Group #25014989 — subgroups

Subgroups — #25014989

Order 11008.

502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14582699	C₂	1	2	yes	maximal, complemented
3	C₂×#14582674	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135459	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₄₄	C₂²	1	2	yes	—
7	C₂×D₆₈₈	—	2	2	no	—
8	C₂×D₆₈₈	—	2	2	no	—
9	C₂×D₆₈₈	C₄	1	4	yes	complemented
10	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₂×#13063245	—	2	2	no	—
12	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
13	#14582800	—	2	2	no	—
14	#14582699	—	2	4	no	—
15	#14582674	—	2	2	no	—
16	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#107×C₄₃	C₂²	1	2	yes	—
18	C₄₃×#367	—	2	2	no	—
19	C₂²×D₁₇₂	—	2	2	no	—
20	C₂×D₃₄₄	—	2	2	no	—
21	C₂×D₃₄₄	—	2	2	no	—
22	C₂×D₃₄₄	—	2	2	no	—
23	C₂×D₃₄₄	—	2	2	no	—
24	C₂×D₃₄₄	—	2	2	no	—
25	C₂×D₃₄₄	C₂×C₄	1	4	yes	—
26	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
27	C₂×(C₂×D₄₃)⋊C₄	—	4	4	no	—
28	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
29	D₆₈₈	—	2	8	no	—
30	C₂×C₄₃⋊C₁₆	—	2	1	no	—
31	C₂×C₄₃⋊C₁₆	—	2	1	no	—
32	C₂×C₄₃⋊C₁₆	D₄	1	2	yes	—
33	#13063245	—	4	4	no	—
34	C₈×Dic₄₃	—	2	1	no	—
35	C₈×Dic₄₃	—	2	1	no	—
36	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
38	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
39	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
40	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
41	#107×C₄₃	—	2	2	no	—
42	#107×C₄₃	—	2	2	no	—
43	C₂³×D₄₃	—	4	2	no	—
44	C₂²×C₄×C₄₃	—	4	2	no	—
45	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×Dic₄₃	D₈	1	2	yes	—
47	C₂×D₁₇₂	—	2	4	no	—
48	C₂×D₁₇₂	—	4	2	no	—
49	C₂×D₁₇₂	—	4	2	no	—
50	C₂×D₁₇₂	—	4	2	no	—
51	C₂×D₁₇₂	—	4	2	no	—
52	C₂×D₁₇₂	—	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×D₄	1	1	yes	characteristic
57	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
58	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
59	C₄⋊C₄×C₄₃	—	4	2	no	—
60	C₄⋊C₄×C₄₃	—	4	2	no	—
61	(C₂×D₄₃)⋊C₄	—	8	8	no	—
62	C₄×Dic₄₃	—	2	1	no	—
63	C₄×Dic₄₃	—	2	1	no	—
64	C₂×C₄₃⋊C₈	—	2	1	no	—
65	C₂×C₄₃⋊C₈	—	2	1	no	—
66	C₂×C₄₃⋊C₈	D₈	1	2	yes	—
67	D₃₄₄	—	2	4	no	—
68	D₃₄₄	—	2	4	no	—
69	D₃₄₄	—	4	2	no	—
70	D₃₄₄	—	4	2	no	—
71	C₁₆×C₄₃	C₂²⋊C₄	1	4	yes	complemented
72	C₄₃⋊C₁₆	—	2	2	no	—
73	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
74	C₂²×D₄₃	—	4	4	no	—
75	C₂²×D₄₃	—	8	2	no	—
76	C₂²×D₄₃	—	8	2	no	—
77	C₂²×D₄₃	—	8	4	no	—
78	C₂²×D₄₃	—	8	4	no	—
79	C₂×C₄×C₄₃	—	8	2	no	—
80	C₂×C₄×C₄₃	—	8	4	no	—
81	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
86	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
87	C₂×Dic₄₃	—	2	2	no	—
88	C₂×Dic₄₃	—	2	4	no	—
89	D₁₇₂	—	4	4	no	—
90	D₁₇₂	—	4	4	no	—
91	D₁₇₂	—	8	2	no	—
92	D₁₇₂	—	8	2	no	—
93	C₈×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
95	C₈×C₄₃	#121	1	1	yes	characteristic
96	C₈×C₄₃	#124	1	1	yes	characteristic
97	C₄₃⋊C₈	—	2	2	no	—
98	#13239	—	43	1	no	maximal, Sylow
99	C₂²×C₄₃	C₄×D₈	1	1	yes	characteristic
100	C₂²×C₄₃	#466	1	1	yes	characteristic
101	C₂²×C₄₃	#493	1	1	yes	characteristic
102	C₂²×C₄₃	#509	1	4	yes	—
103	C₂×D₄₃	—	8	8	no	—
104	C₂×D₄₃	—	8	4	no	—
105	C₂×D₄₃	—	16	4	no	—
106	C₂×D₄₃	—	16	2	no	—
107	C₂×D₄₃	—	16	2	no	—
108	C₄×C₄₃	—	16	2	no	—
109	C₄×C₄₃	#390	1	1	yes	characteristic
110	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
111	C₄×C₄₃	#466	1	1	yes	characteristic
112	C₄×C₄₃	#495	1	1	yes	characteristic
113	Dic₄₃	—	4	2	no	—
114	C₂²×D₁₆	—	43	1	no	—
115	C₂×#367	D₄₃	1	1	yes	characteristic, complemented
116	C₂×#357	—	43	2	no	—
117	C₂×#346	—	43	1	no	—
118	#1970	—	43	2	no	—
119	C₂×C₄₃	#1970	1	1	yes	characteristic
120	C₂×C₄₃	#2177	1	2	yes	—
121	C₂×C₄₃	#2218	1	2	yes	—
122	C₂×C₄₃	#2250	1	2	yes	—
123	D₄₃	—	16	4	no	—
124	C₂²×D₈	—	43	2	no	—
125	C₂×D₁₆	—	43	4	no	—
126	C₂×D₁₆	—	86	2	no	—
127	C₂×D₁₆	—	86	2	no	—
128	C₂²×C₁₆	—	43	1	no	—
129	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
130	C₂×#107	C₂×D₄₃	1	2	yes	—
131	C₂×#102	—	86	2	no	—
132	C₂×C₄×C₈	—	43	1	no	—
133	#390	—	86	2	no	—
134	#367	—	2	2	no	—
135	#357	—	86	4	no	—
136	#346	—	86	2	no	—
137	C₄₃	#13239	1	1	yes	characteristic, complemented, Sylow
138	C₂²×D₄	—	86	2	no	—
139	C₂×D₈	—	43	4	no	—
140	C₂×D₈	—	86	2	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	C₂²×C₈	—	43	1	no	—
146	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₂²⋊C₄	—	172	4	no	—
149	C₂×C₄²	—	43	1	no	—
150	D₁₆	—	86	8	no	—
151	C₂×C₁₆	—	43	2	no	—
152	C₂×C₁₆	—	86	1	no	—
153	C₂×C₁₆	—	86	1	no	—
154	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
155	C₂×C₁₆	D₁₇₂	1	2	yes	—
156	C₂×C₁₆	C₂²⋊D₄₃	1	2	yes	—
157	#107	—	2	2	no	—
158	#107	—	2	2	no	—
159	#102	—	172	4	no	—
160	C₄×C₈	—	86	1	no	—
161	C₄×C₈	—	86	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	—	4	2	no	—
170	C₂²×C₄	—	43	2	no	—
171	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
172	D₈	—	86	4	no	—
173	D₈	—	86	4	no	—
174	D₈	—	172	2	no	—
175	D₈	—	172	2	no	—
176	C₂×C₈	—	43	2	no	—
177	C₂×C₈	—	86	1	no	—
178	C₂×C₈	—	86	1	no	—
179	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
180	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
181	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
182	C₂×C₈	#10621902	1	1	yes	characteristic
183	C₂×C₈	#10621902	1	1	yes	characteristic
184	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₂²⋊C₄	—	344	8	no	—
188	C₄²	—	86	1	no	—
189	C₄²	—	86	1	no	—
190	C₁₆	—	86	2	no	—
191	C₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	complemented
192	C₂³	—	344	4	no	—
193	C₂³	—	344	4	no	—
194	C₂³	—	344	2	no	—
195	C₂³	—	344	2	no	—
196	C₂³	—	172	4	no	—
197	C₂³	D₈×D₄₃	1	1	yes	characteristic
198	D₄	—	344	2	no	—
199	D₄	—	344	2	no	—
200	D₄	—	172	4	no	—
201	D₄	—	172	4	no	—
202	C₂×C₄	—	8	4	no	—
203	C₂×C₄	—	8	2	no	—
204	C₂×C₄	—	86	4	no	—
205	C₂×C₄	—	86	2	no	—
206	C₂×C₄	#13063287	1	1	yes	characteristic
207	C₂×C₄	#13063300	1	1	yes	characteristic
208	C₂×C₄	#13063321	1	1	yes	characteristic
209	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
210	C₂×C₄	#13063348	1	1	yes	characteristic
211	C₂×C₄	#13063348	1	1	yes	characteristic
212	C₈	—	86	2	no	—
213	C₈	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
214	C₈	#13063287	1	1	yes	characteristic
215	C₈	#13063300	1	1	yes	characteristic
216	C₈	#13063314	1	1	yes	characteristic
217	C₂²	—	344	8	no	—
218	C₂²	—	344	4	no	—
219	C₂²	—	688	2	no	—
220	C₂²	—	688	2	no	—
221	C₂²	—	688	4	no	—
222	C₂²	#14582981	1	1	yes	characteristic
223	C₂²	#14583136	1	1	yes	characteristic
224	C₂²	#14583274	1	1	yes	characteristic
225	C₂²	#14583336	1	4	yes	—
226	C₄	—	16	2	no	—
227	C₄	—	172	2	no	—
228	C₄	#14582800	1	1	yes	characteristic
229	C₄	#14582981	1	1	yes	characteristic
230	C₄	#14583136	1	1	yes	characteristic
231	C₄	#14583284	1	1	yes	characteristic
232	C₂	—	688	4	no	—
233	C₂	#19135459	1	1	yes	characteristic
234	C₂	#19136470	1	2	yes	—
235	C₂	#19136699	1	2	yes	—
236	C₂	#19136860	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₆₈₈

C₂

yes

maximal, characteristic

C₂×#14582699

C₂

yes

maximal, complemented

C₂×#14582674

C₂

yes

maximal, characteristic, complemented

#19135459

C₂

yes

maximal, complemented

C₂×C₄₃×#367

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₄₄

C₂²

yes

—

C₂×D₆₈₈

—

C₂×D₆₈₈

—

C₂×D₆₈₈

C₄

yes

complemented

C₂²×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×#13063245

—

C₂×C₈×Dic₄₃

C₂²

yes

—

—

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×#107×C₄₃

C₂²

yes

—

C₄₃×#367

—

C₂²×D₁₇₂

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

—

C₂×C₄×Dic₄₃

D₄

yes

characteristic

D₆₈₈

—

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

D₄

yes

—

#13063245

—

C₈×Dic₄₃

—

C₈×Dic₄₃

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₁₆×C₄₃

D₄

yes

—

C₂×C₁₆×C₄₃

D₄

yes

—

#107×C₄₃

—

#107×C₄₃

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

D₈

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

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×D₄

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₈

yes

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

C₂²⋊C₄

yes

complemented

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×D₄

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

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₄₃

C₄×D₄

yes

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

#13239

—

maximal, Sylow

C₂²×C₄₃

C₄×D₈

yes

characteristic

100

C₂²×C₄₃

#466

yes

characteristic

101

C₂²×C₄₃

#493

yes

characteristic

102

C₂²×C₄₃

#509

yes

—

103

C₂×D₄₃

—

104

C₂×D₄₃

—

105

C₂×D₄₃

—

106

C₂×D₄₃

—

107

C₂×D₄₃

—

108

C₄×C₄₃

—

109

C₄×C₄₃

#390

yes

characteristic

110

C₄×C₄₃

C₄×D₈

yes

characteristic

111

C₄×C₄₃

#466

yes

characteristic

112

C₄×C₄₃

#495

yes

characteristic

113

Dic₄₃

—

114

C₂²×D₁₆

—

115

C₂×#367

D₄₃

yes

characteristic, complemented

116

C₂×#357

—

117

C₂×#346

—

118

#1970

—

119

C₂×C₄₃

#1970

yes

characteristic

120

C₂×C₄₃

#2177

yes

—

121

C₂×C₄₃

#2218

yes

—

122

C₂×C₄₃

#2250

yes

—

123

D₄₃

—

124

C₂²×D₈

—

125

C₂×D₁₆

—

126

C₂×D₁₆

—

127

C₂×D₁₆

—

128

C₂²×C₁₆

—

129

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

130

C₂×#107

C₂×D₄₃

yes

—

131

C₂×#102

—

132

C₂×C₄×C₈

—

133

#390

—

134

#367

—

135

#357

—

136

#346

—

137

C₄₃

#13239

yes

characteristic, complemented, Sylow

138

C₂²×D₄

—

139

C₂×D₈

—

140

C₂×D₈

—

141

C₂×D₈

—

142

C₂×D₈

—

143

C₂×D₈

—

144

C₂×D₈

—

145

C₂²×C₈

—

146

C₂²×C₈

C₂²×D₄₃

yes

characteristic

147

C₂×C₄⋊C₄

—

148

C₂×C₂²⋊C₄

—

172

—

149

C₂×C₄²

—

150

D₁₆

—

151

C₂×C₁₆

—

152

C₂×C₁₆

—

153

C₂×C₁₆

—

154

C₂×C₁₆

C₄×D₄₃

yes

—

155

C₂×C₁₆

D₁₇₂

yes

—

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

—

170

C₂²×C₄

—

171

C₂²×C₄

D₄×D₄₃

yes

characteristic

172

D₈

—

173

D₈

—

174

D₈

—

172

—

175

D₈

—

172

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

180

C₂×C₈

C₂×D₁₇₂

yes

characteristic

181

C₂×C₈

D₄×D₄₃

yes

characteristic

182

C₂×C₈

#10621902

yes

characteristic

183

C₂×C₈

#10621902

yes

characteristic

184

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

344

—

188

C₄²

—

189

C₄²

—

190

C₁₆

—

191

C₁₆

(C₂×D₄₃)⋊C₄

yes

complemented

192

C₂³

—

344

—

193

C₂³

—

344

—

194

C₂³

—

344

—

195

C₂³

—

344

—

196

C₂³

—

172

—

197

C₂³

D₈×D₄₃

yes

characteristic

198

D₄

—

344

—

199

D₄

—

344

—

200

D₄

—

172

—

201

D₄

—

172

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

#13063287

yes

characteristic

207

C₂×C₄

#13063300

yes

characteristic

208

C₂×C₄

#13063321

yes

characteristic

209

C₂×C₄

D₈×D₄₃

yes

characteristic

210

C₂×C₄

#13063348

yes

characteristic

211

C₂×C₄

#13063348

yes

characteristic

212

C₈

—

213

C₈

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

214

C₈

#13063287

yes

characteristic

215

C₈

#13063300

yes

characteristic

216

C₈

#13063314

yes

characteristic

217

C₂²

—

344

—

218

C₂²

—

344

—

219

C₂²

—

688

—

220

C₂²

—

688

—

221

C₂²

—

688

—

222

C₂²

#14582981

yes

characteristic

223

C₂²

#14583136

yes

characteristic

224

C₂²

#14583274

yes

characteristic

225

C₂²

#14583336

yes

—

226

C₄

—

227

C₄

—

172

—

228

C₄

#14582800

yes

characteristic

229

C₄

#14582981

yes

characteristic

230

C₄

#14583136

yes

characteristic

231

C₄

#14583284

yes

characteristic

232

C₂

—

688

—

233

C₂

#19135459

yes

characteristic

234

C₂

#19136470

yes

—

235

C₂

#19136699

yes

—

236

C₂

#19136860

yes

—

	subgroup	G/H
center	C₂³	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#367	C₂
socle	C₂³×C₄₃	C₂×D₈
prime radical	C₂²×D₆₈₈	C₂
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#367	D₄₃
hypocenter	C₄₃	#13239
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#367

subgroup

G/H

center

C₂³

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#367

C₂

socle

C₂³×C₄₃

C₂×D₈

prime radical

C₂²×D₆₈₈

C₂

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#367

N	H ≅ G/N	type
2. C₂×#14582699	C₂	semidirect
3. C₂×#14582674	C₂	semidirect
4. #19135459	C₂	semidirect
5. C₂×C₄₃×#367	C₂	semidirect
9. C₂×D₆₈₈	C₄	semidirect
71. C₁₆×C₄₃	C₂²⋊C₄	semidirect
115. C₂×#367	D₄₃	semidirect
137. C₄₃	#13239	semidirect
191. C₁₆	(C₂×D₄₃)⋊C₄	semidirect

H ≅ G/N

type

2. C₂×#14582699

C₂

semidirect

3. C₂×#14582674

C₂

semidirect

4. #19135459

C₂

semidirect

5. C₂×C₄₃×#367

C₂

semidirect

9. C₂×D₆₈₈

C₄

semidirect

71. C₁₆×C₄₃

C₂²⋊C₄

semidirect

115. C₂×#367

D₄₃

semidirect

137. C₄₃

#13239

semidirect

191. C₁₆

(C₂×D₄₃)⋊C₄

semidirect

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

subgroup	index
C₂²×D₆₈₈	2
C₂×#14582699	2
C₂×#14582674	2
#19135459	2
C₂×C₄₃×#367	2
#13239	43

subgroup

index

C₂²×D₆₈₈

C₂×C₄₃×#367

Subgroups — #25014989

Conjugacy classes of subgroups

Complements

Maximal subgroups