Group #26370778 — subgroups

Subgroups — #26370778

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	C₂×#15689539	C₂	1	1	yes	maximal, characteristic
2	#20253039	C₂	1	2	yes	maximal
3	#20245493	C₂	1	4	yes	maximal, complemented
4	#20245476	C₂	1	4	yes	maximal, complemented
5	#20245172	C₂	1	1	yes	maximal, characteristic, complemented
6	#20245108	C₂	1	2	yes	maximal, complemented
7	C₂²×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13094030	C₂²	1	1	yes	characteristic
9	#15689697	—	2	2	no	—
10	#15689539	—	2	4	no	—
11	C₂×#13093964	C₂²	1	1	yes	characteristic
12	C₂×#13093963	C₂²	1	2	yes	—
13	C₂×C₁₆×D₄₇	C₂²	1	2	yes	—
14	#15689378	—	2	4	no	—
15	#15689361	C₂²	1	8	yes	—
16	#15689161	C₂²	1	2	yes	—
17	#15689132	—	2	2	no	—
18	#15688951	C₂²	1	2	yes	—
19	#15688949	C₂²	1	2	yes	—
20	#15688927	C₂²	1	8	yes	—
21	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
22	C₂×Q₃₂×C₄₇	—	2	4	no	—
23	C₂×Q₃₂×C₄₇	C₂²	1	2	yes	—
24	C₂×Q₃₂×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#10625350	D₄	1	1	yes	characteristic
27	#13094030	—	2	2	no	—
28	#13094030	—	2	2	no	—
29	C₂×#10625329	D₄	1	1	yes	characteristic
30	C₂×#10625324	D₄	1	2	yes	—
31	C₂×C₈×D₄₇	C₂³	1	2	yes	—
32	#13094022	—	4	2	no	—
33	#13094013	—	4	2	no	—
34	#13094007	—	4	4	no	—
35	#13094000	—	2	8	no	—
36	#13093983	—	2	2	no	—
37	#13093964	—	2	2	no	—
38	#13093963	—	2	4	no	—
39	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
40	C₁₆×D₄₇	—	2	4	no	—
41	#13093958	C₂³	1	4	yes	—
42	#13093956	—	2	2	no	—
43	#13093948	—	2	8	no	—
44	C₂²×Q₈×C₄₇	—	2	2	no	—
45	C₂×Q₁₆×C₄₇	—	2	4	no	—
46	C₂×Q₁₆×C₄₇	—	2	2	no	—
47	C₂×Q₁₆×C₄₇	—	2	4	no	—
48	C₂×Q₁₆×C₄₇	C₂³	1	4	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
50	Q₃₂×C₄₇	—	2	4	no	—
51	Q₃₂×C₄₇	—	2	4	no	—
52	C₂×C₁₆×C₄₇	D₄	1	4	yes	—
53	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
55	C₂×Q₈×C₄₇	—	2	4	no	—
56	C₂×Q₈×C₄₇	—	4	2	no	—
57	C₂×Q₈×C₄₇	—	4	4	no	—
58	C₂×Q₈×C₄₇	—	4	4	no	—
59	C₂²×C₄×C₄₇	—	4	2	no	—
60	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂×C₂²⋊D₄₇	D₈	1	2	yes	—
62	#10625350	—	2	2	no	—
63	#10625350	—	2	2	no	—
64	C₂×D₁₈₈	D₈	1	1	yes	characteristic
65	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
66	C₂×Dic₉₄	D₈	1	1	yes	characteristic
67	Q₁₆×C₄₇	—	2	4	no	—
68	Q₁₆×C₄₇	—	2	4	no	—
69	Q₁₆×C₄₇	—	4	4	no	—
70	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₄₇	#41	1	2	yes	—
73	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
74	C₂²⋊Dic₄₇	—	4	2	no	—
75	(C₂×D₄₇)⋊C₄	—	4	8	no	—
76	C₄⋊Dic₄₇	—	2	4	no	—
77	Dic₄₇⋊C₄	—	4	8	no	—
78	C₄×Dic₄₇	—	4	2	no	—
79	#10625329	—	2	2	no	—
80	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
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	Q₈×C₄₇	—	4	4	no	—
90	Q₈×C₄₇	—	4	4	no	—
91	Q₈×C₄₇	—	8	4	no	—
92	C₂×C₄×C₄₇	—	4	4	no	—
93	C₂×C₄×C₄₇	—	8	4	no	—
94	C₂×C₄×C₄₇	#121	1	2	yes	—
95	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
96	C₂×C₄×C₄₇	#135	1	2	yes	—
97	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
98	C₂²⋊D₄₇	—	2	4	no	—
99	C₂×Dic₄₇	—	4	4	no	—
100	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
101	D₁₈₈	—	2	2	no	—
102	C₄×D₄₇	—	2	2	no	—
103	C₄×D₄₇	—	2	2	no	—
104	Dic₉₄	—	2	2	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	D₄₇	1	1	yes	characteristic, complemented
122	C₂×#504	—	47	1	no	—
123	#3059	—	47	2	no	—
124	#2219	—	47	4	no	—
125	#2216	—	47	4	no	—
126	#2158	—	47	1	no	—
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	C₂×D₄₇	1	2	yes	—
133	C₂×#131	—	47	1	no	—
134	#536	—	94	2	no	—
135	C₂×Q₃₂	—	2	4	no	—
136	C₂×Q₃₂	C₂×D₄₇	1	2	yes	—
137	C₂×Q₃₂	C₂×D₄₇	1	2	yes	—
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	—	47	2	no	—
146	#419	—	94	2	no	—
147	#367	—	47	2	no	—
148	#366	—	47	2	no	—
149	#358	—	47	8	no	—
150	C₄₇	#33608	1	1	yes	characteristic, complemented, Sylow
151	C₂×#41	—	47	1	no	—
152	C₂²×Q₈	—	2	2	no	—
153	C₂×Q₁₆	—	2	2	no	—
154	C₂×Q₁₆	—	2	4	no	—
155	C₂×Q₁₆	—	2	4	no	—
156	C₂×Q₁₆	C₂²×D₄₇	1	4	yes	—
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	—	94	2	no	—
168	Q₃₂	—	2	4	no	—
169	Q₃₂	—	2	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	C₂²⋊D₄₇	1	4	yes	—
175	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
176	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
177	#107	—	47	4	no	—
178	#106	—	94	2	no	—
179	#103	—	94	8	no	—
180	#41	—	94	2	no	—
181	#41	—	94	2	no	—
182	C₂×Q₈	—	2	4	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	4	no	—
185	C₂×Q₈	—	4	4	no	—
186	C₂×Q₈	—	47	1	no	—
187	C₂×D₄	—	47	2	no	—
188	C₂×D₄	—	47	1	no	—
189	C₂²×C₄	—	4	2	no	—
190	C₂²×C₄	—	47	2	no	—
191	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
192	Q₁₆	—	2	4	no	—
193	Q₁₆	—	2	4	no	—
194	Q₁₆	—	4	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	D₄×D₄₇	1	1	yes	characteristic
201	C₂×C₈	#10625352	1	2	yes	—
202	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
203	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
204	C₄⋊C₄	—	94	4	no	—
205	C₄⋊C₄	—	188	8	no	—
206	C₂²⋊C₄	—	188	8	no	—
207	C₂²⋊C₄	—	188	2	no	—
208	C₄²	—	188	2	no	—
209	C₁₆	—	94	2	no	—
210	C₁₆	C₂×C₂²⋊D₄₇	1	2	yes	—
211	C₁₆	C₂×C₂²⋊D₄₇	1	2	yes	—
212	C₂³	—	47	2	no	—
213	C₂³	D₈×D₄₇	1	1	yes	characteristic
214	Q₈	—	4	4	no	—
215	Q₈	—	4	4	no	—
216	Q₈	—	8	4	no	—
217	Q₈	—	94	2	no	—
218	D₄	—	94	4	no	—
219	D₄	—	94	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	8	4	no	—
222	C₂×C₄	—	47	2	no	—
223	C₂×C₄	—	94	2	no	—
224	C₂×C₄	—	94	2	no	—
225	C₂×C₄	—	188	4	no	—
226	C₂×C₄	#13093995	1	2	yes	—
227	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
228	C₂×C₄	#13094043	1	2	yes	—
229	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
230	C₈	—	94	2	no	—
231	C₈	#13093995	1	2	yes	—
232	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
233	C₈	C₂×#10625352	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	94	2	no	—
236	C₂²	—	94	4	no	—
237	C₂²	#15689356	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	#15689356	1	2	yes	—
243	C₄	C₂×#13093995	1	1	yes	characteristic
244	C₄	C₂×#13094043	1	1	yes	characteristic
245	C₂	—	2	2	no	—
246	C₂	—	188	2	no	—
247	C₂	C₂×#15689356	1	1	yes	characteristic
248	C₂	#20256537	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689539

C₂

yes

maximal, characteristic

#20253039

C₂

yes

maximal

#20245493

C₂

yes

maximal, complemented

#20245476

C₂

yes

maximal, complemented

#20245172

C₂

yes

maximal, characteristic, complemented

#20245108

C₂

yes

maximal, complemented

C₂²×Q₃₂×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×#13094030

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#13093963

C₂²

yes

—

C₂×C₁₆×D₄₇

C₂²

yes

—

#15689378

—

#15689361

C₂²

yes

—

#15689161

C₂²

yes

—

#15689132

—

#15688951

C₂²

yes

—

#15688949

C₂²

yes

—

#15688927

C₂²

yes

—

C₂²×Q₁₆×C₄₇

C₂²

yes

—

C₂×Q₃₂×C₄₇

—

C₂×Q₃₂×C₄₇

C₂²

yes

—

C₂×Q₃₂×C₄₇

C₂²

yes

—

C₂²×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×#10625350

D₄

yes

—

—

D₄

yes

characteristic

C₂×#10625324

D₄

yes

—

C₂×C₈×D₄₇

C₂³

yes

—

—

—

—

—

—

—

—

C₂×C₄₇⋊C₁₆

C₂³

yes

—

C₁₆×D₄₇

—

#13093958

C₂³

yes

—

#13093956

—

#13093948

—

C₂²×Q₈×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

C₂³

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

Q₃₂×C₄₇

—

Q₃₂×C₄₇

—

C₂×C₁₆×C₄₇

D₄

yes

—

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₇

D₈

yes

—

#10625350

—

#10625350

—

C₂×D₁₈₈

D₈

yes

characteristic

C₂×C₄×D₄₇

C₂×D₄

yes

—

C₂×Dic₉₄

D₈

yes

characteristic

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

#41

yes

—

C₂×C₈×C₄₇

C₂⁴

yes

characteristic

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

C₂×D₄

yes

—

#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

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

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

—

100

C₂×Dic₄₇

C₂×D₈

yes

—

101

D₁₈₈

—

102

C₄×D₄₇

—

103

C₄×D₄₇

—

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

D₄₇

yes

characteristic, complemented

122

C₂×#504

—

123

#3059

—

124

#2219

—

125

#2216

—

126

#2158

—

127

#2141

—

128

C₂×C₄₇

—

129

C₂×C₄₇

C₂×#466

yes

characteristic

130

C₂×C₄₇

#3417

yes

—

131

D₄₇

—

132

C₂²×Q₁₆

C₂×D₄₇

yes

—

133

C₂×#131

—

134

#536

—

135

C₂×Q₃₂

—

136

C₂×Q₃₂

C₂×D₄₇

yes

—

137

C₂×Q₃₂

C₂×D₄₇

yes

—

138

#504

—

139

C₂×M₃₂

—

140

C₂×M₃₂

—

141

C₂²×C₁₆

—

142

C₂²×C₁₆

C₂×D₄₇

yes

characteristic

143

#470

—

144

#467

—

145

#427

—

146

#419

—

147

#367

—

148

#366

—

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

C₂²×D₄₇

yes

—

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

C₂²⋊D₄₇

yes

—

175

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

176

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

177

#107

—

178

#106

—

179

#103

—

180

#41

—

181

#41

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

D₄×D₄₇

yes

characteristic

192

Q₁₆

—

193

Q₁₆

—

194

Q₁₆

—

195

M₁₆

—

196

M₁₆

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

D₄×D₄₇

yes

characteristic

201

C₂×C₈

#10625352

yes

—

202

C₂×C₈

C₂×C₂²⋊D₄₇

yes

—

203

C₂×C₈

C₂³×D₄₇

yes

characteristic

204

C₄⋊C₄

—

205

C₄⋊C₄

—

188

—

206

C₂²⋊C₄

—

188

—

207

C₂²⋊C₄

—

188

—

208

C₄²

—

188

—

209

C₁₆

—

210

C₁₆

C₂×C₂²⋊D₄₇

yes

—

211

C₁₆

C₂×C₂²⋊D₄₇

yes

—

212

C₂³

—

213

C₂³

D₈×D₄₇

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

Q₈

—

218

D₄

—

219

D₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

188

—

226

C₂×C₄

#13093995

yes

—

227

C₂×C₄

D₈×D₄₇

yes

characteristic

228

C₂×C₄

#13094043

yes

—

229

C₂×C₄

C₂×D₄×D₄₇

yes

characteristic

230

C₈

—

231

C₈

#13093995

yes

—

232

C₈

C₂²×C₂²⋊D₄₇

yes

characteristic

233

C₈

C₂×#10625352

yes

characteristic

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

#15689356

yes

—

238

C₂²

C₂×D₈×D₄₇

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

376

—

242

C₄

#15689356

yes

—

243

C₄

C₂×#13093995

yes

characteristic

244

C₄

C₂×#13094043

yes

characteristic

245

C₂

—

246

C₂

—

188

—

247

C₂

C₂×#15689356

yes

characteristic

248

C₂

#20256537

yes

—

	subgroup	G/H
center	C₂²	C₂×D₈×D₄₇
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂²×Q₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×D₈
prime radical	C₂×#10625350	D₄
hypercenter	C₂²×Q₃₂	D₄₇
hypocenter	C₄₇	#33608
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂²

C₂×D₈×D₄₇

commutator, cosocle

C₂×C₈×C₄₇

C₂⁴

Frattini

C₂×C₈

C₂³×D₄₇

Fitting

C₂²×Q₃₂×C₄₇

C₂

socle

C₂²×C₄₇

C₂²×D₈

prime radical

C₂×#10625350

D₄

hypercenter

C₂²×Q₃₂

D₄₇

hypocenter

C₄₇

#33608

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
3. #20245493	C₂	semidirect
4. #20245476	C₂	semidirect
5. #20245172	C₂	semidirect
6. #20245108	C₂	semidirect
7. C₂²×Q₃₂×C₄₇	C₂	semidirect
121. C₂²×Q₃₂	D₄₇	semidirect
150. C₄₇	#33608	semidirect

H ≅ G/N

type

3. #20245493

C₂

semidirect

4. #20245476

C₂

semidirect

5. #20245172

C₂

semidirect

6. #20245108

C₂

semidirect

7. C₂²×Q₃₂×C₄₇

C₂

semidirect

121. C₂²×Q₃₂

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
C₂×#15689539	2
#20253039	2
#20245493	2
#20245476	2
#20245172	2
#20245108	2
C₂²×Q₃₂×C₄₇	2
#33608	47

subgroup

index

C₂²×Q₃₂×C₄₇

Subgroups — #26370778

Conjugacy classes of subgroups

Complements

Maximal subgroups