Group #25016189 — subgroups

Subgroups — #25016189

Order 11008.

482 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 113 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×Dic₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582700	C₂	1	2	yes	maximal, complemented
3	#19135462	C₂	1	2	yes	maximal, complemented
4	#19132687	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂×#13063259	C₂²	1	2	yes	—
8	C₂×#13063246	—	2	2	no	—
9	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
10	#14582802	—	2	2	no	—
11	Dic₄₃⋊C₁₆	—	2	2	no	—
12	#14582700	—	2	4	no	—
13	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
14	C₂×D₁₆×C₄₃	—	2	4	no	—
15	C₂×D₁₆×C₄₃	—	2	2	no	—
16	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
18	C₂×C₄⋊Dic₄₃	—	2	2	no	—
19	C₂×C₂²⋊Dic₄₃	—	4	2	no	—
20	C₂×C₂²⋊Dic₄₃	—	4	2	no	—
21	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
22	C₂×C₄₃⋊C₁₆	—	2	2	no	—
23	C₂×C₄₃⋊C₁₆	—	2	1	no	—
24	#13063259	—	2	2	no	—
25	#13063259	—	2	2	no	—
26	#13063246	—	4	4	no	—
27	C₈×Dic₄₃	—	2	1	no	—
28	C₈×Dic₄₃	—	2	1	no	—
29	C₂²×D₄×C₄₃	—	2	2	no	—
30	C₂×D₈×C₄₃	—	2	2	no	—
31	C₂×D₈×C₄₃	—	2	2	no	—
32	C₂×D₈×C₄₃	—	2	2	no	—
33	C₂×D₈×C₄₃	—	2	2	no	—
34	C₂×D₈×C₄₃	—	2	2	no	—
35	C₂×D₈×C₄₃	D₄	1	4	yes	—
36	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
37	D₁₆×C₄₃	—	2	8	no	—
38	C₂×C₁₆×C₄₃	—	2	2	no	—
39	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
40	C₂⁴×C₄₃	—	4	2	no	—
41	C₂×D₄×C₄₃	—	2	4	no	—
42	C₂×D₄×C₄₃	—	4	2	no	—
43	C₂×D₄×C₄₃	—	4	2	no	—
44	C₂×D₄×C₄₃	—	4	2	no	—
45	C₂×D₄×C₄₃	—	4	2	no	—
46	C₂×D₄×C₄₃	—	4	2	no	—
47	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×Dic₄₃	—	4	2	no	—
49	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
50	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
51	D₈×C₄₃	—	2	4	no	—
52	D₈×C₄₃	—	2	4	no	—
53	D₈×C₄₃	—	4	2	no	—
54	D₈×C₄₃	—	4	2	no	—
55	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
58	C₂×C₈×C₄₃	#41	1	2	yes	—
59	C₂²⋊Dic₄₃	—	8	4	no	—
60	C₂²⋊Dic₄₃	—	8	4	no	—
61	C₄⋊Dic₄₃	—	4	2	no	—
62	C₄⋊Dic₄₃	—	4	2	no	—
63	C₄×Dic₄₃	—	2	1	no	—
64	C₄×Dic₄₃	—	2	1	no	—
65	C₂×C₄₃⋊C₈	—	2	1	no	—
66	C₂×C₄₃⋊C₈	—	2	2	no	—
67	C₁₆×C₄₃	—	2	2	no	—
68	C₄₃⋊C₁₆	—	4	1	no	—
69	C₂³×C₄₃	—	4	4	no	—
70	C₂³×C₄₃	—	8	2	no	—
71	C₂³×C₄₃	—	8	2	no	—
72	C₂³×C₄₃	—	8	2	no	—
73	C₂³×C₄₃	—	8	2	no	—
74	C₂³×C₄₃	—	8	2	no	—
75	C₂³×C₄₃	—	8	2	no	—
76	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
77	D₄×C₄₃	—	4	4	no	—
78	D₄×C₄₃	—	4	4	no	—
79	D₄×C₄₃	—	8	2	no	—
80	D₄×C₄₃	—	8	2	no	—
81	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#121	1	2	yes	—
83	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
84	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
85	C₂×Dic₄₃	—	2	1	no	—
86	C₂×Dic₄₃	—	2	1	no	—
87	C₂×Dic₄₃	—	2	1	no	—
88	C₂×Dic₄₃	—	2	2	no	—
89	C₂×Dic₄₃	—	8	2	no	—
90	C₂×Dic₄₃	—	8	2	no	—
91	C₂×Dic₄₃	—	8	2	no	—
92	C₂×Dic₄₃	D₁₆	1	2	yes	complemented
93	C₈×C₄₃	#120	1	1	yes	characteristic
94	C₈×C₄₃	#123	1	2	yes	—
95	C₈×C₄₃	#124	1	1	yes	characteristic
96	C₄₃⋊C₈	—	4	1	no	—
97	#13448	—	43	1	no	maximal, Sylow
98	C₂²×C₄₃	—	8	4	no	—
99	C₂²×C₄₃	—	8	4	no	—
100	C₂²×C₄₃	—	8	4	no	—
101	C₂²×C₄₃	—	16	2	no	—
102	C₂²×C₄₃	—	16	2	no	—
103	C₂²×C₄₃	—	16	2	no	—
104	C₂²×C₄₃	—	16	2	no	—
105	C₂²×C₄₃	#459	1	2	yes	—
106	C₂²×C₄₃	#466	1	1	yes	characteristic
107	C₂²×C₄₃	C₂×D₁₆	1	1	yes	characteristic
108	C₂²×C₄₃	#508	1	1	yes	characteristic
109	C₂²×C₄₃	#509	1	2	yes	—
110	C₄×C₄₃	#394	1	1	yes	characteristic
111	C₄×C₄₃	#463	1	2	yes	—
112	C₄×C₄₃	#469	1	1	yes	characteristic
113	Dic₄₃	—	2	2	no	—
114	Dic₄₃	—	4	1	no	—
115	Dic₄₃	—	16	2	no	—
116	C₂²×D₁₆	D₄₃	1	1	yes	characteristic
117	C₂×C₄⋊C₁₆	—	43	1	no	—
118	C₂×#357	—	43	2	no	—
119	#1970	—	43	2	no	—
120	#1380	—	43	1	no	—
121	C₂×C₄₃	—	16	4	no	—
122	C₂×C₄₃	#2054	1	1	yes	characteristic
123	C₂×C₄₃	#2206	1	2	yes	—
124	C₂×C₄₃	#2210	1	2	yes	—
125	C₂×C₄₃	#2215	1	1	yes	characteristic
126	C₂×C₄₃	#2218	1	1	yes	characteristic
127	C₂²×D₈	C₂×D₄₃	1	2	yes	—
128	C₂×D₁₆	—	2	4	no	—
129	C₂×D₁₆	—	2	2	no	—
130	C₂²×C₁₆	—	43	1	no	—
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	—	43	1	no	—
135	#390	—	86	2	no	—
136	C₄⋊C₁₆	—	86	2	no	—
137	#357	—	86	4	no	—
138	C₄₃	#13448	1	1	yes	characteristic, complemented, Sylow
139	C₂²×D₄	—	2	2	no	—
140	C₂×D₈	—	2	2	no	—
141	C₂×D₈	—	2	2	no	—
142	C₂×D₈	—	2	2	no	—
143	C₂×D₈	—	2	2	no	—
144	C₂×D₈	—	2	2	no	—
145	C₂×D₈	C₂²⋊D₄₃	1	4	yes	—
146	C₂²×C₈	—	43	1	no	—
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	—	43	1	no	—
152	D₁₆	—	2	8	no	—
153	C₂×C₁₆	—	2	2	no	—
154	C₂×C₁₆	—	86	2	no	—
155	C₂×C₁₆	—	86	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	—	86	1	no	—
161	C₄×C₈	—	86	1	no	—
162	C₂⁴	—	4	2	no	—
163	C₂×D₄	—	2	4	no	—
164	C₂×D₄	—	4	2	no	—
165	C₂×D₄	—	4	2	no	—
166	C₂×D₄	—	4	2	no	—
167	C₂×D₄	—	4	2	no	—
168	C₂×D₄	—	4	2	no	—
169	C₂²×C₄	—	43	1	no	—
170	C₂²×C₄	—	43	1	no	—
171	C₂²×C₄	—	172	2	no	—
172	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
173	D₈	—	2	4	no	—
174	D₈	—	2	4	no	—
175	D₈	—	4	2	no	—
176	D₈	—	4	2	no	—
177	C₂×C₈	—	86	1	no	—
178	C₂×C₈	—	86	2	no	—
179	C₂×C₈	#10621900	1	1	yes	characteristic
180	C₂×C₈	#10621900	1	2	yes	—
181	C₂×C₈	C₂×C₂²⋊D₄₃	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	—	86	1	no	—
188	C₄²	—	86	1	no	—
189	C₁₆	—	2	2	no	—
190	C₁₆	—	172	1	no	—
191	C₂³	—	4	4	no	—
192	C₂³	—	8	2	no	—
193	C₂³	—	8	2	no	—
194	C₂³	—	8	2	no	—
195	C₂³	—	8	2	no	—
196	C₂³	—	8	2	no	—
197	C₂³	—	8	2	no	—
198	C₂³	D₈×D₄₃	1	1	yes	characteristic
199	D₄	—	4	4	no	—
200	D₄	—	4	4	no	—
201	D₄	—	8	2	no	—
202	D₄	—	8	2	no	—
203	C₂×C₄	—	43	2	no	—
204	C₂×C₄	—	86	1	no	—
205	C₂×C₄	—	86	1	no	—
206	C₂×C₄	—	86	2	no	—
207	C₂×C₄	—	86	1	no	—
208	C₂×C₄	—	344	2	no	—
209	C₂×C₄	—	344	2	no	—
210	C₂×C₄	—	344	2	no	—
211	C₂×C₄	#13063296	1	1	yes	characteristic
212	C₂×C₄	#13063297	1	2	yes	—
213	C₂×C₄	#13063344	1	1	yes	characteristic
214	C₂×C₄	#13063349	1	2	yes	—
215	C₈	—	172	1	no	—
216	C₈	#13063294	1	1	yes	characteristic
217	C₈	#13063306	1	2	yes	—
218	C₈	#13063312	1	1	yes	characteristic
219	C₂²	—	8	4	no	—
220	C₂²	—	8	4	no	—
221	C₂²	—	8	4	no	—
222	C₂²	—	16	2	no	—
223	C₂²	—	16	2	no	—
224	C₂²	—	16	2	no	—
225	C₂²	—	16	2	no	—
226	C₂²	#14583092	1	2	yes	—
227	C₂²	#14583132	1	1	yes	characteristic
228	C₂²	D₁₆×D₄₃	1	1	yes	characteristic
229	C₂²	#14583328	1	1	yes	characteristic
230	C₂²	#14583333	1	2	yes	—
231	C₄	—	86	2	no	—
232	C₄	—	172	1	no	—
233	C₄	—	688	2	no	—
234	C₄	#14582813	1	1	yes	characteristic
235	C₄	#14583112	1	2	yes	—
236	C₄	#14583149	1	1	yes	characteristic
237	C₂	—	16	4	no	—
238	C₂	#19135903	1	1	yes	characteristic
239	C₂	#19136628	1	2	yes	—
240	C₂	#19136648	1	2	yes	—
241	C₂	#19136678	1	1	yes	characteristic
242	C₂	#19136695	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×#14582700

C₂

yes

maximal, complemented

#19135462

C₂

yes

maximal, complemented

#19132687

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₆×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×#13063259

C₂²

yes

—

C₂×#13063246

—

C₂×C₈×Dic₄₃

C₂²

yes

characteristic

#14582802

—

Dic₄₃⋊C₁₆

—

#14582700

—

C₂²×D₈×C₄₃

C₂²

yes

—

C₂×D₁₆×C₄₃

—

C₂×D₁₆×C₄₃

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₄₃

—

C₂×C₂²⋊Dic₄₃

—

C₂×C₂²⋊Dic₄₃

—

C₂×C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

—

#13063259

—

#13063259

—

#13063246

—

C₈×Dic₄₃

—

C₈×Dic₄₃

—

C₂²×D₄×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

D₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

D₄

yes

—

C₂⁴×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₈

yes

characteristic

C₂²×Dic₄₃

D₈

yes

characteristic

D₈×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

#121

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

#135

yes

characteristic

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₁₆

yes

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₈×C₄₃

#124

yes

characteristic

C₄₃⋊C₈

—

#13448

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

100

C₂²×C₄₃

—

101

C₂²×C₄₃

—

102

C₂²×C₄₃

—

103

C₂²×C₄₃

—

104

C₂²×C₄₃

—

105

C₂²×C₄₃

#459

yes

—

106

C₂²×C₄₃

#466

yes

characteristic

107

C₂²×C₄₃

C₂×D₁₆

yes

characteristic

108

C₂²×C₄₃

#508

yes

characteristic

109

C₂²×C₄₃

#509

yes

—

110

C₄×C₄₃

#394

yes

characteristic

111

C₄×C₄₃

#463

yes

—

112

C₄×C₄₃

#469

yes

characteristic

113

Dic₄₃

—

114

Dic₄₃

—

115

Dic₄₃

—

116

C₂²×D₁₆

D₄₃

yes

characteristic

117

C₂×C₄⋊C₁₆

—

118

C₂×#357

—

119

#1970

—

120

#1380

—

121

C₂×C₄₃

—

122

C₂×C₄₃

#2054

yes

characteristic

123

C₂×C₄₃

#2206

yes

—

124

C₂×C₄₃

#2210

yes

—

125

C₂×C₄₃

#2215

yes

characteristic

126

C₂×C₄₃

#2218

yes

characteristic

127

C₂²×D₈

C₂×D₄₃

yes

—

128

C₂×D₁₆

—

129

C₂×D₁₆

—

130

C₂²×C₁₆

—

131

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

132

C₂×#107

—

133

C₂×#102

—

134

C₂×C₄×C₈

—

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

C₂²⋊D₄₃

yes

—

146

C₂²×C₈

—

147

C₂²×C₈

C₂²×D₄₃

yes

characteristic

148

C₂×C₄⋊C₄

—

149

C₂×C₂²⋊C₄

—

172

—

150

C₂×C₂²⋊C₄

—

172

—

151

C₂×C₄²

—

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

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

—

172

C₂²×C₄

D₄×D₄₃

yes

characteristic

173

D₈

—

174

D₈

—

175

D₈

—

176

D₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

#10621900

yes

characteristic

180

C₂×C₈

#10621900

yes

—

181

C₂×C₈

C₂×C₂²⋊D₄₃

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

—

172

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

D₈×D₄₃

yes

characteristic

199

D₄

—

200

D₄

—

201

D₄

—

202

D₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

344

—

209

C₂×C₄

—

344

—

210

C₂×C₄

—

344

—

211

C₂×C₄

#13063296

yes

characteristic

212

C₂×C₄

#13063297

yes

—

213

C₂×C₄

#13063344

yes

characteristic

214

C₂×C₄

#13063349

yes

—

215

C₈

—

172

—

216

C₈

#13063294

yes

characteristic

217

C₈

#13063306

yes

—

218

C₈

#13063312

yes

characteristic

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

#14583092

yes

—

227

C₂²

#14583132

yes

characteristic

228

C₂²

D₁₆×D₄₃

yes

characteristic

229

C₂²

#14583328

yes

characteristic

230

C₂²

#14583333

yes

—

231

C₄

—

232

C₄

—

172

—

233

C₄

—

688

—

234

C₄

#14582813

yes

characteristic

235

C₄

#14583112

yes

—

236

C₄

#14583149

yes

characteristic

237

C₂

—

238

C₂

#19135903

yes

characteristic

239

C₂

#19136628

yes

—

240

C₂

#19136648

yes

—

241

C₂

#19136678

yes

characteristic

242

C₂

#19136695

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₄₃
commutator, cosocle	C₂²×C₈×C₄₃	C₂³
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting, prime radical	C₂²×D₁₆×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₈
hypercenter	C₂²×D₁₆	D₄₃
hypocenter	C₄₃	#13448
LCS	G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

subgroup

G/H

center

C₂³

D₈×D₄₃

commutator, cosocle

C₂²×C₈×C₄₃

C₂³

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting, prime radical

C₂²×D₁₆×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₈

hypercenter

C₂²×D₁₆

D₄₃

hypocenter

C₄₃

#13448

LCS

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

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

N	H ≅ G/N	type
1. C₂×Dic₄₃⋊C₁₆	C₂	semidirect
2. C₂×#14582700	C₂	semidirect
3. #19135462	C₂	semidirect
4. #19132687	C₂	semidirect
92. C₂×Dic₄₃	D₁₆	semidirect
138. C₄₃	#13448	semidirect

H ≅ G/N

type

1. C₂×Dic₄₃⋊C₁₆

C₂

semidirect

2. C₂×#14582700

C₂

semidirect

3. #19135462

C₂

semidirect

4. #19132687

C₂

semidirect

92. C₂×Dic₄₃

D₁₆

semidirect

138. C₄₃

#13448

semidirect

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

subgroup	index
C₂×Dic₄₃⋊C₁₆	2
C₂×#14582700	2
#19135462	2
#19132687	2
C₂²×D₁₆×C₄₃	2
#13448	43

subgroup

index

C₂×Dic₄₃⋊C₁₆

C₂²×D₁₆×C₄₃

Subgroups — #25016189

Conjugacy classes of subgroups

Complements

Maximal subgroups