Group #20256102 — subgroups

Subgroups — #20256102

Order 6016.

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

normal subgroups only

This group has 372 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	Q₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689482	C₂	1	2	yes	maximal, complemented
3	#15689473	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689418	C₂	1	2	yes	maximal, complemented
5	#15689403	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689335	C₂	1	2	yes	maximal
7	#15689325	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689254	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689221	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×Q₈×D₄₇	—	2	1	no	—
13	C₂×#10625336	C₂²	1	2	yes	—
14	C₂×#10625334	C₂²	1	1	yes	characteristic
15	#13094024	C₂²	1	1	yes	characteristic
16	#13094024	C₂²	1	2	yes	—
17	#13094004	—	2	1	no	—
18	#13094004	—	2	2	no	—
19	C₄×D₁₈₈	C₂²	1	2	yes	—
20	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
21	#13093957	C₂²	1	2	yes	—
22	#13093957	C₂²	1	1	yes	characteristic
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	#13093935	C₂²	1	2	yes	—
32	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
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	Q₈×D₄₇	—	4	4	no	—
46	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
47	C₂×C₄×D₄₇	—	2	2	no	—
48	C₂×C₄×D₄₇	—	2	1	no	—
49	C₂×Dic₉₄	—	2	2	no	—
50	C₂×Dic₉₄	—	2	1	no	—
51	C₄⋊C₄×C₄₇	—	2	1	no	—
52	C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₄⋊C₄×C₄₇	—	2	1	no	—
54	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
55	C₄⋊C₄×C₄₇	D₄	1	2	yes	—
56	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²⋊C₄×C₄₇	—	2	2	no	—
58	C₂²⋊C₄×C₄₇	—	2	1	no	—
59	C₂²⋊C₄×C₄₇	—	2	2	no	—
60	C₄²×C₄₇	—	2	2	no	—
61	C₄²×C₄₇	C₂³	1	1	yes	characteristic
62	C₄²×C₄₇	C₂³	1	2	yes	—
63	#10625336	—	2	4	no	—
64	#10625334	—	2	2	no	—
65	(C₂×D₄₇)⋊C₄	—	2	2	no	—
66	(C₂×D₄₇)⋊C₄	—	2	1	no	—
67	C₄⋊Dic₄₇	—	2	2	no	—
68	C₄⋊Dic₄₇	—	2	1	no	—
69	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
70	C₄⋊Dic₄₇	C₂³	1	2	yes	—
71	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
74	C₂³×C₄₇	—	2	1	no	—
75	C₂²×D₄₇	—	2	1	no	—
76	Q₈×C₄₇	—	2	2	no	—
77	Q₈×C₄₇	—	2	2	no	—
78	Q₈×C₄₇	—	2	2	no	—
79	D₄×C₄₇	—	2	1	no	—
80	D₄×C₄₇	—	2	1	no	—
81	C₂×C₄×C₄₇	—	2	1	no	—
82	C₂×C₄×C₄₇	—	2	2	no	—
83	C₂×C₄×C₄₇	—	4	2	no	—
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	2	yes	—
87	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
89	C₂×Dic₄₇	—	2	1	no	—
90	C₂×Dic₄₇	—	2	2	no	—
91	D₁₈₈	—	2	1	no	—
92	D₁₈₈	#41	1	2	yes	—
93	C₄×D₄₇	—	4	4	no	—
94	C₄×D₄₇	—	4	2	no	—
95	Dic₉₄	—	4	4	no	—
96	Dic₉₄	—	4	2	no	—
97	C₄₇⋊C₈	—	2	1	no	—
98	C₄₇⋊C₈	—	2	2	no	—
99	C₄₇⋊C₈	—	2	1	no	—
100	C₂²×C₄₇	—	4	1	no	—
101	C₂²×C₄₇	—	4	1	no	—
102	C₂²×C₄₇	—	4	1	no	—
103	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
104	C₂×D₄₇	—	2	2	no	—
105	C₂×D₄₇	—	4	1	no	—
106	C₂×D₄₇	—	4	1	no	—
107	C₄×C₄₇	—	2	2	no	—
108	C₄×C₄₇	—	2	2	no	—
109	C₄×C₄₇	—	2	1	no	—
110	C₄×C₄₇	—	4	2	no	—
111	C₄×C₄₇	—	4	1	no	—
112	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
113	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
114	C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
115	Dic₄₇	—	4	1	no	—
116	Dic₄₇	—	4	2	no	—
117	#3367	—	47	1	no	maximal, Sylow
118	C₂×C₄₇	—	8	1	no	—
119	C₂×C₄₇	#548	1	1	yes	characteristic
120	C₂×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
121	C₂×C₄₇	#578	1	1	yes	characteristic
122	D₄₇	—	4	2	no	—
123	#556	D₄₇	1	1	yes	characteristic, complemented
124	D₄×Q₈	—	47	1	no	—
125	#489	—	47	2	no	—
126	#487	—	47	1	no	—
127	#477	—	47	2	no	—
128	#474	—	47	1	no	—
129	#463	—	47	2	no	—
130	#461	—	47	1	no	—
131	#446	—	47	1	no	—
132	#440	—	47	2	no	—
133	C₄×D₈	—	47	1	no	—
134	C₄₇	#3367	1	1	yes	characteristic, complemented, Sylow
135	C₂²×Q₈	—	94	1	no	—
136	C₂×SD₁₆	—	47	2	no	—
137	C₂×D₈	—	47	1	no	—
138	C₄⋊Q₈	—	47	1	no	—
139	C₄⋊Q₈	—	47	2	no	—
140	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
141	#126	—	2	2	no	—
142	#124	C₂×D₄₇	1	2	yes	—
143	C₂²⋊Q₈	—	2	1	no	—
144	C₂²⋊Q₈	—	94	1	no	—
145	C₂²⋊Q₈	—	94	2	no	—
146	C₄×Q₈	C₂×D₄₇	1	2	yes	—
147	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
148	C₄×D₄	—	47	1	no	—
149	C₄×D₄	—	47	2	no	—
150	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
151	#117	—	2	1	no	—
152	#107	—	47	1	no	—
153	#107	—	47	2	no	—
154	C₄⋊C₈	—	47	1	no	—
155	C₄⋊C₈	—	47	2	no	—
156	#103	—	47	2	no	—
157	#103	—	47	2	no	—
158	#103	—	47	2	no	—
159	#102	—	47	1	no	—
160	#102	—	47	2	no	—
161	#102	—	47	1	no	—
162	#97	—	47	2	no	—
163	C₄×C₈	—	47	1	no	—
164	C₂×Q₈	—	94	2	no	—
165	C₂×Q₈	—	94	1	no	—
166	C₂×Q₈	—	188	4	no	—
167	C₂×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
168	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
169	C₂×D₄	—	47	1	no	—
170	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
171	C₂²×C₄	—	2	1	no	—
172	C₂²×C₄	—	94	2	no	—
173	C₂²×C₄	—	94	1	no	—
174	SD₁₆	—	94	4	no	—
175	D₈	—	94	2	no	—
176	C₂×C₈	—	47	1	no	—
177	C₂×C₈	—	47	1	no	—
178	C₂×C₈	—	47	2	no	—
179	C₄⋊C₄	—	2	1	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	47	1	no	—
183	C₄⋊C₄	—	47	2	no	—
184	C₄⋊C₄	—	94	2	no	—
185	C₄⋊C₄	—	94	1	no	—
186	C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
187	C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
188	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
189	C₂²⋊C₄	—	2	2	no	—
190	C₂²⋊C₄	—	2	1	no	—
191	C₂²⋊C₄	—	2	2	no	—
192	C₂²⋊C₄	—	94	2	no	—
193	C₂²⋊C₄	—	94	1	no	—
194	C₄²	—	2	2	no	—
195	C₄²	C₂²×D₄₇	1	1	yes	characteristic
196	C₄²	C₂²×D₄₇	1	2	yes	—
197	C₂³	—	2	1	no	—
198	C₂³	—	94	1	no	—
199	Q₈	—	2	2	no	—
200	Q₈	—	2	2	no	—
201	Q₈	—	2	2	no	—
202	Q₈	—	188	4	no	—
203	Q₈	—	188	2	no	—
204	D₄	—	2	1	no	—
205	D₄	—	2	1	no	—
206	D₄	—	47	2	no	—
207	D₄	—	94	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	94	2	no	—
212	C₂×C₄	—	94	1	no	—
213	C₂×C₄	—	188	4	no	—
214	C₂×C₄	—	188	2	no	—
215	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
216	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
217	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
218	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
219	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
220	C₈	—	94	1	no	—
221	C₈	—	94	2	no	—
222	C₈	—	94	1	no	—
223	C₂²	—	4	1	no	—
224	C₂²	—	4	1	no	—
225	C₂²	—	4	1	no	—
226	C₂²	—	94	2	no	—
227	C₂²	—	188	1	no	—
228	C₂²	—	188	1	no	—
229	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
230	C₄	—	2	2	no	—
231	C₄	—	2	2	no	—
232	C₄	—	2	1	no	—
233	C₄	—	4	2	no	—
234	C₄	—	4	1	no	—
235	C₄	—	188	2	no	—
236	C₄	—	188	1	no	—
237	C₄	#13094049	1	2	yes	—
238	C₄	#41×D₄₇	1	1	yes	characteristic
239	C₄	#13094071	1	1	yes	characteristic
240	C₂	—	8	1	no	—
241	C₂	—	188	2	no	—
242	C₂	#15689780	1	1	yes	characteristic
243	C₂	C₂×#13094049	1	1	yes	characteristic
244	C₂	#15689938	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×D₁₈₈

C₂

yes

maximal, characteristic, complemented

#15689482

C₂

yes

maximal, complemented

#15689473

C₂

yes

maximal, characteristic, complemented

#15689418

C₂

yes

maximal, complemented

#15689403

C₂

yes

maximal, characteristic, complemented

#15689335

C₂

yes

maximal

#15689325

C₂

yes

maximal, characteristic, complemented

#15689254

C₂

yes

maximal, characteristic, complemented

#15689221

C₂

yes

maximal, complemented

C₄×#10625334

C₂

yes

maximal, characteristic

C₄₇×#556

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₇

—

C₂×#10625336

C₂²

yes

—

C₂×#10625334

C₂²

yes

characteristic

#13094024

C₂²

yes

characteristic

#13094024

C₂²

yes

—

#13094004

—

#13094004

—

C₄×D₁₈₈

C₂²

yes

—

C₄×D₁₈₈

C₂²

yes

characteristic

#13093957

C₂²

yes

—

#13093957

C₂²

yes

characteristic

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

#13093935

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

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

—

Q₈×D₄₇

—

C₂×D₁₈₈

C₂³

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

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

—

C₄⋊Dic₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

C₂³

yes

—

C₂×C₄₇⋊C₈

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

—

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

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

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

—

Dic₉₄

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

100

C₂²×C₄₇

—

101

C₂²×C₄₇

—

102

C₂²×C₄₇

—

103

C₂²×C₄₇

C₂²×D₄

yes

characteristic

104

C₂×D₄₇

—

105

C₂×D₄₇

—

106

C₂×D₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

AGL(1,ℤ/8)

yes

—

113

C₄×C₄₇

C₂×#41

yes

characteristic

114

C₄×C₄₇

2₋¹⁺⁴

yes

characteristic

115

Dic₄₇

—

116

Dic₄₇

—

117

#3367

—

maximal, Sylow

118

C₂×C₄₇

—

119

C₂×C₄₇

#548

yes

characteristic

120

C₂×C₄₇

C₂×AGL(1,ℤ/8)

yes

characteristic

121

C₂×C₄₇

#578

yes

characteristic

122

D₄₇

—

123

#556

D₄₇

yes

characteristic, complemented

124

D₄×Q₈

—

125

#489

—

126

#487

—

127

#477

—

128

#474

—

129

#463

—

130

#461

—

131

#446

—

132

#440

—

133

C₄×D₈

—

134

C₄₇

#3367

yes

characteristic, complemented, Sylow

135

C₂²×Q₈

—

136

C₂×SD₁₆

—

137

C₂×D₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

141

#126

—

142

#124

C₂×D₄₇

yes

—

143

C₂²⋊Q₈

—

144

C₂²⋊Q₈

—

145

C₂²⋊Q₈

—

146

C₄×Q₈

C₂×D₄₇

yes

—

147

C₄×Q₈

C₂×D₄₇

yes

characteristic

148

C₄×D₄

—

149

C₄×D₄

—

150

C₄×D₄

C₂×D₄₇

yes

characteristic

151

#117

—

152

#107

—

153

#107

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

#103

—

157

#103

—

158

#103

—

159

#102

—

160

#102

—

161

#102

—

162

#97

—

163

C₄×C₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

188

—

167

C₂×Q₈

C₂²⋊D₄₇

yes

characteristic

168

C₂×Q₈

C₂²×D₄₇

yes

—

169

C₂×D₄

—

170

C₂×D₄

C₂²×D₄₇

yes

characteristic

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

SD₁₆

—

175

D₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

187

C₄⋊C₄

C₂²⋊D₄₇

yes

—

188

C₄⋊C₄

C₂²×D₄₇

yes

characteristic

189

C₂²⋊C₄

—

190

C₂²⋊C₄

—

191

C₂²⋊C₄

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

194

C₄²

—

195

C₄²

C₂²×D₄₇

yes

characteristic

196

C₄²

C₂²×D₄₇

yes

—

197

C₂³

—

198

C₂³

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

188

—

203

Q₈

—

188

—

204

D₄

—

205

D₄

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

188

—

214

C₂×C₄

—

188

—

215

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

216

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

217

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

218

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

219

C₂×C₄

C₂³×D₄₇

yes

characteristic

220

C₈

—

221

C₈

—

222

C₈

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

188

—

228

C₂²

—

188

—

229

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

188

—

236

C₄

—

188

—

237

C₄

#13094049

yes

—

238

C₄

#41×D₄₇

yes

characteristic

239

C₄

#13094071

yes

characteristic

240

C₂

—

241

C₂

—

188

—

242

C₂

#15689780

yes

characteristic

243

C₂

C₂×#13094049

yes

characteristic

244

C₂

#15689938

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	#3367
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. Q₈×D₁₈₈	C₂	semidirect
2. #15689482	C₂	semidirect
3. #15689473	C₂	semidirect
4. #15689418	C₂	semidirect
5. #15689403	C₂	semidirect
7. #15689325	C₂	semidirect
8. #15689254	C₂	semidirect
9. #15689221	C₂	semidirect
11. C₄₇×#556	C₂	semidirect
123. #556	D₄₇	semidirect
134. C₄₇	#3367	semidirect

H ≅ G/N

type

1. Q₈×D₁₈₈

C₂

semidirect

2. #15689482

C₂

semidirect

3. #15689473

C₂

semidirect

4. #15689418

C₂

semidirect

5. #15689403

C₂

semidirect

7. #15689325

C₂

semidirect

8. #15689254

C₂

semidirect

9. #15689221

C₂

semidirect

11. C₄₇×#556

C₂

semidirect

123. #556

D₄₇

semidirect

134. C₄₇

#3367

semidirect

Subgroups — #20256102

Conjugacy classes of subgroups

Complements