Group #26113676 — subgroups

Subgroups — #26113676

Order 12032.

466 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 115 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	#20252473	C₂	1	1	yes	maximal, characteristic
2	#20248593	C₂	1	1	yes	maximal, characteristic
3	#20242070	C₂	1	2	yes	maximal
4	#20241289	C₂	1	2	yes	maximal
5	C₄₇×#1801	C₂	1	1	yes	maximal, characteristic
6	C₂×#13094024	C₂²	1	1	yes	characteristic
7	#15689254	—	2	4	no	—
8	#15689180	—	2	2	no	—
9	#15689176	C₂²	1	2	yes	—
10	#15689043	C₄	1	4	yes	—
11	#15689030	—	2	1	no	—
12	#15689021	—	2	2	no	—
13	#15688992	—	2	1	no	—
14	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	#15688871	—	2	4	no	—
16	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#423	C₂²	1	2	yes	—
18	C₂×#101×C₄₇	—	2	1	no	—
19	C₄₇×#343	—	2	1	no	—
20	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
21	#13094024	—	2	2	no	—
22	#13094024	—	2	2	no	—
23	C₂×C₄⋊Dic₄₇	—	2	1	no	—
24	C₂×C₄⋊Dic₄₇	—	2	1	no	—
25	C₂×C₄⋊Dic₄₇	—	2	1	no	—
26	C₂×Dic₄₇⋊C₄	—	2	4	no	—
27	C₂×C₄×Dic₄₇	—	2	1	no	—
28	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
29	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
30	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
31	#13093935	—	2	4	no	—
32	C₄×C₄₇⋊C₈	—	2	2	no	—
33	C₄₇⋊#95	—	2	4	no	—
34	C₄₇⋊#95	C₂×C₄	1	2	yes	—
35	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
36	C₂×M₁₆×C₄₇	—	2	2	no	—
37	C₄×Q₈×C₄₇	—	2	2	no	—
38	C₄×Q₈×C₄₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₄₇	D₄	1	2	yes	—
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₇	—	2	2	no	—
44	C₄⋊C₈×C₄₇	—	2	2	no	—
45	#101×C₄₇	—	4	2	no	—
46	C₂×Q₈×C₄₇	—	2	2	no	—
47	C₂×Q₈×C₄₇	—	2	1	no	—
48	C₂×Q₈×C₄₇	—	2	1	no	—
49	C₂×Q₈×C₄₇	—	2	2	no	—
50	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂²×Dic₄₇	—	2	2	no	—
56	C₂²×Dic₄₇	—	2	2	no	—
57	C₂×Dic₉₄	—	2	4	no	—
58	C₂×Dic₉₄	—	8	2	no	—
59	M₁₆×C₄₇	—	4	2	no	—
60	M₁₆×C₄₇	—	4	2	no	—
61	C₂×C₈×C₄₇	—	4	2	no	—
62	C₄⋊C₄×C₄₇	—	2	4	no	—
63	C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₄²×C₄₇	—	2	2	no	—
65	C₄²×C₄₇	—	2	2	no	—
66	C₄²×C₄₇	C₂×D₄	1	2	yes	—
67	C₄²×C₄₇	#41	1	2	yes	—
68	C₄⋊Dic₄₇	—	2	4	no	—
69	C₄⋊Dic₄₇	—	4	1	no	—
70	C₄⋊Dic₄₇	—	4	2	no	—
71	C₄⋊Dic₄₇	—	4	1	no	—
72	Dic₄₇⋊C₄	—	8	4	no	—
73	C₄×Dic₄₇	—	4	1	no	—
74	C₄×Dic₄₇	—	4	1	no	—
75	C₂×C₄₇⋊C₈	—	2	4	no	—
76	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	Q₈×C₄₇	—	4	2	no	—
78	Q₈×C₄₇	—	4	2	no	—
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	—	2	2	no	—
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	—	2	2	no	—
83	C₂×C₄×C₄₇	—	2	2	no	—
84	C₂×C₄×C₄₇	—	4	1	no	—
85	C₂×C₄×C₄₇	—	4	2	no	—
86	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
88	C₂×C₄×C₄₇	#121	1	2	yes	—
89	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
90	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂×C₄×C₄₇	#137	1	2	yes	—
92	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
93	C₂×Dic₄₇	—	2	4	no	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	—	4	2	no	—
96	C₂×Dic₄₇	—	4	4	no	—
97	C₂×Dic₄₇	—	4	2	no	—
98	Dic₉₄	—	8	4	no	—
99	C₈×C₄₇	—	8	2	no	—
100	C₄₇⋊C₈	—	4	4	no	—
101	#9400	—	47	1	no	maximal, Sylow
102	C₂²×C₄₇	—	2	1	no	—
103	C₂²×C₄₇	—	2	1	no	—
104	C₂²×C₄₇	#386	1	1	yes	characteristic
105	C₂²×C₄₇	#417	1	1	yes	characteristic
106	C₂²×C₄₇	#419	1	1	yes	characteristic
107	C₄×C₄₇	—	2	1	no	—
108	C₄×C₄₇	—	2	2	no	—
109	C₄×C₄₇	—	4	2	no	—
110	C₄×C₄₇	—	4	2	no	—
111	C₄×C₄₇	#456	1	2	yes	—
112	C₄×C₄₇	#468	1	2	yes	—
113	C₄×C₄₇	#470	1	2	yes	—
114	Dic₄₇	—	4	4	no	—
115	Dic₄₇	—	8	2	no	—
116	#2983	—	47	1	no	—
117	#2567	—	47	1	no	—
118	#1801	D₄₇	1	1	yes	characteristic
119	#1548	—	47	2	no	—
120	#1303	—	47	2	no	—
121	C₂×C₄₇	—	2	1	no	—
122	C₂×C₄₇	—	2	1	no	—
123	C₂×C₄₇	#1886	1	1	yes	characteristic
124	C₂×C₄₇	#1894	1	1	yes	characteristic
125	C₂×C₄₇	#1914	1	1	yes	characteristic
126	C₂×C₄⋊Q₈	—	47	1	no	—
127	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
128	#446	—	94	4	no	—
129	#432	—	94	2	no	—
130	#431	—	47	2	no	—
131	#423	C₂×D₄₇	1	2	yes	—
132	C₂×#101	—	2	1	no	—
133	#395	—	47	4	no	—
134	#391	—	94	1	no	—
135	#389	—	94	2	no	—
136	#384	—	94	1	no	—
137	C₄×C₄⋊C₄	—	47	1	no	—
138	#343	—	2	1	no	—
139	#333	—	94	4	no	—
140	C₄₇	#9400	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	—	47	2	no	—
142	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
143	C₂×M₁₆	—	2	2	no	—
144	C₄⋊Q₈	—	94	2	no	—
145	C₄⋊Q₈	—	94	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₂×C₄⋊C₄	—	94	1	no	—
149	C₂×C₄⋊C₄	—	94	4	no	—
150	C₂×C₄⋊C₄	—	94	1	no	—
151	C₂×C₄⋊C₄	—	94	1	no	—
152	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
153	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
154	C₂×C₄²	—	94	1	no	—
155	C₂×C₄²	D₁₈₈	1	2	yes	—
156	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	47	4	no	—
160	C₄⋊C₈	—	94	4	no	—
161	#101	—	4	2	no	—
162	C₂²⋊C₈	—	94	2	no	—
163	#97	—	94	4	no	—
164	C₄×C₈	—	94	2	no	—
165	#95	—	47	2	no	—
166	#95	—	94	4	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	1	no	—
171	C₂×Q₈	—	94	4	no	—
172	C₂×Q₈	—	376	2	no	—
173	C₂²×C₄	—	94	2	no	—
174	C₂²×C₄	—	94	2	no	—
175	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
176	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
177	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
180	M₁₆	—	4	2	no	—
181	M₁₆	—	4	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	94	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	94	4	no	—
187	C₄⋊C₄	—	376	4	no	—
188	C₄⋊C₄	—	188	1	no	—
189	C₄⋊C₄	—	188	2	no	—
190	C₄⋊C₄	—	188	1	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	2	2	no	—
193	C₄²	—	188	1	no	—
194	C₄²	—	188	1	no	—
195	C₄²	D₄×D₄₇	1	2	yes	—
196	C₄²	#10625352	1	2	yes	—
197	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
198	Q₈	—	4	2	no	—
199	Q₈	—	4	2	no	—
200	Q₈	—	376	4	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	94	4	no	—
209	C₂×C₄	—	188	4	no	—
210	C₂×C₄	—	188	2	no	—
211	C₂×C₄	—	188	2	no	—
212	C₂×C₄	—	188	2	no	—
213	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
214	C₂×C₄	#13093994	1	1	yes	characteristic
215	C₂×C₄	#13093996	1	2	yes	—
216	C₂×C₄	#13094008	1	1	yes	characteristic
217	C₂×C₄	#13094050	1	1	yes	characteristic
218	C₂×C₄	#13094054	1	2	yes	—
219	C₂×C₄	#13094055	1	1	yes	characteristic
220	C₈	—	8	2	no	—
221	C₈	—	188	4	no	—
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	#15689000	1	1	yes	characteristic
225	C₂²	#15689122	1	1	yes	characteristic
226	C₂²	#15689131	1	1	yes	characteristic
227	C₄	—	2	1	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	2	no	—
231	C₄	—	376	2	no	—
232	C₄	—	188	4	no	—
233	C₄	#15689308	1	2	yes	—
234	C₄	#15689367	1	2	yes	—
235	C₄	#15689379	1	2	yes	—
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	#20243779	1	1	yes	characteristic
239	C₂	#20243819	1	1	yes	characteristic
240	C₂	#20243933	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252473

C₂

yes

maximal, characteristic

#20248593

C₂

yes

maximal, characteristic

#20242070

C₂

yes

maximal

#20241289

C₂

yes

maximal

C₄₇×#1801

C₂

yes

maximal, characteristic

C₂×#13094024

C₂²

yes

—

—

C₂²

yes

—

#15689043

C₄

yes

—

#15689030

—

#15689021

—

#15688992

—

C₄×C₄⋊Dic₄₇

C₂²

yes

characteristic

#15688871

—

C₂×C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄₇×#423

C₂²

yes

—

C₂×#101×C₄₇

—

C₄₇×#343

—

C₂²×Dic₉₄

C₂×C₄

yes

—

#13094024

—

#13094024

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

—

C₄×C₄₇⋊C₈

—

C₄₇⋊#95

—

C₄₇⋊#95

C₂×C₄

yes

—

C₂²×Q₈×C₄₇

D₄

yes

characteristic

C₂×M₁₆×C₄₇

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

#101×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×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

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

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

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

#137

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

C₈×C₄₇

—

100

C₄₇⋊C₈

—

101

#9400

—

maximal, Sylow

102

C₂²×C₄₇

—

103

C₂²×C₄₇

—

104

C₂²×C₄₇

#386

yes

characteristic

105

C₂²×C₄₇

#417

yes

characteristic

106

C₂²×C₄₇

#419

yes

characteristic

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

#456

yes

—

112

C₄×C₄₇

#468

yes

—

113

C₄×C₄₇

#470

yes

—

114

Dic₄₇

—

115

Dic₄₇

—

116

#2983

—

117

#2567

—

118

#1801

D₄₇

yes

characteristic

119

#1548

—

120

#1303

—

121

C₂×C₄₇

—

122

C₂×C₄₇

—

123

C₂×C₄₇

#1886

yes

characteristic

124

C₂×C₄₇

#1894

yes

characteristic

125

C₂×C₄₇

#1914

yes

characteristic

126

C₂×C₄⋊Q₈

—

127

C₂×C₄×Q₈

C₂×D₄₇

yes

characteristic

128

#446

—

129

#432

—

130

#431

—

131

#423

C₂×D₄₇

yes

—

132

C₂×#101

—

133

#395

—

134

#391

—

135

#389

—

136

#384

—

137

C₄×C₄⋊C₄

—

138

#343

—

139

#333

—

140

C₄₇

#9400

yes

characteristic, complemented, Sylow

141

C₂²×Q₈

—

142

C₂²×Q₈

C₂²⋊D₄₇

yes

characteristic

143

C₂×M₁₆

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

C₄×D₄₇

yes

—

153

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

154

C₂×C₄²

—

155

C₂×C₄²

D₁₈₈

yes

—

156

C₂×C₄²

C₂²×D₄₇

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

#101

—

162

C₂²⋊C₈

—

163

#97

—

164

C₄×C₈

—

165

#95

—

166

#95

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

376

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

176

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

177

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

178

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

376

—

188

C₄⋊C₄

—

188

—

189

C₄⋊C₄

—

188

—

190

C₄⋊C₄

—

188

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

188

—

194

C₄²

—

188

—

195

C₄²

D₄×D₄₇

yes

—

196

C₄²

#10625352

yes

—

197

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

376

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

188

—

210

C₂×C₄

—

188

—

211

C₂×C₄

—

188

—

212

C₂×C₄

—

188

—

213

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

214

C₂×C₄

#13093994

yes

characteristic

215

C₂×C₄

#13093996

yes

—

216

C₂×C₄

#13094008

yes

characteristic

217

C₂×C₄

#13094050

yes

characteristic

218

C₂×C₄

#13094054

yes

—

219

C₂×C₄

#13094055

yes

characteristic

220

C₈

—

221

C₈

—

188

—

222

C₂²

—

223

C₂²

—

224

C₂²

#15689000

yes

characteristic

225

C₂²

#15689122

yes

characteristic

226

C₂²

#15689131

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

376

—

232

C₄

—

188

—

233

C₄

#15689308

yes

—

234

C₄

#15689367

yes

—

235

C₄

#15689379

yes

—

236

C₂

—

237

C₂

—

238

C₂

#20243779

yes

characteristic

239

C₂

#20243819

yes

characteristic

240

C₂

#20243933

yes

characteristic

	subgroup	G/H
center	C₂²	#15689000
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1801	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1801	D₄₇
hypocenter	C₄₇	#9400
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#15689000

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1801

C₂

socle

C₂²×C₄₇

#386

prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

N	H ≅ G/N	type
140. C₄₇	#9400	semidirect

H ≅ G/N

type

140. C₄₇

#9400

semidirect

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

subgroup	index
#20252473	2
#20248593	2
#20242070	2
#20241289	2
C₄₇×#1801	2
#9400	47

subgroup

index

C₄₇×#1801

Subgroups — #26113676

Conjugacy classes of subgroups

Complements

Maximal subgroups