Group #26113806 — subgroups

Subgroups — #26113806

Order 12032.

540 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 103 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	#20252459	C₂	1	1	yes	maximal, characteristic, complemented
2	#20242102	C₂	1	2	yes	maximal, complemented
3	#20242023	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241260	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3151	C₂	1	1	yes	maximal, characteristic
6	#15689195	—	2	4	no	—
7	#15689180	C₂²	1	2	yes	—
8	#15689180	C₂²	1	2	yes	—
9	#15689090	—	2	2	no	—
10	#15688867	—	2	4	no	—
11	#15688863	—	2	2	no	—
12	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
13	C₄₇×#532	C₂²	1	1	yes	characteristic
14	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#496	—	2	2	no	—
16	C₄₇×#493	C₄	1	2	yes	—
17	C₄₇×#492	C₄	1	2	yes	—
18	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#10625329	—	2	2	no	—
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
22	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
23	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
24	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
25	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
26	#13093935	—	2	2	no	—
27	#13093935	—	2	2	no	—
28	C₂×#41×C₄₇	D₄	1	2	yes	—
29	C₂²×D₄×C₄₇	—	2	1	no	—
30	C₂²×D₄×C₄₇	—	2	2	no	—
31	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
32	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
33	C₂×SD₁₆×C₄₇	—	2	4	no	—
34	C₂×D₈×C₄₇	—	2	4	no	—
35	C₂×M₁₆×C₄₇	—	2	1	no	—
36	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
37	#127×C₄₇	—	2	1	no	—
38	#127×C₄₇	—	2	2	no	—
39	#127×C₄₇	C₂×C₄	1	2	yes	—
40	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
41	#124×C₄₇	D₄	1	2	yes	—
42	#121×C₄₇	—	2	2	no	—
43	C₄×D₄×C₄₇	—	2	2	no	—
44	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
45	#97×C₄₇	—	2	1	no	—
46	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₂⁴×C₄₇	—	4	1	no	—
48	#41×C₄₇	—	4	2	no	—
49	#41×C₄₇	—	4	2	no	—
50	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
51	C₂×D₄×C₄₇	—	2	2	no	—
52	C₂×D₄×C₄₇	—	2	2	no	—
53	C₂×D₄×C₄₇	—	2	2	no	—
54	C₂×D₄×C₄₇	—	2	4	no	—
55	C₂×D₄×C₄₇	—	4	2	no	—
56	C₂×D₄×C₄₇	—	4	2	no	—
57	C₂×D₄×C₄₇	—	4	1	no	—
58	C₂×D₄×C₄₇	—	4	2	no	—
59	C₂×D₄×C₄₇	—	8	4	no	—
60	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	#41	1	2	yes	—
64	SD₁₆×C₄₇	—	4	8	no	—
65	D₈×C₄₇	—	4	8	no	—
66	M₁₆×C₄₇	—	2	4	no	—
67	C₂×C₈×C₄₇	—	2	2	no	—
68	C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂²⋊C₄×C₄₇	—	2	4	no	—
70	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₄₇	C₂×D₄	1	2	yes	—
73	#10625329	—	8	2	no	—
74	C₂×C₄₇⋊C₈	—	2	4	no	—
75	C₂×C₄₇⋊C₈	—	4	2	no	—
76	C₂×C₄₇⋊C₈	—	8	2	no	—
77	C₂³×C₄₇	—	2	2	no	—
78	C₂³×C₄₇	—	4	2	no	—
79	C₂³×C₄₇	—	8	1	no	—
80	C₂³×C₄₇	—	8	1	no	—
81	C₂³×C₄₇	—	8	4	no	—
82	C₂³×C₄₇	#123	1	1	yes	characteristic
83	Q₈×C₄₇	—	4	2	no	—
84	D₄×C₄₇	—	4	2	no	—
85	D₄×C₄₇	—	4	4	no	—
86	D₄×C₄₇	—	8	2	no	—
87	D₄×C₄₇	—	8	4	no	—
88	D₄×C₄₇	—	8	4	no	—
89	D₄×C₄₇	—	8	2	no	—
90	D₄×C₄₇	—	8	2	no	—
91	C₂×C₄×C₄₇	—	2	2	no	—
92	C₂×C₄×C₄₇	—	2	2	no	—
93	C₂×C₄×C₄₇	—	4	2	no	—
94	C₂×C₄×C₄₇	—	4	2	no	—
95	C₂×C₄×C₄₇	—	4	2	no	—
96	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
99	C₂×C₄×C₄₇	#121	1	2	yes	—
100	C₈×C₄₇	—	2	4	no	—
101	C₄₇⋊C₈	—	4	4	no	—
102	C₄₇⋊C₈	—	8	2	no	—
103	#9423	—	47	1	no	maximal, Sylow
104	C₂²×C₄₇	—	2	1	no	—
105	C₂²×C₄₇	—	2	2	no	—
106	C₂²×C₄₇	—	4	2	no	—
107	C₂²×C₄₇	—	4	4	no	—
108	C₂²×C₄₇	—	8	2	no	—
109	C₂²×C₄₇	—	8	4	no	—
110	C₂²×C₄₇	—	16	2	no	—
111	C₂²×C₄₇	—	16	2	no	—
112	C₂²×C₄₇	#386	1	1	yes	characteristic
113	C₄×C₄₇	—	2	1	no	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	—	2	2	no	—
116	C₄×C₄₇	—	4	2	no	—
117	C₄×C₄₇	#453	1	2	yes	—
118	#3151	D₄₇	1	1	yes	characteristic
119	#2980	—	47	1	no	—
120	#1555	—	47	2	no	—
121	#1536	—	47	1	no	—
122	#1291	—	47	2	no	—
123	C₂×C₄₇	—	4	1	no	—
124	C₂×C₄₇	—	8	2	no	—
125	C₂×C₄₇	—	16	2	no	—
126	C₂×C₄₇	#1887	1	1	yes	characteristic
127	C₂×C₄₇	#1903	1	2	yes	—
128	C₂×AGL(1,ℤ/8)	—	2	2	no	—
129	#532	C₂×D₄₇	1	1	yes	characteristic
130	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
131	#496	—	2	2	no	—
132	#493	Dic₄₇	1	2	yes	—
133	#492	Dic₄₇	1	2	yes	—
134	#435	—	94	4	no	—
135	#432	—	47	2	no	—
136	#432	—	47	2	no	—
137	#408	—	94	2	no	—
138	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
139	#331	—	94	4	no	—
140	#329	—	94	2	no	—
141	C₄₇	#9423	1	1	yes	characteristic, complemented, Sylow
142	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
143	C₂²×D₄	—	2	2	no	—
144	C₂²×D₄	—	2	1	no	—
145	AGL(1,ℤ/8)	—	4	4	no	—
146	AGL(1,ℤ/8)	—	4	4	no	—
147	C₂×SD₁₆	—	2	4	no	—
148	C₂×D₈	—	2	4	no	—
149	C₂×M₁₆	—	2	1	no	—
150	C₂×M₁₆	—	94	2	no	—
151	C₂²×C₈	—	94	2	no	—
152	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
153	#127	—	2	2	no	—
154	#127	—	2	1	no	—
155	#127	C₂×Dic₄₇	1	2	yes	—
156	#127	C₂×Dic₄₇	1	1	yes	characteristic
157	#124	C₂²⋊D₄₇	1	2	yes	—
158	#121	—	2	2	no	—
159	C₄×D₄	—	2	2	no	—
160	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
161	C₄⋊C₈	—	47	4	no	—
162	C₄⋊C₈	—	94	2	no	—
163	C₂²⋊C₈	—	94	4	no	—
164	C₂²⋊C₈	—	94	2	no	—
165	C₂²⋊C₈	—	94	2	no	—
166	#97	—	2	1	no	—
167	#97	—	94	2	no	—
168	#97	—	94	2	no	—
169	C₄×C₈	C₂×Dic₄₇	1	2	yes	—
170	C₂⁴	—	4	1	no	—
171	#41	—	4	2	no	—
172	#41	—	4	2	no	—
173	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	2	no	—
176	C₂×D₄	—	2	2	no	—
177	C₂×D₄	—	2	4	no	—
178	C₂×D₄	—	4	2	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂×D₄	—	4	2	no	—
182	C₂×D₄	—	8	4	no	—
183	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	#10625352	1	2	yes	—
186	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
187	SD₁₆	—	4	8	no	—
188	D₈	—	4	8	no	—
189	M₁₆	—	2	4	no	—
190	M₁₆	—	376	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	94	4	no	—
193	C₂×C₈	—	376	2	no	—
194	C₂×C₈	—	188	2	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₂²⋊C₄	—	2	4	no	—
197	C₄²	D₄×D₄₇	1	2	yes	—
198	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
199	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
200	C₂³	—	2	2	no	—
201	C₂³	—	4	2	no	—
202	C₂³	—	8	1	no	—
203	C₂³	—	8	1	no	—
204	C₂³	—	8	4	no	—
205	C₂³	#13094005	1	1	yes	characteristic
206	Q₈	—	4	2	no	—
207	D₄	—	4	2	no	—
208	D₄	—	4	4	no	—
209	D₄	—	8	2	no	—
210	D₄	—	8	4	no	—
211	D₄	—	8	4	no	—
212	D₄	—	8	2	no	—
213	D₄	—	8	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
220	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
221	C₂×C₄	#13093992	1	1	yes	characteristic
222	C₂×C₄	#13093996	1	2	yes	—
223	C₈	—	2	4	no	—
224	C₈	—	376	2	no	—
225	C₈	—	188	4	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	2	no	—
228	C₂²	—	4	2	no	—
229	C₂²	—	4	4	no	—
230	C₂²	—	8	2	no	—
231	C₂²	—	8	4	no	—
232	C₂²	—	16	2	no	—
233	C₂²	—	16	2	no	—
234	C₂²	#15689003	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	2	no	—
237	C₄	—	2	2	no	—
238	C₄	—	4	2	no	—
239	C₄	#15689290	1	2	yes	—
240	C₂	—	4	1	no	—
241	C₂	—	8	2	no	—
242	C₂	—	16	2	no	—
243	C₂	#20243787	1	1	yes	characteristic
244	C₂	#20243870	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20252459

C₂

yes

maximal, characteristic, complemented

#20242102

C₂

yes

maximal, complemented

#20242023

C₂

yes

maximal, characteristic, complemented

#20241260

C₂

yes

maximal, complemented

C₄₇×#3151

C₂

yes

maximal, characteristic

#15689195

—

#15689180

C₂²

yes

—

#15689180

C₂²

yes

—

#15689090

—

#15688867

—

#15688863

—

C₂×AGL(1,ℤ/8)×C₄₇

—

C₄₇×#532

C₂²

yes

characteristic

C₂×#127×C₄₇

C₂²

yes

characteristic

C₄₇×#496

—

C₄₇×#493

C₄

yes

—

C₄₇×#492

C₄

yes

—

C₄×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

—

#13093935

—

C₂×#41×C₄₇

D₄

yes

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

AGL(1,ℤ/8)×C₄₇

—

AGL(1,ℤ/8)×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×D₈×C₄₇

—

C₂×M₁₆×C₄₇

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

characteristic

#127×C₄₇

—

#127×C₄₇

—

#127×C₄₇

C₂×C₄

yes

—

#127×C₄₇

C₂×C₄

yes

characteristic

#124×C₄₇

D₄

yes

—

#121×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#97×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

—

C₂⁴×C₄₇

—

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

C₂²⋊C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

—

SD₁₆×C₄₇

—

D₈×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#123

yes

characteristic

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

100

C₈×C₄₇

—

101

C₄₇⋊C₈

—

102

C₄₇⋊C₈

—

103

#9423

—

maximal, Sylow

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

—

111

C₂²×C₄₇

—

112

C₂²×C₄₇

#386

yes

characteristic

113

C₄×C₄₇

—

114

C₄×C₄₇

—

115

C₄×C₄₇

—

116

C₄×C₄₇

—

117

C₄×C₄₇

#453

yes

—

118

#3151

D₄₇

yes

characteristic

119

#2980

—

120

#1555

—

121

#1536

—

122

#1291

—

123

C₂×C₄₇

—

124

C₂×C₄₇

—

125

C₂×C₄₇

—

126

C₂×C₄₇

#1887

yes

characteristic

127

C₂×C₄₇

#1903

yes

—

128

C₂×AGL(1,ℤ/8)

—

129

#532

C₂×D₄₇

yes

characteristic

130

C₂×#127

C₂×D₄₇

yes

characteristic

131

#496

—

132

#493

Dic₄₇

yes

—

133

#492

Dic₄₇

yes

—

134

#435

—

135

#432

—

136

#432

—

137

#408

—

138

C₄×M₁₆

C₂×D₄₇

yes

characteristic

139

#331

—

140

#329

—

141

C₄₇

#9423

yes

characteristic, complemented, Sylow

142

C₂×#41

C₂²⋊D₄₇

yes

—

143

C₂²×D₄

—

144

C₂²×D₄

—

145

AGL(1,ℤ/8)

—

146

AGL(1,ℤ/8)

—

147

C₂×SD₁₆

—

148

C₂×D₈

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

151

C₂²×C₈

—

152

C₄⋊Q₈

C₂×Dic₄₇

yes

characteristic

153

#127

—

154

#127

—

155

#127

C₂×Dic₄₇

yes

—

156

#127

C₂×Dic₄₇

yes

characteristic

157

#124

C₂²⋊D₄₇

yes

—

158

#121

—

159

C₄×D₄

—

160

C₂×C₄²

C₂²×D₄₇

yes

characteristic

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₂²⋊C₈

—

164

C₂²⋊C₈

—

165

C₂²⋊C₈

—

166

#97

—

167

#97

—

168

#97

—

169

C₄×C₈

C₂×Dic₄₇

yes

—

170

C₂⁴

—

171

#41

—

172

#41

—

173

C₂×Q₈

C₂²⋊Dic₄₇

yes

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

C₂²⋊Dic₄₇

yes

—

184

C₂²×C₄

—

185

C₂²×C₄

#10625352

yes

—

186

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

187

SD₁₆

—

188

D₈

—

189

M₁₆

—

190

M₁₆

—

376

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

376

—

194

C₂×C₈

—

188

—

195

C₄⋊C₄

—

196

C₂²⋊C₄

—

197

C₄²

D₄×D₄₇

yes

—

198

C₄²

C₂²×Dic₄₇

yes

characteristic

199

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

#13094005

yes

characteristic

206

Q₈

—

207

D₄

—

208

D₄

—

209

D₄

—

210

D₄

—

211

D₄

—

212

D₄

—

213

D₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

220

C₂×C₄

D₄×Dic₄₇

yes

—

221

C₂×C₄

#13093992

yes

characteristic

222

C₂×C₄

#13093996

yes

—

223

C₈

—

224

C₈

—

376

—

225

C₈

—

188

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

#15689003

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

#15689290

yes

—

240

C₂

—

241

C₂

—

242

C₂

—

243

C₂

#20243787

yes

characteristic

244

C₂

#20243870

yes

—

	subgroup	G/H
center	C₂²	#15689003
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting, prime radical	C₄₇×#3151	C₂
socle	C₂²×C₄₇	#386
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#3151	D₄₇
hypocenter	C₄₇	#9423
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3151

subgroup

G/H

center

C₂²

#15689003

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting, prime radical

C₄₇×#3151

C₂

socle

C₂²×C₄₇

#386

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3151

N	H ≅ G/N	type
1. #20252459	C₂	semidirect
2. #20242102	C₂	semidirect
3. #20242023	C₂	semidirect
4. #20241260	C₂	semidirect
141. C₄₇	#9423	semidirect

H ≅ G/N

type

1. #20252459

C₂

semidirect

2. #20242102

C₂

semidirect

3. #20242023

C₂

semidirect

4. #20241260

C₂

semidirect

141. C₄₇

#9423

semidirect

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

subgroup	index
#20252459	2
#20242102	2
#20242023	2
#20241260	2
C₄₇×#3151	2
#9423	47

subgroup

index

C₄₇×#3151

Subgroups — #26113806

Conjugacy classes of subgroups

Complements

Maximal subgroups