Group #26109544 — subgroups

Subgroups — #26109544

Order 12032.

346 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 119 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	#20252322	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688874	C₂	1	1	yes	maximal, characteristic
3	#20242079	C₂	1	2	yes	maximal
4	#20241262	C₂	1	2	yes	maximal
5	C₄₇×#1837	C₂	1	1	yes	maximal, characteristic
6	#15689680	C₂²	1	1	yes	characteristic
7	#15689253	—	2	1	no	—
8	#15689253	C₄	1	2	yes	—
9	C₈×Dic₉₄	—	2	1	no	—
10	C₈×Dic₉₄	C₄	1	2	yes	—
11	#15689149	—	2	1	no	—
12	#15689147	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	#15689078	—	2	1	no	—
15	#15688874	—	2	1	no	—
16	#15688874	—	2	1	no	—
17	#15688871	—	2	2	no	—
18	#15688868	—	2	2	no	—
19	C₄₇×#423	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#341	—	2	1	no	—
22	C₄₇×#341	—	2	1	no	—
23	C₂×#10625329	—	2	1	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	#13094024	D₄	1	1	yes	characteristic
26	#13094024	D₄	1	1	yes	characteristic
27	#13094016	—	2	1	no	—
28	#13094003	—	2	1	no	—
29	#13094003	Q₈	1	2	yes	—
30	C₄×Dic₉₄	—	2	1	no	—
31	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
32	#13093983	—	2	1	no	—
33	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
34	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
35	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
36	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
37	Dic₄₇⋊C₈	—	2	2	no	—
38	Dic₄₇⋊C₈	—	2	2	no	—
39	#13093934	—	2	2	no	—
40	C₈×Dic₄₇	—	2	2	no	—
41	C₂×M₁₆×C₄₇	—	2	2	no	—
42	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₄₇	—	2	2	no	—
46	C₄⋊C₈×C₄₇	—	2	2	no	—
47	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
50	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
53	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
54	C₂×Dic₉₄	—	2	1	no	—
55	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
56	M₁₆×C₄₇	—	4	2	no	—
57	M₁₆×C₄₇	—	4	2	no	—
58	C₂×C₈×C₄₇	—	2	2	no	—
59	C₂×C₈×C₄₇	—	2	2	no	—
60	C₂×C₈×C₄₇	—	4	2	no	—
61	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₄₇	#41	1	1	yes	characteristic
69	C₂²⋊Dic₄₇	—	2	2	no	—
70	C₄⋊Dic₄₇	—	2	1	no	—
71	C₄⋊Dic₄₇	—	2	1	no	—
72	C₄⋊Dic₄₇	—	2	1	no	—
73	C₄⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
74	Dic₄₇⋊C₄	—	2	2	no	—
75	Dic₄₇⋊C₄	—	2	2	no	—
76	C₄×Dic₄₇	—	2	2	no	—
77	#10625329	—	4	2	no	—
78	C₂×C₄₇⋊C₈	—	2	2	no	—
79	C₂×C₄₇⋊C₈	—	4	2	no	—
80	C₂×C₄₇⋊C₈	—	8	2	no	—
81	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂×C₄×C₄₇	—	2	2	no	—
83	C₂×C₄×C₄₇	—	4	1	no	—
84	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
87	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
88	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
89	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#135	1	2	yes	—
91	C₂×C₄×C₄₇	#137	1	2	yes	—
92	C₂×Dic₄₇	—	2	2	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	Dic₉₄	—	4	2	no	—
95	Dic₉₄	—	4	2	no	—
96	C₈×C₄₇	—	2	1	no	—
97	C₈×C₄₇	—	2	1	no	—
98	C₈×C₄₇	—	2	1	no	—
99	C₈×C₄₇	—	2	1	no	—
100	C₈×C₄₇	—	8	2	no	—
101	C₄₇⋊C₈	—	4	2	no	—
102	C₄₇⋊C₈	—	8	2	no	—
103	#8687	—	47	1	no	maximal, Sylow
104	C₂²×C₄₇	—	2	1	no	—
105	C₂²×C₄₇	—	2	1	no	—
106	C₂²×C₄₇	#380	1	1	yes	characteristic
107	C₂²×C₄₇	#479	1	2	yes	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	—	2	1	no	—
110	C₄×C₄₇	—	2	1	no	—
111	C₄×C₄₇	#416	1	1	yes	characteristic
112	C₄×C₄₇	#419	1	1	yes	characteristic
113	C₄×C₄₇	#464	1	2	yes	—
114	C₄×C₄₇	#471	1	2	yes	—
115	Dic₄₇	—	4	2	no	—
116	Dic₄₇	—	4	2	no	—
117	#2960	—	47	1	no	—
118	#1837	D₄₇	1	1	yes	characteristic
119	C₂×#334	—	47	1	no	—
120	#1550	—	47	2	no	—
121	#1292	—	47	2	no	—
122	C₂×C₄₇	—	2	2	no	—
123	C₂×C₄₇	#1805	1	1	yes	characteristic
124	C₂×C₄₇	#1813	1	1	yes	characteristic
125	C₂×C₄₇	#1815	1	1	yes	characteristic
126	#533	—	47	1	no	—
127	#446	—	47	2	no	—
128	#446	—	94	1	no	—
129	C₈×Q₈	—	47	2	no	—
130	C₈×Q₈	—	94	1	no	—
131	#424	—	94	1	no	—
132	#423	—	47	1	no	—
133	#423	C₂×D₄₇	1	2	yes	—
134	C₂×C₄⋊C₈	—	47	2	no	—
135	#405	—	94	1	no	—
136	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
137	#341	—	2	1	no	—
138	#341	—	2	1	no	—
139	#334	—	94	1	no	—
140	#334	—	94	1	no	—
141	#333	—	94	2	no	—
142	#332	—	94	2	no	—
143	C₄₇	#8687	1	1	yes	characteristic, complemented, Sylow
144	C₂×M₁₆	—	2	2	no	—
145	C₂×M₁₆	—	94	1	no	—
146	C₂²×C₈	—	94	2	no	—
147	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
148	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
149	C₄⋊Q₈	—	47	1	no	—
150	C₄⋊Q₈	—	47	1	no	—
151	#125	—	94	1	no	—
152	C₂²⋊Q₈	—	47	2	no	—
153	C₂²⋊Q₈	—	94	1	no	—
154	C₄×Q₈	—	47	2	no	—
155	C₄×Q₈	—	94	1	no	—
156	#117	—	94	1	no	—
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	2	no	—
161	C₄⋊C₈	—	94	2	no	—
162	C₄⋊C₈	—	94	2	no	—
163	C₄⋊C₈	—	94	1	no	—
164	C₄⋊C₈	—	94	2	no	—
165	C₄⋊C₈	—	94	2	no	—
166	#97	—	94	2	no	—
167	C₄×C₈	—	94	2	no	—
168	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
169	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
170	C₄×C₈	D₁₈₈	1	1	yes	characteristic
171	C₄×C₈	D₁₈₈	1	1	yes	characteristic
172	C₂×Q₈	—	47	2	no	—
173	C₂×Q₈	—	94	1	no	—
174	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
175	C₂²×C₄	#10625354	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
177	M₁₆	—	4	2	no	—
178	M₁₆	—	4	2	no	—
179	M₁₆	—	188	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	94	2	no	—
184	C₂×C₈	—	376	2	no	—
185	C₂×C₈	—	188	2	no	—
186	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
187	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
188	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
189	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
190	C₄⋊C₄	—	47	2	no	—
191	C₄⋊C₄	—	94	2	no	—
192	C₄⋊C₄	—	94	1	no	—
193	C₄⋊C₄	—	94	1	no	—
194	C₄⋊C₄	—	94	1	no	—
195	C₄⋊C₄	—	94	2	no	—
196	C₂²⋊C₄	—	94	2	no	—
197	C₄²	—	94	2	no	—
198	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
199	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
200	C₄²	D₄×D₄₇	1	1	yes	characteristic
201	C₄²	#10625352	1	1	yes	characteristic
202	C₂³	#13094000	1	1	yes	characteristic
203	Q₈	—	188	2	no	—
204	Q₈	—	188	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	94	2	no	—
208	C₂×C₄	—	94	2	no	—
209	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
210	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
211	C₂×C₄	#13093982	1	1	yes	characteristic
212	C₂×C₄	#13093995	1	1	yes	characteristic
213	C₂×C₄	#13093999	1	1	yes	characteristic
214	C₂×C₄	#13094004	1	1	yes	characteristic
215	C₂×C₄	#13094044	1	2	yes	—
216	C₂×C₄	#13094054	1	2	yes	—
217	C₈	—	2	1	no	—
218	C₈	—	2	1	no	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	8	2	no	—
222	C₈	—	376	2	no	—
223	C₈	—	188	2	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	#15688980	1	1	yes	characteristic
227	C₂²	#15689427	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	188	2	no	—
232	C₄	—	188	2	no	—
233	C₄	#15689117	1	1	yes	characteristic
234	C₄	#15689131	1	1	yes	characteristic
235	C₄	#15689342	1	2	yes	—
236	C₄	#15689387	1	2	yes	—
237	C₂	—	2	2	no	—
238	C₂	#20243400	1	1	yes	characteristic
239	C₂	#20243435	1	1	yes	characteristic
240	C₂	#20243444	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252322

C₂

yes

maximal, characteristic

C₂×#15688874

C₂

yes

maximal, characteristic

#20242079

C₂

yes

maximal

#20241262

C₂

yes

maximal

C₄₇×#1837

C₂

yes

maximal, characteristic

#15689680

C₂²

yes

characteristic

#15689253

—

#15689253

C₄

yes

—

C₈×Dic₉₄

—

C₈×Dic₉₄

C₄

yes

—

#15689149

—

#15689147

C₂²

yes

characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

—

—

—

—

—

C₄₇×#423

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#341

—

C₄₇×#341

—

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

#13094024

D₄

yes

characteristic

#13094024

D₄

yes

—

—

Q₈

yes

—

C₄×Dic₉₄

—

C₄×Dic₉₄

C₂×C₄

yes

—

#13093983

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

Dic₄₇⋊C₈

—

Dic₄₇⋊C₈

—

#13093934

—

C₈×Dic₄₇

—

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

C₄⋊C₄

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

#41

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₄⋊C₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

100

C₈×C₄₇

—

101

C₄₇⋊C₈

—

102

C₄₇⋊C₈

—

103

#8687

—

maximal, Sylow

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

#380

yes

characteristic

107

C₂²×C₄₇

#479

yes

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

#416

yes

characteristic

112

C₄×C₄₇

#419

yes

characteristic

113

C₄×C₄₇

#464

yes

—

114

C₄×C₄₇

#471

yes

—

115

Dic₄₇

—

116

Dic₄₇

—

117

#2960

—

118

#1837

D₄₇

yes

characteristic

119

C₂×#334

—

120

#1550

—

121

#1292

—

122

C₂×C₄₇

—

123

C₂×C₄₇

#1805

yes

characteristic

124

C₂×C₄₇

#1813

yes

characteristic

125

C₂×C₄₇

#1815

yes

characteristic

126

#533

—

127

#446

—

128

#446

—

129

C₈×Q₈

—

130

C₈×Q₈

—

131

#424

—

132

#423

—

133

#423

C₂×D₄₇

yes

—

134

C₂×C₄⋊C₈

—

135

#405

—

136

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

137

#341

—

138

#341

—

139

#334

—

140

#334

—

141

#333

—

142

#332

—

143

C₄₇

#8687

yes

characteristic, complemented, Sylow

144

C₂×M₁₆

—

145

C₂×M₁₆

—

146

C₂²×C₈

—

147

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

148

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

151

#125

—

152

C₂²⋊Q₈

—

153

C₂²⋊Q₈

—

154

C₄×Q₈

—

155

C₄×Q₈

—

156

#117

—

157

C₂×C₄²

C₂²×D₄₇

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#97

—

167

C₄×C₈

—

168

C₄×C₈

C₄×D₄₇

yes

characteristic

169

C₄×C₈

C₄×D₄₇

yes

characteristic

170

C₄×C₈

D₁₈₈

yes

characteristic

171

C₄×C₈

D₁₈₈

yes

characteristic

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂²×C₄

Q₈×D₄₇

yes

characteristic

175

C₂²×C₄

#10625354

yes

characteristic

176

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

177

M₁₆

—

178

M₁₆

—

179

M₁₆

—

188

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

376

—

185

C₂×C₈

—

188

—

186

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

187

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

188

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

189

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₂²⋊C₄

—

197

C₄²

—

198

C₄²

C₂×C₄×D₄₇

yes

characteristic

199

C₄²

C₂×D₁₈₈

yes

characteristic

200

C₄²

D₄×D₄₇

yes

characteristic

201

C₄²

#10625352

yes

characteristic

202

C₂³

#13094000

yes

characteristic

203

Q₈

—

188

—

204

Q₈

—

188

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

210

C₂×C₄

C₄⋊C₄×D₄₇

yes

characteristic

211

C₂×C₄

#13093982

yes

characteristic

212

C₂×C₄

#13093995

yes

characteristic

213

C₂×C₄

#13093999

yes

characteristic

214

C₂×C₄

#13094004

yes

characteristic

215

C₂×C₄

#13094044

yes

—

216

C₂×C₄

#13094054

yes

—

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

376

—

223

C₈

—

188

—

224

C₂²

—

225

C₂²

—

226

C₂²

#15688980

yes

characteristic

227

C₂²

#15689427

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

188

—

232

C₄

—

188

—

233

C₄

#15689117

yes

characteristic

234

C₄

#15689131

yes

characteristic

235

C₄

#15689342

yes

—

236

C₄

#15689387

yes

—

237

C₂

—

238

C₂

#20243400

yes

characteristic

239

C₂

#20243435

yes

characteristic

240

C₂

#20243444

yes

characteristic

	subgroup	G/H
center	C₂²	#15688980
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1837	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂³×C₄₇	C₂²⋊Q₈
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1837	D₄₇
hypocenter	C₄₇	#8687
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂²

#15688980

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1837

C₂

socle

C₂²×C₄₇

#380

prime radical

C₂³×C₄₇

C₂²⋊Q₈

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
143. C₄₇	#8687	semidirect

H ≅ G/N

type

143. C₄₇

#8687

semidirect

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

subgroup	index
#20252322	2
C₂×#15688874	2
#20242079	2
#20241262	2
C₄₇×#1837	2
#8687	47

subgroup

index

C₄₇×#1837

Subgroups — #26109544

Conjugacy classes of subgroups

Complements

Maximal subgroups