Group #25016192 — subgroups

Subgroups — #25016192

Order 11008.

482 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 115 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×D₆₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582701	C₂	1	2	yes	maximal, complemented
3	#19135461	C₂	1	2	yes	maximal, complemented
4	#19132687	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₄₄	C₂²	1	2	yes	—
7	C₂×D₆₈₈	—	2	4	no	—
8	C₂×D₆₈₈	—	2	2	no	—
9	C₂×#13063259	C₂²	1	2	yes	—
10	C₂×#13063247	—	2	2	no	—
11	#14582801	—	2	2	no	—
12	#14582701	—	2	4	no	—
13	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×C₄⋊C₁₆	—	2	2	no	—
17	C₂²×D₁₇₂	—	2	2	no	—
18	C₂×D₃₄₄	—	2	2	no	—
19	C₂×D₃₄₄	—	2	2	no	—
20	C₂×D₃₄₄	—	2	2	no	—
21	C₂×D₃₄₄	—	2	2	no	—
22	C₂×D₃₄₄	—	2	2	no	—
23	C₂×D₃₄₄	D₄	1	4	yes	—
24	C₂×C₄⋊Dic₄₃	—	2	2	no	—
25	C₂×(C₂×D₄₃)⋊C₄	—	4	2	no	—
26	C₂×(C₂×D₄₃)⋊C₄	—	4	2	no	—
27	D₆₈₈	—	2	8	no	—
28	#13063259	—	2	2	no	—
29	#13063259	—	2	2	no	—
30	#13063247	—	4	4	no	—
31	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
33	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
34	C₂×C₁₆×C₄₃	—	2	2	no	—
35	C₂×C₁₆×C₄₃	—	2	1	no	—
36	C₂×C₁₆×C₄₃	—	2	2	no	—
37	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
38	C₄×C₈×C₄₃	—	2	1	no	—
39	C₄×C₈×C₄₃	—	2	1	no	—
40	C₂³×D₄₃	—	4	2	no	—
41	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
43	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×Dic₄₃	—	4	2	no	—
45	C₂×D₁₇₂	—	2	4	no	—
46	C₂×D₁₇₂	—	4	2	no	—
47	C₂×D₁₇₂	—	4	2	no	—
48	C₂×D₁₇₂	—	4	2	no	—
49	C₂×D₁₇₂	—	4	2	no	—
50	C₂×D₁₇₂	—	4	2	no	—
51	C₂×C₈×C₄₃	—	2	1	no	—
52	C₂×C₈×C₄₃	—	2	2	no	—
53	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
54	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
56	C₂×C₈×C₄₃	#41	1	2	yes	—
57	C₄²×C₄₃	—	2	1	no	—
58	C₄²×C₄₃	—	2	1	no	—
59	(C₂×D₄₃)⋊C₄	—	8	4	no	—
60	(C₂×D₄₃)⋊C₄	—	8	4	no	—
61	C₄⋊Dic₄₃	—	4	2	no	—
62	C₄⋊Dic₄₃	—	4	2	no	—
63	D₃₄₄	—	2	4	no	—
64	D₃₄₄	—	2	4	no	—
65	D₃₄₄	—	4	2	no	—
66	D₃₄₄	—	4	2	no	—
67	C₁₆×C₄₃	—	2	2	no	—
68	C₁₆×C₄₃	—	4	1	no	—
69	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
70	C₂²×D₄₃	—	4	4	no	—
71	C₂²×D₄₃	—	8	2	no	—
72	C₂²×D₄₃	—	8	2	no	—
73	C₂²×D₄₃	—	8	2	no	—
74	C₂²×D₄₃	—	8	2	no	—
75	C₂²×D₄₃	—	8	2	no	—
76	C₂²×D₄₃	—	8	2	no	—
77	C₂×C₄×C₄₃	—	2	1	no	—
78	C₂×C₄×C₄₃	—	2	1	no	—
79	C₂×C₄×C₄₃	—	2	1	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	D₁₆	1	2	yes	complemented
82	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#121	1	2	yes	—
84	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
85	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
86	C₂×Dic₄₃	—	8	2	no	—
87	C₂×Dic₄₃	—	8	2	no	—
88	C₂×Dic₄₃	—	8	2	no	—
89	D₁₇₂	—	4	4	no	—
90	D₁₇₂	—	4	4	no	—
91	D₁₇₂	—	8	2	no	—
92	D₁₇₂	—	8	2	no	—
93	C₈×C₄₃	—	4	1	no	—
94	C₈×C₄₃	#120	1	1	yes	characteristic
95	C₈×C₄₃	#123	1	2	yes	—
96	C₈×C₄₃	#124	1	1	yes	characteristic
97	#13448	—	43	1	no	maximal, Sylow
98	C₂²×C₄₃	#459	1	2	yes	—
99	C₂²×C₄₃	#466	1	1	yes	characteristic
100	C₂²×C₄₃	C₂×D₁₆	1	1	yes	characteristic
101	C₂²×C₄₃	#508	1	1	yes	characteristic
102	C₂²×C₄₃	#509	1	2	yes	—
103	C₂×D₄₃	—	8	4	no	—
104	C₂×D₄₃	—	8	4	no	—
105	C₂×D₄₃	—	8	4	no	—
106	C₂×D₄₃	—	16	2	no	—
107	C₂×D₄₃	—	16	2	no	—
108	C₂×D₄₃	—	16	2	no	—
109	C₂×D₄₃	—	16	2	no	—
110	C₄×C₄₃	—	2	2	no	—
111	C₄×C₄₃	—	4	1	no	—
112	C₄×C₄₃	#394	1	1	yes	characteristic
113	C₄×C₄₃	#463	1	2	yes	—
114	C₄×C₄₃	#469	1	1	yes	characteristic
115	Dic₄₃	—	16	2	no	—
116	C₂²×D₁₆	—	43	1	no	—
117	C₂×C₄⋊C₁₆	D₄₃	1	1	yes	characteristic, complemented
118	C₂×#357	—	43	2	no	—
119	#1970	—	43	2	no	—
120	#1380	—	43	1	no	—
121	C₂×C₄₃	#2054	1	1	yes	characteristic
122	C₂×C₄₃	#2206	1	2	yes	—
123	C₂×C₄₃	#2210	1	2	yes	—
124	C₂×C₄₃	#2215	1	1	yes	characteristic
125	C₂×C₄₃	#2218	1	1	yes	characteristic
126	D₄₃	—	16	4	no	—
127	C₂²×D₈	—	43	2	no	—
128	C₂×D₁₆	—	86	4	no	—
129	C₂×D₁₆	—	86	2	no	—
130	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
131	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
132	C₂×#107	—	43	2	no	—
133	C₂×#102	—	86	2	no	—
134	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
135	#390	—	86	2	no	—
136	C₄⋊C₁₆	—	2	2	no	—
137	#357	—	86	4	no	—
138	C₄₃	#13448	1	1	yes	characteristic, complemented, Sylow
139	C₂²×D₄	—	86	2	no	—
140	C₂×D₈	—	43	4	no	—
141	C₂×D₈	—	86	2	no	—
142	C₂×D₈	—	86	2	no	—
143	C₂×D₈	—	86	2	no	—
144	C₂×D₈	—	86	2	no	—
145	C₂×D₈	—	86	2	no	—
146	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
147	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
148	C₂×C₄⋊C₄	—	86	2	no	—
149	C₂×C₂²⋊C₄	—	172	2	no	—
150	C₂×C₂²⋊C₄	—	172	2	no	—
151	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
152	D₁₆	—	86	8	no	—
153	C₂×C₁₆	—	2	2	no	—
154	C₂×C₁₆	—	2	2	no	—
155	C₂×C₁₆	—	2	1	no	—
156	C₂×C₁₆	C₂²⋊D₄₃	1	2	yes	—
157	#107	—	86	2	no	—
158	#107	—	86	2	no	—
159	#102	—	172	4	no	—
160	C₄×C₈	—	2	1	no	—
161	C₄×C₈	—	2	1	no	—
162	C₂⁴	—	172	2	no	—
163	C₂×D₄	—	86	4	no	—
164	C₂×D₄	—	172	2	no	—
165	C₂×D₄	—	172	2	no	—
166	C₂×D₄	—	172	2	no	—
167	C₂×D₄	—	172	2	no	—
168	C₂×D₄	—	172	2	no	—
169	C₂²×C₄	—	172	2	no	—
170	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
171	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
172	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
173	D₈	—	86	4	no	—
174	D₈	—	86	4	no	—
175	D₈	—	172	2	no	—
176	D₈	—	172	2	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	#10621898	1	1	yes	characteristic
180	C₂×C₈	D₄×D₄₃	1	2	yes	—
181	C₂×C₈	#10621902	1	2	yes	—
182	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
183	C₄⋊C₄	—	172	2	no	—
184	C₄⋊C₄	—	172	2	no	—
185	C₂²⋊C₄	—	344	4	no	—
186	C₂²⋊C₄	—	344	4	no	—
187	C₄²	—	2	1	no	—
188	C₄²	—	2	1	no	—
189	C₁₆	—	2	2	no	—
190	C₁₆	—	4	1	no	—
191	C₂³	—	344	2	no	—
192	C₂³	—	344	2	no	—
193	C₂³	—	344	2	no	—
194	C₂³	—	344	2	no	—
195	C₂³	—	344	2	no	—
196	C₂³	—	344	2	no	—
197	C₂³	—	172	4	no	—
198	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
199	D₄	—	344	2	no	—
200	D₄	—	344	2	no	—
201	D₄	—	172	4	no	—
202	D₄	—	172	4	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	344	2	no	—
208	C₂×C₄	—	344	2	no	—
209	C₂×C₄	—	344	2	no	—
210	C₂×C₄	D₆₈₈	1	2	yes	complemented
211	C₂×C₄	#13063299	1	1	yes	characteristic
212	C₂×C₄	#13063300	1	2	yes	—
213	C₂×C₄	#13063347	1	1	yes	characteristic
214	C₂×C₄	#13063353	1	2	yes	—
215	C₈	—	4	1	no	—
216	C₈	#13063293	1	1	yes	characteristic
217	C₈	#13063310	1	2	yes	—
218	C₈	#13063314	1	1	yes	characteristic
219	C₂²	—	344	4	no	—
220	C₂²	—	344	4	no	—
221	C₂²	—	344	4	no	—
222	C₂²	—	688	2	no	—
223	C₂²	—	688	2	no	—
224	C₂²	—	688	2	no	—
225	C₂²	—	688	2	no	—
226	C₂²	#14583095	1	2	yes	—
227	C₂²	#14583135	1	1	yes	characteristic
228	C₂²	C₂×D₆₈₈	1	1	yes	characteristic
229	C₂²	#14583331	1	1	yes	characteristic
230	C₂²	#14583337	1	2	yes	—
231	C₄	—	2	2	no	—
232	C₄	—	4	1	no	—
233	C₄	—	688	2	no	—
234	C₄	#14582816	1	1	yes	characteristic
235	C₄	#14583115	1	2	yes	—
236	C₄	#14583152	1	1	yes	characteristic
237	C₂	—	688	4	no	—
238	C₂	#19135906	1	1	yes	characteristic
239	C₂	#19136631	1	2	yes	—
240	C₂	#19136651	1	2	yes	—
241	C₂	#19136681	1	1	yes	characteristic
242	C₂	#19136698	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₆₈₈

C₂

yes

maximal, characteristic

C₂×#14582701

C₂

yes

maximal, complemented

#19135461

C₂

yes

maximal, complemented

#19132687

C₂

yes

maximal, characteristic, complemented

C₂×C₄₃×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₄₄

C₂²

yes

—

C₂×D₆₈₈

—

C₂×D₆₈₈

—

C₂×#13063259

C₂²

yes

—

C₂×#13063247

—

#14582801

—

#14582701

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

—

C₂²×D₁₇₂

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

D₄

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

—

D₆₈₈

—

#13063259

—

#13063259

—

#13063247

—

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×C₁₆×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₁₆

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

#135

yes

characteristic

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₈×C₄₃

#120

yes

characteristic

C₈×C₄₃

#123

yes

—

C₈×C₄₃

yes

—

C₂²×C₄₃

yes

—

C₂²×C₄₃

#466

yes

characteristic

100

C₂²×C₄₃

C₂×D₁₆

yes

characteristic

101

C₂²×C₄₃

#508

yes

characteristic

102

C₂²×C₄₃

#509

yes

—

103

C₂×D₄₃

—

104

C₂×D₄₃

—

105

C₂×D₄₃

—

106

C₂×D₄₃

—

107

C₂×D₄₃

—

108

C₂×D₄₃

—

109

C₂×D₄₃

—

110

C₄×C₄₃

—

111

C₄×C₄₃

—

112

C₄×C₄₃

#394

yes

characteristic

113

C₄×C₄₃

#463

yes

—

114

C₄×C₄₃

#469

yes

characteristic

115

Dic₄₃

—

116

C₂²×D₁₆

—

117

C₂×C₄⋊C₁₆

D₄₃

yes

characteristic, complemented

118

C₂×#357

—

119

#1970

—

120

#1380

—

121

C₂×C₄₃

#2054

yes

characteristic

122

C₂×C₄₃

#2206

yes

—

123

C₂×C₄₃

#2210

yes

—

124

C₂×C₄₃

#2215

yes

characteristic

125

C₂×C₄₃

#2218

yes

characteristic

126

D₄₃

—

127

C₂²×D₈

—

128

C₂×D₁₆

—

129

C₂×D₁₆

—

130

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

131

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

132

C₂×#107

—

133

C₂×#102

—

134

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

135

#390

—

136

C₄⋊C₁₆

—

137

#357

—

138

C₄₃

#13448

yes

characteristic, complemented, Sylow

139

C₂²×D₄

—

140

C₂×D₈

—

141

C₂×D₈

—

142

C₂×D₈

—

143

C₂×D₈

—

144

C₂×D₈

—

145

C₂×D₈

—

146

C₂²×C₈

D₁₇₂

yes

characteristic

147

C₂²×C₈

C₂²×D₄₃

yes

characteristic

148

C₂×C₄⋊C₄

—

149

C₂×C₂²⋊C₄

—

172

—

150

C₂×C₂²⋊C₄

—

172

—

151

C₂×C₄²

D₁₇₂

yes

characteristic

152

D₁₆

—

153

C₂×C₁₆

—

154

C₂×C₁₆

—

155

C₂×C₁₆

—

156

C₂×C₁₆

C₂²⋊D₄₃

yes

—

157

#107

—

158

#107

—

159

#102

—

172

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₂⁴

—

172

—

163

C₂×D₄

—

164

C₂×D₄

—

172

—

165

C₂×D₄

—

172

—

166

C₂×D₄

—

172

—

167

C₂×D₄

—

172

—

168

C₂×D₄

—

172

—

169

C₂²×C₄

—

172

—

170

C₂²×C₄

D₃₄₄

yes

characteristic

171

C₂²×C₄

D₃₄₄

yes

characteristic

172

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

173

D₈

—

174

D₈

—

175

D₈

—

172

—

176

D₈

—

172

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

#10621898

yes

characteristic

180

C₂×C₈

D₄×D₄₃

yes

—

181

C₂×C₈

#10621902

yes

—

182

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

183

C₄⋊C₄

—

172

—

184

C₄⋊C₄

—

172

—

185

C₂²⋊C₄

—

344

—

186

C₂²⋊C₄

—

344

—

187

C₄²

—

188

C₄²

—

189

C₁₆

—

190

C₁₆

—

191

C₂³

—

344

—

192

C₂³

—

344

—

193

C₂³

—

344

—

194

C₂³

—

344

—

195

C₂³

—

344

—

196

C₂³

—

344

—

197

C₂³

—

172

—

198

C₂³

C₂×D₃₄₄

yes

characteristic

199

D₄

—

344

—

200

D₄

—

344

—

201

D₄

—

172

—

202

D₄

—

172

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

344

—

208

C₂×C₄

—

344

—

209

C₂×C₄

—

344

—

210

C₂×C₄

D₆₈₈

yes

complemented

211

C₂×C₄

#13063299

yes

characteristic

212

C₂×C₄

#13063300

yes

—

213

C₂×C₄

#13063347

yes

characteristic

214

C₂×C₄

#13063353

yes

—

215

C₈

—

216

C₈

#13063293

yes

characteristic

217

C₈

#13063310

yes

—

218

C₈

#13063314

yes

characteristic

219

C₂²

—

344

—

220

C₂²

—

344

—

221

C₂²

—

344

—

222

C₂²

—

688

—

223

C₂²

—

688

—

224

C₂²

—

688

—

225

C₂²

—

688

—

226

C₂²

#14583095

yes

—

227

C₂²

#14583135

yes

characteristic

228

C₂²

C₂×D₆₈₈

yes

characteristic

229

C₂²

#14583331

yes

characteristic

230

C₂²

#14583337

yes

—

231

C₄

—

232

C₄

—

233

C₄

—

688

—

234

C₄

#14582816

yes

characteristic

235

C₄

#14583115

yes

—

236

C₄

#14583152

yes

characteristic

237

C₂

—

688

—

238

C₂

#19135906

yes

characteristic

239

C₂

#19136631

yes

—

240

C₂

#19136651

yes

—

241

C₂

#19136681

yes

characteristic

242

C₂

#19136698

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₄₄
commutator, cosocle	C₂²×C₈×C₄₃	C₂³
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×C₄⋊C₁₆	C₂
socle	C₂³×C₄₃	C₂×D₈
prime radical	C₂²×D₆₈₈	C₂
hypercenter	C₂×C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#13448
LCS	G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center

C₂³

C₂×D₃₄₄

commutator, cosocle

C₂²×C₈×C₄₃

C₂³

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×C₄⋊C₁₆

C₂

socle

C₂³×C₄₃

C₂×D₈

prime radical

C₂²×D₆₈₈

C₂

hypercenter

C₂×C₄⋊C₁₆

D₄₃

hypocenter

C₄₃

#13448

LCS

G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
2. C₂×#14582701	C₂	semidirect
3. #19135461	C₂	semidirect
4. #19132687	C₂	semidirect
5. C₂×C₄₃×C₄⋊C₁₆	C₂	semidirect
81. C₂×C₄×C₄₃	D₁₆	semidirect
117. C₂×C₄⋊C₁₆	D₄₃	semidirect
138. C₄₃	#13448	semidirect
210. C₂×C₄	D₆₈₈	semidirect

H ≅ G/N

type

2. C₂×#14582701

C₂

semidirect

3. #19135461

C₂

semidirect

4. #19132687

C₂

semidirect

5. C₂×C₄₃×C₄⋊C₁₆

C₂

semidirect

81. C₂×C₄×C₄₃

D₁₆

semidirect

117. C₂×C₄⋊C₁₆

D₄₃

semidirect

138. C₄₃

#13448

semidirect

210. C₂×C₄

D₆₈₈

semidirect

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

subgroup	index
C₂²×D₆₈₈	2
C₂×#14582701	2
#19135461	2
#19132687	2
C₂×C₄₃×C₄⋊C₁₆	2
#13448	43

subgroup

index

C₂²×D₆₈₈

C₂×C₄₃×C₄⋊C₁₆

Subgroups — #25016192

Conjugacy classes of subgroups

Complements

Maximal subgroups