Group #26119839 — subgroups

Subgroups — #26119839

Order 12032.

478 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 127 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	#20248761	C₂	1	1	yes	maximal, characteristic
2	#20243390	C₂	1	2	yes	maximal
3	C₂×#15688855	C₂	1	2	yes	maximal
4	#20241271	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1845	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	C₂×#13093947	—	2	2	no	—
9	#15689053	—	2	2	no	—
10	#15689028	—	2	2	no	—
11	#15689022	—	2	2	no	—
12	#15688885	—	2	2	no	—
13	#15688855	—	2	4	no	—
14	C₂×#107×C₄₇	—	2	2	no	—
15	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#384	C₂²	1	1	yes	characteristic
17	C₄₇×#384	C₂²	1	1	yes	characteristic
18	C₂²×Dic₉₄	D₄	1	2	yes	—
19	C₂²×C₄₇⋊C₈	—	2	2	no	—
20	C₄×Dic₉₄	—	2	2	no	—
21	C₄×Dic₉₄	—	2	2	no	—
22	C₄×Dic₉₄	—	2	2	no	—
23	C₄×Dic₉₄	—	2	2	no	—
24	C₂×C₄⋊Dic₄₇	—	2	2	no	—
25	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
26	C₂×Dic₄₇⋊C₄	—	2	2	no	—
27	C₂×C₄×Dic₄₇	—	2	2	no	—
28	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
29	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
30	#13093947	—	4	4	no	—
31	C₄₇⋊#95	—	2	4	no	—
32	C₄₇⋊#95	—	2	2	no	—
33	C₂²×C₈×C₄₇	—	2	1	no	—
34	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
37	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
38	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
39	#107×C₄₇	—	4	4	no	—
40	C₄×C₈×C₄₇	—	2	1	no	—
41	C₄×C₈×C₄₇	D₄	1	2	yes	—
42	C₂²×C₄×C₄₇	—	2	2	no	—
43	C₂²×C₄×C₄₇	—	4	1	no	—
44	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
46	C₂²×Dic₄₇	—	2	2	no	—
47	C₂²×Dic₄₇	—	2	2	no	—
48	C₂×Dic₉₄	—	2	2	no	—
49	C₂×Dic₉₄	—	2	2	no	—
50	C₂×Dic₉₄	—	2	2	no	—
51	C₂×Dic₉₄	—	2	2	no	—
52	C₂×Dic₉₄	—	2	2	no	—
53	C₂×Dic₉₄	Q₁₆	1	4	yes	—
54	C₂×C₈×C₄₇	—	2	2	no	—
55	C₂×C₈×C₄₇	—	2	2	no	—
56	C₂×C₈×C₄₇	—	2	2	no	—
57	C₄⋊C₄×C₄₇	—	4	2	no	—
58	C₄⋊C₄×C₄₇	—	4	2	no	—
59	C₄⋊C₄×C₄₇	—	4	2	no	—
60	C₄⋊C₄×C₄₇	—	4	2	no	—
61	C₄⋊C₄×C₄₇	—	4	2	no	—
62	C₄⋊C₄×C₄₇	—	4	2	no	—
63	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₄₇	#41	1	1	yes	characteristic
65	C₄²×C₄₇	#41	1	2	yes	—
66	C₄⋊Dic₄₇	—	2	2	no	—
67	C₄⋊Dic₄₇	—	2	2	no	—
68	C₄⋊Dic₄₇	—	8	2	no	—
69	Dic₄₇⋊C₄	—	4	2	no	—
70	Dic₄₇⋊C₄	—	4	2	no	—
71	C₄×Dic₄₇	—	4	2	no	—
72	C₄×Dic₄₇	—	4	2	no	—
73	C₂×C₄₇⋊C₈	—	4	2	no	—
74	C₂×C₄₇⋊C₈	—	4	2	no	—
75	C₂×C₄₇⋊C₈	—	4	2	no	—
76	C₂³×C₄₇	#120	1	1	yes	characteristic
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	1	no	—
79	C₂×C₄×C₄₇	—	4	4	no	—
80	C₂×C₄×C₄₇	—	4	2	no	—
81	C₂×C₄×C₄₇	—	8	2	no	—
82	C₂×C₄×C₄₇	—	8	1	no	—
83	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
84	C₂×C₄×C₄₇	#121	1	2	yes	—
85	C₂×C₄×C₄₇	#123	1	2	yes	—
86	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
87	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
88	C₂×C₄×C₄₇	#135	1	2	yes	—
89	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
90	C₂×C₄×C₄₇	#137	1	2	yes	—
91	C₂×Dic₄₇	—	2	4	no	—
92	C₂×Dic₄₇	—	4	2	no	—
93	C₂×Dic₄₇	—	4	2	no	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	—	4	2	no	—
96	C₂×Dic₄₇	—	4	2	no	—
97	Dic₉₄	—	2	4	no	—
98	Dic₉₄	—	2	4	no	—
99	Dic₉₄	—	4	2	no	—
100	Dic₉₄	—	4	2	no	—
101	C₈×C₄₇	—	2	4	no	—
102	C₄₇⋊C₈	—	8	2	no	—
103	#10439	—	47	1	no	maximal, Sylow
104	C₂²×C₄₇	#394	1	1	yes	characteristic
105	C₂²×C₄₇	#449	1	2	yes	—
106	C₂²×C₄₇	#451	1	2	yes	—
107	C₂²×C₄₇	#453	1	1	yes	characteristic
108	C₂²×C₄₇	#456	1	1	yes	characteristic
109	C₄×C₄₇	—	2	1	no	—
110	C₄×C₄₇	—	2	1	no	—
111	C₄×C₄₇	—	8	2	no	—
112	C₄×C₄₇	—	16	1	no	—
113	C₄×C₄₇	#467	1	2	yes	—
114	C₄×C₄₇	#468	1	2	yes	—
115	C₄×C₄₇	#484	1	2	yes	—
116	C₄×C₄₇	#485	1	2	yes	—
117	Dic₄₇	—	4	4	no	—
118	Dic₄₇	—	8	2	no	—
119	#2582	—	47	1	no	—
120	#1845	D₄₇	1	1	yes	characteristic
121	#1803	—	47	2	no	—
122	C₂×Q₈⋊C₈	—	47	2	no	—
123	#1296	—	47	1	no	—
124	C₂×C₄₇	#1620	1	1	yes	characteristic
125	C₂×C₄₇	#1633	1	1	yes	characteristic
126	C₂×C₄₇	#1648	1	2	yes	—
127	C₂×C₄₇	#2036	1	2	yes	—
128	C₂×C₄₇	#2039	1	1	yes	characteristic
129	C₂×C₄×Q₈	—	47	2	no	—
130	C₂×#107	—	2	2	no	—
131	C₂×C₄⋊C₈	—	47	2	no	—
132	C₂×#103	—	94	2	no	—
133	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
134	#398	—	94	2	no	—
135	#391	—	94	2	no	—
136	#389	—	94	2	no	—
137	#384	C₂×D₄₇	1	1	yes	characteristic
138	#384	C₂×D₄₇	1	1	yes	characteristic
139	#340	—	94	2	no	—
140	Q₈⋊C₈	—	94	4	no	—
141	C₄₇	#10439	1	1	yes	characteristic, complemented, Sylow
142	C₂²×Q₈	—	47	2	no	—
143	C₂²×C₈	—	2	1	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	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	1	no	—
152	C₂×C₄⋊C₄	—	47	2	no	—
153	C₂×C₄⋊C₄	—	94	2	no	—
154	C₂×C₄⋊C₄	—	94	2	no	—
155	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
156	C₂×C₄²	—	94	2	no	—
157	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
158	#107	—	4	4	no	—
159	C₄⋊C₈	—	94	2	no	—
160	C₄⋊C₈	—	94	2	no	—
161	#103	—	188	4	no	—
162	C₄×C₈	—	2	1	no	—
163	C₄×C₈	D₁₈₈	1	2	yes	—
164	#95	—	94	4	no	—
165	#95	—	94	2	no	—
166	C₂×Q₈	—	47	4	no	—
167	C₂×Q₈	—	94	2	no	—
168	C₂×Q₈	—	94	2	no	—
169	C₂×Q₈	—	94	2	no	—
170	C₂×Q₈	—	94	2	no	—
171	C₂×Q₈	—	94	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	4	1	no	—
174	C₂²×C₄	—	94	2	no	—
175	C₂²×C₄	—	94	2	no	—
176	C₂²×C₄	D₄×D₄₇	1	2	yes	—
177	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	188	2	no	—
182	C₂×C₈	—	188	2	no	—
183	C₂×C₈	—	188	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	94	2	no	—
191	C₄⋊C₄	—	94	2	no	—
192	C₄⋊C₄	—	376	2	no	—
193	C₄⋊C₄	—	188	2	no	—
194	C₄⋊C₄	—	188	2	no	—
195	C₄²	—	188	2	no	—
196	C₄²	—	188	2	no	—
197	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
198	C₄²	#10625350	1	1	yes	characteristic
199	C₄²	#10625354	1	2	yes	—
200	C₂³	#13093992	1	1	yes	characteristic
201	Q₈	—	94	4	no	—
202	Q₈	—	94	4	no	—
203	Q₈	—	188	2	no	—
204	Q₈	—	188	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	8	2	no	—
210	C₂×C₄	—	8	1	no	—
211	C₂×C₄	—	94	4	no	—
212	C₂×C₄	—	188	2	no	—
213	C₂×C₄	—	188	2	no	—
214	C₂×C₄	—	188	2	no	—
215	C₂×C₄	—	188	2	no	—
216	C₂×C₄	—	188	2	no	—
217	C₂×C₄	#13093998	1	1	yes	characteristic
218	C₂×C₄	#13093999	1	2	yes	—
219	C₂×C₄	#13094009	1	2	yes	—
220	C₂×C₄	#13094013	1	1	yes	characteristic
221	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
222	C₂×C₄	#13094043	1	2	yes	—
223	C₂×C₄	#13094048	1	2	yes	—
224	C₂×C₄	#13094056	1	2	yes	—
225	C₈	—	2	4	no	—
226	C₈	—	376	2	no	—
227	C₂²	#15689040	1	1	yes	characteristic
228	C₂²	#15689265	1	2	yes	—
229	C₂²	#15689277	1	2	yes	—
230	C₂²	#15689290	1	1	yes	characteristic
231	C₂²	#15689305	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	8	2	no	—
235	C₄	—	16	1	no	—
236	C₄	—	376	2	no	—
237	C₄	—	188	4	no	—
238	C₄	#15689365	1	2	yes	—
239	C₄	#15689370	1	2	yes	—
240	C₄	#15689460	1	2	yes	—
241	C₄	#15689466	1	2	yes	—
242	C₂	#20242445	1	1	yes	characteristic
243	C₂	#20242526	1	1	yes	characteristic
244	C₂	#20242627	1	2	yes	—
245	C₂	#20244593	1	2	yes	—
246	C₂	#20244612	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20248761

C₂

yes

maximal, characteristic

#20243390

C₂

yes

maximal

C₂×#15688855

C₂

yes

maximal

#20241271

C₂

yes

maximal, characteristic

C₄₇×#1845

C₂

yes

maximal, characteristic

C₂×C₄×Dic₉₄

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

—

—

—

—

—

—

C₂×#107×C₄₇

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#384

C₂²

yes

characteristic

C₄₇×#384

C₂²

yes

characteristic

C₂²×Dic₉₄

D₄

yes

—

C₂²×C₄₇⋊C₈

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093947

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#107×C₄₇

—

C₄×C₈×C₄₇

—

C₄×C₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

Q₁₆

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

C₄²×C₄₇

yes

C₄²×C₄₇

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#121

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

#123

yes

—

C₂×C₄×C₄₇

#124

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₁₆

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

100

Dic₉₄

—

101

C₈×C₄₇

—

102

C₄₇⋊C₈

—

103

#10439

—

maximal, Sylow

104

C₂²×C₄₇

#394

yes

characteristic

105

C₂²×C₄₇

#449

yes

—

106

C₂²×C₄₇

#451

yes

—

107

C₂²×C₄₇

#453

yes

characteristic

108

C₂²×C₄₇

#456

yes

characteristic

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

#467

yes

—

114

C₄×C₄₇

#468

yes

—

115

C₄×C₄₇

#484

yes

—

116

C₄×C₄₇

#485

yes

—

117

Dic₄₇

—

118

Dic₄₇

—

119

#2582

—

120

#1845

D₄₇

yes

characteristic

121

#1803

—

122

C₂×Q₈⋊C₈

—

123

#1296

—

124

C₂×C₄₇

#1620

yes

characteristic

125

C₂×C₄₇

#1633

yes

characteristic

126

C₂×C₄₇

#1648

yes

—

127

C₂×C₄₇

#2036

yes

—

128

C₂×C₄₇

#2039

yes

characteristic

129

C₂×C₄×Q₈

—

130

C₂×#107

—

131

C₂×C₄⋊C₈

—

132

C₂×#103

—

133

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

134

#398

—

135

#391

—

136

#389

—

137

#384

C₂×D₄₇

yes

characteristic

138

#384

C₂×D₄₇

yes

characteristic

139

#340

—

140

Q₈⋊C₈

—

141

C₄₇

#10439

yes

characteristic, complemented, Sylow

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×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

—

156

C₂×C₄²

—

157

C₂×C₄²

C₂²×D₄₇

yes

characteristic

158

#107

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

#103

—

188

—

162

C₄×C₈

—

163

C₄×C₈

D₁₈₈

yes

—

164

#95

—

165

#95

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

D₄×D₄₇

yes

—

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

C₂×C₈

—

188

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

376

—

193

C₄⋊C₄

—

188

—

194

C₄⋊C₄

—

188

—

195

C₄²

—

188

—

196

C₄²

—

188

—

197

C₄²

C₂×D₁₈₈

yes

characteristic

198

C₄²

#10625350

yes

characteristic

199

C₄²

#10625354

yes

—

200

C₂³

#13093992

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

188

—

204

Q₈

—

188

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

188

—

213

C₂×C₄

—

188

—

214

C₂×C₄

—

188

—

215

C₂×C₄

—

188

—

216

C₂×C₄

—

188

—

217

C₂×C₄

#13093998

yes

characteristic

218

C₂×C₄

#13093999

yes

—

219

C₂×C₄

#13094009

yes

—

220

C₂×C₄

#13094013

yes

characteristic

221

C₂×C₄

Q₁₆×D₄₇

yes

—

222

C₂×C₄

#13094043

yes

—

223

C₂×C₄

#13094048

yes

—

224

C₂×C₄

#13094056

yes

—

225

C₈

—

226

C₈

—

376

—

227

C₂²

#15689040

yes

characteristic

228

C₂²

#15689265

yes

—

229

C₂²

#15689277

yes

—

230

C₂²

#15689290

yes

characteristic

231

C₂²

#15689305

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

376

—

237

C₄

—

188

—

238

C₄

#15689365

yes

—

239

C₄

#15689370

yes

—

240

C₄

#15689460

yes

—

241

C₄

#15689466

yes

—

242

C₂

#20242445

yes

characteristic

243

C₂

#20242526

yes

characteristic

244

C₂

#20242627

yes

—

245

C₂

#20244593

yes

—

246

C₂

#20244612

yes

characteristic

	subgroup	G/H
center	C₂³	#13093992
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1845	C₂
socle, prime radical	C₂³×C₄₇	#120
hypercenter	#1845	D₄₇
hypocenter	C₄₇	#10439
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

subgroup

G/H

center

C₂³

#13093992

commutator, cosocle

C₂×C₄²×C₄₇

C₂³

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1845

C₂

C₂³×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

N	H ≅ G/N	type
141. C₄₇	#10439	semidirect

H ≅ G/N

type

141. C₄₇

#10439

semidirect

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

subgroup	index
#20248761	2
#20243390	2
C₂×#15688855	2
#20241271	2
C₄₇×#1845	2
#10439	47

subgroup

index

C₄₇×#1845

Subgroups — #26119839

Conjugacy classes of subgroups

Complements

Maximal subgroups