Group #26115075 — subgroups

Subgroups — #26115075

Order 12032.

546 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 179 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×#13094024	C₂	1	1	yes	maximal, characteristic
2	#20243134	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688853	C₂	1	4	yes	maximal
4	C₄₇×#1842	C₂	1	1	yes	maximal, characteristic
5	C₂×#13094024	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
7	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
8	#15689029	C₄	1	2	yes	—
9	#15689021	—	2	2	no	—
10	#15688993	C₄	1	1	yes	characteristic
11	C₄×C₄⋊Dic₄₇	—	2	2	no	—
12	#15688878	—	2	2	no	—
13	#15688853	—	2	8	no	—
14	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
15	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
16	C₄³×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
18	C₂²×C₄₇⋊C₈	—	2	2	no	—
19	#13094024	—	2	4	no	—
20	C₄×Dic₉₄	—	2	4	no	—
21	C₄×Dic₉₄	—	2	4	no	—
22	C₂×C₄⋊Dic₄₇	—	2	2	no	—
23	C₂×C₄⋊Dic₄₇	—	2	2	no	—
24	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
25	C₂×Dic₄₇⋊C₄	—	2	2	no	—
26	C₂×C₄×Dic₄₇	—	2	2	no	—
27	C₄×C₄₇⋊C₈	—	2	2	no	—
28	C₄×C₄₇⋊C₈	D₄	1	4	yes	—
29	C₄₇⋊#95	—	2	4	no	—
30	C₂²×C₈×C₄₇	—	2	2	no	—
31	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₄₇	D₄	1	2	yes	—
34	C₂×C₄²×C₄₇	D₄	1	2	yes	—
35	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
36	C₄⋊C₈×C₄₇	—	2	4	no	—
37	C₄⋊C₈×C₄₇	—	4	4	no	—
38	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₄₇	—	2	2	no	—
44	C₂²×Dic₄₇	—	2	2	no	—
45	C₂×Dic₉₄	—	2	4	no	—
46	C₂×Dic₉₄	—	2	4	no	—
47	C₂×Dic₉₄	—	2	2	no	—
48	C₂×Dic₉₄	M₁₆	1	4	yes	—
49	C₂×C₈×C₄₇	—	4	2	no	—
50	C₂×C₈×C₄₇	—	4	4	no	—
51	C₄²×C₄₇	—	2	2	no	—
52	C₄²×C₄₇	—	2	2	no	—
53	C₄²×C₄₇	—	4	2	no	—
54	C₄²×C₄₇	SD₁₆	1	4	yes	—
55	C₄²×C₄₇	Q₁₆	1	4	yes	—
56	C₄²×C₄₇	C₂×D₄	1	2	yes	—
57	C₄²×C₄₇	#41	1	2	yes	—
58	C₄⋊Dic₄₇	—	2	8	no	—
59	C₄⋊Dic₄₇	—	2	4	no	—
60	C₄⋊Dic₄₇	—	4	4	no	—
61	Dic₄₇⋊C₄	—	4	4	no	—
62	C₄×Dic₄₇	—	4	2	no	—
63	C₄×Dic₄₇	—	4	2	no	—
64	C₂×C₄₇⋊C₈	—	2	4	no	—
65	C₂×C₄₇⋊C₈	—	4	4	no	—
66	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₄₇	—	2	2	no	—
68	C₂×C₄×C₄₇	—	2	2	no	—
69	C₂×C₄×C₄₇	—	2	2	no	—
70	C₂×C₄×C₄₇	—	2	2	no	—
71	C₂×C₄×C₄₇	—	2	2	no	—
72	C₂×C₄×C₄₇	#103	1	4	yes	—
73	C₂×C₄×C₄₇	#103	1	4	yes	—
74	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
75	C₂×C₄×C₄₇	#121	1	2	yes	—
76	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
77	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
78	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
79	C₂×C₄×C₄₇	#131	1	2	yes	—
80	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
81	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
82	C₂×Dic₄₇	—	2	4	no	—
83	C₂×Dic₄₇	—	4	2	no	—
84	C₂×Dic₄₇	—	4	2	no	—
85	C₂×Dic₄₇	—	4	2	no	—
86	C₂×Dic₄₇	—	4	4	no	—
87	Dic₉₄	—	2	8	no	—
88	Dic₉₄	—	4	4	no	—
89	C₈×C₄₇	—	8	2	no	—
90	C₄₇⋊C₈	—	4	4	no	—
91	#9643	—	47	1	no	maximal, Sylow
92	C₂²×C₄₇	#390	1	1	yes	characteristic
93	C₂²×C₄₇	#407	1	1	yes	characteristic
94	C₂²×C₄₇	#408	1	1	yes	characteristic
95	C₂²×C₄₇	C₂×#103	1	2	yes	—
96	C₂²×C₄₇	#421	1	2	yes	—
97	C₄×C₄₇	—	2	2	no	—
98	C₄×C₄₇	—	2	4	no	—
99	C₄×C₄₇	—	2	4	no	—
100	C₄×C₄₇	#435	1	4	yes	—
101	C₄×C₄₇	#487	1	2	yes	—
102	C₄×C₄₇	#492	1	1	yes	characteristic
103	C₄×C₄₇	#494	1	1	yes	characteristic
104	Dic₄₇	—	4	4	no	—
105	Dic₄₇	—	8	2	no	—
106	C₄×C₄⋊Q₈	—	47	1	no	—
107	#1842	D₄₇	1	1	yes	characteristic
108	#1744	—	47	1	no	—
109	C₂×Q₈⋊C₈	—	47	4	no	—
110	C₂×C₄₇	#1481	1	2	yes	—
111	C₂×C₄₇	#1487	1	2	yes	—
112	C₂×C₄₇	#1955	1	1	yes	characteristic
113	C₂×C₄₇	#1956	1	1	yes	characteristic
114	C₂×C₄₇	#1963	1	1	yes	characteristic
115	C₂×C₄⋊Q₈	—	47	1	no	—
116	C₂×C₄×Q₈	—	47	2	no	—
117	C₂×C₄⋊C₈	—	2	2	no	—
118	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
119	C₂×C₄×C₈	—	47	2	no	—
120	#391	—	47	2	no	—
121	#389	—	94	2	no	—
122	#384	—	47	1	no	—
123	C₄×C₄⋊C₄	—	94	2	no	—
124	C₄³	C₂×D₄₇	1	1	yes	characteristic
125	#336	—	94	2	no	—
126	Q₈⋊C₈	—	94	8	no	—
127	C₄₇	#9643	1	1	yes	characteristic, complemented, Sylow
128	C₂²×Q₈	—	47	2	no	—
129	C₂²×C₈	—	2	2	no	—
130	C₂²×C₈	—	94	2	no	—
131	C₄⋊Q₈	—	94	4	no	—
132	C₄×Q₈	—	94	4	no	—
133	C₄×Q₈	—	94	4	no	—
134	C₂×C₄⋊C₄	—	47	2	no	—
135	C₂×C₄⋊C₄	—	94	2	no	—
136	C₂×C₄⋊C₄	—	94	2	no	—
137	C₂×C₄⋊C₄	—	94	2	no	—
138	C₂×C₄²	—	94	2	no	—
139	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
140	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
141	C₂×C₄²	D₁₈₈	1	2	yes	—
142	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
143	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
144	C₄⋊C₈	—	2	4	no	—
145	C₄⋊C₈	—	4	4	no	—
146	C₄×C₈	—	47	4	no	—
147	C₄×C₈	—	94	2	no	—
148	#95	—	94	4	no	—
149	C₂×Q₈	—	47	4	no	—
150	C₂×Q₈	—	94	2	no	—
151	C₂×Q₈	—	94	4	no	—
152	C₂×Q₈	—	94	4	no	—
153	C₂²×C₄	—	94	2	no	—
154	C₂²×C₄	—	94	2	no	—
155	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
156	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
157	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
158	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
159	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
160	C₂×C₈	—	4	2	no	—
161	C₂×C₈	—	4	4	no	—
162	C₂×C₈	—	94	4	no	—
163	C₂×C₈	—	188	4	no	—
164	C₄⋊C₄	—	94	8	no	—
165	C₄⋊C₄	—	94	4	no	—
166	C₄⋊C₄	—	188	4	no	—
167	C₄⋊C₄	—	188	4	no	—
168	C₄²	—	2	2	no	—
169	C₄²	—	2	2	no	—
170	C₄²	—	4	2	no	—
171	C₄²	—	188	2	no	—
172	C₄²	—	188	2	no	—
173	C₄²	#10625335	1	4	yes	—
174	C₄²	#10625337	1	4	yes	—
175	C₄²	D₄×D₄₇	1	2	yes	—
176	C₄²	#10625354	1	2	yes	—
177	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
178	Q₈	—	94	8	no	—
179	Q₈	—	188	4	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	94	4	no	—
186	C₂×C₄	—	188	2	no	—
187	C₂×C₄	—	188	4	no	—
188	C₂×C₄	—	188	2	no	—
189	C₂×C₄	—	188	2	no	—
190	C₂×C₄	#13093947	1	4	yes	—
191	C₂×C₄	#13093947	1	4	yes	—
192	C₂×C₄	#13093986	1	2	yes	—
193	C₂×C₄	#13093999	1	2	yes	—
194	C₂×C₄	#13094013	1	1	yes	characteristic
195	C₂×C₄	#13094020	1	1	yes	characteristic
196	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
197	C₂×C₄	#13094030	1	2	yes	—
198	C₂×C₄	C₂×#10625335	1	2	yes	—
199	C₂×C₄	C₂×#10625337	1	2	yes	—
200	C₈	—	8	2	no	—
201	C₈	—	188	4	no	—
202	C₂²	#15689024	1	1	yes	characteristic
203	C₂²	#15689086	1	1	yes	characteristic
204	C₂²	#15689089	1	1	yes	characteristic
205	C₂²	C₂×#13093947	1	2	yes	—
206	C₂²	#15689139	1	2	yes	—
207	C₄	—	2	4	no	—
208	C₄	—	2	4	no	—
209	C₄	—	2	2	no	—
210	C₄	—	376	2	no	—
211	C₄	—	188	4	no	—
212	C₄	#15689193	1	4	yes	—
213	C₄	#15689475	1	2	yes	—
214	C₄	#15689495	1	1	yes	characteristic
215	C₄	#15689502	1	1	yes	characteristic
216	C₂	#20241790	1	2	yes	—
217	C₂	#20241816	1	2	yes	—
218	C₂	#20244185	1	1	yes	characteristic
219	C₂	#20244189	1	1	yes	characteristic
220	C₂	#20244219	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13094024

C₂

yes

maximal, characteristic

#20243134

C₂

yes

maximal, characteristic

C₂×#15688853

C₂

yes

maximal

C₄₇×#1842

C₂

yes

maximal, characteristic

C₂×#13094024

C₄

yes

characteristic

C₂×C₄×Dic₉₄

C₂²

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

#15689029

C₄

yes

—

#15689021

—

#15688993

C₄

yes

characteristic

C₄×C₄⋊Dic₄₇

—

#15688878

—

#15688853

—

C₂×C₄⋊C₈×C₄₇

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄³×C₄₇

C₂²

yes

characteristic

C₂²×Dic₉₄

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

—

#13094024

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

M₁₆

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

SD₁₆

yes

—

C₄²×C₄₇

Q₁₆

yes

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

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

#103

yes

—

C₂×C₄×C₄₇

#103

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

#131

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

C₂×C₄×C₄₇

C₂×Q₁₆

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#421

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

100

C₄×C₄₇

#435

yes

—

101

C₄×C₄₇

#487

yes

—

102

C₄×C₄₇

#492

yes

characteristic

103

C₄×C₄₇

#494

yes

characteristic

104

Dic₄₇

—

105

Dic₄₇

—

106

C₄×C₄⋊Q₈

—

107

#1842

D₄₇

yes

characteristic

108

#1744

—

109

C₂×Q₈⋊C₈

—

110

C₂×C₄₇

#1481

yes

—

111

C₂×C₄₇

#1487

yes

—

112

C₂×C₄₇

#1955

yes

characteristic

113

C₂×C₄₇

#1956

yes

characteristic

114

C₂×C₄₇

#1963

yes

characteristic

115

C₂×C₄⋊Q₈

—

116

C₂×C₄×Q₈

—

117

C₂×C₄⋊C₈

—

118

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

119

C₂×C₄×C₈

—

120

#391

—

121

#389

—

122

#384

—

123

C₄×C₄⋊C₄

—

124

C₄³

C₂×D₄₇

yes

characteristic

125

#336

—

126

Q₈⋊C₈

—

127

C₄₇

#9643

yes

characteristic, complemented, Sylow

128

C₂²×Q₈

—

129

C₂²×C₈

—

130

C₂²×C₈

—

131

C₄⋊Q₈

—

132

C₄×Q₈

—

133

C₄×Q₈

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄²

—

139

C₂×C₄²

C₄×D₄₇

yes

characteristic

140

C₂×C₄²

C₄×D₄₇

yes

characteristic

141

C₂×C₄²

D₁₈₈

yes

—

142

C₂×C₄²

C₂²⋊D₄₇

yes

—

143

C₂×C₄²

C₂²×D₄₇

yes

characteristic

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄×C₈

—

147

C₄×C₈

—

148

#95

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

156

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

157

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

158

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

159

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

188

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

188

—

167

C₄⋊C₄

—

188

—

168

C₄²

—

169

C₄²

—

170

C₄²

—

171

C₄²

—

188

—

172

C₄²

—

188

—

173

C₄²

#10625335

yes

—

174

C₄²

#10625337

yes

—

175

C₄²

D₄×D₄₇

yes

—

176

C₄²

#10625354

yes

—

177

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

178

Q₈

—

179

Q₈

—

188

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

188

—

187

C₂×C₄

—

188

—

188

C₂×C₄

—

188

—

189

C₂×C₄

—

188

—

190

C₂×C₄

#13093947

yes

—

191

C₂×C₄

#13093947

yes

—

192

C₂×C₄

#13093986

yes

—

193

C₂×C₄

#13093999

yes

—

194

C₂×C₄

#13094013

yes

characteristic

195

C₂×C₄

#13094020

yes

characteristic

196

C₂×C₄

M₁₆×D₄₇

yes

—

197

C₂×C₄

#13094030

yes

—

198

C₂×C₄

C₂×#10625335

yes

—

199

C₂×C₄

C₂×#10625337

yes

—

200

C₈

—

201

C₈

—

188

—

202

C₂²

#15689024

yes

characteristic

203

C₂²

#15689086

yes

characteristic

204

C₂²

#15689089

yes

characteristic

205

C₂²

C₂×#13093947

yes

—

206

C₂²

#15689139

yes

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

376

—

211

C₄

—

188

—

212

C₄

#15689193

yes

—

213

C₄

#15689475

yes

—

214

C₄

#15689495

yes

characteristic

215

C₄

#15689502

yes

characteristic

216

C₂

#20241790

yes

—

217

C₂

#20241816

yes

—

218

C₂

#20244185

yes

characteristic

219

C₂

#20244189

yes

characteristic

220

C₂

#20244219

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1842	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1842	D₄₇
hypocenter	C₄₇	#9643
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₄₇

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1842

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

N	H ≅ G/N	type
127. C₄₇	#9643	semidirect

H ≅ G/N

type

127. C₄₇

#9643

semidirect

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

subgroup	index
C₄×#13094024	2
#20243134	2
C₂×#15688853	2
C₄₇×#1842	2
#9643	47

subgroup

index

C₄₇×#1842

Subgroups — #26115075

Conjugacy classes of subgroups

Complements

Maximal subgroups