Group #25012809 — subgroups

Subgroups — #25012809

Order 11008.

454 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14582854	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#19132672	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10621877	C₄	1	1	yes	characteristic
6	C₂×#13063284	C₄	1	1	yes	characteristic
7	C₂²×C₄₃⋊C₁₆	C₂²	1	2	yes	—
8	#14582854	—	2	2	no	—
9	#14582854	—	2	2	no	—
10	C₂×#13063235	C₄	1	2	yes	—
11	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
12	C₂²⋊(C₄₃⋊C₁₆)	—	2	2	no	—
13	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
15	C₄₃×C₂²⋊C₁₆	—	2	2	no	—
16	C₂×#10621877	—	2	2	no	—
17	C₂×#10621877	—	2	4	no	—
18	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
19	#13063284	—	2	2	no	—
20	#13063284	—	2	2	no	—
21	C₂×C₄⋊Dic₄₃	C₈	1	1	yes	characteristic
22	C₂×C₄⋊Dic₄₃	C₈	1	1	yes	characteristic
23	C₂×C₂²⋊Dic₄₃	C₈	1	2	yes	—
24	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₄₃⋊C₁₆	—	2	2	no	—
26	C₂×C₄₃⋊C₁₆	—	2	4	no	—
27	#13063235	—	2	4	no	—
28	C₈×Dic₄₃	—	2	2	no	—
29	C₈×Dic₄₃	—	2	2	no	—
30	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₄₃	—	2	4	no	—
32	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₄₃	D₄	1	2	yes	—
34	C₂²×C₈×C₄₃	D₄	1	2	yes	—
35	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
36	C₂×C₁₆×C₄₃	—	2	2	no	—
37	C₂×C₁₆×C₄₃	—	2	4	no	—
38	C₂⁴×C₄₃	C₂×C₈	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	—	2	2	no	—
40	C₂²×C₄×C₄₃	—	2	2	no	—
41	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
42	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
43	C₂²×C₄×C₄₃	M₁₆	1	2	yes	—
44	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×Dic₄₃	C₂×C₈	1	2	yes	—
46	C₂²×Dic₄₃	C₂×C₈	1	2	yes	—
47	C₂×C₈×C₄₃	—	2	2	no	—
48	C₂×C₈×C₄₃	—	2	4	no	—
49	C₂×C₈×C₄₃	—	2	4	no	—
50	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₈×C₄₃	#41	1	4	yes	—
54	C₂²⋊Dic₄₃	—	2	4	no	—
55	C₄⋊Dic₄₃	—	2	2	no	—
56	C₄⋊Dic₄₃	—	2	2	no	—
57	C₄×Dic₄₃	—	2	2	no	—
58	C₄×Dic₄₃	—	2	2	no	—
59	#10621877	—	2	8	no	—
60	C₂×C₄₃⋊C₈	—	2	2	no	—
61	C₂×C₄₃⋊C₈	—	2	2	no	—
62	C₂×C₄₃⋊C₈	M₁₆	1	4	yes	—
63	C₁₆×C₄₃	—	4	2	no	—
64	C₄₃⋊C₁₆	—	4	2	no	—
65	C₂³×C₄₃	—	2	2	no	—
66	C₂³×C₄₃	—	2	2	no	—
67	C₂³×C₄₃	—	2	2	no	—
68	C₂³×C₄₃	C₂²⋊C₈	1	2	yes	—
69	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
70	C₂×C₄×C₄₃	—	2	2	no	—
71	C₂×C₄×C₄₃	—	2	2	no	—
72	C₂×C₄×C₄₃	—	2	2	no	—
73	C₂×C₄×C₄₃	—	2	4	no	—
74	C₂×C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
75	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₄₃	#117	1	2	yes	—
77	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
78	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
79	C₂×Dic₄₃	—	2	2	no	—
80	C₂×Dic₄₃	—	2	2	no	—
81	C₂×Dic₄₃	—	2	4	no	—
82	C₂×Dic₄₃	—	2	4	no	—
83	C₈×C₄₃	—	2	2	no	—
84	C₈×C₄₃	#123	1	2	yes	—
85	C₈×C₄₃	#123	1	2	yes	—
86	C₄₃⋊C₈	—	2	4	no	—
87	#12845	—	43	1	no	maximal, Sylow
88	C₂²×C₄₃	—	2	2	no	—
89	C₂²×C₄₃	—	2	2	no	—
90	C₂²×C₄₃	—	2	2	no	—
91	C₂²×C₄₃	—	4	4	no	—
92	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
93	C₂²×C₄₃	#431	1	2	yes	—
94	C₂²×C₄₃	#504	1	2	yes	—
95	C₂²×C₄₃	#504	1	2	yes	—
96	C₄×C₄₃	—	2	2	no	—
97	C₄×C₄₃	#381	1	1	yes	characteristic
98	C₄×C₄₃	#407	1	1	yes	characteristic
99	C₄×C₄₃	#432	1	2	yes	—
100	Dic₄₃	—	4	2	no	—
101	Dic₄₃	—	4	2	no	—
102	C₂×#405	—	43	1	no	—
103	C₂×C₂²⋊C₁₆	—	43	1	no	—
104	C₂×C₂²⋊C₁₆	D₄₃	1	1	yes	characteristic
105	#1374	—	43	4	no	—
106	C₂×C₄₃	—	4	2	no	—
107	C₂×C₄₃	#1817	1	1	yes	characteristic
108	C₂×C₄₃	#2113	1	1	yes	characteristic
109	C₂×C₄₃	#2113	1	1	yes	characteristic
110	C₂×C₄₃	#2164	1	4	yes	—
111	C₂²×M₁₆	—	43	1	no	—
112	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
113	C₂×#117	—	43	1	no	—
114	C₂²×C₁₆	—	43	2	no	—
115	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
116	#405	—	86	2	no	—
117	#405	—	86	2	no	—
118	C₂×#97	—	43	2	no	—
119	C₂×C₄×C₈	—	43	2	no	—
120	C₂²⋊C₁₆	—	2	2	no	—
121	C₂²⋊C₁₆	—	86	2	no	—
122	C₄₃	#12845	1	1	yes	characteristic, complemented, Sylow
123	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
124	C₂×M₁₆	—	86	4	no	—
125	C₂×M₁₆	—	86	2	no	—
126	C₂²×C₈	—	2	4	no	—
127	C₂²×C₈	—	43	2	no	—
128	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
129	C₂²×C₈	D₁₇₂	1	2	yes	—
130	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
131	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
132	#117	—	86	2	no	—
133	#117	—	86	2	no	—
134	C₂×C₄⋊C₄	—	43	1	no	—
135	C₂×C₄⋊C₄	—	43	1	no	—
136	C₂×C₂²⋊C₄	—	43	2	no	—
137	C₂×C₄²	—	43	2	no	—
138	C₂×C₁₆	—	2	4	no	—
139	C₂×C₁₆	—	2	2	no	—
140	C₂×C₁₆	—	86	2	no	—
141	C₂×C₁₆	—	86	4	no	—
142	#97	—	86	4	no	—
143	C₄×C₈	—	86	2	no	—
144	C₄×C₈	—	86	2	no	—
145	C₂⁴	C₈×D₄₃	1	1	yes	characteristic
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	43	2	no	—
149	C₂²×C₄	—	43	2	no	—
150	C₂²×C₄	C₈×D₄₃	1	1	yes	characteristic
151	C₂²×C₄	#10621872	1	2	yes	—
152	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
153	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
154	M₁₆	—	86	8	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	2	4	no	—
158	C₂×C₈	—	43	4	no	—
159	C₂×C₈	—	86	2	no	—
160	C₂×C₈	—	86	2	no	—
161	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
162	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
163	C₂×C₈	#10621900	1	4	yes	—
164	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
165	C₄⋊C₄	—	86	2	no	—
166	C₄⋊C₄	—	86	2	no	—
167	C₂²⋊C₄	—	86	4	no	—
168	C₄²	—	86	2	no	—
169	C₄²	—	86	2	no	—
170	C₁₆	—	4	2	no	—
171	C₁₆	—	172	2	no	—
172	C₂³	—	2	2	no	—
173	C₂³	—	2	2	no	—
174	C₂³	—	2	2	no	—
175	C₂³	(C₂×D₄₃)⋊C₈	1	2	yes	—
176	C₂³	C₂×C₈×D₄₃	1	1	yes	characteristic
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	86	4	no	—
182	C₂×C₄	—	86	4	no	—
183	C₂×C₄	—	86	2	no	—
184	C₂×C₄	—	86	2	no	—
185	C₂×C₄	(C₂×D₄₃)⋊C₈	1	2	yes	—
186	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
187	C₂×C₄	#13063281	1	2	yes	—
188	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
189	C₂×C₄	C₂×#10621872	1	1	yes	characteristic
190	C₈	—	2	2	no	—
191	C₈	—	86	4	no	—
192	C₈	#13063306	1	2	yes	—
193	C₈	#13063309	1	2	yes	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	4	4	no	—
198	C₂²	C₂×(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
199	C₂²	#14582949	1	2	yes	—
200	C₂²	#14583315	1	2	yes	—
201	C₂²	#14583317	1	2	yes	—
202	C₄	—	2	2	no	—
203	C₄	—	172	2	no	—
204	C₄	—	172	2	no	—
205	C₄	#14582760	1	1	yes	characteristic
206	C₄	#14582862	1	1	yes	characteristic
207	C₄	#14582953	1	2	yes	—
208	C₂	—	4	2	no	—
209	C₂	#19134661	1	1	yes	characteristic
210	C₂	#19136208	1	1	yes	characteristic
211	C₂	#19136210	1	1	yes	characteristic
212	C₂	#19136399	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14582854

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₄₃⋊C₁₆)

C₂

yes

maximal, characteristic

#19132672

C₂

yes

maximal, complemented

C₂×C₄₃×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×#10621877

C₄

yes

characteristic

C₂×#13063284

C₄

yes

characteristic

C₂²×C₄₃⋊C₁₆

C₂²

yes

—

#14582854

—

#14582854

—

C₂×#13063235

C₄

yes

—

C₂×C₈×Dic₄₃

C₂²

yes

—

C₂²⋊(C₄₃⋊C₁₆)

—

C₂³×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₁₆×C₄₃

C₂²

yes

—

C₄₃×C₂²⋊C₁₆

—

C₂×#10621877

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

#13063284

—

#13063284

—

C₂×C₄⋊Dic₄₃

C₈

yes

characteristic

C₂×C₄⋊Dic₄₃

C₈

yes

characteristic

C₂×C₂²⋊Dic₄₃

C₈

yes

—

C₂×C₄×Dic₄₃

C₂×C₄

yes

—

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

—

#13063235

—

C₈×Dic₄₃

—

C₈×Dic₄₃

—

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂⁴×C₄₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₃

M₁₆

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×Dic₄₃

C₂×C₈

yes

—

C₂²×Dic₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

M₁₆

yes

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²⋊C₈

yes

—

C₂³×C₄₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#123

yes

—

C₈×C₄₃

#123

yes

—

C₄₃⋊C₈

—

#12845

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₄₃

#431

yes

—

C₂²×C₄₃

#504

yes

—

C₂²×C₄₃

#504

yes

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

100

Dic₄₃

—

101

Dic₄₃

—

102

C₂×#405

—

103

C₂×C₂²⋊C₁₆

—

104

C₂×C₂²⋊C₁₆

D₄₃

yes

characteristic

105

#1374

—

106

C₂×C₄₃

—

107

C₂×C₄₃

#1817

yes

characteristic

108

C₂×C₄₃

#2113

yes

characteristic

109

C₂×C₄₃

#2113

yes

characteristic

110

C₂×C₄₃

#2164

yes

—

111

C₂²×M₁₆

—

112

C₂³×C₈

C₂×D₄₃

yes

characteristic

113

C₂×#117

—

114

C₂²×C₁₆

—

115

C₂²×C₁₆

C₂×D₄₃

yes

—

116

#405

—

117

#405

—

118

C₂×#97

—

119

C₂×C₄×C₈

—

120

C₂²⋊C₁₆

—

121

C₂²⋊C₁₆

—

122

C₄₃

#12845

yes

characteristic, complemented, Sylow

123

C₂³×C₄

C₄×D₄₃

yes

characteristic

124

C₂×M₁₆

—

125

C₂×M₁₆

—

126

C₂²×C₈

—

127

C₂²×C₈

—

128

C₂²×C₈

C₄×D₄₃

yes

characteristic

129

C₂²×C₈

D₁₇₂

yes

—

130

C₂²×C₈

C₂²⋊D₄₃

yes

—

131

C₂²×C₈

C₂²×D₄₃

yes

characteristic

132

#117

—

133

#117

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₄²

—

138

C₂×C₁₆

—

139

C₂×C₁₆

—

140

C₂×C₁₆

—

141

C₂×C₁₆

—

142

#97

—

143

C₄×C₈

—

144

C₄×C₈

—

145

C₂⁴

C₈×D₄₃

yes

characteristic

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

C₈×D₄₃

yes

characteristic

151

C₂²×C₄

#10621872

yes

—

152

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

153

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

154

M₁₆

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

162

C₂×C₈

C₂×D₁₇₂

yes

characteristic

163

C₂×C₈

#10621900

yes

—

164

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₂²⋊C₄

—

168

C₄²

—

169

C₄²

—

170

C₁₆

—

171

C₁₆

—

172

—

172

C₂³

—

173

C₂³

—

174

C₂³

—

175

C₂³

(C₂×D₄₃)⋊C₈

yes

—

176

C₂³

C₂×C₈×D₄₃

yes

characteristic

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

—

186

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

187

C₂×C₄

#13063281

yes

—

188

C₂×C₄

M₁₆×D₄₃

yes

—

189

C₂×C₄

C₂×#10621872

yes

characteristic

190

C₈

—

191

C₈

—

192

C₈

#13063306

yes

—

193

C₈

#13063309

yes

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

C₂×(C₂×D₄₃)⋊C₈

yes

characteristic

199

C₂²

#14582949

yes

—

200

C₂²

#14583315

yes

—

201

C₂²

#14583317

yes

—

202

C₄

—

203

C₄

—

172

—

204

C₄

—

172

—

205

C₄

#14582760

yes

characteristic

206

C₄

#14582862

yes

characteristic

207

C₄

#14582953

yes

—

208

C₂

—

209

C₂

#19134661

yes

characteristic

210

C₂

#19136208

yes

characteristic

211

C₂

#19136210

yes

characteristic

212

C₂

#19136399

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₄₃
commutator, socle	C₂³×C₄₃	C₂²×C₈
Fitting	C₂×C₄₃×C₂²⋊C₁₆	C₂
prime radical	C₂⁴×C₄₃	C₂×C₈
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×C₂²⋊C₁₆	D₄₃
hypocenter	C₄₃	#12845
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₁₆

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₄₃

commutator, socle

C₂³×C₄₃

C₂²×C₈

Fitting

C₂×C₄₃×C₂²⋊C₁₆

C₂

prime radical

C₂⁴×C₄₃

C₂×C₈

cosocle

C₂²×C₈×C₄₃

C₂³

hypercenter

C₂×C₂²⋊C₁₆

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₁₆

N	H ≅ G/N	type
3. #19132672	C₂	semidirect
122. C₄₃	#12845	semidirect

H ≅ G/N

type

3. #19132672

C₂

semidirect

122. C₄₃

#12845

semidirect

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

subgroup	index
C₂×#14582854	2
C₂×C₂²⋊(C₄₃⋊C₁₆)	2
#19132672	2
C₂×C₄₃×C₂²⋊C₁₆	2
#12845	43

subgroup

index

C₂×#14582854

C₂×C₂²⋊(C₄₃⋊C₁₆)

#19132672

C₂×C₄₃×C₂²⋊C₁₆

#12845

Subgroups — #25012809

Conjugacy classes of subgroups

Complements

Maximal subgroups