—

102

C₄×C₄₇

—

103

C₄×C₄₇

#496

yes

—

104

C₄×C₄₇

#497

yes

—

105

C₄×C₄₇

C₂×C₄⋊Q₈

yes

—

106

Dic₄₇

—

107

C₂×#500

—

108

C₂×#498

—

109

#2868

—

110

#2862

D₄₇

yes

characteristic

111

#1847

—

112

C₄×#97

—

113

C₂×C₄₇

#2868

yes

characteristic

114

C₂×C₄₇

C₂×#496

yes

characteristic

115

C₂×C₄₇

C₂×#497

yes

characteristic

116

C₂×C₄₇

#3165

yes

—

117

C₂×C₄⋊Q₈

—

118

C₂×C₄⋊Q₈

—

119

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

120

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

121

#500

—

122

#498

—

123

C₂×#107

—

124

C₂×#106

—

125

C₂×#97

—

126

C₂×C₄×C₈

—

127

#391

—

128

#391

—

129

#384

—

130

#384

—

131

#382

C₂×D₄₇

yes

—

132

C₄³

C₂×D₄₇

yes

characteristic

133

C₄₇

#33314

yes

characteristic, complemented, Sylow

134

C₂²×Q₈

—

135

C₂²×Q₈

—

136

C₂²×Q₈

—

137

C₂²×C₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

188

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

C₂²×D₄₇

yes

—

149

C₂×C₄⋊C₄

C₂²×D₄₇

yes

—

150

C₂×C₄²

C₂²⋊D₄₇

yes

—

151

C₂×C₄²

C₂²⋊D₄₇

yes

—

152

C₂×C₄²

C₂²×D₄₇

yes

characteristic

153

C₂×C₄²

C₂²×D₄₇

yes

—

154

#107

—

155

#106

—

156

#97

—

157

C₄×C₈

—

158

#95

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

188

—

164

C₂×Q₈

—

188

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

—

169

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

170

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

171

C₂²×C₄

C₂³×D₄₇

yes

characteristic

172

C₂×C₈

—

173

C₂×C₈

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

188

—

181

C₄⋊C₄

—

188

—

182

C₄²

—

183

C₄²

—

184

C₄²

D₄×D₄₇

yes

—

185

C₄²

Q₈×D₄₇

yes

—

186

C₂³

C₂²×C₂²⋊D₄₇

yes

characteristic

187

Q₈

—

188

Q₈

—

189

Q₈

—

376

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

188

—

197

C₂×C₄

—

188

—

198

C₂×C₄

#13094020

yes

—

199

C₂×C₄

#13094020

yes

—

200

C₂×C₄

#13094022

yes

—

201

C₂×C₄

#13094049

yes

—

202

C₂×C₄

#13094054

yes

—

203

C₂×C₄

C₂×D₄×D₄₇

yes

—

204

C₂×C₄

C₂×Q₈×D₄₇

yes

—

205

C₈

—

206

C₂²

C₂×#13094020

yes

characteristic

207

C₂²

C₂×#13094022

yes

—

208

C₂²

C₂×#13094049

yes

—

209

C₂²

C₂×#13094054

yes

—

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

—

376

—

214

C₄

#15689513

yes

—

215

C₄

#15689518

yes

—

216

C₄

C₄⋊Q₈×D₄₇

yes

—

217

C₂

#20251784

yes

characteristic

218

C₂

C₂×#15689513

yes

characteristic

219

C₂

C₂×#15689518

yes

characteristic

220

C₂

#20253935

yes

—

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2862	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
hypercenter	#2862	D₄₇
hypocenter	C₄₇	#33314
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

subgroup

G/H

center

C₂³

C₂²×C₂²⋊D₄₇

commutator, cosocle

C₂²×C₄×C₄₇

C₂⁴

Frattini

C₂²×C₄

C₂³×D₄₇

Fitting

C₄₇×#2862

C₂

socle, prime radical

C₂³×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

N	H ≅ G/N	type
33. #13093935	Q₈	semidirect
94. C₄₇⋊C₈	C₄⋊Q₈	semidirect
133. C₄₇	#33314	semidirect

H ≅ G/N

type

33. #13093935

Q₈

semidirect

94. C₄₇⋊C₈

C₄⋊Q₈

semidirect

133. C₄₇

#33314

semidirect

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

subgroup	index
C₂×#15689526	2
C₂×#15689519	2
#20251786	2
#20243557	2
C₄×#13093935	2
C₄₇×#2862	2
#33314	47

subgroup

index

C₄₇×#2862

Subgroups — #26368865

Conjugacy classes of subgroups

Complements

Maximal subgroups