Group #26048421 — subgroups

Subgroups — C₄₇×#8723 #26048421

Order 12032.

630 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 206 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×C₄₇×#384	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1797	C₂	1	2	yes	maximal
3	C₄₇×#1296	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄⋊C₄×C₄₇	—	2	2	no	—
5	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
6	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	—
8	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
9	C₄₇×#384	—	2	2	no	—
10	C₄₇×#384	C₄	1	2	yes	—
11	C₄₇×#384	C₂²	1	2	yes	—
12	C₄₇×#336	—	2	2	no	—
13	C₂³×C₄×C₄₇	—	2	2	no	—
14	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₄₇	D₄	1	2	yes	—
16	C₂²×C₈×C₄₇	—	2	4	no	—
17	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
18	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
19	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
20	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
21	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
22	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
23	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₄₇	—	2	4	no	—
25	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₄₇	D₄	1	2	yes	—
27	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
28	C₄⋊C₈×C₄₇	—	2	8	no	—
29	C₂²⋊C₈×C₄₇	—	4	4	no	—
30	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₄₇	—	2	2	no	—
32	C₂²×C₄×C₄₇	—	2	2	no	—
33	C₂²×C₄×C₄₇	—	2	2	no	—
34	C₂²×C₄×C₄₇	—	2	4	no	—
35	C₂²×C₄×C₄₇	—	2	4	no	—
36	C₂²×C₄×C₄₇	—	2	4	no	—
37	C₂²×C₄×C₄₇	—	4	4	no	—
38	C₂²×C₄×C₄₇	—	4	8	no	—
39	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
41	C₂²×C₄×C₄₇	D₈	1	4	yes	—
42	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
43	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
45	C₂×C₈×C₄₇	—	4	4	no	—
46	C₂×C₈×C₄₇	—	4	4	no	—
47	C₂×C₈×C₄₇	—	4	4	no	—
48	C₄⋊C₄×C₄₇	—	4	4	no	—
49	C₄⋊C₄×C₄₇	—	4	4	no	—
50	C₄⋊C₄×C₄₇	—	4	8	no	—
51	C₄⋊C₄×C₄₇	—	4	4	no	—
52	C₄⋊C₄×C₄₇	—	4	4	no	—
53	C₄²×C₄₇	—	2	2	no	—
54	C₄²×C₄₇	—	2	4	no	—
55	C₄²×C₄₇	#41	1	4	yes	—
56	C₂³×C₄₇	—	2	1	no	—
57	C₂³×C₄₇	—	2	1	no	—
58	C₂³×C₄₇	—	2	2	no	—
59	C₂³×C₄₇	#100	1	2	yes	—
60	C₂³×C₄₇	#102	1	4	yes	—
61	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₄₇	—	2	8	no	—
63	C₂×C₄×C₄₇	—	2	1	no	—
64	C₂×C₄×C₄₇	—	2	2	no	—
65	C₂×C₄×C₄₇	—	2	1	no	—
66	C₂×C₄×C₄₇	—	2	1	no	—
67	C₂×C₄×C₄₇	—	2	1	no	—
68	C₂×C₄×C₄₇	—	2	2	no	—
69	C₂×C₄×C₄₇	—	2	8	no	—
70	C₂×C₄×C₄₇	—	2	8	no	—
71	C₂×C₄×C₄₇	—	4	4	no	—
72	C₂×C₄×C₄₇	—	4	8	no	—
73	C₂×C₄×C₄₇	—	8	8	no	—
74	C₂×C₄×C₄₇	#101	1	2	yes	—
75	C₂×C₄×C₄₇	#102	1	4	yes	—
76	C₂×C₄×C₄₇	#117	1	2	yes	—
77	C₂×C₄×C₄₇	#123	1	4	yes	—
78	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
79	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
80	C₂×C₄×C₄₇	#137	1	4	yes	—
81	C₈×C₄₇	—	8	4	no	—
82	#8723	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂²×C₄₇	—	2	4	no	—
84	C₂²×C₄₇	—	2	2	no	—
85	C₂²×C₄₇	—	2	2	no	—
86	C₂²×C₄₇	—	2	4	no	—
87	C₂²×C₄₇	#331	1	4	yes	—
88	C₂²×C₄₇	#381	1	1	yes	characteristic
89	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
90	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
91	C₂²×C₄₇	C₂×#102	1	2	yes	—
92	C₂²×C₄₇	#419	1	2	yes	—
93	C₄×C₄₇	—	2	2	no	—
94	C₄×C₄₇	—	2	2	no	—
95	C₄×C₄₇	—	2	4	no	—
96	C₄×C₄₇	—	8	4	no	—
97	C₄×C₄₇	#480	1	4	yes	—
98	C₄×C₄₇	#483	1	4	yes	—
99	C₂×#384	C₂×C₄₇	1	1	yes	characteristic
100	#1797	C₂×C₄₇	1	2	yes	—
101	#1296	C₂×C₄₇	1	4	yes	complemented
102	C₂×C₄₇	—	2	4	no	—
103	C₂×C₄₇	C₂×#331	1	1	yes	characteristic
104	C₂×C₄₇	#1546	1	2	yes	—
105	C₂×C₄₇	#1558	1	1	yes	characteristic
106	C₂×C₄₇	#1821	1	1	yes	characteristic
107	C₂×C₄₇	#1823	1	2	yes	—
108	C₂²×C₄⋊C₄	—	2	2	no	—
109	C₂²×C₄⋊C₄	C₄×C₄₇	1	2	yes	—
110	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
111	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	—
112	C₂×C₂²⋊C₈	—	2	2	no	—
113	#384	—	2	2	no	—
114	#384	C₄×C₄₇	1	2	yes	—
115	#384	C₂²×C₄₇	1	2	yes	—
116	#336	—	2	2	no	—
117	C₄₇	#8723	1	1	yes	characteristic, direct product factor, Sylow
118	C₂³×C₄	—	2	2	no	—
119	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
120	C₂³×C₄	D₄×C₄₇	1	2	yes	—
121	C₂²×C₈	—	2	4	no	—
122	C₂×C₄⋊C₄	—	2	4	no	—
123	C₂×C₄⋊C₄	—	2	2	no	—
124	C₂×C₄⋊C₄	—	2	4	no	—
125	C₂×C₄⋊C₄	—	4	4	no	—
126	C₂×C₄⋊C₄	—	4	4	no	—
127	C₂×C₄⋊C₄	—	4	4	no	—
128	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
129	C₂×C₄²	—	2	4	no	—
130	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
131	C₂×C₄²	D₄×C₄₇	1	2	yes	—
132	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
133	C₄⋊C₈	—	2	8	no	—
134	C₂²⋊C₈	—	4	4	no	—
135	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	—	2	4	no	—
140	C₂²×C₄	—	2	2	no	—
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	—	4	4	no	—
143	C₂²×C₄	—	4	8	no	—
144	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
145	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
146	C₂²×C₄	D₈×C₄₇	1	4	yes	—
147	C₂²×C₄	SD₁₆×C₄₇	1	4	yes	—
148	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
149	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
150	C₂×C₈	—	4	4	no	—
151	C₂×C₈	—	4	4	no	—
152	C₂×C₈	—	4	4	no	—
153	C₄⋊C₄	—	4	4	no	—
154	C₄⋊C₄	—	4	4	no	—
155	C₄⋊C₄	—	4	4	no	—
156	C₄⋊C₄	—	4	4	no	—
157	C₄⋊C₄	—	4	8	no	—
158	C₄²	—	2	2	no	—
159	C₄²	—	2	4	no	—
160	C₄²	#41×C₄₇	1	4	yes	—
161	C₂³	—	2	1	no	—
162	C₂³	—	2	1	no	—
163	C₂³	—	2	2	no	—
164	C₂³	#100×C₄₇	1	2	yes	—
165	C₂³	#102×C₄₇	1	4	yes	—
166	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
167	C₂×C₄	—	2	8	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	8	no	—
175	C₂×C₄	—	2	8	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	—	4	8	no	—
178	C₂×C₄	—	8	8	no	—
179	C₂×C₄	#101×C₄₇	1	2	yes	—
180	C₂×C₄	#102×C₄₇	1	4	yes	—
181	C₂×C₄	#117×C₄₇	1	2	yes	—
182	C₂×C₄	#123×C₄₇	1	4	yes	—
183	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
184	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
185	C₂×C₄	#137×C₄₇	1	4	yes	—
186	C₈	—	8	4	no	—
187	C₂²	—	2	4	no	—
188	C₂²	—	2	2	no	—
189	C₂²	—	2	2	no	—
190	C₂²	—	2	4	no	—
191	C₂²	C₄₇×#331	1	4	yes	—
192	C₂²	C₄₇×#381	1	1	yes	characteristic
193	C₂²	C₂×#100×C₄₇	1	1	yes	characteristic
194	C₂²	C₂×#101×C₄₇	1	1	yes	characteristic
195	C₂²	C₂×#102×C₄₇	1	2	yes	—
196	C₂²	C₄₇×#419	1	2	yes	—
197	C₄	—	2	2	no	—
198	C₄	—	2	2	no	—
199	C₄	—	2	4	no	—
200	C₄	—	8	4	no	—
201	C₄	C₄₇×#480	1	4	yes	—
202	C₄	C₄₇×#483	1	4	yes	—
203	C₂	—	2	4	no	—
204	C₂	C₂×C₄₇×#331	1	1	yes	characteristic
205	C₂	C₄₇×#1546	1	2	yes	—
206	C₂	C₄₇×#1558	1	1	yes	characteristic
207	C₂	C₄₇×#1821	1	1	yes	characteristic
208	C₂	C₄₇×#1823	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄₇×#384

C₂

yes

maximal, characteristic

C₄₇×#1797

C₂

yes

maximal

C₄₇×#1296

C₂

yes

maximal, complemented

C₂²×C₄⋊C₄×C₄₇

—

C₂²×C₄⋊C₄×C₄₇

C₄

yes

—

C₂²×C₄²×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×C₂²⋊C₈×C₄₇

—

C₄₇×#384

—

C₄₇×#384

C₄

yes

—

C₄₇×#384

C₂²

yes

—

C₄₇×#336

—

C₂³×C₄×C₄₇

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

D₈

yes

—

C₂²×C₄×C₄₇

SD₁₆

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

#41

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#100

yes

—

C₂³×C₄₇

#102

yes

—

C₂³×C₄₇

C₂×C₂²⋊C₄

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

#101

yes

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

#117

yes

—

C₂×C₄×C₄₇

#123

yes

—

C₂×C₄×C₄₇

C₂×D₈

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₈×C₄₇

—

#8723

C₄₇

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#331

yes

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#419

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#480

yes

—

C₄×C₄₇

#483

yes

—

C₂×#384

C₂×C₄₇

yes

characteristic

100

#1797

C₂×C₄₇

yes

—

101

#1296

C₂×C₄₇

yes

complemented

102

C₂×C₄₇

—

103

C₂×C₄₇

C₂×#331

yes

characteristic

104

C₂×C₄₇

#1546

yes

—

105

C₂×C₄₇

#1558

yes

characteristic

106

C₂×C₄₇

#1821

yes

characteristic

107

C₂×C₄₇

#1823

yes

—

108

C₂²×C₄⋊C₄

—

109

C₂²×C₄⋊C₄

C₄×C₄₇

yes

—

110

C₂²×C₄²

C₂²×C₄₇

yes

characteristic

111

C₂×C₄⋊C₈

C₂²×C₄₇

yes

—

112

C₂×C₂²⋊C₈

—

113

#384

—

114

#384

C₄×C₄₇

yes

—

115

#384

C₂²×C₄₇

yes

—

116

#336

—

117

C₄₇

#8723

yes

characteristic, direct product factor, Sylow

118

C₂³×C₄

—

119

C₂³×C₄

C₂×C₄×C₄₇

yes

characteristic

120

C₂³×C₄

D₄×C₄₇

yes

—

121

C₂²×C₈

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

C₂×C₄×C₄₇

yes

—

129

C₂×C₄²

—

130

C₂×C₄²

C₂×C₄×C₄₇

yes

characteristic

131

C₂×C₄²

D₄×C₄₇

yes

—

132

C₂×C₄²

C₂³×C₄₇

yes

characteristic

133

C₄⋊C₈

—

134

C₂²⋊C₈

—

135

C₂⁴

C₂²⋊C₄×C₄₇

yes

characteristic

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

C₂²⋊C₄×C₄₇

yes

characteristic

145

C₂²×C₄

C₂²⋊C₄×C₄₇

yes

—

146

C₂²×C₄

D₈×C₄₇

yes

—

147

C₂²×C₄

SD₁₆×C₄₇

yes

—

148

C₂²×C₄

C₂²×C₄×C₄₇

yes

characteristic

149

C₂²×C₄

C₂×D₄×C₄₇

yes

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄²

—

159

C₄²

—

160

C₄²

#41×C₄₇

yes

—

161

C₂³

—

162

C₂³

—

163

C₂³

—

164

C₂³

#100×C₄₇

yes

—

165

C₂³

#102×C₄₇

yes

—

166

C₂³

C₂×C₂²⋊C₄×C₄₇

yes

characteristic

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

#101×C₄₇

yes

—

180

C₂×C₄

#102×C₄₇

yes

—

181

C₂×C₄

#117×C₄₇

yes

—

182

C₂×C₄

#123×C₄₇

yes

—

183

C₂×C₄

C₂×D₈×C₄₇

yes

—

184

C₂×C₄

C₂×SD₁₆×C₄₇

yes

—

185

C₂×C₄

#137×C₄₇

yes

—

186

C₈

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

C₄₇×#331

yes

—

192

C₂²

C₄₇×#381

yes

characteristic

193

C₂²

C₂×#100×C₄₇

yes

characteristic

194

C₂²

C₂×#101×C₄₇

yes

characteristic

195

C₂²

C₂×#102×C₄₇

yes

—

196

C₂²

C₄₇×#419

yes

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

C₄₇×#480

yes

—

202

C₄

C₄₇×#483

yes

—

203

C₂

—

204

C₂

C₂×C₄₇×#331

yes

characteristic

205

C₂

C₄₇×#1546

yes

—

206

C₂

C₄₇×#1558

yes

characteristic

207

C₂

C₄₇×#1821

yes

characteristic

208

C₂

C₄₇×#1823

yes

—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₇
Frattini, cosocle	C₂×C₄²	C₂³×C₄₇
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

subgroup

G/H

center, socle

C₂³×C₄₇

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₄₇

Frattini, cosocle

C₂×C₄²

C₂³×C₄₇

prime radical

C₂⁴×C₄₇

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

N	H ≅ G/N	type
3. C₄₇×#1296	C₂	semidirect
82. #8723	C₄₇	direct (N × H)
101. #1296	C₂×C₄₇	semidirect
117. C₄₇	#8723	direct (N × H)

H ≅ G/N

type

3. C₄₇×#1296

C₂

semidirect

82. #8723

C₄₇

direct (N × H)

101. #1296

C₂×C₄₇

semidirect

117. C₄₇

#8723

direct (N × H)

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

subgroup	index
C₂×C₄₇×#384	2
C₄₇×#1797	2
C₄₇×#1296	2
#8723	47

subgroup

index

C₂×C₄₇×#384

C₄₇×#1797

C₄₇×#1296

#8723

Subgroups — C₄₇×#8723 #26048421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C47×#8723 #26048421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#8723 #26048421