Group #26230162 — subgroups

Subgroups — #26230162

Order 12032.

818 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 211 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	#20253834	C₂	1	1	yes	maximal, characteristic
2	#20252101	C₂	1	2	yes	maximal, complemented
3	#20244220	C₂	1	2	yes	maximal, complemented
4	#20243714	C₂	1	8	yes	maximal, complemented
5	#20243529	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13094046	C₂²	1	4	yes	—
8	C₂×#13094030	C₂²	1	4	yes	—
9	#15689673	C₂²	1	2	yes	—
10	#15689517	C₄	1	4	yes	complemented
11	#15689512	C₄	1	4	yes	complemented
12	#15689202	—	2	2	no	—
13	#15689202	—	2	2	no	—
14	C₈×D₁₈₈	—	2	2	no	—
15	C₈×D₁₈₈	—	2	2	no	—
16	#15689147	C₂²	1	2	yes	—
17	C₂×#13093952	C₂²	1	8	yes	—
18	#15689089	C₂²	1	4	yes	—
19	#15688888	C₂²	1	4	yes	—
20	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#376	C₂²	1	1	yes	characteristic
23	C₄₇×#336	C₂²	1	4	yes	—
24	C₂×#10625350	C₂³	1	4	yes	—
25	#13094046	—	4	8	no	—
26	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	—
27	C₂×#10625325	C₂×C₄	1	8	yes	—
28	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
29	#13094030	—	4	8	no	—
30	C₂×#10625329	C₂³	1	4	yes	—
31	C₂×#10625324	—	2	4	no	—
32	C₂×C₈×D₄₇	—	2	4	no	—
33	#13094024	C₂×C₄	1	2	yes	—
34	#13094021	C₂×C₄	1	2	yes	—
35	#13094012	C₂×C₄	1	4	yes	—
36	#13093998	—	2	2	no	—
37	#13093998	—	2	2	no	—
38	C₄×D₁₈₈	—	2	2	no	—
39	C₄×D₁₈₈	—	2	2	no	—
40	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
41	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
42	#13093952	—	4	8	no	—
43	(C₂×D₄₇)⋊C₈	—	2	4	no	—
44	(C₂×D₄₇)⋊C₈	—	2	4	no	—
45	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
47	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
48	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
49	#97×C₄₇	C₂×C₄	1	4	yes	—
50	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
51	C₄×C₈×C₄₇	D₄	1	2	yes	—
52	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
53	#95×C₄₇	—	2	2	no	—
54	C₂²×C₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	#41	1	2	yes	—
56	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
57	C₂×C₂²⋊D₄₇	—	2	4	no	—
58	#10625350	—	2	8	no	—
59	#10625350	—	2	8	no	—
60	C₂×D₁₈₈	—	2	2	no	—
61	C₂×D₁₈₈	—	2	2	no	—
62	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
63	C₂×C₄×D₄₇	—	2	4	no	—
64	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
65	C₂×C₈×C₄₇	—	2	4	no	—
66	C₂×C₈×C₄₇	—	2	4	no	—
67	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
68	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
70	C₄²×C₄₇	—	2	4	no	—
71	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
72	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
74	(C₂×D₄₇)⋊C₄	—	2	4	no	—
75	(C₂×D₄₇)⋊C₄	—	2	4	no	—
76	C₄⋊Dic₄₇	—	2	2	no	—
77	C₄⋊Dic₄₇	—	2	2	no	—
78	#10625329	—	2	8	no	—
79	C₂×C₄₇⋊C₈	—	2	4	no	—
80	Dic₁₈₈	—	4	4	no	—
81	D₃₇₆	—	4	4	no	—
82	#10625325	—	4	8	no	—
83	#10625324	—	4	8	no	—
84	C₈×D₄₇	—	4	8	no	—
85	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
86	C₂²×D₄₇	—	2	4	no	—
87	C₂×C₄×C₄₇	—	4	2	no	—
88	C₂×C₄×C₄₇	—	4	4	no	—
89	C₂×C₄×C₄₇	—	4	2	no	—
90	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
93	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
94	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
95	C₂²⋊D₄₇	—	4	8	no	—
96	C₂×Dic₄₇	—	2	4	no	—
97	D₁₈₈	—	2	8	no	—
98	D₁₈₈	—	4	4	no	—
99	D₁₈₈	—	4	4	no	—
100	C₄×D₄₇	—	4	4	no	—
101	C₄×D₄₇	—	4	4	no	—
102	Dic₉₄	—	2	8	no	—
103	C₈×C₄₇	—	2	4	no	—
104	C₈×C₄₇	—	2	2	no	—
105	C₈×C₄₇	—	2	2	no	—
106	C₄₇⋊C₈	—	4	4	no	—
107	#22281	—	47	1	no	maximal, Sylow
108	C₂²×C₄₇	—	2	2	no	—
109	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
110	C₂²×C₄₇	#540	1	2	yes	—
111	C₂×D₄₇	—	4	4	no	—
112	C₂×D₄₇	—	4	4	no	—
113	C₂×D₄₇	—	4	4	no	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	—	2	2	no	—
116	C₄×C₄₇	—	8	2	no	—
117	C₄×C₄₇	#518	1	2	yes	—
118	C₄×C₄₇	#535	1	2	yes	—
119	Dic₄₇	—	4	4	no	—
120	#3150	—	47	1	no	—
121	#2931	—	47	2	no	—
122	#1963	—	47	2	no	—
123	#1876	—	47	8	no	—
124	#1838	—	47	1	no	—
125	#1746	D₄₇	1	1	yes	characteristic, complemented
126	C₂×C₄₇	—	2	2	no	—
127	C₂×C₄₇	#2328	1	1	yes	characteristic
128	C₂×C₄₇	#2955	1	2	yes	—
129	D₄₇	—	8	4	no	—
130	C₂×#135	—	47	4	no	—
131	C₂×#131	—	47	4	no	—
132	#532	—	47	2	no	—
133	#497	—	47	4	no	—
134	#496	—	47	4	no	—
135	#436	—	94	2	no	—
136	#436	—	94	2	no	—
137	C₈×D₄	—	94	2	no	—
138	C₈×D₄	—	94	2	no	—
139	#423	—	47	2	no	—
140	C₂×#104	—	47	8	no	—
141	#408	—	47	4	no	—
142	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
143	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
144	#376	C₂×D₄₇	1	1	yes	characteristic
145	#341	—	47	4	no	—
146	#336	C₂×D₄₇	1	4	yes	—
147	C₄₇	#22281	1	1	yes	characteristic, complemented, Sylow
148	C₂×#41	—	47	4	no	—
149	#135	—	188	8	no	—
150	C₂×Q₁₆	—	47	4	no	—
151	C₂×SD₁₆	—	47	8	no	—
152	C₂×D₈	—	47	4	no	—
153	#131	—	188	8	no	—
154	C₂×M₁₆	—	47	4	no	—
155	C₂×M₁₆	—	94	4	no	—
156	C₂²×C₈	—	94	4	no	—
157	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
158	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
159	C₄⋊Q₈	—	47	2	no	—
160	#127	—	47	2	no	—
161	#124	—	47	4	no	—
162	#121	—	94	2	no	—
163	#121	—	94	2	no	—
164	C₄×D₄	—	94	2	no	—
165	C₄×D₄	—	94	2	no	—
166	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
167	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
168	C₄⋊C₈	—	94	2	no	—
169	C₄⋊C₈	—	94	2	no	—
170	#104	—	188	8	no	—
171	C₂²⋊C₈	—	94	4	no	—
172	C₂²⋊C₈	—	94	4	no	—
173	#97	C₄×D₄₇	1	4	yes	—
174	C₄×C₈	D₁₈₈	1	1	yes	characteristic
175	C₄×C₈	D₁₈₈	1	2	yes	—
176	C₄×C₈	D₁₈₈	1	1	yes	characteristic
177	#95	—	2	2	no	—
178	#41	—	94	8	no	—
179	#41	—	94	8	no	—
180	C₂×Q₈	—	47	4	no	—
181	C₂×D₄	—	47	4	no	—
182	C₂×D₄	—	94	4	no	—
183	C₂×D₄	—	94	2	no	—
184	C₂×D₄	—	94	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	94	4	no	—
187	C₂²×C₄	#10625350	1	2	yes	—
188	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
189	Q₁₆	—	188	4	no	—
190	SD₁₆	—	188	8	no	—
191	D₈	—	188	4	no	—
192	M₁₆	—	94	8	no	—
193	M₁₆	—	188	8	no	—
194	C₂×C₈	—	2	4	no	—
195	C₂×C₈	—	2	4	no	—
196	C₂×C₈	—	94	4	no	—
197	C₂×C₈	—	188	8	no	—
198	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
199	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
200	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
201	C₄⋊C₄	—	94	2	no	—
202	C₄⋊C₄	—	94	2	no	—
203	C₂²⋊C₄	—	94	4	no	—
204	C₂²⋊C₄	—	94	4	no	—
205	C₄²	—	2	4	no	—
206	C₄²	C₂×C₄×D₄₇	1	2	yes	—
207	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
208	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
209	C₂³	—	94	4	no	—
210	C₂³	C₂×#10625350	1	1	yes	characteristic
211	Q₈	—	94	8	no	—
212	D₄	—	94	8	no	—
213	D₄	—	188	4	no	—
214	D₄	—	188	4	no	—
215	D₄	—	188	8	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	4	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	94	4	no	—
220	C₂×C₄	—	188	4	no	—
221	C₂×C₄	—	188	4	no	—
222	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
223	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
224	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
225	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
226	C₂×C₄	#13094070	1	4	yes	—
227	C₈	—	2	4	no	—
228	C₈	—	2	2	no	—
229	C₈	—	2	2	no	—
230	C₈	—	188	4	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	188	4	no	—
233	C₂²	—	188	4	no	—
234	C₂²	—	188	4	no	—
235	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
236	C₂²	#15689728	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	8	2	no	—
240	C₄	—	188	4	no	—
241	C₄	#15689597	1	2	yes	—
242	C₄	#15689692	1	2	yes	—
243	C₂	—	2	2	no	—
244	C₂	—	376	4	no	—
245	C₂	#20246113	1	1	yes	characteristic
246	C₂	#20252292	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20253834

C₂

yes

maximal, characteristic

#20252101

C₂

yes

maximal, complemented

#20244220

C₂

yes

maximal, complemented

#20243714

C₂

yes

maximal, complemented

#20243529

C₂

yes

maximal, characteristic, complemented

C₄₇×#1746

C₂

yes

maximal, characteristic, complemented

C₂×#13094046

C₂²

yes

—

C₂×#13094030

C₂²

yes

—

#15689673

C₂²

yes

—

#15689517

C₄

yes

complemented

#15689512

C₄

yes

complemented

#15689202

—

#15689202

—

C₈×D₁₈₈

—

C₈×D₁₈₈

—

#15689147

C₂²

yes

—

C₂×#13093952

C₂²

yes

—

#15689089

C₂²

yes

—

#15688888

C₂²

yes

—

C₂×#97×C₄₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#376

C₂²

yes

characteristic

C₄₇×#336

C₂²

yes

—

C₂×#10625350

C₂³

yes

—

#13094046

—

C₂×Dic₁₈₈

C₂×C₄

yes

—

C₂×#10625325

C₂×C₄

yes

—

C₂×D₃₇₆

C₂×C₄

yes

—

#13094030

—

C₂×#10625329

C₂³

yes

—

C₂×#10625324

—

C₂×C₈×D₄₇

—

#13094024

C₂×C₄

yes

—

#13094021

C₂×C₄

yes

—

#13094012

C₂×C₄

yes

—

#13093998

—

#13093998

—

C₄×D₁₈₈

—

C₄×D₁₈₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093952

—

(C₂×D₄₇)⋊C₈

—

(C₂×D₄₇)⋊C₈

—

C₂²×C₈×C₄₇

C₂³

yes

—

C₂²×C₈×C₄₇

C₂³

yes

—

C₂×C₄²×C₄₇

C₂³

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#97×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

—

C₄×C₈×C₄₇

D₄

yes

characteristic

#95×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

#41

yes

—

C₂²×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂²×C₄

yes

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

C₂²×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²×C₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

D₃₇₆

—

#10625325

—

#10625324

—

C₈×D₄₇

—

C₂³×C₄₇

C₂×#41

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₂³×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×D₄

yes

characteristic

C₂×C₄×C₄₇

H(5,𝔽₂)

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

100

C₄×D₄₇

—

101

C₄×D₄₇

—

102

Dic₉₄

—

103

C₈×C₄₇

—

104

C₈×C₄₇

—

105

C₈×C₄₇

—

106

C₄₇⋊C₈

—

107

#22281

—

maximal, Sylow

108

C₂²×C₄₇

—

109

C₂²×C₄₇

C₂×C₄×D₄

yes

characteristic

110

C₂²×C₄₇

#540

yes

—

111

C₂×D₄₇

—

112

C₂×D₄₇

—

113

C₂×D₄₇

—

114

C₄×C₄₇

—

115

C₄×C₄₇

—

116

C₄×C₄₇

—

117

C₄×C₄₇

#518

yes

—

118

C₄×C₄₇

#535

yes

—

119

Dic₄₇

—

120

#3150

—

121

#2931

—

122

#1963

—

123

#1876

—

124

#1838

—

125

#1746

D₄₇

yes

characteristic, complemented

126

C₂×C₄₇

—

127

C₂×C₄₇

#2328

yes

characteristic

128

C₂×C₄₇

#2955

yes

—

129

D₄₇

—

130

C₂×#135

—

131

C₂×#131

—

132

#532

—

133

#497

—

134

#496

—

135

#436

—

136

#436

—

137

C₈×D₄

—

138

C₈×D₄

—

139

#423

—

140

C₂×#104

—

141

#408

—

142

C₂×#97

C₂×D₄₇

yes

characteristic

143

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

144

#376

C₂×D₄₇

yes

characteristic

145

#341

—

146

#336

C₂×D₄₇

yes

—

147

C₄₇

#22281

yes

characteristic, complemented, Sylow

148

C₂×#41

—

149

#135

—

188

—

150

C₂×Q₁₆

—

151

C₂×SD₁₆

—

152

C₂×D₈

—

153

#131

—

188

—

154

C₂×M₁₆

—

155

C₂×M₁₆

—

156

C₂²×C₈

—

157

C₂²×C₈

C₂²×D₄₇

yes

—

158

C₂²×C₈

C₂²×D₄₇

yes

—

159

C₄⋊Q₈

—

160

#127

—

161

#124

—

162

#121

—

163

#121

—

164

C₄×D₄

—

165

C₄×D₄

—

166

C₂×C₄²

C₂²×D₄₇

yes

—

167

C₂×C₄²

C₂²×D₄₇

yes

characteristic

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

#104

—

188

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

173

#97

C₄×D₄₇

yes

—

174

C₄×C₈

D₁₈₈

yes

characteristic

175

C₄×C₈

D₁₈₈

yes

—

176

C₄×C₈

D₁₈₈

yes

characteristic

177

#95

—

178

#41

—

179

#41

—

180

C₂×Q₈

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

#10625350

yes

—

188

C₂²×C₄

C₂³×D₄₇

yes

characteristic

189

Q₁₆

—

188

—

190

SD₁₆

—

188

—

191

D₈

—

188

—

192

M₁₆

—

193

M₁₆

—

188

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

188

—

198

C₂×C₈

C₂×C₄×D₄₇

yes

—

199

C₂×C₈

C₂×D₁₈₈

yes

—

200

C₂×C₈

C₂×D₁₈₈

yes

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

—

206

C₄²

C₂×C₄×D₄₇

yes

—

207

C₄²

C₂×D₁₈₈

yes

characteristic

208

C₄²

C₂×D₁₈₈

yes

characteristic

209

C₂³

—

210

C₂³

C₂×#10625350

yes

characteristic

211

Q₈

—

212

D₄

—

213

D₄

—

188

—

214

D₄

—

188

—

215

D₄

—

188

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

188

—

221

C₂×C₄

—

188

—

222

C₂×C₄

C₄×D₁₈₈

yes

—

223

C₂×C₄

C₄×D₁₈₈

yes

—

224

C₂×C₄

C₂²×C₄×D₄₇

yes

characteristic

225

C₂×C₄

C₂²×D₁₈₈

yes

characteristic

226

C₂×C₄

#13094070

yes

—

227

C₈

—

228

C₈

—

229

C₈

—

230

C₈

—

188

—

231

C₂²

—

232

C₂²

—

188

—

233

C₂²

—

188

—

234

C₂²

—

188

—

235

C₂²

C₂×C₄×D₁₈₈

yes

characteristic

236

C₂²

#15689728

yes

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

188

—

241

C₄

#15689597

yes

—

242

C₄

#15689692

yes

—

243

C₂

—

244

C₂

—

376

—

245

C₂

#20246113

yes

characteristic

246

C₂

#20252292

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1746	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253834	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1746	D₄₇
hypocenter	C₄₇	#22281
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1746

subgroup

G/H

center

C₂×C₄

C₂²×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂³×C₄

Frattini

C₂²×C₄

C₂³×D₄₇

Fitting

C₄₇×#1746

C₂

socle

C₂²×C₄₇

C₂×C₄×D₄

prime radical

#20253834

C₂

cosocle

C₂²×C₄×C₄₇

C₂⁴

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1746

N	H ≅ G/N	type
2. #20252101	C₂	semidirect
3. #20244220	C₂	semidirect
4. #20243714	C₂	semidirect
5. #20243529	C₂	semidirect
6. C₄₇×#1746	C₂	semidirect
10. #15689517	C₄	semidirect
11. #15689512	C₄	semidirect
125. #1746	D₄₇	semidirect
147. C₄₇	#22281	semidirect

H ≅ G/N

type

2. #20252101

C₂

semidirect

3. #20244220

C₂

semidirect

4. #20243714

C₂

semidirect

5. #20243529

C₂

semidirect

6. C₄₇×#1746

C₂

semidirect

10. #15689517

C₄

semidirect

11. #15689512

C₄

semidirect

125. #1746

D₄₇

semidirect

147. C₄₇

#22281

semidirect

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

subgroup	index
#20253834	2
#20252101	2
#20244220	2
#20243714	2
#20243529	2
C₄₇×#1746	2
#22281	47

subgroup

index

C₄₇×#1746

Subgroups — #26230162

Conjugacy classes of subgroups

Complements

Maximal subgroups