Group #26115389 — subgroups

Subgroups — #26115389

Order 12032.

466 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 143 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	#20251766	C₂	1	1	yes	maximal, characteristic
2	#20243241	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688871	C₂	1	2	yes	maximal
4	C₂×#15688868	C₂	1	2	yes	maximal
5	C₄₇×#1831	C₂	1	1	yes	maximal, characteristic
6	C₂×#13094024	C₂²	1	1	yes	characteristic
7	C₂×#13094024	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
9	C₂×#13093935	—	2	1	no	—
10	#15689029	—	2	1	no	—
11	#15689029	—	2	1	no	—
12	#15689029	C₄	1	4	yes	—
13	#15688989	—	2	2	no	—
14	#15688878	—	2	1	no	—
15	#15688871	—	2	4	no	—
16	#15688868	—	2	4	no	—
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₄³×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#336	—	2	2	no	—
20	C₂²×Dic₉₄	—	2	1	no	—
21	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	#13094024	—	2	2	no	—
24	#13094024	—	2	2	no	—
25	#13094024	—	2	2	no	—
26	#13094024	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	1	no	—
28	C₂×C₄⋊Dic₄₇	—	2	1	no	—
29	C₂×C₄⋊Dic₄₇	—	2	1	no	—
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
31	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
33	#13093935	—	4	2	no	—
34	C₄₇⋊#95	—	2	4	no	—
35	C₄₇⋊#95	—	2	4	no	—
36	C₂²×C₈×C₄₇	—	2	2	no	—
37	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₄₇	D₄	1	2	yes	—
41	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₄₇	—	2	2	no	—
43	C₄⋊C₈×C₄₇	—	2	2	no	—
44	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂²×Dic₄₇	—	2	2	no	—
50	C₂²×Dic₄₇	—	2	2	no	—
51	C₂×Dic₉₄	—	2	4	no	—
52	C₂×Dic₉₄	—	4	2	no	—
53	C₂×Dic₉₄	—	4	2	no	—
54	C₂×Dic₉₄	—	4	1	no	—
55	C₂×Dic₉₄	—	4	1	no	—
56	C₂×Dic₉₄	—	4	4	no	—
57	C₂×C₈×C₄₇	—	4	2	no	—
58	C₂×C₈×C₄₇	—	4	4	no	—
59	C₄²×C₄₇	—	2	2	no	—
60	C₄²×C₄₇	—	2	1	no	—
61	C₄²×C₄₇	—	2	1	no	—
62	C₄²×C₄₇	—	2	4	no	—
63	C₄²×C₄₇	—	4	2	no	—
64	C₄²×C₄₇	C₂×D₄	1	2	yes	—
65	C₄²×C₄₇	#41	1	2	yes	—
66	C₄⋊Dic₄₇	—	2	4	no	—
67	C₄⋊Dic₄₇	—	4	2	no	—
68	C₄⋊Dic₄₇	—	4	1	no	—
69	C₄⋊Dic₄₇	—	4	1	no	—
70	C₄⋊Dic₄₇	—	4	1	no	—
71	C₄⋊Dic₄₇	—	4	1	no	—
72	C₂×C₄₇⋊C₈	—	2	4	no	—
73	C₂×C₄₇⋊C₈	—	4	2	no	—
74	C₂×C₄₇⋊C₈	—	4	2	no	—
75	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₄₇	—	2	2	no	—
77	C₂×C₄×C₄₇	—	2	2	no	—
78	C₂×C₄×C₄₇	—	2	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	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₄₇	#121	1	2	yes	—
85	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
86	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
87	C₂×C₄×C₄₇	#135	1	2	yes	—
88	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#137	1	4	yes	—
90	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
91	C₂×Dic₄₇	—	4	2	no	—
92	C₂×Dic₄₇	—	4	2	no	—
93	C₂×Dic₄₇	—	4	4	no	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	—	4	2	no	—
96	Dic₉₄	—	8	2	no	—
97	Dic₉₄	—	8	2	no	—
98	Dic₉₄	—	8	4	no	—
99	C₈×C₄₇	—	8	2	no	—
100	C₄₇⋊C₈	—	4	4	no	—
101	#9709	—	47	1	no	maximal, Sylow
102	C₂²×C₄₇	#390	1	1	yes	characteristic
103	C₂²×C₄₇	#413	1	2	yes	—
104	C₂²×C₄₇	#416	1	1	yes	characteristic
105	C₂²×C₄₇	#417	1	1	yes	characteristic
106	C₂²×C₄₇	#419	1	2	yes	—
107	C₄×C₄₇	—	2	2	no	—
108	C₄×C₄₇	—	4	2	no	—
109	C₄×C₄₇	—	4	2	no	—
110	C₄×C₄₇	#463	1	2	yes	—
111	C₄×C₄₇	#464	1	2	yes	—
112	C₄×C₄₇	#491	1	2	yes	—
113	C₄×C₄₇	#497	1	2	yes	—
114	Dic₄₇	—	8	2	no	—
115	Dic₄₇	—	8	2	no	—
116	#2862	—	47	1	no	—
117	#1831	D₄₇	1	1	yes	characteristic
118	#1767	—	47	1	no	—
119	C₂×#333	—	47	2	no	—
120	C₂×#332	—	47	2	no	—
121	C₂×C₄₇	#1554	1	2	yes	—
122	C₂×C₄₇	#1559	1	2	yes	—
123	C₂×C₄₇	#1960	1	1	yes	characteristic
124	C₂×C₄₇	#1967	1	1	yes	characteristic
125	C₂×C₄₇	#1983	1	1	yes	characteristic
126	C₂×C₄⋊Q₈	—	47	1	no	—
127	C₂×C₄⋊Q₈	—	47	1	no	—
128	C₂×C₄⋊C₈	—	47	2	no	—
129	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
130	C₂×#97	—	94	1	no	—
131	#391	—	47	4	no	—
132	#391	—	94	1	no	—
133	#391	—	94	1	no	—
134	#382	—	94	2	no	—
135	C₄³	C₂×D₄₇	1	1	yes	characteristic
136	#336	—	2	2	no	—
137	#336	—	94	1	no	—
138	#333	—	94	4	no	—
139	#332	—	94	4	no	—
140	C₄₇	#9709	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	—	47	2	no	—
142	C₂²×Q₈	—	94	1	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	94	2	no	—
145	C₄⋊Q₈	—	94	2	no	—
146	C₄⋊Q₈	—	94	2	no	—
147	C₄⋊Q₈	—	94	2	no	—
148	C₄⋊Q₈	—	94	2	no	—
149	C₂×C₄⋊C₄	—	47	2	no	—
150	C₂×C₄⋊C₄	—	94	1	no	—
151	C₂×C₄⋊C₄	—	94	1	no	—
152	C₂×C₄⋊C₄	—	94	1	no	—
153	C₂×C₄²	C₄×D₄₇	1	2	yes	—
154	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
155	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
156	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
157	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	47	4	no	—
161	C₄⋊C₈	—	94	2	no	—
162	#97	—	188	2	no	—
163	#95	—	94	4	no	—
164	#95	—	94	4	no	—
165	C₂×Q₈	—	94	4	no	—
166	C₂×Q₈	—	188	4	no	—
167	C₂×Q₈	—	188	2	no	—
168	C₂×Q₈	—	188	2	no	—
169	C₂×Q₈	—	188	1	no	—
170	C₂×Q₈	—	188	1	no	—
171	C₂²×C₄	—	94	2	no	—
172	C₂²×C₄	—	94	2	no	—
173	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
174	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
175	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	4	4	no	—
180	C₂×C₈	—	94	4	no	—
181	C₂×C₈	—	188	2	no	—
182	C₂×C₈	—	188	2	no	—
183	C₄⋊C₄	—	94	4	no	—
184	C₄⋊C₄	—	188	2	no	—
185	C₄⋊C₄	—	188	1	no	—
186	C₄⋊C₄	—	188	1	no	—
187	C₄⋊C₄	—	188	1	no	—
188	C₄⋊C₄	—	188	1	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	2	4	no	—
192	C₄²	—	2	1	no	—
193	C₄²	—	4	2	no	—
194	C₄²	D₄×D₄₇	1	2	yes	—
195	C₄²	#10625354	1	2	yes	—
196	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
197	Q₈	—	376	4	no	—
198	Q₈	—	376	2	no	—
199	Q₈	—	376	2	no	—
200	C₂×C₄	—	2	2	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	—	2	2	no	—
207	C₂×C₄	—	188	2	no	—
208	C₂×C₄	—	188	2	no	—
209	C₂×C₄	—	188	4	no	—
210	C₂×C₄	—	188	2	no	—
211	C₂×C₄	—	188	2	no	—
212	C₂×C₄	#13093986	1	2	yes	—
213	C₂×C₄	#13093999	1	2	yes	—
214	C₂×C₄	#13094013	1	1	yes	characteristic
215	C₂×C₄	#13094020	1	1	yes	characteristic
216	C₂×C₄	#13094046	1	2	yes	—
217	C₂×C₄	#13094052	1	1	yes	characteristic
218	C₂×C₄	#13094054	1	4	yes	—
219	C₂×C₄	#13094057	1	1	yes	characteristic
220	C₈	—	8	2	no	—
221	C₈	—	188	4	no	—
222	C₂²	#15689024	1	1	yes	characteristic
223	C₂²	#15689105	1	2	yes	—
224	C₂²	#15689120	1	1	yes	characteristic
225	C₂²	#15689125	1	1	yes	characteristic
226	C₂²	#15689131	1	2	yes	—
227	C₄	—	2	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	376	2	no	—
231	C₄	—	376	2	no	—
232	C₄	#15689339	1	2	yes	—
233	C₄	#15689346	1	2	yes	—
234	C₄	#15689493	1	2	yes	—
235	C₄	#15689518	1	2	yes	—
236	C₂	#20242096	1	2	yes	—
237	C₂	#20242119	1	2	yes	—
238	C₂	#20244207	1	1	yes	characteristic
239	C₂	#20244235	1	1	yes	characteristic
240	C₂	#20244318	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20251766

C₂

yes

maximal, characteristic

#20243241

C₂

yes

maximal, characteristic

C₂×#15688871

C₂

yes

maximal

C₂×#15688868

C₂

yes

maximal

C₄₇×#1831

C₂

yes

maximal, characteristic

C₂×#13094024

C₂²

yes

characteristic

C₂×#13094024

C₂²

yes

characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

—

—

—

C₄

yes

—

—

—

—

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄³×C₄₇

C₂²

yes

characteristic

C₄₇×#336

—

C₂²×Dic₉₄

—

C₂²×Dic₉₄

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

—

—

—

—

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

#13093935

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

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

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

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

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

#137

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

100

C₄₇⋊C₈

—

101

#9709

—

maximal, Sylow

102

C₂²×C₄₇

#390

yes

characteristic

103

C₂²×C₄₇

#413

yes

—

104

C₂²×C₄₇

#416

yes

characteristic

105

C₂²×C₄₇

#417

yes

characteristic

106

C₂²×C₄₇

#419

yes

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

#463

yes

—

111

C₄×C₄₇

#464

yes

—

112

C₄×C₄₇

#491

yes

—

113

C₄×C₄₇

#497

yes

—

114

Dic₄₇

—

115

Dic₄₇

—

116

#2862

—

117

#1831

D₄₇

yes

characteristic

118

#1767

—

119

C₂×#333

—

120

C₂×#332

—

121

C₂×C₄₇

#1554

yes

—

122

C₂×C₄₇

#1559

yes

—

123

C₂×C₄₇

#1960

yes

characteristic

124

C₂×C₄₇

#1967

yes

characteristic

125

C₂×C₄₇

#1983

yes

characteristic

126

C₂×C₄⋊Q₈

—

127

C₂×C₄⋊Q₈

—

128

C₂×C₄⋊C₈

—

129

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

130

C₂×#97

—

131

#391

—

132

#391

—

133

#391

—

134

#382

—

135

C₄³

C₂×D₄₇

yes

characteristic

136

#336

—

137

#336

—

138

#333

—

139

#332

—

140

C₄₇

#9709

yes

characteristic, complemented, Sylow

141

C₂²×Q₈

—

142

C₂²×Q₈

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

C₄×D₄₇

yes

—

154

C₂×C₄²

D₁₈₈

yes

characteristic

155

C₂×C₄²

D₁₈₈

yes

characteristic

156

C₂×C₄²

C₂²⋊D₄₇

yes

—

157

C₂×C₄²

C₂²×D₄₇

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

#97

—

188

—

163

#95

—

164

#95

—

165

C₂×Q₈

—

166

C₂×Q₈

—

188

—

167

C₂×Q₈

—

188

—

168

C₂×Q₈

—

188

—

169

C₂×Q₈

—

188

—

170

C₂×Q₈

—

188

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

174

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

175

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

176

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

177

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

188

—

182

C₂×C₈

—

188

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

188

—

185

C₄⋊C₄

—

188

—

186

C₄⋊C₄

—

188

—

187

C₄⋊C₄

—

188

—

188

C₄⋊C₄

—

188

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

D₄×D₄₇

yes

—

195

C₄²

#10625354

yes

—

196

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

197

Q₈

—

376

—

198

Q₈

—

376

—

199

Q₈

—

376

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

188

—

208

C₂×C₄

—

188

—

209

C₂×C₄

—

188

—

210

C₂×C₄

—

188

—

211

C₂×C₄

—

188

—

212

C₂×C₄

#13093986

yes

—

213

C₂×C₄

#13093999

yes

—

214

C₂×C₄

#13094013

yes

characteristic

215

C₂×C₄

#13094020

yes

characteristic

216

C₂×C₄

#13094046

yes

—

217

C₂×C₄

#13094052

yes

characteristic

218

C₂×C₄

#13094054

yes

—

219

C₂×C₄

#13094057

yes

characteristic

220

C₈

—

221

C₈

—

188

—

222

C₂²

#15689024

yes

characteristic

223

C₂²

#15689105

yes

—

224

C₂²

#15689120

yes

characteristic

225

C₂²

#15689125

yes

characteristic

226

C₂²

#15689131

yes

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

376

—

231

C₄

—

376

—

232

C₄

#15689339

yes

—

233

C₄

#15689346

yes

—

234

C₄

#15689493

yes

—

235

C₄

#15689518

yes

—

236

C₂

#20242096

yes

—

237

C₂

#20242119

yes

—

238

C₂

#20244207

yes

characteristic

239

C₂

#20244235

yes

characteristic

240

C₂

#20244318

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1831	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1831	D₄₇
hypocenter	C₄₇	#9709
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂³

C₂×(C₂×D₄₇)⋊C₄

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1831

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
140. C₄₇	#9709	semidirect

H ≅ G/N

type

140. C₄₇

#9709

semidirect

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

subgroup	index
#20251766	2
#20243241	2
C₂×#15688871	2
C₂×#15688868	2
C₄₇×#1831	2
#9709	47

subgroup

index

C₄₇×#1831

Subgroups — #26115389

Conjugacy classes of subgroups

Complements

Maximal subgroups