Group #25011827 — subgroups

Subgroups — #25011827

Order 11008.

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

normal subgroups only

This group has 442 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	C₄×#13063347	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582707	C₂	1	2	yes	maximal
3	C₄×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132691	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063347	C₂²	1	1	yes	characteristic
7	C₄×#10621898	—	2	1	no	—
8	C₄×Dic₁₇₂	C₄	1	2	yes	—
9	C₄×#10621873	—	2	2	no	—
10	C₄×D₃₄₄	C₄	1	2	yes	—
11	C₂×#13063261	C₂²	1	2	yes	—
12	#14582937	C₂²	1	1	yes	characteristic
13	#14582896	—	2	1	no	—
14	C₄×#10621877	—	2	1	no	—
15	#14582707	C₄	1	8	yes	complemented
16	#14582664	—	2	1	no	—
17	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#346	—	2	2	no	—
20	C₂×#10621898	—	2	1	no	—
21	#13063347	—	2	2	no	—
22	#13063347	C₂×C₄	1	4	yes	—
23	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
24	C₂×#10621873	—	2	1	no	—
25	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
26	C₂×#10621877	—	2	2	no	—
27	C₄×Dic₈₆	—	2	2	no	—
28	C₄×D₁₇₂	—	2	2	no	—
29	C₄×C₂²⋊D₄₃	—	4	2	no	—
30	#13063284	—	2	1	no	—
31	#13063282	—	4	1	no	—
32	C₄²×D₄₃	—	4	1	no	—
33	#13063261	—	2	2	no	—
34	#13063261	C₂×C₄	1	4	yes	complemented
35	#13063259	C₂×C₄	1	2	yes	—
36	#13063257	—	2	1	no	—
37	#13063250	—	2	2	no	—
38	#13063247	—	2	2	no	—
39	#13063236	—	4	1	no	—
40	C₄×C₄₃⋊C₈	—	4	1	no	—
41	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
43	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
44	C₂×C₁₆×C₄₃	—	2	2	no	—
45	C₂×C₁₆×C₄₃	—	2	2	no	—
46	C₂×C₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
47	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
48	C₄×C₈×C₄₃	D₄	1	2	yes	—
49	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
50	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₂²⋊D₄₃	—	4	1	no	—
52	#10621898	—	2	4	no	—
53	#10621898	—	4	2	no	—
54	C₂×D₁₇₂	—	2	1	no	—
55	C₂×C₄×D₄₃	—	4	1	no	—
56	C₂×C₄×D₄₃	—	4	2	no	—
57	C₂×Dic₈₆	—	2	1	no	—
58	C₂×C₈×C₄₃	—	2	2	no	—
59	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
62	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₄₃	#41	1	2	yes	—
64	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₄₃	D₈	1	1	yes	characteristic
66	C₄²×C₄₃	D₈	1	1	yes	characteristic
67	C₂²⋊Dic₄₃	—	4	1	no	—
68	(C₂×D₄₃)⋊C₄	—	4	2	no	—
69	C₄⋊Dic₄₃	—	2	2	no	—
70	Dic₄₃⋊C₄	—	4	2	no	—
71	C₄×Dic₄₃	—	4	2	no	—
72	C₄×Dic₄₃	—	4	1	no	—
73	#10621877	—	2	4	no	—
74	#10621877	—	4	2	no	—
75	C₂×C₄₃⋊C₈	—	4	2	no	—
76	Dic₁₇₂	—	2	1	no	—
77	Dic₁₇₂	C₄²	1	2	yes	—
78	D₃₄₄	—	2	1	no	—
79	D₃₄₄	C₄²	1	2	yes	—
80	#10621873	—	2	4	no	—
81	C₁₆×C₄₃	—	2	4	no	—
82	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
83	C₂²×D₄₃	—	4	1	no	—
84	C₂×C₄×C₄₃	—	4	2	no	—
85	C₂×C₄×C₄₃	#102	1	2	yes	—
86	C₂×C₄×C₄₃	#102	1	2	yes	—
87	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
89	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₄₃	#135	1	2	yes	—
91	C₂²⋊D₄₃	—	4	4	no	—
92	C₂×Dic₄₃	—	4	1	no	—
93	C₂×Dic₄₃	—	4	2	no	—
94	D₁₇₂	—	2	2	no	—
95	D₁₇₂	—	4	1	no	—
96	C₄×D₄₃	—	4	4	no	—
97	C₄×D₄₃	—	8	4	no	—
98	Dic₈₆	—	2	2	no	—
99	Dic₈₆	—	4	1	no	—
100	C₈×C₄₃	—	2	2	no	—
101	C₈×C₄₃	C₂×C₄²	1	1	yes	characteristic
102	C₈×C₄₃	#117	1	1	yes	characteristic
103	C₈×C₄₃	C₄×D₄	1	2	yes	—
104	C₄₃⋊C₈	—	4	4	no	—
105	#12640	—	43	1	no	maximal, Sylow
106	C₂²×C₄₃	—	2	2	no	—
107	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
108	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
109	C₂×D₄₃	—	4	2	no	—
110	C₂×D₄₃	—	8	2	no	—
111	C₄×C₄₃	—	2	2	no	—
112	C₄×C₄₃	—	2	2	no	—
113	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
114	C₄×C₄₃	#416	1	1	yes	characteristic
115	C₄×C₄₃	C₄×D₈	1	2	yes	—
116	Dic₄₃	—	4	2	no	—
117	Dic₄₃	—	8	2	no	—
118	C₄×#135	—	43	1	no	—
119	C₂×#359	—	43	2	no	—
120	C₂×#346	D₄₃	1	1	yes	characteristic, complemented
121	C₄×#108	—	43	1	no	—
122	#1382	—	43	2	no	—
123	C₂×C₄₃	—	2	2	no	—
124	C₂×C₄₃	C₄×#102	1	1	yes	characteristic
125	C₂×C₄₃	#2143	1	2	yes	—
126	D₄₃	—	8	2	no	—
127	C₂×#135	—	43	1	no	—
128	C₄×#41	—	86	1	no	—
129	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
130	C₄×Q₁₆	—	43	2	no	—
131	C₄×SD₁₆	—	86	2	no	—
132	C₄×D₈	—	43	2	no	—
133	C₂×#108	—	43	2	no	—
134	#427	—	43	1	no	—
135	#416	—	86	1	no	—
136	C₄×M₁₆	—	86	1	no	—
137	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
138	#359	—	43	8	no	—
139	#346	—	2	2	no	—
140	#341	—	86	1	no	—
141	C₄₃	#12640	1	1	yes	characteristic, complemented, Sylow
142	C₂×#41	—	86	1	no	—
143	#135	—	43	4	no	—
144	#135	—	86	2	no	—
145	C₂×Q₁₆	—	43	1	no	—
146	C₂×SD₁₆	—	86	1	no	—
147	C₂×D₈	—	43	1	no	—
148	C₂×M₁₆	—	86	2	no	—
149	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
150	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
151	C₄×Q₈	—	86	2	no	—
152	C₄×D₄	—	86	2	no	—
153	C₄×D₄	—	172	2	no	—
154	#117	—	86	1	no	—
155	#117	—	172	1	no	—
156	C₂×C₄²	—	172	1	no	—
157	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
158	C₂×C₁₆	—	2	2	no	—
159	C₂×C₁₆	—	2	2	no	—
160	C₂×C₁₆	C₄×D₄₃	1	4	yes	complemented
161	#108	—	43	4	no	—
162	#108	—	86	2	no	—
163	#107	—	43	2	no	—
164	#106	—	86	1	no	—
165	#103	—	86	2	no	—
166	#102	—	86	2	no	—
167	#97	—	172	1	no	—
168	C₄×C₈	—	172	1	no	—
169	C₄×C₈	C₄×D₄₃	1	2	yes	—
170	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
171	#41	—	86	4	no	—
172	#41	—	172	2	no	—
173	C₂×Q₈	—	86	1	no	—
174	C₂×D₄	—	86	1	no	—
175	C₂×D₄	—	172	1	no	—
176	C₂²×C₄	—	172	2	no	—
177	C₂²×C₄	—	172	1	no	—
178	C₂²×C₄	#10621873	1	2	yes	—
179	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
180	Q₁₆	—	43	2	no	—
181	Q₁₆	—	86	1	no	—
182	SD₁₆	—	86	4	no	—
183	D₈	—	43	2	no	—
184	D₈	—	86	1	no	—
185	M₁₆	—	86	4	no	—
186	M₁₆	—	172	2	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	172	2	no	—
189	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
190	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
191	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
192	C₂×C₈	#10621898	1	2	yes	—
193	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
194	C₄⋊C₄	—	86	2	no	—
195	C₄⋊C₄	—	172	2	no	—
196	C₂²⋊C₄	—	172	1	no	—
197	C₂²⋊C₄	—	172	2	no	—
198	C₄²	—	172	2	no	—
199	C₄²	—	172	1	no	—
200	C₄²	D₃₄₄	1	1	yes	characteristic
201	C₄²	D₃₄₄	1	1	yes	characteristic
202	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
203	C₁₆	—	2	4	no	—
204	C₂³	—	172	1	no	—
205	C₂³	C₂×#10621873	1	1	yes	characteristic
206	Q₈	—	86	2	no	—
207	Q₈	—	172	1	no	—
208	D₄	—	86	2	no	—
209	D₄	—	172	4	no	—
210	D₄	—	172	1	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	344	4	no	—
213	C₂×C₄	—	172	2	no	—
214	C₂×C₄	—	172	1	no	—
215	C₂×C₄	—	172	4	no	—
216	C₂×C₄	#13063247	1	2	yes	—
217	C₂×C₄	#13063247	1	2	yes	—
218	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
219	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
220	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
221	C₂×C₄	#13063347	1	2	yes	—
222	C₈	—	2	2	no	—
223	C₈	—	172	4	no	—
224	C₈	C₄²×D₄₃	1	1	yes	characteristic
225	C₈	#13063282	1	1	yes	characteristic
226	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
227	C₂²	—	2	2	no	—
228	C₂²	—	344	2	no	—
229	C₂²	—	172	2	no	—
230	C₂²	C₂×#13063247	1	1	yes	characteristic
231	C₂²	C₄×#10621873	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	344	2	no	—
235	C₄	—	172	2	no	—
236	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
237	C₄	#14582896	1	1	yes	characteristic
238	C₄	C₄×D₃₄₄	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	—	344	2	no	—
241	C₂	C₄×#13063247	1	1	yes	characteristic
242	C₂	#19136324	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063347

C₂

yes

maximal, characteristic

C₂×#14582707

C₂

yes

maximal

C₄×#13063261

C₂

yes

maximal, characteristic, complemented

#19132691

C₂

yes

maximal, complemented

C₂×C₄₃×#346

C₂

yes

maximal, characteristic, complemented

C₂×#13063347

C₂²

yes

characteristic

C₄×#10621898

—

C₄×Dic₁₇₂

C₄

yes

—

C₄×#10621873

—

C₄×D₃₄₄

C₄

yes

—

C₂×#13063261

C₂²

yes

—

#14582937

C₂²

yes

—

—

C₄

yes

complemented

#14582664

—

C₂²×C₁₆×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#346

—

C₂×#10621898

—

#13063347

—

#13063347

C₂×C₄

yes

—

C₂×Dic₁₇₂

C₂×C₄

yes

characteristic

C₂×#10621873

—

C₂×D₃₄₄

C₂×C₄

yes

characteristic

C₂×#10621877

—

C₄×Dic₈₆

—

C₄×D₁₇₂

—

C₄×C₂²⋊D₄₃

—

#13063284

—

#13063282

—

C₄²×D₄₃

—

#13063261

—

#13063261

C₂×C₄

yes

complemented

#13063259

C₂×C₄

yes

—

—

—

—

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

complemented

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

SD₁₆

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

#10621898

—

#10621898

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₄²×C₄₃

C₂²⋊C₄

yes

—

C₄²×C₄₃

D₈

yes

characteristic

C₄²×C₄₃

D₈

yes

characteristic

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

Dic₁₇₂

C₄²

yes

—

D₃₄₄

—

D₃₄₄

C₄²

yes

—

#10621873

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×SD₁₆

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

#135

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

100

C₈×C₄₃

—

101

C₈×C₄₃

C₂×C₄²

yes

characteristic

102

C₈×C₄₃

#117

yes

characteristic

103

C₈×C₄₃

C₄×D₄

yes

—

104

C₄₃⋊C₈

—

105

#12640

—

maximal, Sylow

106

C₂²×C₄₃

—

107

C₂²×C₄₃

C₂×#102

yes

characteristic

108

C₂²×C₄₃

C₄×SD₁₆

yes

—

109

C₂×D₄₃

—

110

C₂×D₄₃

—

111

C₄×C₄₃

—

112

C₄×C₄₃

—

113

C₄×C₄₃

C₄×C₂²⋊C₄

yes

characteristic

114

C₄×C₄₃

#416

yes

characteristic

115

C₄×C₄₃

C₄×D₈

yes

—

116

Dic₄₃

—

117

Dic₄₃

—

118

C₄×#135

—

119

C₂×#359

—

120

C₂×#346

D₄₃

yes

characteristic, complemented

121

C₄×#108

—

122

#1382

—

123

C₂×C₄₃

—

124

C₂×C₄₃

C₄×#102

yes

characteristic

125

C₂×C₄₃

#2143

yes

—

126

D₄₃

—

127

C₂×#135

—

128

C₄×#41

—

129

C₂²×C₁₆

C₂×D₄₃

yes

—

130

C₄×Q₁₆

—

131

C₄×SD₁₆

—

132

C₄×D₈

—

133

C₂×#108

—

134

#427

—

135

#416

—

136

C₄×M₁₆

—

137

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

138

#359

—

139

#346

—

140

#341

—

141

C₄₃

#12640

yes

characteristic, complemented, Sylow

142

C₂×#41

—

143

#135

—

144

#135

—

145

C₂×Q₁₆

—

146

C₂×SD₁₆

—

147

C₂×D₈

—

148

C₂×M₁₆

—

149

C₂²×C₈

D₁₇₂

yes

characteristic

150

C₂²×C₈

C₂²×D₄₃

yes

characteristic

151

C₄×Q₈

—

152

C₄×D₄

—

153

C₄×D₄

—

172

—

154

#117

—

155

#117

—

172

—

156

C₂×C₄²

—

172

—

157

C₂×C₄²

D₁₇₂

yes

characteristic

158

C₂×C₁₆

—

159

C₂×C₁₆

—

160

C₂×C₁₆

C₄×D₄₃

yes

complemented

161

#108

—

162

#108

—

163

#107

—

164

#106

—

165

#103

—

166

#102

—

167

#97

—

172

—

168

C₄×C₈

—

172

—

169

C₄×C₈

C₄×D₄₃

yes

—

170

C₄×C₈

C₂²⋊D₄₃

yes

—

171

#41

—

172

#41

—

172

—

173

C₂×Q₈

—

174

C₂×D₄

—

175

C₂×D₄

—

172

—

176

C₂²×C₄

—

172

—

177

C₂²×C₄

—

172

—

178

C₂²×C₄

#10621873

yes

—

179

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

180

Q₁₆

—

181

Q₁₆

—

182

SD₁₆

—

183

D₈

—

184

D₈

—

185

M₁₆

—

186

M₁₆

—

172

—

187

C₂×C₈

—

188

C₂×C₈

—

172

—

189

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

190

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

191

C₂×C₈

C₂×C₄×D₄₃

yes

—

192

C₂×C₈

#10621898

yes

—

193

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

194

C₄⋊C₄

—

195

C₄⋊C₄

—

172

—

196

C₂²⋊C₄

—

172

—

197

C₂²⋊C₄

—

172

—

198

C₄²

—

172

—

199

C₄²

—

172

—

200

C₄²

D₃₄₄

yes

characteristic

201

C₄²

D₃₄₄

yes

characteristic

202

C₄²

(C₂×D₄₃)⋊C₄

yes

—

203

C₁₆

—

204

C₂³

—

172

—

205

C₂³

C₂×#10621873

yes

characteristic

206

Q₈

—

207

Q₈

—

172

—

208

D₄

—

209

D₄

—

172

—

210

D₄

—

172

—

211

C₂×C₄

—

212

C₂×C₄

—

344

—

213

C₂×C₄

—

172

—

214

C₂×C₄

—

172

—

215

C₂×C₄

—

172

—

216

C₂×C₄

#13063247

yes

—

217

C₂×C₄

#13063247

yes

—

218

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

219

C₂×C₄

C₄×D₁₇₂

yes

—

220

C₂×C₄

C₂×D₃₄₄

yes

characteristic

221

C₂×C₄

#13063347

yes

—

222

C₈

—

223

C₈

—

172

—

224

C₈

C₄²×D₄₃

yes

characteristic

225

C₈

#13063282

yes

characteristic

226

C₈

C₄×C₂²⋊D₄₃

yes

—

227

C₂²

—

228

C₂²

—

344

—

229

C₂²

—

172

—

230

C₂²

C₂×#13063247

yes

characteristic

231

C₂²

C₄×#10621873

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

344

—

235

C₄

—

172

—

236

C₄

C₄×(C₂×D₄₃)⋊C₄

yes

characteristic

237

C₄

#14582896

yes

characteristic

238

C₄

C₄×D₃₄₄

yes

—

239

C₂

—

240

C₂

—

344

—

241

C₂

C₄×#13063247

yes

characteristic

242

C₂

#19136324

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₃₄₄
commutator	C₈×C₄₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#346	C₂
socle	C₂²×C₄₃	C₂×#102
prime radical	C₂×#13063347	C₂²
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#346	D₄₃
hypocenter	C₄₃	#12640
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

C₂×D₃₄₄

commutator

C₈×C₄₃

C₂×C₄²

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#346

C₂

C₂²×C₄₃

C₂²

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
3. C₄×#13063261	C₂	semidirect
4. #19132691	C₂	semidirect
5. C₂×C₄₃×#346	C₂	semidirect
15. #14582707	C₄	semidirect
34. #13063261	C₂×C₄	semidirect
46. C₂×C₁₆×C₄₃	C₂×C₄	semidirect
120. C₂×#346	D₄₃	semidirect
141. C₄₃	#12640	semidirect
160. C₂×C₁₆	C₄×D₄₃	semidirect

H ≅ G/N

type

3. C₄×#13063261

C₂

semidirect

4. #19132691

C₂

semidirect

5. C₂×C₄₃×#346

C₂

semidirect

15. #14582707

C₄

semidirect

34. #13063261

C₂×C₄

semidirect

46. C₂×C₁₆×C₄₃

C₂×C₄

semidirect

120. C₂×#346

D₄₃

semidirect

141. C₄₃

#12640

semidirect

160. C₂×C₁₆

C₄×D₄₃

semidirect

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

subgroup	index
C₄×#13063347	2
C₂×#14582707	2
C₄×#13063261	2
#19132691	2
C₂×C₄₃×#346	2
#12640	43

subgroup

index

C₂×C₄₃×#346

Subgroups — #25011827

Conjugacy classes of subgroups

Complements

Maximal subgroups