Group #26116243 — subgroups

Subgroups — #26116243

Order 12032.

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

normal subgroups only

This group has 498 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	#20243526	C₂	1	1	yes	maximal, characteristic, complemented
2	#20241839	C₂	1	2	yes	maximal, complemented
3	#20241839	C₂	1	2	yes	maximal, complemented
4	C₂×#15688845	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#3147	C₂	1	1	yes	maximal, characteristic
6	#15689147	C₂²	1	2	yes	—
7	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
9	#15688888	—	2	2	no	—
10	D₄⋊(C₄₇⋊C₈)	—	2	4	no	—
11	D₄⋊(C₄₇⋊C₈)	—	2	4	no	—
12	#15688845	—	2	2	no	—
13	C₂×#135×C₄₇	—	2	2	no	—
14	C₄₇×#532	C₂²	1	2	yes	—
15	C₄₇×#495	—	2	2	no	—
16	C₄₇×#494	C₄	1	1	yes	characteristic
17	C₄₇×#493	C₄	1	1	yes	characteristic
18	C₄₇×#492	C₄	1	2	yes	—
19	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#10625329	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	2	1	no	—
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
25	C₄×C₄₇⋊C₈	—	2	1	no	—
26	C₄×C₄₇⋊C₈	—	2	1	no	—
27	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
28	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
29	C₂×#41×C₄₇	—	2	2	no	—
30	#135×C₄₇	—	4	8	no	—
31	C₂×Q₁₆×C₄₇	—	2	2	no	—
32	C₂×SD₁₆×C₄₇	—	2	4	no	—
33	C₂×D₈×C₄₇	—	2	2	no	—
34	C₂²×C₈×C₄₇	D₄	1	2	yes	—
35	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
36	#127×C₄₇	C₂×C₄	1	2	yes	—
37	#124×C₄₇	—	2	2	no	—
38	#121×C₄₇	—	2	2	no	—
39	#121×C₄₇	—	2	2	no	—
40	C₄×D₄×C₄₇	—	2	2	no	—
41	C₄×D₄×C₄₇	—	2	2	no	—
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₄₇	D₄	1	2	yes	—
46	#41×C₄₇	—	4	8	no	—
47	C₂×Q₈×C₄₇	—	2	2	no	—
48	C₂×D₄×C₄₇	—	2	2	no	—
49	C₂×D₄×C₄₇	—	2	2	no	—
50	C₂×D₄×C₄₇	—	2	2	no	—
51	C₂×D₄×C₄₇	—	4	2	no	—
52	C₂²×C₄×C₄₇	—	4	2	no	—
53	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
56	Q₁₆×C₄₇	—	4	4	no	—
57	SD₁₆×C₄₇	—	4	8	no	—
58	D₈×C₄₇	—	4	4	no	—
59	C₂×C₈×C₄₇	—	2	4	no	—
60	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
62	C₄⋊C₄×C₄₇	—	2	2	no	—
63	C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂²⋊C₄×C₄₇	—	4	2	no	—
65	C₂²⋊C₄×C₄₇	—	4	2	no	—
66	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
70	#10625329	—	4	4	no	—
71	C₂×C₄₇⋊C₈	—	2	4	no	—
72	C₂×C₄₇⋊C₈	—	2	2	no	—
73	C₂×C₄₇⋊C₈	—	2	2	no	—
74	C₂×C₄₇⋊C₈	—	4	2	no	—
75	C₂×C₄₇⋊C₈	—	4	2	no	—
76	C₂³×C₄₇	—	4	2	no	—
77	C₂³×C₄₇	#124	1	1	yes	characteristic
78	Q₈×C₄₇	—	4	4	no	—
79	D₄×C₄₇	—	4	4	no	—
80	D₄×C₄₇	—	4	4	no	—
81	D₄×C₄₇	—	4	4	no	—
82	D₄×C₄₇	—	8	4	no	—
83	C₂×C₄×C₄₇	—	2	2	no	—
84	C₂×C₄×C₄₇	—	2	2	no	—
85	C₂×C₄×C₄₇	—	4	2	no	—
86	C₂×C₄×C₄₇	—	8	4	no	—
87	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
89	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
91	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
92	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
93	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
94	C₈×C₄₇	—	2	2	no	—
95	C₈×C₄₇	—	2	2	no	—
96	C₄₇⋊C₈	—	2	4	no	—
97	C₄₇⋊C₈	—	4	2	no	—
98	C₄₇⋊C₈	—	8	2	no	—
99	#9860	—	47	1	no	maximal, Sylow
100	C₂²×C₄₇	—	2	1	no	—
101	C₂²×C₄₇	—	2	1	no	—
102	C₂²×C₄₇	—	8	2	no	—
103	C₂²×C₄₇	—	8	2	no	—
104	C₂²×C₄₇	—	8	2	no	—
105	C₂²×C₄₇	#390	1	1	yes	characteristic
106	C₂²×C₄₇	#490	1	2	yes	—
107	C₄×C₄₇	—	2	1	no	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	—	8	2	no	—
110	C₄×C₄₇	#418	1	2	yes	—
111	C₄×C₄₇	#443	1	2	yes	—
112	C₄×C₄₇	#444	1	2	yes	—
113	C₄×C₄₇	#496	1	2	yes	—
114	#3147	D₄₇	1	1	yes	characteristic
115	#1837	—	47	1	no	—
116	#1492	—	47	2	no	—
117	#1492	—	47	2	no	—
118	C₂×#322	—	47	1	no	—
119	C₂×C₄₇	—	2	2	no	—
120	C₂×C₄₇	—	16	2	no	—
121	C₂×C₄₇	#1961	1	1	yes	characteristic
122	C₂×C₄₇	#1974	1	1	yes	characteristic
123	C₂×C₄₇	#1975	1	1	yes	characteristic
124	C₂×#135	—	2	2	no	—
125	#532	C₂×D₄₇	1	2	yes	—
126	#495	—	2	2	no	—
127	#494	Dic₄₇	1	1	yes	characteristic
128	#493	Dic₄₇	1	1	yes	characteristic
129	#492	Dic₄₇	1	2	yes	—
130	#423	—	47	2	no	—
131	C₂×C₄×C₈	—	47	1	no	—
132	C₂×C₄×C₈	—	47	1	no	—
133	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
134	#341	—	94	2	no	—
135	D₄⋊C₈	—	94	4	no	—
136	D₄⋊C₈	—	94	4	no	—
137	#322	—	94	2	no	—
138	C₄₇	#9860	1	1	yes	characteristic, complemented, Sylow
139	C₂×#41	—	2	2	no	—
140	#135	—	4	8	no	—
141	C₂×Q₁₆	—	2	2	no	—
142	C₂×SD₁₆	—	2	4	no	—
143	C₂×D₈	—	2	2	no	—
144	C₂×M₁₆	—	94	2	no	—
145	C₂²×C₈	—	94	1	no	—
146	C₂²×C₈	—	94	1	no	—
147	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
148	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
149	#127	C₂×Dic₄₇	1	2	yes	—
150	#124	—	2	2	no	—
151	#121	—	2	2	no	—
152	#121	—	2	2	no	—
153	C₄×D₄	—	2	2	no	—
154	C₄×D₄	—	2	2	no	—
155	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
156	C₄⋊C₈	—	94	2	no	—
157	C₄⋊C₈	—	94	2	no	—
158	C₄×C₈	—	47	2	no	—
159	C₄×C₈	—	47	2	no	—
160	C₄×C₈	—	94	1	no	—
161	C₄×C₈	—	94	1	no	—
162	C₄×C₈	C₂×Dic₄₇	1	1	yes	characteristic
163	C₄×C₈	C₂×Dic₄₇	1	1	yes	characteristic
164	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
165	#41	—	4	8	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×D₄	—	2	2	no	—
168	C₂×D₄	—	2	2	no	—
169	C₂×D₄	—	2	2	no	—
170	C₂×D₄	—	4	2	no	—
171	C₂²×C₄	—	4	2	no	—
172	C₂²×C₄	#10625352	1	1	yes	characteristic
173	C₂²×C₄	#10625352	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
175	Q₁₆	—	4	4	no	—
176	SD₁₆	—	4	8	no	—
177	D₈	—	4	4	no	—
178	M₁₆	—	188	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	94	4	no	—
181	C₂×C₈	—	94	2	no	—
182	C₂×C₈	—	94	2	no	—
183	C₂×C₈	—	188	2	no	—
184	C₂×C₈	—	188	2	no	—
185	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
186	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	—	2	2	no	—
189	C₂²⋊C₄	—	4	2	no	—
190	C₂²⋊C₄	—	4	2	no	—
191	C₄²	D₄×D₄₇	1	1	yes	characteristic
192	C₄²	D₄×D₄₇	1	1	yes	characteristic
193	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
194	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
195	C₂³	—	4	2	no	—
196	C₂³	#13094011	1	1	yes	characteristic
197	Q₈	—	4	4	no	—
198	D₄	—	4	4	no	—
199	D₄	—	4	4	no	—
200	D₄	—	4	4	no	—
201	D₄	—	8	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	8	4	no	—
206	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
207	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
208	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
209	C₂×C₄	#13093995	1	1	yes	characteristic
210	C₂×C₄	#13093995	1	1	yes	characteristic
211	C₂×C₄	#13094020	1	1	yes	characteristic
212	C₂×C₄	#13094050	1	4	yes	—
213	C₈	—	2	2	no	—
214	C₈	—	2	2	no	—
215	C₈	—	94	4	no	—
216	C₈	—	376	2	no	—
217	C₈	—	188	2	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	8	2	no	—
221	C₂²	—	8	2	no	—
222	C₂²	—	8	2	no	—
223	C₂²	#15689026	1	1	yes	characteristic
224	C₂²	#15689487	1	2	yes	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	8	2	no	—
228	C₄	#15689128	1	2	yes	—
229	C₄	#15689240	1	2	yes	—
230	C₄	#15689245	1	2	yes	—
231	C₄	#15689510	1	2	yes	—
232	C₂	—	2	2	no	—
233	C₂	—	16	2	no	—
234	C₂	#20244213	1	1	yes	characteristic
235	C₂	#20244277	1	1	yes	characteristic
236	C₂	#20244282	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20243526

C₂

yes

maximal, characteristic, complemented

#20241839

C₂

yes

maximal, complemented

#20241839

C₂

yes

maximal, complemented

C₂×#15688845

C₂

yes

maximal, characteristic, complemented

C₄₇×#3147

C₂

yes

maximal, characteristic

#15689147

C₂²

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

#15688888

—

D₄⋊(C₄₇⋊C₈)

—

D₄⋊(C₄₇⋊C₈)

—

#15688845

—

C₂×#135×C₄₇

—

C₄₇×#532

C₂²

yes

—

C₄₇×#495

—

C₄₇×#494

C₄

yes

characteristic

C₄₇×#493

C₄

yes

characteristic

C₄₇×#492

C₄

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₂×#41×C₄₇

—

#135×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×D₈×C₄₇

—

C₂²×C₈×C₄₇

D₄

yes

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

—

#127×C₄₇

C₂×C₄

yes

—

#124×C₄₇

—

#121×C₄₇

—

#121×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×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

—

#41×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

C₂²×C₄×C₄₇

yes

C₂²×C₄×C₄₇

yes

Q₁₆×C₄₇

—

SD₁₆×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

#124

yes

characteristic

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

#9860

—

maximal, Sylow

100

C₂²×C₄₇

—

101

C₂²×C₄₇

—

102

C₂²×C₄₇

—

103

C₂²×C₄₇

—

104

C₂²×C₄₇

—

105

C₂²×C₄₇

#390

yes

characteristic

106

C₂²×C₄₇

#490

yes

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

#418

yes

—

111

C₄×C₄₇

#443

yes

—

112

C₄×C₄₇

#444

yes

—

113

C₄×C₄₇

#496

yes

—

114

#3147

D₄₇

yes

characteristic

115

#1837

—

116

#1492

—

117

#1492

—

118

C₂×#322

—

119

C₂×C₄₇

—

120

C₂×C₄₇

—

121

C₂×C₄₇

#1961

yes

characteristic

122

C₂×C₄₇

#1974

yes

characteristic

123

C₂×C₄₇

#1975

yes

characteristic

124

C₂×#135

—

125

#532

C₂×D₄₇

yes

—

126

#495

—

127

#494

Dic₄₇

yes

characteristic

128

#493

Dic₄₇

yes

characteristic

129

#492

Dic₄₇

yes

—

130

#423

—

131

C₂×C₄×C₈

—

132

C₂×C₄×C₈

—

133

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

134

#341

—

135

D₄⋊C₈

—

136

D₄⋊C₈

—

137

#322

—

138

C₄₇

#9860

yes

characteristic, complemented, Sylow

139

C₂×#41

—

140

#135

—

141

C₂×Q₁₆

—

142

C₂×SD₁₆

—

143

C₂×D₈

—

144

C₂×M₁₆

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

C₂²⋊D₄₇

yes

—

148

C₄⋊Q₈

C₂×Dic₄₇

yes

—

149

#127

C₂×Dic₄₇

yes

—

150

#124

—

151

#121

—

152

#121

—

153

C₄×D₄

—

154

C₄×D₄

—

155

C₂×C₄²

C₂²×D₄₇

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₄×C₈

C₂×Dic₄₇

yes

characteristic

163

C₄×C₈

C₂×Dic₄₇

yes

characteristic

164

C₄×C₈

C₂²⋊D₄₇

yes

—

165

#41

—

166

C₂×Q₈

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂²×C₄

—

172

C₂²×C₄

#10625352

yes

characteristic

173

C₂²×C₄

#10625352

yes

characteristic

174

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

175

Q₁₆

—

176

SD₁₆

—

177

D₈

—

178

M₁₆

—

188

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

188

—

184

C₂×C₈

—

188

—

185

C₂×C₈

C₂²⋊Dic₄₇

yes

—

186

C₂×C₈

C₂²⋊Dic₄₇

yes

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₂²⋊C₄

—

190

C₂²⋊C₄

—

191

C₄²

D₄×D₄₇

yes

characteristic

192

C₄²

D₄×D₄₇

yes

characteristic

193

C₄²

C₂²×Dic₄₇

yes

characteristic

194

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

195

C₂³

—

196

C₂³

#13094011

yes

characteristic

197

Q₈

—

198

D₄

—

199

D₄

—

200

D₄

—

201

D₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

207

C₂×C₄

D₄×Dic₄₇

yes

characteristic

208

C₂×C₄

D₄×Dic₄₇

yes

characteristic

209

C₂×C₄

#13093995

yes

characteristic

210

C₂×C₄

#13093995

yes

characteristic

211

C₂×C₄

#13094020

yes

characteristic

212

C₂×C₄

#13094050

yes

—

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

—

376

—

217

C₈

—

188

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

#15689026

yes

characteristic

224

C₂²

#15689487

yes

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

#15689128

yes

—

229

C₄

#15689240

yes

—

230

C₄

#15689245

yes

—

231

C₄

#15689510

yes

—

232

C₂

—

233

C₂

—

234

C₂

#20244213

yes

characteristic

235

C₂

#20244277

yes

characteristic

236

C₂

#20244282

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13094020
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting, prime radical	C₄₇×#3147	C₂
socle	C₂²×C₄₇	#390
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#3147	D₄₇
hypocenter	C₄₇	#9860
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3147

subgroup

G/H

center

C₂×C₄

#13094020

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting, prime radical

C₄₇×#3147

C₂

socle

C₂²×C₄₇

#390

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3147

N	H ≅ G/N	type
1. #20243526	C₂	semidirect
2. #20241839	C₂	semidirect
3. #20241839	C₂	semidirect
4. C₂×#15688845	C₂	semidirect
138. C₄₇	#9860	semidirect

H ≅ G/N

type

1. #20243526

C₂

semidirect

2. #20241839

C₂

semidirect

3. #20241839

C₂

semidirect

4. C₂×#15688845

C₂

semidirect

138. C₄₇

#9860

semidirect

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

subgroup	index
#20243526	2
#20241839	2
C₂×#15688845	2
C₄₇×#3147	2
#9860	47

subgroup

index

C₄₇×#3147

Subgroups — #26116243

Conjugacy classes of subgroups

Complements

Maximal subgroups