Group #26110322 — subgroups

Subgroups — #26110322

Order 12032.

348 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 111 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	#20244329	C₂	1	1	yes	maximal, characteristic
3	#20242173	C₂	1	2	yes	maximal
4	#20241288	C₂	1	2	yes	maximal
5	C₄₇×#1461	C₂	1	1	yes	maximal, characteristic
6	#15689254	—	2	2	no	—
7	#15689254	—	2	2	no	—
8	#15689180	—	2	1	no	—
9	#15689180	C₂²	1	2	yes	—
10	#15689176	—	2	1	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#13093935	C₂²	1	1	yes	characteristic
13	#15688878	—	2	1	no	—
14	#15688878	—	2	1	no	—
15	#15688876	—	2	2	no	—
16	#15688874	—	2	2	no	—
17	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#431	C₂²	1	2	yes	—
19	C₄₇×#324	C₄	1	2	yes	—
20	C₄₇×#324	C₄	1	2	yes	—
21	C₂²×C₄₇⋊C₈	—	2	1	no	—
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
24	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
25	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
26	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
27	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
29	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
30	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
31	#13093935	—	2	2	no	—
32	#13093935	—	2	2	no	—
33	#13093935	—	2	2	no	—
34	C₄×C₄₇⋊C₈	—	2	2	no	—
35	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
36	C₄×Q₈×C₄₇	—	2	2	no	—
37	C₄×Q₈×C₄₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
41	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₄₇	—	2	2	no	—
45	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
46	C₄×C₈×C₄₇	—	2	2	no	—
47	C₂×Q₈×C₄₇	—	2	2	no	—
48	C₂×Q₈×C₄₇	—	2	2	no	—
49	C₂×Q₈×C₄₇	—	4	1	no	—
50	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
57	C₂×C₈×C₄₇	—	2	4	no	—
58	C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₄⋊C₄×C₄₇	—	2	2	no	—
61	C₄²×C₄₇	—	2	1	no	—
62	C₄²×C₄₇	—	2	1	no	—
63	C₄²×C₄₇	—	2	1	no	—
64	C₄²×C₄₇	—	2	1	no	—
65	C₄²×C₄₇	C₂×D₄	1	2	yes	—
66	C₄²×C₄₇	#41	1	2	yes	—
67	C₂×C₄₇⋊C₈	—	2	2	no	—
68	C₂×C₄₇⋊C₈	—	2	2	no	—
69	C₂×C₄₇⋊C₈	—	2	2	no	—
70	C₂×C₄₇⋊C₈	—	4	1	no	—
71	C₂×C₄₇⋊C₈	—	4	1	no	—
72	C₂×C₄₇⋊C₈	—	4	2	no	—
73	C₂×C₄₇⋊C₈	—	4	1	no	—
74	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
75	Q₈×C₄₇	—	4	4	no	—
76	C₂×C₄×C₄₇	—	2	1	no	—
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	1	no	—
79	C₂×C₄×C₄₇	—	2	1	no	—
80	C₂×C₄×C₄₇	—	2	1	no	—
81	C₂×C₄×C₄₇	—	2	1	no	—
82	C₂×C₄×C₄₇	—	2	1	no	—
83	C₂×C₄×C₄₇	—	2	1	no	—
84	C₂×C₄×C₄₇	—	2	1	no	—
85	C₂×C₄×C₄₇	—	2	1	no	—
86	C₂×C₄×C₄₇	—	2	1	no	—
87	C₂×C₄×C₄₇	—	4	1	no	—
88	C₂×C₄×C₄₇	—	4	1	no	—
89	C₂×C₄×C₄₇	—	4	1	no	—
90	C₂×C₄×C₄₇	#108	1	2	yes	—
91	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
93	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
94	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
95	C₈×C₄₇	—	4	4	no	—
96	C₄₇⋊C₈	—	4	2	no	—
97	C₄₇⋊C₈	—	4	2	no	—
98	C₄₇⋊C₈	—	4	2	no	—
99	C₄₇⋊C₈	—	8	1	no	—
100	#8865	—	47	1	no	maximal, Sylow
101	C₂²×C₄₇	—	2	1	no	—
102	C₂²×C₄₇	—	2	1	no	—
103	C₂²×C₄₇	#385	1	1	yes	characteristic
104	C₂²×C₄₇	C₂×#108	1	1	yes	characteristic
105	C₂²×C₄₇	#430	1	1	yes	characteristic
106	C₄×C₄₇	—	2	2	no	—
107	C₄×C₄₇	—	2	2	no	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	—	2	2	no	—
110	C₄×C₄₇	—	4	1	no	—
111	C₄×C₄₇	—	4	1	no	—
112	C₄×C₄₇	—	4	1	no	—
113	C₄×C₄₇	#454	1	1	yes	characteristic
114	C₄×C₄₇	#456	1	1	yes	characteristic
115	#2983	—	47	1	no	—
116	#1985	—	47	1	no	—
117	#1573	—	47	2	no	—
118	#1461	D₄₇	1	1	yes	characteristic
119	#1302	—	47	2	no	—
120	C₂×C₄₇	—	2	1	no	—
121	C₂×C₄₇	—	2	1	no	—
122	C₂×C₄₇	#1855	1	1	yes	characteristic
123	C₂×C₄₇	#1857	1	1	yes	characteristic
124	C₂×C₄₇	#1868	1	1	yes	characteristic
125	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
126	#446	—	94	2	no	—
127	#446	—	94	2	no	—
128	#432	—	47	2	no	—
129	#432	—	94	1	no	—
130	#431	—	94	1	no	—
131	#431	C₂×D₄₇	1	2	yes	—
132	C₂×C₄⋊C₈	—	47	1	no	—
133	C₂×#97	—	47	1	no	—
134	#336	—	94	1	no	—
135	#336	—	94	1	no	—
136	#335	—	94	2	no	—
137	#334	—	94	2	no	—
138	#324	Dic₄₇	1	2	yes	—
139	#324	Dic₄₇	1	2	yes	—
140	C₄₇	#8865	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
142	C₂²×C₈	—	94	1	no	—
143	C₂²×C₈	—	94	1	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₂×C₄⋊C₄	Dic₉₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
148	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
149	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
150	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
151	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	—	47	2	no	—
154	C₄⋊C₈	—	47	2	no	—
155	C₄⋊C₈	—	94	1	no	—
156	C₄⋊C₈	—	94	1	no	—
157	C₄⋊C₈	—	94	1	no	—
158	C₄⋊C₈	—	94	1	no	—
159	C₄⋊C₈	—	94	2	no	—
160	C₂²⋊C₈	—	94	2	no	—
161	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	—
162	#97	—	94	2	no	—
163	#97	—	94	2	no	—
164	#97	—	94	2	no	—
165	C₄×C₈	—	2	2	no	—
166	C₄×C₈	—	94	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	4	1	no	—
170	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
171	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
172	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
173	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
174	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
175	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
176	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	94	2	no	—
179	C₂×C₈	—	94	2	no	—
180	C₂×C₈	—	94	2	no	—
181	C₂×C₈	—	188	2	no	—
182	C₂×C₈	—	188	1	no	—
183	C₂×C₈	—	188	1	no	—
184	C₂×C₈	—	188	1	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	2	1	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	2	1	no	—
192	C₄²	D₄×D₄₇	1	2	yes	—
193	C₄²	#10625352	1	2	yes	—
194	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	#13093960	1	2	yes	—
211	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
212	C₂×C₄	#13093994	1	1	yes	characteristic
213	C₂×C₄	#13094001	1	2	yes	—
214	C₂×C₄	#13094008	1	1	yes	characteristic
215	C₈	—	4	4	no	—
216	C₈	—	376	1	no	—
217	C₈	—	188	2	no	—
218	C₈	—	188	2	no	—
219	C₈	—	188	2	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	#15688998	1	1	yes	characteristic
223	C₂²	C₂×#13093960	1	1	yes	characteristic
224	C₂²	#15689172	1	1	yes	characteristic
225	C₄	—	2	2	no	—
226	C₄	—	2	2	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	1	no	—
230	C₄	—	4	1	no	—
231	C₄	—	4	1	no	—
232	C₄	#15689298	1	1	yes	characteristic
233	C₄	#15689308	1	1	yes	characteristic
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#20243595	1	1	yes	characteristic
237	C₂	#20243605	1	1	yes	characteristic
238	C₂	#20243676	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252473

C₂

yes

maximal, characteristic

#20244329

C₂

yes

maximal, characteristic

#20242173

C₂

yes

maximal

#20241288

C₂

yes

maximal

C₄₇×#1461

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#15689176

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₂×#13093935

C₂²

yes

—

—

—

—

C₂×C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄₇×#431

C₂²

yes

—

C₄₇×#324

C₄

yes

—

C₄₇×#324

C₄

yes

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

—

#13093935

—

#13093935

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

Q₈

yes

characteristic

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₄₇

Q₈

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₄⋊C₄

yes

characteristic

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

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#108

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

#123

yes

characteristic

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

100

#8865

—

maximal, Sylow

101

C₂²×C₄₇

—

102

C₂²×C₄₇

—

103

C₂²×C₄₇

#385

yes

characteristic

104

C₂²×C₄₇

C₂×#108

yes

characteristic

105

C₂²×C₄₇

#430

yes

characteristic

106

C₄×C₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

#454

yes

characteristic

114

C₄×C₄₇

#456

yes

characteristic

115

#2983

—

116

#1985

—

117

#1573

—

118

#1461

D₄₇

yes

characteristic

119

#1302

—

120

C₂×C₄₇

—

121

C₂×C₄₇

—

122

C₂×C₄₇

#1855

yes

characteristic

123

C₂×C₄₇

#1857

yes

characteristic

124

C₂×C₄₇

#1868

yes

characteristic

125

C₂×C₄×Q₈

C₂×D₄₇

yes

characteristic

126

#446

—

127

#446

—

128

#432

—

129

#432

—

130

#431

—

131

#431

C₂×D₄₇

yes

—

132

C₂×C₄⋊C₈

—

133

C₂×#97

—

134

#336

—

135

#336

—

136

#335

—

137

#334

—

138

#324

Dic₄₇

yes

—

139

#324

Dic₄₇

yes

—

140

C₄₇

#8865

yes

characteristic, complemented, Sylow

141

C₂²×Q₈

Dic₉₄

yes

characteristic

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

146

C₂×C₄⋊C₄

Dic₉₄

yes

characteristic

147

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

characteristic

148

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

characteristic

149

C₂×C₄²

D₁₈₈

yes

characteristic

150

C₂×C₄²

D₁₈₈

yes

characteristic

151

C₂×C₄²

C₂²×D₄₇

yes

characteristic

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₂²⋊C₈

—

161

C₂²⋊C₈

C₂×Dic₄₇

yes

—

162

#97

—

163

#97

—

164

#97

—

165

C₄×C₈

—

166

C₄×C₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂²×C₄

C₄⋊Dic₄₇

yes

characteristic

171

C₂²×C₄

C₄⋊Dic₄₇

yes

characteristic

172

C₂²×C₄

C₄⋊Dic₄₇

yes

characteristic

173

C₂²×C₄

C₄⋊Dic₄₇

yes

characteristic

174

C₂²×C₄

C₂×Dic₉₄

yes

characteristic

175

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

176

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

188

—

182

C₂×C₈

—

188

—

183

C₂×C₈

—

188

—

184

C₂×C₈

—

188

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

D₄×D₄₇

yes

—

193

C₄²

#10625352

yes

—

194

C₂³

C₂×C₄⋊Dic₄₇

yes

characteristic

195

Q₈

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

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

—

210

C₂×C₄

#13093960

yes

—

211

C₂×C₄

D₄×Dic₄₇

yes

—

212

C₂×C₄

#13093994

yes

characteristic

213

C₂×C₄

#13094001

yes

—

214

C₂×C₄

#13094008

yes

characteristic

215

C₈

—

216

C₈

—

376

—

217

C₈

—

188

—

218

C₈

—

188

—

219

C₈

—

188

—

220

C₂²

—

221

C₂²

—

222

C₂²

#15688998

yes

characteristic

223

C₂²

C₂×#13093960

yes

characteristic

224

C₂²

#15689172

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

#15689298

yes

characteristic

233

C₄

#15689308

yes

characteristic

234

C₂

—

235

C₂

—

236

C₂

#20243595

yes

characteristic

237

C₂

#20243605

yes

characteristic

238

C₂

#20243676

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13093994
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1461	C₂
socle	C₂²×C₄₇	#385
prime radical	C₂³×C₄₇	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1461	D₄₇
hypocenter	C₄₇	#8865
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1461

subgroup

G/H

center

C₂×C₄

#13093994

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1461

C₂

socle

C₂²×C₄₇

#385

prime radical

C₂³×C₄₇

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1461

N	H ≅ G/N	type
140. C₄₇	#8865	semidirect

H ≅ G/N

type

140. C₄₇

#8865

semidirect

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

subgroup	index
#20252473	2
#20244329	2
#20242173	2
#20241288	2
C₄₇×#1461	2
#8865	47

subgroup

index

C₄₇×#1461

Subgroups — #26110322

Conjugacy classes of subgroups

Complements

Maximal subgroups