Group #26109230 — subgroups

Subgroups — #26109230

Order 12032.

450 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 113 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	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#20242149	C₂	1	2	yes	maximal, complemented
3	#20241729	C₂	1	1	yes	maximal, characteristic
4	#20241257	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1466	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₄	1	2	yes	—
7	D₄×C₄₇⋊C₈	—	2	2	no	—
8	D₄×C₄₇⋊C₈	—	2	2	no	—
9	#15689180	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	2	yes	—
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	#15688875	—	2	2	no	—
14	#15688873	—	2	2	no	—
15	#15688847	—	2	2	no	—
16	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#432	C₂²	1	2	yes	—
18	C₄₇×#323	—	2	2	no	—
19	C₂²×C₄₇⋊C₈	—	2	2	no	—
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	4	4	no	—
22	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
24	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
26	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
28	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
29	#13093935	—	2	2	no	—
30	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
31	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
32	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
33	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
34	C₄×D₄×C₄₇	—	2	2	no	—
35	C₄×D₄×C₄₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
38	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₄₇	—	2	2	no	—
40	C₂²⋊C₈×C₄₇	—	2	2	no	—
41	#97×C₄₇	—	2	2	no	—
42	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
43	C₂×D₄×C₄₇	—	2	4	no	—
44	C₂×D₄×C₄₇	—	2	2	no	—
45	C₂²×C₄×C₄₇	—	2	2	no	—
46	C₂²×C₄×C₄₇	—	2	2	no	—
47	C₂²×C₄×C₄₇	—	4	2	no	—
48	C₂²×C₄×C₄₇	—	4	2	no	—
49	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₄₇	C₂²×C₄	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	C₂×C₈×C₄₇	—	4	2	no	—
54	C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂²⋊C₄×C₄₇	—	2	4	no	—
56	C₄²×C₄₇	C₂×D₄	1	2	yes	—
57	C₄²×C₄₇	#41	1	2	yes	—
58	C₂×C₄₇⋊C₈	—	2	2	no	—
59	C₂×C₄₇⋊C₈	—	2	2	no	—
60	C₂×C₄₇⋊C₈	—	4	1	no	—
61	C₂×C₄₇⋊C₈	—	4	4	no	—
62	C₂×C₄₇⋊C₈	—	4	4	no	—
63	C₂×C₄₇⋊C₈	—	4	2	no	—
64	C₂×C₄₇⋊C₈	—	4	2	no	—
65	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
66	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
68	C₂³×C₄₇	—	2	2	no	—
69	C₂³×C₄₇	—	2	2	no	—
70	C₂³×C₄₇	—	4	2	no	—
71	C₂³×C₄₇	—	4	2	no	—
72	C₂³×C₄₇	#108	1	4	yes	—
73	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
74	D₄×C₄₇	—	2	8	no	—
75	C₂×C₄×C₄₇	—	2	2	no	—
76	C₂×C₄×C₄₇	—	2	1	no	—
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
79	C₂×C₄×C₄₇	—	4	1	no	—
80	C₂×C₄×C₄₇	—	4	4	no	—
81	C₂×C₄×C₄₇	—	4	2	no	—
82	C₂×C₄×C₄₇	—	4	2	no	—
83	C₂×C₄×C₄₇	—	4	2	no	—
84	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
86	C₂×C₄×C₄₇	#121	1	2	yes	—
87	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
88	C₈×C₄₇	—	8	2	no	—
89	C₄₇⋊C₈	—	2	1	no	—
90	C₄₇⋊C₈	—	2	2	no	—
91	C₄₇⋊C₈	—	4	2	no	—
92	C₄₇⋊C₈	—	8	2	no	—
93	C₄₇⋊C₈	#100	1	2	yes	—
94	#8622	—	47	1	no	maximal, Sylow
95	C₂²×C₄₇	—	2	1	no	—
96	C₂²×C₄₇	—	2	1	no	—
97	C₂²×C₄₇	—	2	4	no	—
98	C₂²×C₄₇	—	4	4	no	—
99	C₂²×C₄₇	—	4	4	no	—
100	C₂²×C₄₇	—	4	2	no	—
101	C₂²×C₄₇	—	4	2	no	—
102	C₂²×C₄₇	#380	1	1	yes	characteristic
103	C₂²×C₄₇	C₂×#108	1	2	yes	—
104	C₄×C₄₇	—	2	1	no	—
105	C₄×C₄₇	—	2	2	no	—
106	C₄×C₄₇	—	2	2	no	—
107	C₄×C₄₇	—	4	2	no	—
108	C₄×C₄₇	C₂×#100	1	1	yes	characteristic
109	C₄×C₄₇	#413	1	1	yes	characteristic
110	C₂×C₈×D₄	—	47	1	no	—
111	#1568	—	47	2	no	—
112	#1466	—	47	1	no	—
113	#1466	D₄₇	1	1	yes	characteristic
114	#1290	—	47	2	no	—
115	C₂×C₄₇	—	2	2	no	—
116	C₂×C₄₇	—	4	4	no	—
117	C₂×C₄₇	#1800	1	1	yes	characteristic
118	C₂×C₄₇	#1810	1	1	yes	characteristic
119	C₂×C₄₇	#1812	1	1	yes	characteristic
120	C₂³×C₈	—	47	2	no	—
121	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
122	C₈×D₄	—	94	2	no	—
123	C₈×D₄	—	94	2	no	—
124	#432	—	47	2	no	—
125	#432	C₂×D₄₇	1	2	yes	—
126	C₂×C₄⋊C₈	—	47	1	no	—
127	C₂×C₂²⋊C₈	—	47	2	no	—
128	C₂×C₄×C₈	—	47	1	no	—
129	#335	—	94	2	no	—
130	#334	—	94	2	no	—
131	#323	—	2	2	no	—
132	#323	—	94	2	no	—
133	C₄₇	#8622	1	1	yes	characteristic, complemented, Sylow
134	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
135	C₂³×C₄	C₄×D₄₇	1	2	yes	—
136	C₂²×C₈	—	47	1	no	—
137	C₂²×C₈	—	47	1	no	—
138	C₂²×C₈	—	47	2	no	—
139	C₂²×C₈	—	94	2	no	—
140	C₂²×C₈	—	94	2	no	—
141	C₂²×C₈	—	188	4	no	—
142	C₄×D₄	—	2	2	no	—
143	C₄×D₄	—	2	2	no	—
144	C₂×C₄⋊C₄	Dic₉₄	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
146	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	94	2	no	—
149	C₄⋊C₈	—	94	2	no	—
150	C₂²⋊C₈	—	2	2	no	—
151	C₂²⋊C₈	—	94	4	no	—
152	C₂²⋊C₈	—	94	2	no	—
153	#97	—	2	2	no	—
154	#97	—	94	2	no	—
155	C₄×C₈	—	47	2	no	—
156	C₄×C₈	—	47	2	no	—
157	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
158	C₂×D₄	—	2	4	no	—
159	C₂×D₄	—	2	2	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	2	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
165	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
167	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	—	47	1	no	—
170	C₂×C₈	—	47	2	no	—
171	C₂×C₈	—	47	1	no	—
172	C₂×C₈	—	94	2	no	—
173	C₂×C₈	—	94	2	no	—
174	C₂×C₈	—	188	4	no	—
175	C₂×C₈	—	188	1	no	—
176	C₂×C₈	—	188	4	no	—
177	C₂×C₈	—	188	2	no	—
178	C₂×C₈	—	188	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₂²⋊C₄	—	2	4	no	—
181	C₄²	D₄×D₄₇	1	2	yes	—
182	C₄²	#10625352	1	2	yes	—
183	C₂³	—	2	2	no	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	2	no	—
186	C₂³	—	4	2	no	—
187	C₂³	#13093959	1	4	yes	—
188	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
189	D₄	—	2	8	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
200	C₂×C₄	#13093980	1	1	yes	characteristic
201	C₂×C₄	#13093996	1	2	yes	—
202	C₂×C₄	#13094001	1	2	yes	—
203	C₈	—	8	2	no	—
204	C₈	—	47	2	no	—
205	C₈	—	94	1	no	—
206	C₈	—	94	2	no	—
207	C₈	—	376	2	no	—
208	C₈	—	188	2	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	4	no	—
212	C₂²	—	4	4	no	—
213	C₂²	—	4	4	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	4	2	no	—
216	C₂²	#15688981	1	1	yes	characteristic
217	C₂²	C₂×#13093959	1	2	yes	—
218	C₄	—	2	1	no	—
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	#100×D₄₇	1	1	yes	characteristic
223	C₄	#15689104	1	1	yes	characteristic
224	C₂	—	2	2	no	—
225	C₂	—	4	4	no	—
226	C₂	#20243378	1	1	yes	characteristic
227	C₂	#20243424	1	1	yes	characteristic
228	C₂	#20243432	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×C₄₇⋊C₈

C₂

yes

maximal, characteristic

#20242149

C₂

yes

maximal, complemented

#20241729

C₂

yes

maximal, characteristic

#20241257

C₂

yes

maximal, complemented

C₄₇×#1466

C₂

yes

maximal, characteristic

C₂³×C₄₇⋊C₈

C₄

yes

—

D₄×C₄₇⋊C₈

—

D₄×C₄₇⋊C₈

—

#15689180

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₂×C₂²⋊(C₄₇⋊C₈)

C₄

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

—

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₄₇×#432

C₂²

yes

—

C₄₇×#323

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₂²×D₄×C₄₇

Q₈

yes

characteristic

C₂³×C₄×C₄₇

C₂×C₄

yes

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

Q₈

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

—

#97×C₄₇

—

C₂⁴×C₄₇

C₄⋊C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

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

—

C₂²⋊C₄×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

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#108

yes

—

C₂³×C₄₇

C₂×C₄⋊C₄

yes

characteristic

D₄×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×C₂²⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

#100

yes

—

#8622

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

100

C₂²×C₄₇

—

101

C₂²×C₄₇

—

102

C₂²×C₄₇

#380

yes

characteristic

103

C₂²×C₄₇

C₂×#108

yes

—

104

C₄×C₄₇

—

105

C₄×C₄₇

—

106

C₄×C₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

C₂×#100

yes

characteristic

109

C₄×C₄₇

#413

yes

characteristic

110

C₂×C₈×D₄

—

111

#1568

—

112

#1466

—

113

#1466

D₄₇

yes

characteristic

114

#1290

—

115

C₂×C₄₇

—

116

C₂×C₄₇

—

117

C₂×C₄₇

#1800

yes

characteristic

118

C₂×C₄₇

#1810

yes

characteristic

119

C₂×C₄₇

#1812

yes

characteristic

120

C₂³×C₈

—

121

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

122

C₈×D₄

—

123

C₈×D₄

—

124

#432

—

125

#432

C₂×D₄₇

yes

—

126

C₂×C₄⋊C₈

—

127

C₂×C₂²⋊C₈

—

128

C₂×C₄×C₈

—

129

#335

—

130

#334

—

131

#323

—

132

#323

—

133

C₄₇

#8622

yes

characteristic, complemented, Sylow

134

C₂²×D₄

Dic₉₄

yes

characteristic

135

C₂³×C₄

C₄×D₄₇

yes

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₂²×C₈

—

188

—

142

C₄×D₄

—

143

C₄×D₄

—

144

C₂×C₄⋊C₄

Dic₉₄

yes

characteristic

145

C₂×C₂²⋊C₄

C₂²⋊D₄₇

yes

—

146

C₂×C₄²

C₂²×D₄₇

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

C₂²⋊C₈

—

151

C₂²⋊C₈

—

152

C₂²⋊C₈

—

153

#97

—

154

#97

—

155

C₄×C₈

—

156

C₄×C₈

—

157

C₂⁴

Dic₄₇⋊C₄

yes

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

Dic₄₇⋊C₄

yes

—

165

C₂²×C₄

C₂×Dic₉₄

yes

characteristic

166

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

167

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

188

—

175

C₂×C₈

—

188

—

176

C₂×C₈

—

188

—

177

C₂×C₈

—

188

—

178

C₂×C₈

—

188

—

179

C₄⋊C₄

—

180

C₂²⋊C₄

—

181

C₄²

D₄×D₄₇

yes

—

182

C₄²

#10625352

yes

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

#13093959

yes

—

188

C₂³

C₂×Dic₄₇⋊C₄

yes

characteristic

189

D₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

C₂²⋊C₄×D₄₇

yes

characteristic

200

C₂×C₄

#13093980

yes

characteristic

201

C₂×C₄

#13093996

yes

—

202

C₂×C₄

#13094001

yes

—

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

207

C₈

—

376

—

208

C₈

—

188

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

#15688981

yes

characteristic

217

C₂²

C₂×#13093959

yes

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

#100×D₄₇

yes

characteristic

223

C₄

#15689104

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

#20243378

yes

characteristic

227

C₂

#20243424

yes

characteristic

228

C₂

#20243432

yes

characteristic

	subgroup	G/H
center	C₂²	#15688981
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1466	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂²×D₄×C₄₇	Q₈
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1466	D₄₇
hypocenter	C₄₇	#8622
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1466

subgroup

G/H

center

C₂²

#15688981

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1466

C₂

socle

C₂²×C₄₇

#380

prime radical

C₂²×D₄×C₄₇

Q₈

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1466

N	H ≅ G/N	type
2. #20242149	C₂	semidirect
4. #20241257	C₂	semidirect
133. C₄₇	#8622	semidirect

H ≅ G/N

type

2. #20242149

C₂

semidirect

4. #20241257

C₂

semidirect

133. C₄₇

#8622

semidirect

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
#20242149	2
#20241729	2
#20241257	2
C₄₇×#1466	2
#8622	47

subgroup

index

C₂×D₄×C₄₇⋊C₈

C₄₇×#1466

Subgroups — #26109230

Conjugacy classes of subgroups

Complements

Maximal subgroups