Group #26370783 — subgroups

Subgroups — #26370783

Order 12032.

650 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 171 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	C₂²×Dic₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689539	C₂	1	1	yes	maximal, characteristic
3	#20253044	C₂	1	2	yes	maximal
4	#20245497	C₂	1	4	yes	maximal, complemented
5	#20245480	C₂	1	4	yes	maximal, complemented
6	#20245107	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2158	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₁₈₈	C₂²	1	2	yes	—
9	C₂×#13094030	C₂²	1	1	yes	characteristic
10	#15689699	—	2	2	no	—
11	C₂×Dic₃₇₆	—	2	4	no	—
12	C₂×Dic₃₇₆	C₂²	1	2	yes	—
13	C₂×Dic₃₇₆	C₂²	1	2	yes	—
14	#15689539	—	2	4	no	—
15	C₂×#13093964	C₂²	1	1	yes	characteristic
16	C₂×#13093963	C₂²	1	2	yes	—
17	C₂×C₁₆×D₄₇	C₂²	1	2	yes	—
18	#15689382	—	2	4	no	—
19	#15689365	C₂²	1	8	yes	—
20	#15689131	—	2	2	no	—
21	#15688926	C₂²	1	8	yes	—
22	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#427	C₂²	1	2	yes	—
24	C₄₇×#367	C₂²	1	2	yes	—
25	C₄₇×#366	C₂²	1	2	yes	—
26	C₂×#10625350	D₄	1	1	yes	characteristic
27	C₂²×Dic₉₄	—	2	2	no	—
28	C₂×Dic₁₈₈	—	2	4	no	—
29	C₂×Dic₁₈₈	—	2	4	no	—
30	C₂×Dic₁₈₈	—	2	2	no	—
31	C₂×Dic₁₈₈	C₂³	1	4	yes	—
32	#13094030	—	2	2	no	—
33	#13094030	—	2	2	no	—
34	C₂×#10625329	D₄	1	1	yes	characteristic
35	C₂×#10625324	D₄	1	2	yes	—
36	C₂×C₈×D₄₇	C₂³	1	2	yes	—
37	#13094024	—	4	2	no	—
38	#13094012	—	4	2	no	—
39	#13094008	—	4	4	no	—
40	#13094004	—	2	8	no	—
41	Dic₃₇₆	—	2	4	no	—
42	Dic₃₇₆	—	2	4	no	—
43	#13093964	—	2	2	no	—
44	#13093963	—	2	4	no	—
45	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
46	C₁₆×D₄₇	—	2	4	no	—
47	#13093947	—	2	8	no	—
48	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
49	#117×C₄₇	—	2	2	no	—
50	C₂×C₁₆×C₄₇	D₄	1	4	yes	—
51	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
53	#107×C₄₇	C₂³	1	4	yes	—
54	#106×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂×C₂²⋊D₄₇	D₈	1	2	yes	—
57	C₂²×Dic₄₇	—	4	2	no	—
58	#10625350	—	2	2	no	—
59	#10625350	—	2	2	no	—
60	C₂×D₁₈₈	D₈	1	1	yes	characteristic
61	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
62	C₂×Dic₉₄	—	2	4	no	—
63	C₂×Dic₉₄	—	4	4	no	—
64	C₂×Dic₉₄	—	4	4	no	—
65	C₂×Dic₉₄	—	4	2	no	—
66	C₂×Dic₉₄	D₈	1	1	yes	characteristic
67	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₄₇	#41	1	2	yes	—
70	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
71	C₄⋊C₄×C₄₇	—	2	4	no	—
72	C₂²⋊C₄×C₄₇	—	4	2	no	—
73	C₄²×C₄₇	—	4	2	no	—
74	(C₂×D₄₇)⋊C₄	—	4	8	no	—
75	C₄⋊Dic₄₇	—	4	8	no	—
76	#10625329	—	2	2	no	—
77	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
78	Dic₁₈₈	—	2	4	no	—
79	Dic₁₈₈	—	2	4	no	—
80	Dic₁₈₈	—	4	4	no	—
81	#10625324	—	2	4	no	—
82	C₈×D₄₇	—	2	2	no	—
83	C₈×D₄₇	—	2	2	no	—
84	C₁₆×C₄₇	C₂×D₄	1	2	yes	—
85	C₁₆×C₄₇	C₂×D₄	1	2	yes	—
86	C₄₇⋊C₁₆	—	2	2	no	—
87	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
88	C₂²×D₄₇	C₂×D₈	1	2	yes	—
89	C₂×C₄×C₄₇	—	4	4	no	—
90	C₂×C₄×C₄₇	#121	1	2	yes	—
91	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
92	C₂×C₄×C₄₇	#135	1	2	yes	—
93	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
94	C₂²⋊D₄₇	—	2	4	no	—
95	C₂×Dic₄₇	—	4	4	no	—
96	C₂×Dic₄₇	—	8	4	no	—
97	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
98	D₁₈₈	—	2	2	no	—
99	C₄×D₄₇	—	2	2	no	—
100	C₄×D₄₇	—	2	2	no	—
101	Dic₉₄	—	2	2	no	—
102	Dic₉₄	—	4	4	no	—
103	Dic₉₄	—	4	4	no	—
104	Dic₉₄	—	8	4	no	—
105	C₈×C₄₇	#121	1	2	yes	—
106	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
107	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
108	C₄₇⋊C₈	—	2	2	no	—
109	#33608	—	47	1	no	maximal, Sylow
110	C₂²×C₄₇	—	2	2	no	—
111	C₂²×C₄₇	#466	1	2	yes	—
112	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
113	C₂×D₄₇	—	2	4	no	—
114	C₂×D₄₇	—	2	2	no	—
115	C₄×C₄₇	—	8	4	no	—
116	C₄×C₄₇	#466	1	2	yes	—
117	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
118	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
119	Dic₄₇	—	2	2	no	—
120	Dic₄₇	—	8	4	no	—
121	C₂²×Q₃₂	—	47	1	no	—
122	C₂×#504	—	47	1	no	—
123	#3059	—	47	2	no	—
124	#2219	—	47	4	no	—
125	#2216	—	47	4	no	—
126	#2158	D₄₇	1	1	yes	characteristic, complemented
127	#2141	—	47	2	no	—
128	C₂×C₄₇	—	2	2	no	—
129	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
130	C₂×C₄₇	#3417	1	2	yes	—
131	D₄₇	—	4	2	no	—
132	C₂²×Q₁₆	—	47	2	no	—
133	C₂×#131	—	47	1	no	—
134	#536	—	94	2	no	—
135	C₂×Q₃₂	—	47	2	no	—
136	C₂×Q₃₂	—	47	2	no	—
137	C₂×Q₃₂	—	94	4	no	—
138	#504	—	94	4	no	—
139	C₂×M₃₂	—	47	1	no	—
140	C₂×M₃₂	—	47	2	no	—
141	C₂²×C₁₆	—	47	2	no	—
142	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
143	#470	—	94	4	no	—
144	#467	—	47	8	no	—
145	#427	C₂×D₄₇	1	2	yes	—
146	#419	—	94	2	no	—
147	#367	C₂×D₄₇	1	2	yes	—
148	#366	C₂×D₄₇	1	2	yes	—
149	#358	—	47	8	no	—
150	C₄₇	#33608	1	1	yes	characteristic, complemented, Sylow
151	C₂×#41	—	47	1	no	—
152	C₂²×Q₈	—	94	2	no	—
153	C₂×Q₁₆	—	47	4	no	—
154	C₂×Q₁₆	—	94	4	no	—
155	C₂×Q₁₆	—	94	2	no	—
156	C₂×Q₁₆	—	94	4	no	—
157	#131	—	94	2	no	—
158	#131	—	94	2	no	—
159	C₂×M₁₆	—	47	1	no	—
160	C₂×M₁₆	—	47	2	no	—
161	C₂²×C₈	—	47	2	no	—
162	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
163	C₄⋊Q₈	—	188	2	no	—
164	#124	—	188	2	no	—
165	#123	—	188	4	no	—
166	C₂²⋊Q₈	—	94	8	no	—
167	#117	—	2	2	no	—
168	Q₃₂	—	94	4	no	—
169	Q₃₂	—	94	4	no	—
170	M₃₂	—	94	2	no	—
171	M₃₂	—	94	4	no	—
172	C₂×C₁₆	—	47	2	no	—
173	C₂×C₁₆	—	94	4	no	—
174	C₂×C₁₆	D₁₈₈	1	4	yes	—
175	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
176	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
177	#107	C₂²×D₄₇	1	4	yes	—
178	#106	—	2	2	no	—
179	#103	—	94	8	no	—
180	#41	—	94	2	no	—
181	#41	—	94	2	no	—
182	C₂×Q₈	—	47	1	no	—
183	C₂×Q₈	—	94	4	no	—
184	C₂×Q₈	—	188	4	no	—
185	C₂×Q₈	—	188	4	no	—
186	C₂×Q₈	—	188	2	no	—
187	C₂×D₄	—	47	2	no	—
188	C₂×D₄	—	47	1	no	—
189	C₂²×C₄	—	47	2	no	—
190	C₂²×C₄	—	188	2	no	—
191	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
192	Q₁₆	—	94	4	no	—
193	Q₁₆	—	94	4	no	—
194	Q₁₆	—	188	4	no	—
195	M₁₆	—	94	2	no	—
196	M₁₆	—	94	4	no	—
197	C₂×C₈	—	47	2	no	—
198	C₂×C₈	—	94	2	no	—
199	C₂×C₈	—	94	2	no	—
200	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
201	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
202	C₂×C₈	#10625354	1	2	yes	—
203	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
204	C₄⋊C₄	—	2	4	no	—
205	C₄⋊C₄	—	188	8	no	—
206	C₂²⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	188	8	no	—
208	C₄²	—	4	2	no	—
209	C₁₆	—	94	2	no	—
210	C₁₆	C₂×D₁₈₈	1	2	yes	—
211	C₁₆	C₂×D₁₈₈	1	2	yes	—
212	C₂³	—	47	2	no	—
213	C₂³	D₈×D₄₇	1	1	yes	characteristic
214	Q₈	—	94	2	no	—
215	Q₈	—	376	4	no	—
216	Q₈	—	188	4	no	—
217	Q₈	—	188	4	no	—
218	D₄	—	94	4	no	—
219	D₄	—	94	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	47	2	no	—
222	C₂×C₄	—	94	2	no	—
223	C₂×C₄	—	94	2	no	—
224	C₂×C₄	—	376	4	no	—
225	C₂×C₄	—	188	4	no	—
226	C₂×C₄	#13093999	1	2	yes	—
227	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
228	C₂×C₄	#13094047	1	2	yes	—
229	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
230	C₈	—	94	2	no	—
231	C₈	#13093999	1	2	yes	—
232	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
233	C₈	C₂×#10625354	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	94	4	no	—
236	C₂²	—	94	2	no	—
237	C₂²	#15689360	1	2	yes	—
238	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
239	C₄	—	8	4	no	—
240	C₄	—	94	2	no	—
241	C₄	—	376	4	no	—
242	C₄	#15689360	1	2	yes	—
243	C₄	C₂×#13093999	1	1	yes	characteristic
244	C₄	C₂×#13094047	1	1	yes	characteristic
245	C₂	—	2	2	no	—
246	C₂	—	188	2	no	—
247	C₂	C₂×#15689360	1	1	yes	characteristic
248	C₂	#20256538	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₃₇₆

C₂

yes

maximal, characteristic, complemented

C₂×#15689539

C₂

yes

maximal, characteristic

#20253044

C₂

yes

maximal

#20245497

C₂

yes

maximal, complemented

#20245480

C₂

yes

maximal, complemented

#20245107

C₂

yes

maximal, complemented

C₄₇×#2158

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₁₈₈

C₂²

yes

—

C₂×#13094030

C₂²

yes

characteristic

#15689699

—

C₂×Dic₃₇₆

—

C₂×Dic₃₇₆

C₂²

yes

—

C₂×Dic₃₇₆

C₂²

yes

—

#15689539

—

C₂×#13093964

C₂²

yes

characteristic

C₂×#13093963

C₂²

yes

—

C₂×C₁₆×D₄₇

C₂²

yes

—

#15689382

—

#15689365

C₂²

yes

—

#15689131

—

#15688926

C₂²

yes

—

C₂²×C₁₆×C₄₇

C₂²

yes

characteristic

C₄₇×#427

C₂²

yes

—

C₄₇×#367

C₂²

yes

—

C₄₇×#366

C₂²

yes

—

C₂×#10625350

D₄

yes

characteristic

C₂²×Dic₉₄

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂³

yes

—

#13094030

—

#13094030

—

C₂×#10625329

D₄

yes

characteristic

C₂×#10625324

D₄

yes

—

C₂×C₈×D₄₇

C₂³

yes

—

—

—

—

—

Dic₃₇₆

—

Dic₃₇₆

—

#13093964

—

#13093963

—

C₂×C₄₇⋊C₁₆

C₂³

yes

—

C₁₆×D₄₇

—

#13093947

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

#117×C₄₇

—

C₂×C₁₆×C₄₇

D₄

yes

—

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

#107×C₄₇

C₂³

yes

—

#106×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₇

D₈

yes

—

C₂²×Dic₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

D₈

yes

characteristic

C₂×C₄×D₄₇

C₂×D₄

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

D₈

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

#41

yes

—

C₂×C₈×C₄₇

C₂⁴

yes

characteristic

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

C₂×D₄

yes

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

#10625324

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

C₂×D₄

yes

—

C₁₆×C₄₇

C₂×D₄

yes

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

C₂²×D₄₇

C₂×D₈

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

C₂²×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₈

yes

—

D₁₈₈

—

C₄×D₄₇

—

100

C₄×D₄₇

—

101

Dic₉₄

—

102

Dic₉₄

—

103

Dic₉₄

—

104

Dic₉₄

—

105

C₈×C₄₇

#121

yes

—

106

C₈×C₄₇

C₂²×D₄

yes

characteristic

107

C₈×C₄₇

C₂×#41

yes

characteristic

108

C₄₇⋊C₈

—

109

#33608

—

maximal, Sylow

110

C₂²×C₄₇

—

111

C₂²×C₄₇

#466

yes

—

112

C₂²×C₄₇

C₂²×D₈

yes

characteristic

113

C₂×D₄₇

—

114

C₂×D₄₇

—

115

C₄×C₄₇

—

116

C₄×C₄₇

#466

yes

—

117

C₄×C₄₇

C₂×#121

yes

characteristic

118

C₄×C₄₇

C₂×#135

yes

characteristic

119

Dic₄₇

—

120

Dic₄₇

—

121

C₂²×Q₃₂

—

122

C₂×#504

—

123

#3059

—

124

#2219

—

125

#2216

—

126

#2158

D₄₇

yes

characteristic, complemented

127

#2141

—

128

C₂×C₄₇

—

129

C₂×C₄₇

C₂×#466

yes

characteristic

130

C₂×C₄₇

#3417

yes

—

131

D₄₇

—

132

C₂²×Q₁₆

—

133

C₂×#131

—

134

#536

—

135

C₂×Q₃₂

—

136

C₂×Q₃₂

—

137

C₂×Q₃₂

—

138

#504

—

139

C₂×M₃₂

—

140

C₂×M₃₂

—

141

C₂²×C₁₆

—

142

C₂²×C₁₆

C₂×D₄₇

yes

characteristic

143

#470

—

144

#467

—

145

#427

C₂×D₄₇

yes

—

146

#419

—

147

#367

C₂×D₄₇

yes

—

148

#366

C₂×D₄₇

yes

—

149

#358

—

150

C₄₇

#33608

yes

characteristic, complemented, Sylow

151

C₂×#41

—

152

C₂²×Q₈

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

#131

—

158

#131

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

C₂²×D₄₇

yes

characteristic

163

C₄⋊Q₈

—

188

—

164

#124

—

188

—

165

#123

—

188

—

166

C₂²⋊Q₈

—

167

#117

—

168

Q₃₂

—

169

Q₃₂

—

170

M₃₂

—

171

M₃₂

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

174

C₂×C₁₆

D₁₈₈

yes

—

175

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

176

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

177

#107

C₂²×D₄₇

yes

—

178

#106

—

179

#103

—

180

#41

—

181

#41

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

188

—

185

C₂×Q₈

—

188

—

186

C₂×Q₈

—

188

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

188

—

191

C₂²×C₄

D₄×D₄₇

yes

characteristic

192

Q₁₆

—

193

Q₁₆

—

194

Q₁₆

—

188

—

195

M₁₆

—

196

M₁₆

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

C₂×D₁₈₈

yes

—

201

C₂×C₈

D₄×D₄₇

yes

characteristic

202

C₂×C₈

#10625354

yes

—

203

C₂×C₈

C₂³×D₄₇

yes

characteristic

204

C₄⋊C₄

—

205

C₄⋊C₄

—

188

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

188

—

208

C₄²

—

209

C₁₆

—

210

C₁₆

C₂×D₁₈₈

yes

—

211

C₁₆

C₂×D₁₈₈

yes

—

212

C₂³

—

213

C₂³

D₈×D₄₇

yes

characteristic

214

Q₈

—

215

Q₈

—

376

—

216

Q₈

—

188

—

217

Q₈

—

188

—

218

D₄

—

219

D₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

376

—

225

C₂×C₄

—

188

—

226

C₂×C₄

#13093999

yes

—

227

C₂×C₄

D₈×D₄₇

yes

characteristic

228

C₂×C₄

#13094047

yes

—

229

C₂×C₄

C₂×D₄×D₄₇

yes

characteristic

230

C₈

—

231

C₈

#13093999

yes

—

232

C₈

C₂²×D₁₈₈

yes

characteristic

233

C₈

C₂×#10625354

yes

characteristic

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

#15689360

yes

—

238

C₂²

C₂×D₈×D₄₇

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

376

—

242

C₄

#15689360

yes

—

243

C₄

C₂×#13093999

yes

characteristic

244

C₄

C₂×#13094047

yes

characteristic

245

C₂

—

246

C₂

—

188

—

247

C₂

C₂×#15689360

yes

characteristic

248

C₂

#20256538

yes

—

	subgroup	G/H
center	C₂²	C₂×D₈×D₄₇
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2158	C₂
socle	C₂²×C₄₇	C₂²×D₈
prime radical	C₂×#10625350	D₄
hypercenter	#2158	D₄₇
hypocenter	C₄₇	#33608
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2158

subgroup

G/H

center

C₂²

C₂×D₈×D₄₇

commutator, cosocle

C₂×C₈×C₄₇

C₂⁴

Frattini

C₂×C₈

C₂³×D₄₇

Fitting

C₄₇×#2158

C₂

socle

C₂²×C₄₇

C₂²×D₈

D₄

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2158

N	H ≅ G/N	type
1. C₂²×Dic₃₇₆	C₂	semidirect
4. #20245497	C₂	semidirect
5. #20245480	C₂	semidirect
6. #20245107	C₂	semidirect
7. C₄₇×#2158	C₂	semidirect
126. #2158	D₄₇	semidirect
150. C₄₇	#33608	semidirect

H ≅ G/N

type

1. C₂²×Dic₃₇₆

C₂

semidirect

4. #20245497

C₂

semidirect

5. #20245480

C₂

semidirect

6. #20245107

C₂

semidirect

7. C₄₇×#2158

C₂

semidirect

126. #2158

D₄₇

semidirect

150. C₄₇

#33608

semidirect

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

subgroup	index
C₂²×Dic₃₇₆	2
C₂×#15689539	2
#20253044	2
#20245497	2
#20245480	2
#20245107	2
C₄₇×#2158	2
#33608	47

subgroup

index

C₂²×Dic₃₇₆

C₄₇×#2158

Subgroups — #26370783

Conjugacy classes of subgroups

Complements

Maximal subgroups