Group #26109504 — subgroups

Subgroups — #26109504

Order 12032.

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

normal subgroups only

This group has 350 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	#20252322	C₂	1	1	yes	maximal, characteristic
2	#20242136	C₂	1	1	yes	maximal, characteristic
3	#20241951	C₂	1	2	yes	maximal
4	#20241246	C₂	1	2	yes	maximal
5	C₄₇×#1835	C₂	1	1	yes	maximal, characteristic
6	#15689680	C₂²	1	1	yes	characteristic
7	#15689253	—	2	1	no	—
8	#15689253	C₄	1	2	yes	complemented
9	C₈×Dic₉₄	—	2	1	no	—
10	C₈×Dic₉₄	C₄	1	2	yes	complemented
11	#15689176	C₂²	1	2	yes	—
12	#15689149	—	2	1	no	—
13	#15689147	C₂²	1	1	yes	characteristic
14	#15689078	—	2	1	no	—
15	#15688876	—	2	1	no	—
16	#15688874	—	2	1	no	—
17	#15688859	—	2	4	no	—
18	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#382	C₂²	1	2	yes	—
20	C₄₇×#340	—	2	1	no	—
21	C₄₇×#340	—	2	1	no	—
22	C₂×#10625329	—	2	1	no	—
23	#13094024	Q₈	1	1	yes	characteristic
24	#13094024	Q₈	1	1	yes	characteristic
25	#13094016	—	2	1	no	—
26	#13094003	—	2	1	no	—
27	#13094003	D₄	1	2	yes	—
28	C₄×Dic₉₄	—	2	1	no	—
29	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
30	#13093983	—	2	1	no	—
31	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
34	Dic₄₇⋊C₈	—	2	2	no	—
35	Dic₄₇⋊C₈	—	2	2	no	—
36	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
37	#13093934	—	2	2	no	—
38	C₄×C₄₇⋊C₈	—	2	2	no	—
39	C₈×Dic₄₇	—	2	2	no	—
40	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
44	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
47	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
48	#95×C₄₇	—	2	2	no	—
49	#95×C₄₇	—	2	2	no	—
50	C₂²×C₄×C₄₇	—	4	2	no	—
51	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	C₂×D₄	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	C₂×C₈×C₄₇	—	2	2	no	—
57	C₂×C₈×C₄₇	—	2	2	no	—
58	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
62	C₄⋊C₄×C₄₇	—	4	2	no	—
63	C₄⋊C₄×C₄₇	—	4	2	no	—
64	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₄₇	#41	1	1	yes	characteristic
68	C₂²⋊Dic₄₇	—	2	2	no	—
69	C₄⋊Dic₄₇	—	2	1	no	—
70	C₄⋊Dic₄₇	—	2	1	no	—
71	C₄⋊Dic₄₇	—	2	1	no	—
72	C₄⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
73	Dic₄₇⋊C₄	—	2	2	no	—
74	Dic₄₇⋊C₄	—	2	2	no	—
75	C₄×Dic₄₇	—	2	2	no	—
76	#10625329	—	4	2	no	—
77	C₂×C₄₇⋊C₈	—	2	2	no	—
78	C₂×C₄₇⋊C₈	—	4	2	no	—
79	C₂³×C₄₇	#121	1	1	yes	characteristic
80	C₂×C₄×C₄₇	—	4	1	no	—
81	C₂×C₄×C₄₇	—	4	1	no	—
82	C₂×C₄×C₄₇	—	8	2	no	—
83	C₂×C₄×C₄₇	—	8	2	no	—
84	C₂×C₄×C₄₇	—	8	2	no	—
85	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₄₇	#117	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	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₄₇	#135	1	2	yes	—
92	C₂×C₄×C₄₇	#137	1	2	yes	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	—	2	2	no	—
95	Dic₉₄	—	4	2	no	—
96	Dic₉₄	—	4	2	no	—
97	C₈×C₄₇	—	2	1	no	—
98	C₈×C₄₇	—	2	1	no	—
99	C₈×C₄₇	—	2	1	no	—
100	C₈×C₄₇	—	2	1	no	—
101	C₄₇⋊C₈	—	4	2	no	—
102	C₄₇⋊C₈	—	8	2	no	—
103	#8679	—	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	#464	1	2	yes	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	—	2	1	no	—
110	C₄×C₄₇	—	2	1	no	—
111	C₄×C₄₇	—	2	1	no	—
112	C₄×C₄₇	—	16	2	no	—
113	C₄×C₄₇	#416	1	1	yes	characteristic
114	C₄×C₄₇	#419	1	1	yes	characteristic
115	C₄×C₄₇	#479	1	2	yes	—
116	Dic₄₇	—	4	2	no	—
117	Dic₄₇	—	4	2	no	—
118	#2960	—	47	1	no	—
119	#1835	D₄₇	1	1	yes	characteristic
120	#1564	—	47	1	no	—
121	#1518	—	47	2	no	—
122	#1286	—	47	2	no	—
123	C₂×C₄₇	—	2	2	no	—
124	C₂×C₄₇	#1805	1	1	yes	characteristic
125	C₂×C₄₇	#1812	1	1	yes	characteristic
126	C₂×C₄₇	#1814	1	1	yes	characteristic
127	#533	—	47	1	no	—
128	#446	—	47	2	no	—
129	#446	—	94	1	no	—
130	C₈×Q₈	—	47	2	no	—
131	C₈×Q₈	—	94	1	no	—
132	#431	—	47	2	no	—
133	#424	—	94	1	no	—
134	#423	—	47	1	no	—
135	#405	—	94	1	no	—
136	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
137	#382	C₂×D₄₇	1	2	yes	—
138	#340	—	2	1	no	—
139	#340	—	2	1	no	—
140	#335	—	94	1	no	—
141	#334	—	94	1	no	—
142	#328	—	94	4	no	—
143	C₄₇	#8679	1	1	yes	characteristic, complemented, Sylow
144	C₂×M₁₆	—	94	1	no	—
145	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
146	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
147	C₄⋊Q₈	—	47	1	no	—
148	C₄⋊Q₈	—	47	1	no	—
149	#125	—	94	1	no	—
150	C₂²⋊Q₈	—	47	2	no	—
151	C₂²⋊Q₈	—	94	1	no	—
152	C₄×Q₈	—	47	2	no	—
153	C₄×Q₈	—	94	1	no	—
154	#117	—	94	1	no	—
155	C₂×C₄⋊C₄	—	2	2	no	—
156	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
157	C₄⋊C₈	—	47	2	no	—
158	C₄⋊C₈	—	94	2	no	—
159	C₄⋊C₈	—	94	2	no	—
160	C₄⋊C₈	—	94	1	no	—
161	C₄⋊C₈	—	94	2	no	—
162	C₂²⋊C₈	—	94	2	no	—
163	#97	—	94	2	no	—
164	C₄×C₈	—	94	2	no	—
165	C₄×C₈	—	94	2	no	—
166	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
167	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
168	C₄×C₈	D₁₈₈	1	1	yes	characteristic
169	C₄×C₈	D₁₈₈	1	1	yes	characteristic
170	#95	—	2	2	no	—
171	#95	—	2	2	no	—
172	C₂×Q₈	—	47	2	no	—
173	C₂×Q₈	—	94	1	no	—
174	C₂²×C₄	—	4	2	no	—
175	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
176	C₂²×C₄	#10625352	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
178	M₁₆	—	188	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	94	2	no	—
182	C₂×C₈	—	188	2	no	—
183	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
184	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
185	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
186	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	47	2	no	—
190	C₄⋊C₄	—	94	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	C₂²⋊C₄	—	94	2	no	—
196	C₄²	—	94	2	no	—
197	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
198	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
199	C₄²	Q₈×D₄₇	1	1	yes	characteristic
200	C₄²	#10625354	1	1	yes	characteristic
201	C₂³	#13093995	1	1	yes	characteristic
202	Q₈	—	188	2	no	—
203	Q₈	—	188	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	8	2	no	—
207	C₂×C₄	—	8	2	no	—
208	C₂×C₄	—	8	2	no	—
209	C₂×C₄	—	94	2	no	—
210	C₂×C₄	—	94	2	no	—
211	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
213	C₂×C₄	#13093982	1	1	yes	characteristic
214	C₂×C₄	#13093999	1	1	yes	characteristic
215	C₂×C₄	#13094000	1	1	yes	characteristic
216	C₂×C₄	#13094004	1	1	yes	characteristic
217	C₂×C₄	#13094044	1	2	yes	—
218	C₂×C₄	#13094054	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	376	2	no	—
224	C₈	—	188	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#15688980	1	1	yes	characteristic
228	C₂²	#15689342	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	16	2	no	—
234	C₄	—	188	2	no	—
235	C₄	—	188	2	no	—
236	C₄	#15689117	1	1	yes	characteristic
237	C₄	#15689131	1	1	yes	characteristic
238	C₄	#15689427	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#20243400	1	1	yes	characteristic
241	C₂	#20243431	1	1	yes	characteristic
242	C₂	#20243439	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252322

C₂

yes

maximal, characteristic

#20242136

C₂

yes

maximal, characteristic

#20241951

C₂

yes

maximal

#20241246

C₂

yes

maximal

C₄₇×#1835

C₂

yes

maximal, characteristic

#15689680

C₂²

yes

characteristic

#15689253

—

#15689253

C₄

yes

complemented

C₈×Dic₉₄

—

C₈×Dic₉₄

C₄

yes

complemented

#15689176

C₂²

yes

—

#15689149

—

#15689147

C₂²

yes

—

—

—

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#382

C₂²

yes

—

C₄₇×#340

—

C₄₇×#340

—

C₂×#10625329

—

#13094024

Q₈

yes

characteristic

#13094024

Q₈

yes

—

—

D₄

yes

—

C₄×Dic₉₄

—

C₄×Dic₉₄

C₂×C₄

yes

—

#13093983

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

Dic₄₇⋊C₈

—

Dic₄₇⋊C₈

—

C₂²⋊(C₄₇⋊C₈)

—

#13093934

—

C₄×C₄₇⋊C₈

—

C₈×Dic₄₇

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

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

#95×C₄₇

—

#95×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

C₄⋊C₄

yes

—

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

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×Q₈

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

—

C₂³×C₄₇

#121

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

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

C₂²⋊Q₈

yes

characteristic

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

—

100

C₈×C₄₇

—

101

C₄₇⋊C₈

—

102

C₄₇⋊C₈

—

103

#8679

—

maximal, Sylow

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

#380

yes

characteristic

107

C₂²×C₄₇

#464

yes

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

#416

yes

characteristic

114

C₄×C₄₇

#419

yes

characteristic

115

C₄×C₄₇

#479

yes

—

116

Dic₄₇

—

117

Dic₄₇

—

118

#2960

—

119

#1835

D₄₇

yes

characteristic

120

#1564

—

121

#1518

—

122

#1286

—

123

C₂×C₄₇

—

124

C₂×C₄₇

#1805

yes

characteristic

125

C₂×C₄₇

#1812

yes

characteristic

126

C₂×C₄₇

#1814

yes

characteristic

127

#533

—

128

#446

—

129

#446

—

130

C₈×Q₈

—

131

C₈×Q₈

—

132

#431

—

133

#424

—

134

#423

—

135

#405

—

136

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

137

#382

C₂×D₄₇

yes

—

138

#340

—

139

#340

—

140

#335

—

141

#334

—

142

#328

—

143

C₄₇

#8679

yes

characteristic, complemented, Sylow

144

C₂×M₁₆

—

145

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

146

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

#125

—

150

C₂²⋊Q₈

—

151

C₂²⋊Q₈

—

152

C₄×Q₈

—

153

C₄×Q₈

—

154

#117

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄²

C₂²×D₄₇

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₂²⋊C₈

—

163

#97

—

164

C₄×C₈

—

165

C₄×C₈

—

166

C₄×C₈

C₄×D₄₇

yes

characteristic

167

C₄×C₈

C₄×D₄₇

yes

characteristic

168

C₄×C₈

D₁₈₈

yes

characteristic

169

C₄×C₈

D₁₈₈

yes

characteristic

170

#95

—

171

#95

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂²×C₄

—

175

C₂²×C₄

D₄×D₄₇

yes

characteristic

176

C₂²×C₄

#10625352

yes

characteristic

177

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

178

M₁₆

—

188

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

188

—

183

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

184

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

185

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

186

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₂²⋊C₄

—

196

C₄²

—

197

C₄²

C₂×C₄×D₄₇

yes

characteristic

198

C₄²

C₂×D₁₈₈

yes

characteristic

199

C₄²

Q₈×D₄₇

yes

characteristic

200

C₄²

#10625354

yes

characteristic

201

C₂³

#13093995

yes

characteristic

202

Q₈

—

188

—

203

Q₈

—

188

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

212

C₂×C₄

C₄⋊C₄×D₄₇

yes

characteristic

213

C₂×C₄

#13093982

yes

characteristic

214

C₂×C₄

#13093999

yes

characteristic

215

C₂×C₄

#13094000

yes

characteristic

216

C₂×C₄

#13094004

yes

characteristic

217

C₂×C₄

#13094044

yes

—

218

C₂×C₄

#13094054

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

376

—

224

C₈

—

188

—

225

C₂²

—

226

C₂²

—

227

C₂²

#15688980

yes

characteristic

228

C₂²

#15689342

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

188

—

235

C₄

—

188

—

236

C₄

#15689117

yes

characteristic

237

C₄

#15689131

yes

characteristic

238

C₄

#15689427

yes

—

239

C₂

—

240

C₂

#20243400

yes

characteristic

241

C₂

#20243431

yes

characteristic

242

C₂

#20243439

yes

characteristic

	subgroup	G/H
center	C₂²	#15688980
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1835	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂³×C₄₇	#121
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1835	D₄₇
hypocenter	C₄₇	#8679
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

subgroup

G/H

center

C₂²

#15688980

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1835

C₂

C₂²×C₄₇

C₂³×C₄₇

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

N	H ≅ G/N	type
8. #15689253	C₄	semidirect
10. C₈×Dic₉₄	C₄	semidirect
143. C₄₇	#8679	semidirect

H ≅ G/N

type

8. #15689253

C₄

semidirect

10. C₈×Dic₉₄

C₄

semidirect

143. C₄₇

#8679

semidirect

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

subgroup	index
#20252322	2
#20242136	2
#20241951	2
#20241246	2
C₄₇×#1835	2
#8679	47

subgroup

index

C₄₇×#1835

Subgroups — #26109504

Conjugacy classes of subgroups

Complements

Maximal subgroups