Group #20256033 — subgroups

Subgroups — #20256033

Order 6016.

350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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	#15689833	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689477	C₂	1	2	yes	maximal, complemented
3	#15689473	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689430	C₂	1	2	yes	maximal, complemented
5	#15689413	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689335	C₂	1	2	yes	maximal
7	#15689325	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#10625336	C₂	1	2	yes	maximal, complemented
10	C₄×#10625334	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10625336	C₂²	1	2	yes	—
13	C₂×#10625334	C₂²	1	1	yes	characteristic
14	#13094024	C₂²	1	1	yes	characteristic
15	#13094016	C₂²	1	2	yes	—
16	#13094002	—	2	2	no	—
17	#13094000	—	2	1	no	—
18	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
19	C₄×D₁₈₈	C₂²	1	2	yes	—
20	C₄⋊C₄×D₄₇	—	2	1	no	—
21	#13093957	C₂²	1	1	yes	characteristic
22	#13093955	C₂²	1	2	yes	—
23	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
25	#13093948	C₂²	1	2	yes	—
26	#13093948	C₂²	1	2	yes	—
27	#13093948	C₂²	1	2	yes	—
28	#13093945	C₂²	1	1	yes	characteristic
29	#13093945	C₂²	1	2	yes	—
30	#13093944	C₂²	1	1	yes	characteristic
31	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
34	#126×C₄₇	—	2	2	no	—
35	#124×C₄₇	C₂²	1	2	yes	—
36	C₂²⋊Q₈×C₄₇	—	2	1	no	—
37	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
38	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
40	#117×C₄₇	—	2	1	no	—
41	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
42	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
43	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	—	2	1	no	—
45	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
46	C₂×C₄×D₄₇	—	2	1	no	—
47	C₂×C₄×D₄₇	—	2	2	no	—
48	C₂×Dic₉₄	—	2	1	no	—
49	C₄⋊C₄×C₄₇	—	2	1	no	—
50	C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₄⋊C₄×C₄₇	—	2	1	no	—
52	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
53	C₄⋊C₄×C₄₇	D₄	1	2	yes	—
54	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂²⋊C₄×C₄₇	—	2	2	no	—
56	C₂²⋊C₄×C₄₇	—	2	1	no	—
57	C₂²⋊C₄×C₄₇	—	2	2	no	—
58	C₄²×C₄₇	—	2	2	no	—
59	C₄²×C₄₇	C₂³	1	1	yes	characteristic
60	C₄²×C₄₇	C₂³	1	2	yes	—
61	#10625336	—	2	4	no	—
62	#10625334	—	2	2	no	—
63	(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	(C₂×D₄₇)⋊C₄	—	2	1	no	—
65	C₄⋊Dic₄₇	—	2	1	no	—
66	C₄⋊Dic₄₇	C₂³	1	2	yes	—
67	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
68	Dic₄₇⋊C₄	—	2	2	no	—
69	Dic₄₇⋊C₄	—	2	2	no	—
70	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
72	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
73	C₂³×C₄₇	—	2	1	no	—
74	C₂²×D₄₇	—	2	1	no	—
75	Q₈×C₄₇	—	2	2	no	—
76	Q₈×C₄₇	—	2	2	no	—
77	Q₈×C₄₇	—	2	2	no	—
78	D₄×C₄₇	—	2	1	no	—
79	D₄×C₄₇	—	2	1	no	—
80	C₂×C₄×C₄₇	—	2	1	no	—
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	—	4	2	no	—
83	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
85	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
88	C₂×Dic₄₇	—	2	1	no	—
89	C₂×Dic₄₇	—	2	2	no	—
90	D₁₈₈	—	2	1	no	—
91	D₁₈₈	#41	1	2	yes	—
92	C₄×D₄₇	—	4	2	no	—
93	C₄×D₄₇	—	8	2	no	—
94	Dic₉₄	—	8	1	no	—
95	C₄₇⋊C₈	—	2	1	no	—
96	C₄₇⋊C₈	—	2	2	no	—
97	C₄₇⋊C₈	—	2	1	no	—
98	C₂²×C₄₇	—	4	1	no	—
99	C₂²×C₄₇	—	4	1	no	—
100	C₂²×C₄₇	—	4	1	no	—
101	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
102	C₂×D₄₇	—	2	2	no	—
103	C₂×D₄₇	—	4	1	no	—
104	C₂×D₄₇	—	4	1	no	—
105	C₄×C₄₇	—	2	2	no	—
106	C₄×C₄₇	—	2	1	no	—
107	C₄×C₄₇	—	2	2	no	—
108	C₄×C₄₇	—	4	2	no	—
109	C₄×C₄₇	—	4	1	no	—
110	C₄×C₄₇	#135	1	2	yes	—
111	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
112	C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
113	Dic₄₇	—	4	1	no	—
114	Dic₄₇	—	4	2	no	—
115	#3360	—	47	1	no	maximal, Sylow
116	C₂×C₄₇	—	8	1	no	—
117	C₂×C₄₇	#548	1	1	yes	characteristic
118	C₂×C₄₇	C₂×#135	1	1	yes	characteristic
119	C₂×C₄₇	#577	1	1	yes	characteristic
120	D₄₇	—	4	2	no	—
121	#556	D₄₇	1	1	yes	characteristic, complemented
122	#554	—	47	1	no	—
123	#488	—	47	2	no	—
124	#487	—	47	1	no	—
125	#479	—	47	2	no	—
126	#476	—	47	1	no	—
127	#463	—	47	2	no	—
128	#461	—	47	1	no	—
129	C₈×Q₈	—	47	1	no	—
130	C₄×SD₁₆	—	47	2	no	—
131	C₄×D₈	—	47	1	no	—
132	C₄₇	#3360	1	1	yes	characteristic, complemented, Sylow
133	C₂×SD₁₆	—	47	2	no	—
134	C₂×D₈	—	47	1	no	—
135	C₄⋊Q₈	—	47	1	no	—
136	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
137	#126	—	2	2	no	—
138	#125	—	47	2	no	—
139	#124	C₂×D₄₇	1	2	yes	—
140	C₂²⋊Q₈	—	2	1	no	—
141	C₂²⋊Q₈	—	94	1	no	—
142	C₂²⋊Q₈	—	94	2	no	—
143	C₄×Q₈	C₂×D₄₇	1	2	yes	—
144	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
145	C₄×D₄	—	47	1	no	—
146	C₄×D₄	—	47	2	no	—
147	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
148	#117	—	2	1	no	—
149	C₂×C₄⋊C₄	—	94	1	no	—
150	#107	—	47	1	no	—
151	#106	—	47	2	no	—
152	C₄⋊C₈	—	47	1	no	—
153	C₄⋊C₈	—	47	2	no	—
154	#103	—	47	2	no	—
155	#103	—	47	2	no	—
156	#103	—	47	2	no	—
157	#102	—	47	1	no	—
158	#102	—	47	2	no	—
159	#102	—	47	1	no	—
160	C₄×C₈	—	47	1	no	—
161	C₄×C₈	—	47	2	no	—
162	C₂×Q₈	—	94	1	no	—
163	C₂×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
164	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
165	C₂×D₄	—	47	1	no	—
166	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	94	2	no	—
169	C₂²×C₄	—	94	1	no	—
170	SD₁₆	—	94	4	no	—
171	D₈	—	94	2	no	—
172	C₂×C₈	—	47	1	no	—
173	C₂×C₈	—	47	2	no	—
174	C₂×C₈	—	47	1	no	—
175	C₄⋊C₄	—	2	1	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	1	no	—
178	C₄⋊C₄	—	47	2	no	—
179	C₄⋊C₄	—	47	1	no	—
180	C₄⋊C₄	—	94	2	no	—
181	C₄⋊C₄	—	94	2	no	—
182	C₄⋊C₄	—	94	1	no	—
183	C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
184	C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
185	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
186	C₂²⋊C₄	—	2	2	no	—
187	C₂²⋊C₄	—	2	1	no	—
188	C₂²⋊C₄	—	2	2	no	—
189	C₂²⋊C₄	—	94	1	no	—
190	C₂²⋊C₄	—	94	2	no	—
191	C₄²	—	2	2	no	—
192	C₄²	C₂²×D₄₇	1	1	yes	characteristic
193	C₄²	C₂²×D₄₇	1	2	yes	—
194	C₂³	—	2	1	no	—
195	C₂³	—	94	1	no	—
196	Q₈	—	2	2	no	—
197	Q₈	—	2	2	no	—
198	Q₈	—	2	2	no	—
199	Q₈	—	376	1	no	—
200	D₄	—	2	1	no	—
201	D₄	—	2	1	no	—
202	D₄	—	47	2	no	—
203	D₄	—	94	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	94	1	no	—
208	C₂×C₄	—	94	2	no	—
209	C₂×C₄	—	376	2	no	—
210	C₂×C₄	—	188	2	no	—
211	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
212	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
213	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
214	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
215	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
216	C₈	—	94	1	no	—
217	C₈	—	94	2	no	—
218	C₈	—	94	1	no	—
219	C₂²	—	4	1	no	—
220	C₂²	—	4	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	94	2	no	—
223	C₂²	—	188	1	no	—
224	C₂²	—	188	1	no	—
225	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	2	1	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	1	no	—
231	C₄	—	188	1	no	—
232	C₄	—	188	2	no	—
233	C₄	#13094044	1	2	yes	—
234	C₄	#41×D₄₇	1	1	yes	characteristic
235	C₄	#13094071	1	1	yes	characteristic
236	C₂	—	8	1	no	—
237	C₂	—	188	2	no	—
238	C₂	#15689780	1	1	yes	characteristic
239	C₂	C₂×#13094044	1	1	yes	characteristic
240	C₂	#15689931	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689833

C₂

yes

maximal, characteristic, complemented

#15689477

C₂

yes

maximal, complemented

#15689473

C₂

yes

maximal, characteristic, complemented

#15689430

C₂

yes

maximal, complemented

#15689413

C₂

yes

maximal, characteristic, complemented

#15689335

C₂

yes

maximal

#15689325

C₂

yes

maximal, characteristic, complemented

Q₈×C₄₇⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#10625336

C₂

yes

maximal, complemented

C₄×#10625334

C₂

yes

maximal, characteristic

C₄₇×#556

C₂

yes

maximal, characteristic, complemented

C₂×#10625336

C₂²

yes

—

C₂×#10625334

C₂²

yes

characteristic

#13094024

C₂²

yes

characteristic

#13094016

C₂²

yes

—

#13094002

—

#13094000

—

C₄×D₁₈₈

C₂²

yes

characteristic

C₄×D₁₈₈

C₂²

yes

—

C₄⋊C₄×D₄₇

—

#13093957

C₂²

yes

characteristic

#13093955

C₂²

yes

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093948

C₂²

yes

—

#13093948

C₂²

yes

—

#13093948

C₂²

yes

—

#13093945

C₂²

yes

characteristic

#13093945

C₂²

yes

—

#13093944

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

#126×C₄₇

—

#124×C₄₇

C₂²

yes

—

C₂²⋊Q₈×C₄₇

—

C₄×Q₈×C₄₇

C₂²

yes

—

C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄×D₄×C₄₇

C₂²

yes

characteristic

#117×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

characteristic

C₂×Q₈×C₄₇

C₂³

yes

—

C₂×D₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂×D₁₈₈

C₂³

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

D₄

yes

—

C₄⋊C₄×C₄₇

C₂³

yes

characteristic

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂³

yes

—

#10625336

—

#10625334

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

characteristic

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₂×C₄₇⋊C₈

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂×C₄₇⋊C₈

C₂³

yes

characteristic

C₂³×C₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

#41

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

100

C₂²×C₄₇

—

101

C₂²×C₄₇

C₂²×D₄

yes

characteristic

102

C₂×D₄₇

—

103

C₂×D₄₇

—

104

C₂×D₄₇

—

105

C₄×C₄₇

—

106

C₄×C₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

#135

yes

—

111

C₄×C₄₇

C₂×#41

yes

characteristic

112

C₄×C₄₇

2₋¹⁺⁴

yes

characteristic

113

Dic₄₇

—

114

Dic₄₇

—

115

#3360

—

maximal, Sylow

116

C₂×C₄₇

—

117

C₂×C₄₇

#548

yes

characteristic

118

C₂×C₄₇

C₂×#135

yes

characteristic

119

C₂×C₄₇

#577

yes

characteristic

120

D₄₇

—

121

#556

D₄₇

yes

characteristic, complemented

122

#554

—

123

#488

—

124

#487

—

125

#479

—

126

#476

—

127

#463

—

128

#461

—

129

C₈×Q₈

—

130

C₄×SD₁₆

—

131

C₄×D₈

—

132

C₄₇

#3360

yes

characteristic, complemented, Sylow

133

C₂×SD₁₆

—

134

C₂×D₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

137

#126

—

138

#125

—

139

#124

C₂×D₄₇

yes

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

142

C₂²⋊Q₈

—

143

C₄×Q₈

C₂×D₄₇

yes

—

144

C₄×Q₈

C₂×D₄₇

yes

characteristic

145

C₄×D₄

—

146

C₄×D₄

—

147

C₄×D₄

C₂×D₄₇

yes

characteristic

148

#117

—

149

C₂×C₄⋊C₄

—

150

#107

—

151

#106

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#103

—

155

#103

—

156

#103

—

157

#102

—

158

#102

—

159

#102

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₂×Q₈

—

163

C₂×Q₈

C₂²⋊D₄₇

yes

characteristic

164

C₂×Q₈

C₂²×D₄₇

yes

—

165

C₂×D₄

—

166

C₂×D₄

C₂²×D₄₇

yes

characteristic

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

SD₁₆

—

171

D₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

184

C₄⋊C₄

C₂²⋊D₄₇

yes

—

185

C₄⋊C₄

C₂²×D₄₇

yes

characteristic

186

C₂²⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

189

C₂²⋊C₄

—

190

C₂²⋊C₄

—

191

C₄²

—

192

C₄²

C₂²×D₄₇

yes

characteristic

193

C₄²

C₂²×D₄₇

yes

—

194

C₂³

—

195

C₂³

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

Q₈

—

376

—

200

D₄

—

201

D₄

—

202

D₄

—

203

D₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

376

—

210

C₂×C₄

—

188

—

211

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

212

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

213

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

214

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

215

C₂×C₄

C₂³×D₄₇

yes

characteristic

216

C₈

—

217

C₈

—

218

C₈

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

188

—

224

C₂²

—

188

—

225

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

188

—

232

C₄

—

188

—

233

C₄

#13094044

yes

—

234

C₄

#41×D₄₇

yes

characteristic

235

C₄

#13094071

yes

characteristic

236

C₂

—

237

C₂

—

188

—

238

C₂

#15689780

yes

characteristic

239

C₂

C₂×#13094044

yes

characteristic

240

C₂

#15689931

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#556	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#556	D₄₇
hypocenter	C₄₇	#3360
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#556

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

N	H ≅ G/N	type
1. #15689833	C₂	semidirect
2. #15689477	C₂	semidirect
3. #15689473	C₂	semidirect
4. #15689430	C₂	semidirect
5. #15689413	C₂	semidirect
7. #15689325	C₂	semidirect
8. Q₈×C₄₇⋊C₈	C₂	semidirect
9. C₄×#10625336	C₂	semidirect
11. C₄₇×#556	C₂	semidirect
121. #556	D₄₇	semidirect
132. C₄₇	#3360	semidirect

H ≅ G/N

type

1. #15689833

C₂

semidirect

2. #15689477

C₂

semidirect

3. #15689473

C₂

semidirect

4. #15689430

C₂

semidirect

5. #15689413

C₂

semidirect

7. #15689325

C₂

semidirect

8. Q₈×C₄₇⋊C₈

C₂

semidirect

9. C₄×#10625336

C₂

semidirect

11. C₄₇×#556

C₂

semidirect

121. #556

D₄₇

semidirect

132. C₄₇

#3360

semidirect

Subgroups — #20256033

Conjugacy classes of subgroups

Complements