Group #25016193 — subgroups

Subgroups — #25016193

Order 11008.

482 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 109 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×Dic₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14582699	C₂	1	2	yes	maximal, complemented
4	#19135459	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1380	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	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×#13063245	—	2	2	no	—
11	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
12	#14582800	—	2	2	no	—
13	Dic₄₃⋊C₁₆	—	2	2	no	—
14	#14582699	—	2	4	no	—
15	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#107×C₄₃	C₂²	1	2	yes	—
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	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
25	C₂×(C₂×D₄₃)⋊C₄	—	4	2	no	—
26	C₂×(C₂×D₄₃)⋊C₄	—	4	2	no	—
27	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
28	D₆₈₈	—	2	8	no	—
29	C₂×C₄₃⋊C₁₆	—	2	2	no	—
30	C₂×C₄₃⋊C₁₆	—	2	1	no	—
31	#13063245	—	4	4	no	—
32	C₈×Dic₄₃	—	2	1	no	—
33	C₈×Dic₄₃	—	2	1	no	—
34	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
36	C₂×C₁₆×C₄₃	—	2	2	no	—
37	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
38	#107×C₄₃	—	2	2	no	—
39	#107×C₄₃	—	2	2	no	—
40	C₂³×D₄₃	—	4	2	no	—
41	C₂²×C₄×C₄₃	—	4	2	no	—
42	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
44	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₄₃	#41	1	2	yes	—
54	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
55	C₄⋊C₄×C₄₃	—	4	2	no	—
56	C₄⋊C₄×C₄₃	—	4	2	no	—
57	(C₂×D₄₃)⋊C₄	—	8	4	no	—
58	(C₂×D₄₃)⋊C₄	—	8	4	no	—
59	C₄×Dic₄₃	—	2	1	no	—
60	C₄×Dic₄₃	—	2	1	no	—
61	C₂×C₄₃⋊C₈	—	2	1	no	—
62	C₂×C₄₃⋊C₈	—	2	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	C₄₃⋊C₁₆	—	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	—	8	2	no	—
78	C₂×C₄×C₄₃	—	8	2	no	—
79	C₂×C₄×C₄₃	—	8	2	no	—
80	C₂×C₄×C₄₃	#121	1	2	yes	—
81	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
83	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
84	C₂×Dic₄₃	—	2	1	no	—
85	C₂×Dic₄₃	—	2	1	no	—
86	C₂×Dic₄₃	—	2	1	no	—
87	C₂×Dic₄₃	—	2	2	no	—
88	C₂×Dic₄₃	D₁₆	1	2	yes	complemented
89	D₁₇₂	—	4	4	no	—
90	D₁₇₂	—	4	4	no	—
91	D₁₇₂	—	8	2	no	—
92	D₁₇₂	—	8	2	no	—
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	#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	—	16	2	no	—
111	C₄×C₄₃	#394	1	1	yes	characteristic
112	C₄×C₄₃	#463	1	2	yes	—
113	C₄×C₄₃	#469	1	1	yes	characteristic
114	Dic₄₃	—	2	2	no	—
115	Dic₄₃	—	4	1	no	—
116	C₂²×D₁₆	—	43	1	no	—
117	C₂×C₄⋊C₁₆	—	43	1	no	—
118	C₂×#357	—	43	2	no	—
119	#1970	—	43	2	no	—
120	#1380	D₄₃	1	1	yes	characteristic, complemented
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	—	43	1	no	—
131	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
132	C₂×#107	C₂×D₄₃	1	2	yes	—
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	—	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	—	43	1	no	—
147	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₂²⋊C₄	—	172	2	no	—
150	C₂×C₂²⋊C₄	—	172	2	no	—
151	C₂×C₄²	—	43	1	no	—
152	D₁₆	—	86	8	no	—
153	C₂×C₁₆	—	2	2	no	—
154	C₂×C₁₆	—	86	1	no	—
155	C₂×C₁₆	—	86	2	no	—
156	C₂×C₁₆	D₁₇₂	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	1	no	—
171	C₂²×C₄	—	43	1	no	—
172	C₂²×C₄	D₄×D₄₃	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	—	86	1	no	—
178	C₂×C₈	—	86	2	no	—
179	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
180	C₂×C₈	#10621898	1	2	yes	—
181	C₂×C₈	D₄×D₄₃	1	2	yes	—
182	C₂×C₈	#10621902	1	1	yes	characteristic
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	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	—	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	D₈×D₄₃	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	—	8	2	no	—
204	C₂×C₄	—	8	2	no	—
205	C₂×C₄	—	8	2	no	—
206	C₂×C₄	—	43	2	no	—
207	C₂×C₄	—	86	1	no	—
208	C₂×C₄	—	86	1	no	—
209	C₂×C₄	—	86	2	no	—
210	C₂×C₄	—	86	1	no	—
211	C₂×C₄	#13063298	1	2	yes	—
212	C₂×C₄	#13063300	1	1	yes	characteristic
213	C₂×C₄	#13063348	1	1	yes	characteristic
214	C₂×C₄	#13063352	1	2	yes	—
215	C₈	—	172	1	no	—
216	C₈	#13063295	1	1	yes	characteristic
217	C₈	#13063310	1	2	yes	—
218	C₈	#13063313	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	#14583093	1	2	yes	—
227	C₂²	#14583136	1	1	yes	characteristic
228	C₂²	D₁₆×D₄₃	1	1	yes	characteristic
229	C₂²	#14583332	1	1	yes	characteristic
230	C₂²	#14583336	1	2	yes	—
231	C₄	—	16	2	no	—
232	C₄	—	86	2	no	—
233	C₄	—	172	1	no	—
234	C₄	#14582817	1	1	yes	characteristic
235	C₄	#14583117	1	2	yes	—
236	C₄	#14583153	1	1	yes	characteristic
237	C₂	—	688	4	no	—
238	C₂	#19135907	1	1	yes	characteristic
239	C₂	#19136629	1	2	yes	—
240	C₂	#19136653	1	2	yes	—
241	C₂	#19136682	1	1	yes	characteristic
242	C₂	#19136699	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₆₈₈

C₂

yes

maximal, characteristic

C₂×Dic₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×#14582699

C₂

yes

maximal, complemented

#19135459

C₂

yes

maximal, complemented

C₄₃×#1380

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₄₄

C₂²

yes

—

C₂×D₆₈₈

—

C₂×D₆₈₈

—

C₂²×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×#13063245

—

C₂×C₈×Dic₄₃

C₂²

yes

characteristic

#14582800

—

Dic₄₃⋊C₁₆

—

#14582699

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×#107×C₄₃

C₂²

yes

—

C₂²×D₁₇₂

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

D₄

yes

—

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×C₄×Dic₄₃

D₄

yes

characteristic

D₆₈₈

—

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

—

#13063245

—

C₈×Dic₄₃

—

C₈×Dic₄₃

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₃

—

C₂×C₁₆×C₄₃

—

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

characteristic

C₂²×Dic₄₃

D₈

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

#41

yes

—

C₂×C₈×C₄₃

#41

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

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

#121

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₁₆

yes

complemented

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

#120

yes

characteristic

C₈×C₄₃

#123

yes

—

C₈×C₄₃

#124

yes

characteristic

C₄₃⋊C₈

—

#13448

—

maximal, Sylow

C₂²×C₄₃

#459

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

#394

yes

characteristic

112

C₄×C₄₃

#463

yes

—

113

C₄×C₄₃

#469

yes

characteristic

114

Dic₄₃

—

115

Dic₄₃

—

116

C₂²×D₁₆

—

117

C₂×C₄⋊C₁₆

—

118

C₂×#357

—

119

#1970

—

120

#1380

D₄₃

yes

characteristic, complemented

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

—

131

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

132

C₂×#107

C₂×D₄₃

yes

—

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

—

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

D₁₇₂

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

—

172

C₂²×C₄

D₄×D₄₃

yes

characteristic

173

D₈

—

174

D₈

—

175

D₈

—

172

—

176

D₈

—

172

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

C₂×D₁₇₂

yes

characteristic

180

C₂×C₈

#10621898

yes

—

181

C₂×C₈

D₄×D₄₃

yes

—

182

C₂×C₈

#10621902

yes

characteristic

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

344

—

186

C₂²⋊C₄

—

344

—

187

C₄²

—

188

C₄²

—

189

C₁₆

—

190

C₁₆

—

172

—

191

C₂³

—

344

—

192

C₂³

—

344

—

193

C₂³

—

344

—

194

C₂³

—

344

—

195

C₂³

—

344

—

196

C₂³

—

344

—

197

C₂³

—

172

—

198

C₂³

D₈×D₄₃

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

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

#13063298

yes

—

212

C₂×C₄

#13063300

yes

characteristic

213

C₂×C₄

#13063348

yes

characteristic

214

C₂×C₄

#13063352

yes

—

215

C₈

—

172

—

216

C₈

#13063295

yes

characteristic

217

C₈

#13063310

yes

—

218

C₈

#13063313

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

#14583093

yes

—

227

C₂²

#14583136

yes

characteristic

228

C₂²

D₁₆×D₄₃

yes

characteristic

229

C₂²

#14583332

yes

characteristic

230

C₂²

#14583336

yes

—

231

C₄

—

232

C₄

—

233

C₄

—

172

—

234

C₄

#14582817

yes

characteristic

235

C₄

#14583117

yes

—

236

C₄

#14583153

yes

characteristic

237

C₂

—

688

—

238

C₂

#19135907

yes

characteristic

239

C₂

#19136629

yes

—

240

C₂

#19136653

yes

—

241

C₂

#19136682

yes

characteristic

242

C₂

#19136699

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₄₃
commutator, cosocle	C₂²×C₈×C₄₃	C₂³
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1380	C₂
socle	C₂³×C₄₃	C₂×D₈
prime radical	C₂²×D₆₈₈	C₂
hypercenter	#1380	D₄₃
hypocenter	C₄₃	#13448
LCS	G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

subgroup

G/H

center

C₂³

D₈×D₄₃

commutator, cosocle

C₂²×C₈×C₄₃

C₂³

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#1380

C₂

socle

C₂³×C₄₃

C₂×D₈

prime radical

C₂²×D₆₈₈

C₂

D₄₃

C₄₃

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

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

N	H ≅ G/N	type
2. C₂×Dic₄₃⋊C₁₆	C₂	semidirect
3. C₂×#14582699	C₂	semidirect
4. #19135459	C₂	semidirect
5. C₄₃×#1380	C₂	semidirect
88. C₂×Dic₄₃	D₁₆	semidirect
120. #1380	D₄₃	semidirect
138. C₄₃	#13448	semidirect

H ≅ G/N

type

2. C₂×Dic₄₃⋊C₁₆

C₂

semidirect

3. C₂×#14582699

C₂

semidirect

4. #19135459

C₂

semidirect

5. C₄₃×#1380

C₂

semidirect

88. C₂×Dic₄₃

D₁₆

semidirect

120. #1380

D₄₃

semidirect

138. C₄₃

#13448

semidirect

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

subgroup	index
C₂²×D₆₈₈	2
C₂×Dic₄₃⋊C₁₆	2
C₂×#14582699	2
#19135459	2
C₄₃×#1380	2
#13448	43

subgroup

index

C₂²×D₆₈₈

C₂×Dic₄₃⋊C₁₆

C₂×#14582699

#19135459

C₄₃×#1380

#13448

Subgroups — #25016193

Conjugacy classes of subgroups

Complements

Maximal subgroups