Group #25012779 — subgroups

Subgroups — #25012779

Order 11008.

374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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×#13063264	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582729	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134630	C₂	1	2	yes	maximal
4	#19132688	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
7	C₂×#13063264	—	2	2	no	—
8	C₂×#13063264	—	2	2	no	—
9	C₂×#13063264	C₄	1	4	yes	—
10	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₂×#13063261	C₂²	1	2	yes	—
12	#14582862	—	2	2	no	—
13	#14582729	—	2	2	no	—
14	#14582663	—	2	2	no	—
15	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#108×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#368	—	2	2	no	—
18	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
19	C₂×#10621877	—	2	2	no	—
20	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
21	C₂×C₈×D₄₃	—	2	1	no	—
22	C₂×C₈×D₄₃	—	2	1	no	—
23	C₂×C₈×D₄₃	—	2	1	no	—
24	C₂×C₈×D₄₃	—	2	1	no	—
25	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
26	C₂×C₈×D₄₃	Q₈	1	2	yes	—
27	#13063264	—	2	8	no	—
28	C₂×C₄₃⋊C₁₆	—	2	1	no	—
29	C₂×C₄₃⋊C₁₆	—	2	1	no	—
30	C₂×C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
31	#13063261	—	2	2	no	—
32	#13063261	—	2	2	no	—
33	(C₂×D₄₃)⋊C₈	—	4	4	no	—
34	C₂×M₁₆×C₄₃	—	2	2	no	—
35	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
36	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
37	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
38	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
39	#108×C₄₃	—	2	2	no	—
40	#108×C₄₃	—	2	2	no	—
41	C₂³×D₄₃	Q₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₄₃	Q₁₆	1	1	yes	characteristic
44	C₂×C₄×D₄₃	—	2	1	no	—
45	C₂×C₄×D₄₃	—	2	1	no	—
46	C₂×C₄×D₄₃	—	2	1	no	—
47	C₂×C₄×D₄₃	—	2	1	no	—
48	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
49	C₂×C₄×D₄₃	D₈	1	2	yes	—
50	M₁₆×C₄₃	—	4	2	no	—
51	M₁₆×C₄₃	—	4	2	no	—
52	C₂×C₈×C₄₃	—	4	2	no	—
53	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
57	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
58	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
59	#10621877	—	4	2	no	—
60	#10621877	—	4	2	no	—
61	C₂×C₄₃⋊C₈	—	2	1	no	—
62	C₂×C₄₃⋊C₈	—	2	1	no	—
63	C₂×C₄₃⋊C₈	—	4	2	no	—
64	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
65	C₈×D₄₃	—	2	2	no	—
66	C₈×D₄₃	—	2	2	no	—
67	C₈×D₄₃	—	2	2	no	—
68	C₈×D₄₃	—	2	2	no	—
69	C₁₆×C₄₃	C₂²⋊C₄	1	4	yes	—
70	C₄₃⋊C₁₆	—	2	2	no	—
71	C₂³×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
72	C₂²×D₄₃	—	2	1	no	—
73	C₂²×D₄₃	—	2	1	no	—
74	C₂²×D₄₃	—	4	2	no	—
75	C₂²×D₄₃	#107	1	2	yes	—
76	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
78	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
79	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
81	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
82	C₂×Dic₄₃	—	2	1	no	—
83	C₂×Dic₄₃	—	2	1	no	—
84	C₂×Dic₄₃	#107	1	2	yes	—
85	C₄×D₄₃	—	2	2	no	—
86	C₄×D₄₃	—	2	2	no	—
87	C₄×D₄₃	—	2	2	no	—
88	C₄×D₄₃	—	2	2	no	—
89	C₈×C₄₃	—	8	2	no	—
90	C₈×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₈×C₄₃	#117	1	1	yes	characteristic
92	C₈×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
93	C₈×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
94	C₄₃⋊C₈	—	2	2	no	—
95	C₄₃⋊C₈	—	8	2	no	—
96	#12838	—	43	1	no	maximal, Sylow
97	C₂²×C₄₃	—	2	2	no	—
98	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
99	C₂²×C₄₃	#467	1	1	yes	characteristic
100	C₂²×C₄₃	#467	1	1	yes	characteristic
101	C₂×D₄₃	—	2	2	no	—
102	C₂×D₄₃	—	2	4	no	—
103	C₂×D₄₃	—	4	2	no	—
104	C₂×D₄₃	—	4	2	no	—
105	C₄×C₄₃	#380	1	1	yes	characteristic
106	C₄×C₄₃	#427	1	1	yes	characteristic
107	C₄×C₄₃	#466	1	1	yes	characteristic
108	C₄×C₄₃	#466	1	1	yes	characteristic
109	Dic₄₃	—	2	2	no	—
110	C₂²×M₃₂	—	43	1	no	—
111	C₂×#368	—	43	1	no	—
112	C₂×#368	D₄₃	1	1	yes	characteristic, complemented
113	#1810	—	43	2	no	—
114	#1381	—	43	2	no	—
115	C₂×C₄₃	—	2	1	no	—
116	C₂×C₄₃	—	2	1	no	—
117	C₂×C₄₃	#1808	1	1	yes	characteristic
118	C₂×C₄₃	#2161	1	2	yes	—
119	D₄₃	—	4	2	no	—
120	C₂³×C₈	—	43	1	no	—
121	C₂×M₃₂	—	43	4	no	—
122	C₂×M₃₂	—	86	2	no	—
123	C₂×M₃₂	—	86	2	no	—
124	C₂²×C₁₆	—	43	1	no	—
125	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
126	C₂×#108	—	43	2	no	—
127	C₂×#108	C₂×D₄₃	1	2	yes	—
128	#407	—	86	2	no	—
129	#368	—	2	2	no	—
130	#368	—	86	2	no	—
131	#341	—	86	2	no	—
132	C₄₃	#12838	1	1	yes	characteristic, complemented, Sylow
133	C₂³×C₄	—	43	1	no	—
134	C₂×M₁₆	—	2	2	no	—
135	C₂×M₁₆	—	86	2	no	—
136	C₂²×C₈	—	43	1	no	—
137	C₂²×C₈	—	43	2	no	—
138	C₂²×C₈	—	43	2	no	—
139	C₂²×C₈	—	86	1	no	—
140	C₂²×C₈	—	86	1	no	—
141	C₂²×C₈	—	86	1	no	—
142	C₂²×C₈	—	86	1	no	—
143	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
144	M₃₂	—	86	8	no	—
145	C₂×C₁₆	—	43	2	no	—
146	C₂×C₁₆	—	86	1	no	—
147	C₂×C₁₆	—	86	1	no	—
148	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
149	C₂×C₁₆	D₁₇₂	1	2	yes	—
150	C₂×C₁₆	C₂²⋊D₄₃	1	2	yes	—
151	#108	—	2	2	no	—
152	#108	—	2	2	no	—
153	#108	—	86	2	no	—
154	#108	—	86	2	no	—
155	C₂²⋊C₈	—	172	4	no	—
156	C₂⁴	—	43	1	no	—
157	C₂²×C₄	—	43	1	no	—
158	C₂²×C₄	—	43	2	no	—
159	C₂²×C₄	—	43	2	no	—
160	C₂²×C₄	—	86	1	no	—
161	C₂²×C₄	—	86	1	no	—
162	C₂²×C₄	—	86	1	no	—
163	C₂²×C₄	—	86	1	no	—
164	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
165	M₁₆	—	4	2	no	—
166	M₁₆	—	4	2	no	—
167	M₁₆	—	172	2	no	—
168	M₁₆	—	172	2	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	43	2	no	—
171	C₂×C₈	—	86	1	no	—
172	C₂×C₈	—	86	1	no	—
173	C₂×C₈	—	86	2	no	—
174	C₂×C₈	—	86	2	no	—
175	C₂×C₈	—	86	2	no	—
176	C₂×C₈	—	86	2	no	—
177	C₂×C₈	—	172	2	no	—
178	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
179	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
180	C₂×C₈	#10621900	1	1	yes	characteristic
181	C₂×C₈	Q₈×D₄₃	1	1	yes	characteristic
182	C₂×C₈	#10621902	1	1	yes	characteristic
183	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
184	C₁₆	—	86	2	no	—
185	C₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	—
186	C₂³	—	43	2	no	—
187	C₂³	—	86	1	no	—
188	C₂³	—	86	1	no	—
189	C₂³	—	172	2	no	—
190	C₂³	Q₁₆×D₄₃	1	1	yes	characteristic
191	C₂×C₄	—	43	2	no	—
192	C₂×C₄	—	86	1	no	—
193	C₂×C₄	—	86	1	no	—
194	C₂×C₄	—	86	2	no	—
195	C₂×C₄	—	86	2	no	—
196	C₂×C₄	—	86	2	no	—
197	C₂×C₄	—	86	2	no	—
198	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
199	C₂×C₄	#13063296	1	1	yes	characteristic
200	C₂×C₄	#13063300	1	1	yes	characteristic
201	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
202	C₂×C₄	#13063344	1	1	yes	characteristic
203	C₂×C₄	#13063348	1	1	yes	characteristic
204	C₈	—	8	2	no	—
205	C₈	—	86	2	no	—
206	C₈	—	344	2	no	—
207	C₈	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
208	C₈	#13063283	1	1	yes	characteristic
209	C₈	#13063301	1	1	yes	characteristic
210	C₈	#13063305	1	1	yes	characteristic
211	C₂²	—	2	2	no	—
212	C₂²	—	86	4	no	—
213	C₂²	—	86	2	no	—
214	C₂²	—	172	2	no	—
215	C₂²	—	172	2	no	—
216	C₂²	#107×D₄₃	1	1	yes	characteristic
217	C₂²	#14583137	1	1	yes	characteristic
218	C₂²	#14583141	1	1	yes	characteristic
219	C₄	—	86	2	no	—
220	C₄	#14582756	1	1	yes	characteristic
221	C₄	#14582936	1	1	yes	characteristic
222	C₄	#14583132	1	1	yes	characteristic
223	C₄	#14583136	1	1	yes	characteristic
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	—	172	2	no	—
227	C₂	#19134621	1	1	yes	characteristic
228	C₂	#19136388	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#13063264

C₂

yes

maximal, characteristic

C₂×#14582729

C₂

yes

maximal, characteristic, complemented

#19134630

C₂

yes

maximal

#19132688

C₂

yes

maximal, complemented

C₂×C₄₃×#368

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₄₃

C₂²

yes

—

—

C₄

yes

—

C₂²×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×#13063261

C₂²

yes

—

#14582862

—

#14582729

—

#14582663

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×#108×C₄₃

C₂²

yes

—

C₄₃×#368

—

C₂²×C₄×D₄₃

D₄

yes

characteristic

C₂×#10621877

—

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

C₂×C₄

yes

—

C₂×C₈×D₄₃

Q₈

yes

—

#13063264

—

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

#13063261

—

#13063261

—

(C₂×D₄₃)⋊C₈

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₁₆×C₄₃

D₄

yes

—

C₂×C₁₆×C₄₃

D₄

yes

—

#108×C₄₃

—

#108×C₄₃

—

C₂³×D₄₃

Q₁₆

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

Q₁₆

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₄⋊C₄

yes

—

C₂×C₄×D₄₃

D₈

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×Q₈

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

—

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

C₂²⋊C₄

yes

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×Q₁₆

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

#107

yes

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×D₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#107

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₄₃

#117

yes

characteristic

C₈×C₄₃

C₂²⋊Q₈

yes

characteristic

C₈×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#12838

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

100

C₂²×C₄₃

#467

yes

characteristic

101

C₂×D₄₃

—

102

C₂×D₄₃

—

103

C₂×D₄₃

—

104

C₂×D₄₃

—

105

C₄×C₄₃

#380

yes

characteristic

106

C₄×C₄₃

#427

yes

characteristic

107

C₄×C₄₃

#466

yes

characteristic

108

C₄×C₄₃

#466

yes

characteristic

109

Dic₄₃

—

110

C₂²×M₃₂

—

111

C₂×#368

—

112

C₂×#368

D₄₃

yes

characteristic, complemented

113

#1810

—

114

#1381

—

115

C₂×C₄₃

—

116

C₂×C₄₃

—

117

C₂×C₄₃

#1808

yes

characteristic

118

C₂×C₄₃

#2161

yes

—

119

D₄₃

—

120

C₂³×C₈

—

121

C₂×M₃₂

—

122

C₂×M₃₂

—

123

C₂×M₃₂

—

124

C₂²×C₁₆

—

125

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

126

C₂×#108

—

127

C₂×#108

C₂×D₄₃

yes

—

128

#407

—

129

#368

—

130

#368

—

131

#341

—

132

C₄₃

#12838

yes

characteristic, complemented, Sylow

133

C₂³×C₄

—

134

C₂×M₁₆

—

135

C₂×M₁₆

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₂²×C₈

C₂²×D₄₃

yes

characteristic

144

M₃₂

—

145

C₂×C₁₆

—

146

C₂×C₁₆

—

147

C₂×C₁₆

—

148

C₂×C₁₆

C₄×D₄₃

yes

—

149

C₂×C₁₆

D₁₇₂

yes

—

150

C₂×C₁₆

C₂²⋊D₄₃

yes

—

151

#108

—

152

#108

—

153

#108

—

154

#108

—

155

C₂²⋊C₈

—

172

—

156

C₂⁴

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

D₄×D₄₃

yes

characteristic

165

M₁₆

—

166

M₁₆

—

167

M₁₆

—

172

—

168

M₁₆

—

172

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

172

—

178

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

179

C₂×C₈

C₂×D₁₇₂

yes

characteristic

180

C₂×C₈

#10621900

yes

characteristic

181

C₂×C₈

Q₈×D₄₃

yes

characteristic

182

C₂×C₈

#10621902

yes

characteristic

183

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

184

C₁₆

—

185

C₁₆

(C₂×D₄₃)⋊C₄

yes

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

172

—

190

C₂³

Q₁₆×D₄₃

yes

characteristic

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

C₄⋊C₄×D₄₃

yes

characteristic

199

C₂×C₄

#13063296

yes

characteristic

200

C₂×C₄

#13063300

yes

characteristic

201

C₂×C₄

D₈×D₄₃

yes

characteristic

202

C₂×C₄

#13063344

yes

characteristic

203

C₂×C₄

#13063348

yes

characteristic

204

C₈

—

205

C₈

—

206

C₈

—

344

—

207

C₈

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

208

C₈

#13063283

yes

characteristic

209

C₈

#13063301

yes

characteristic

210

C₈

#13063305

yes

characteristic

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

172

—

215

C₂²

—

172

—

216

C₂²

#107×D₄₃

yes

characteristic

217

C₂²

#14583137

yes

characteristic

218

C₂²

#14583141

yes

characteristic

219

C₄

—

220

C₄

#14582756

yes

characteristic

221

C₄

#14582936

yes

characteristic

222

C₄

#14583132

yes

characteristic

223

C₄

#14583136

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

—

172

—

227

C₂

#19134621

yes

characteristic

228

C₂

#19136388

yes

—

	subgroup	G/H
center	C₂×C₄	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#368	C₂
socle	C₂²×C₄₃	C₂×#107
prime radical	C₂³×D₄₃	Q₁₆
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#368	D₄₃
hypocenter	C₄₃	#12838
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

subgroup

G/H

center

C₂×C₄

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#368

C₂

socle

C₂²×C₄₃

C₂×#107

prime radical

C₂³×D₄₃

Q₁₆

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

N	H ≅ G/N	type
2. C₂×#14582729	C₂	semidirect
4. #19132688	C₂	semidirect
5. C₂×C₄₃×#368	C₂	semidirect
112. C₂×#368	D₄₃	semidirect
132. C₄₃	#12838	semidirect

H ≅ G/N

type

2. C₂×#14582729

C₂

semidirect

4. #19132688

C₂

semidirect

5. C₂×C₄₃×#368

C₂

semidirect

112. C₂×#368

D₄₃

semidirect

132. C₄₃

#12838

semidirect

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

subgroup	index
C₂²×#13063264	2
C₂×#14582729	2
#19134630	2
#19132688	2
C₂×C₄₃×#368	2
#12838	43

subgroup

index

C₂×C₄₃×#368

Subgroups — #25012779

Conjugacy classes of subgroups

Complements

Maximal subgroups