Group #25007544 — subgroups

Subgroups — #25007544

Order 11008.

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

normal subgroups only

This group has 334 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	#19145181	C₂	1	1	yes	maximal, characteristic
2	#19134723	C₂	1	1	yes	maximal, characteristic
3	#19132608	C₂	1	4	yes	maximal
4	C₄₃×#2162	C₂	1	1	yes	maximal, characteristic
5	#14583456	—	2	1	no	—
6	#14583304	C₄	1	1	yes	characteristic, complemented
7	#14583279	C₄	1	1	yes	characteristic, complemented
8	#14583250	—	2	1	no	—
9	#14583140	—	2	1	no	—
10	#14583140	C₂²	1	2	yes	—
11	C₄×Dic₁₇₂	—	2	1	no	—
12	C₄×Dic₁₇₂	C₄	1	2	yes	complemented
13	#14582769	—	2	1	no	—
14	#14582662	—	2	1	no	—
15	#14582662	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×C₄⋊C₁₆	—	2	1	no	—
18	C₄₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
19	C₄×C₁₆×C₄₃	—	2	1	no	—
20	C₂×Dic₁₇₂	—	2	1	no	—
21	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
22	#13063325	—	2	1	no	—
23	#13063325	—	2	1	no	—
24	#13063317	—	4	1	no	—
25	#13063304	—	2	2	no	—
26	#13063304	—	4	1	no	—
27	C₄×Dic₈₆	—	2	2	no	—
28	C₄×Dic₈₆	—	4	1	no	—
29	#13063284	—	4	1	no	—
30	C₂×C₄⋊Dic₄₃	—	2	2	no	—
31	C₂×C₄⋊Dic₄₃	—	4	1	no	—
32	C₂×C₄⋊Dic₄₃	—	4	1	no	—
33	#13063259	—	2	1	no	—
34	#13063259	C₂×C₄	1	2	yes	—
35	#13063250	—	2	2	no	—
36	#13063250	—	2	2	no	—
37	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
39	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
40	C₂×C₁₆×C₄₃	—	2	2	no	—
41	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
44	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×Dic₄₃	—	4	2	no	—
49	C₂×Dic₈₆	—	2	2	no	—
50	C₂×Dic₈₆	—	4	1	no	—
51	C₂×C₈×C₄₃	—	4	1	no	—
52	C₂×C₈×C₄₃	—	4	1	no	—
53	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
60	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
61	C₂²⋊Dic₄₃	—	4	2	no	—
62	C₄⋊Dic₄₃	—	2	2	no	—
63	C₄⋊Dic₄₃	—	4	1	no	—
64	C₄⋊Dic₄₃	—	4	1	no	—
65	C₄⋊Dic₄₃	—	4	1	no	—
66	C₄⋊Dic₄₃	—	4	2	no	—
67	C₄⋊Dic₄₃	—	4	2	no	—
68	C₄⋊Dic₄₃	—	8	2	no	—
69	C₄⋊Dic₄₃	—	8	2	no	—
70	Dic₄₃⋊C₄	—	4	2	no	—
71	Dic₄₃⋊C₄	—	4	2	no	—
72	C₄×Dic₄₃	—	4	2	no	—
73	Dic₁₇₂	—	4	2	no	—
74	Dic₁₇₂	—	4	2	no	—
75	C₁₆×C₄₃	—	4	2	no	—
76	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
77	C₂×C₄×C₄₃	—	2	2	no	—
78	C₂×C₄×C₄₃	—	2	1	no	—
79	C₂×C₄×C₄₃	—	2	1	no	—
80	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
81	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
84	C₂×C₄×C₄₃	SD₃₂	1	2	yes	—
85	C₂×C₄×C₄₃	Q₃₂	1	2	yes	—
86	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
88	C₂×Dic₄₃	—	4	2	no	—
89	C₂×Dic₄₃	—	4	2	no	—
90	C₂×Dic₄₃	—	8	2	no	—
91	C₂×Dic₄₃	—	8	2	no	—
92	C₂×Dic₄₃	—	8	2	no	—
93	Dic₈₆	—	4	2	no	—
94	Dic₈₆	—	4	2	no	—
95	Dic₈₆	—	8	2	no	—
96	C₈×C₄₃	—	2	1	no	—
97	C₈×C₄₃	—	2	1	no	—
98	C₈×C₄₃	—	2	1	no	—
99	C₈×C₄₃	—	2	1	no	—
100	#11857	—	43	1	no	maximal, Sylow
101	C₂²×C₄₃	—	2	1	no	—
102	C₂²×C₄₃	—	2	1	no	—
103	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
104	C₂²×C₄₃	C₂×SD₃₂	1	1	yes	characteristic
105	C₂²×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
106	C₄×C₄₃	—	2	1	no	—
107	C₄×C₄₃	—	2	1	no	—
108	C₄×C₄₃	#358	1	2	yes	—
109	C₄×C₄₃	#358	1	2	yes	—
110	C₄×C₄₃	#360	1	2	yes	—
111	C₄×C₄₃	#410	1	1	yes	characteristic
112	C₄×C₄₃	#421	1	1	yes	characteristic
113	Dic₄₃	—	8	2	no	—
114	Dic₄₃	—	8	2	no	—
115	Dic₄₃	—	16	2	no	—
116	#3170	—	43	1	no	—
117	#2162	D₄₃	1	1	yes	characteristic
118	#1834	—	43	1	no	—
119	#1348	—	43	4	no	—
120	C₂×C₄₃	—	2	1	no	—
121	C₂×C₄₃	—	2	1	no	—
122	C₂×C₄₃	#1517	1	1	yes	characteristic
123	C₂×C₄₃	C₂×#358	1	1	yes	characteristic
124	C₂×C₄₃	C₂×#360	1	1	yes	characteristic
125	#533	—	86	1	no	—
126	#500	—	43	1	no	—
127	#494	—	43	1	no	—
128	#487	—	86	1	no	—
129	#467	—	43	2	no	—
130	#467	—	86	1	no	—
131	C₄×Q₁₆	—	43	2	no	—
132	C₄×Q₁₆	—	86	1	no	—
133	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
134	#384	—	86	1	no	—
135	C₄⋊C₁₆	—	2	1	no	—
136	C₂²⋊C₁₆	C₂×D₄₃	1	2	yes	—
137	C₄×C₁₆	—	2	1	no	—
138	#340	—	43	2	no	—
139	#340	—	86	1	no	—
140	C₄₃	#11857	1	1	yes	characteristic, complemented, Sylow
141	C₂×Q₁₆	—	43	2	no	—
142	C₂×Q₁₆	—	86	1	no	—
143	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
144	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
145	C₄⋊Q₈	—	86	1	no	—
146	C₄⋊Q₈	—	86	1	no	—
147	#125	—	172	1	no	—
148	C₂²⋊Q₈	—	86	2	no	—
149	C₂²⋊Q₈	—	172	1	no	—
150	C₄×Q₈	—	86	2	no	—
151	C₄×Q₈	—	172	1	no	—
152	#117	—	172	1	no	—
153	C₂×C₄⋊C₄	—	86	2	no	—
154	C₂×C₄⋊C₄	—	172	1	no	—
155	C₂×C₄⋊C₄	—	172	1	no	—
156	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
157	C₂×C₁₆	—	2	2	no	—
158	#107	—	43	2	no	—
159	#107	—	86	1	no	—
160	#103	—	86	2	no	—
161	#103	—	86	2	no	—
162	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
163	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
164	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
166	C₂×Q₈	—	86	2	no	—
167	C₂×Q₈	—	172	1	no	—
168	C₂²×C₄	—	172	2	no	—
169	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
170	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
171	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
172	Q₁₆	—	172	2	no	—
173	Q₁₆	—	172	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
177	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
178	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
179	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
180	C₄⋊C₄	—	86	2	no	—
181	C₄⋊C₄	—	344	2	no	—
182	C₄⋊C₄	—	344	2	no	—
183	C₄⋊C₄	—	172	2	no	—
184	C₄⋊C₄	—	172	2	no	—
185	C₄⋊C₄	—	172	1	no	—
186	C₄⋊C₄	—	172	1	no	—
187	C₄⋊C₄	—	172	2	no	—
188	C₄⋊C₄	—	172	1	no	—
189	C₄⋊C₄	—	172	2	no	—
190	C₂²⋊C₄	—	172	2	no	—
191	C₄²	—	172	2	no	—
192	C₄²	#10621873	1	1	yes	characteristic
193	C₄²	#10621873	1	1	yes	characteristic
194	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
195	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
196	C₁₆	—	4	2	no	—
197	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
198	Q₈	—	344	2	no	—
199	Q₈	—	172	2	no	—
200	Q₈	—	172	2	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	344	2	no	—
205	C₂×C₄	—	344	2	no	—
206	C₂×C₄	—	344	2	no	—
207	C₂×C₄	—	172	2	no	—
208	C₂×C₄	—	172	2	no	—
209	C₂×C₄	#13063247	1	1	yes	characteristic
210	C₂×C₄	#13063247	1	1	yes	characteristic
211	C₂×C₄	#13063247	1	1	yes	characteristic
212	C₂×C₄	#13063247	1	1	yes	characteristic
213	C₂×C₄	#13063270	1	2	yes	—
214	C₂×C₄	Dic₃₄₄	1	2	yes	—
215	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
216	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	2	1	no	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	—	2	1	no	—
223	C₂²	C₂×#13063247	1	1	yes	characteristic
224	C₂²	C₂×#13063270	1	1	yes	characteristic
225	C₂²	C₂×Dic₃₄₄	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	344	2	no	—
229	C₄	—	344	2	no	—
230	C₄	—	688	2	no	—
231	C₄	#14582704	1	2	yes	—
232	C₄	#14582704	1	2	yes	—
233	C₄	#14582710	1	2	yes	—
234	C₄	#14582872	1	1	yes	characteristic
235	C₄	#14582915	1	1	yes	characteristic
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	#19133156	1	1	yes	characteristic
239	C₂	C₂×#14582704	1	1	yes	characteristic
240	C₂	C₂×#14582710	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19145181

C₂

yes

maximal, characteristic

#19134723

C₂

yes

maximal, characteristic

#19132608

C₂

yes

maximal

C₄₃×#2162

C₂

yes

maximal, characteristic

#14583456

—

#14583304

C₄

yes

characteristic, complemented

#14583279

C₄

yes

characteristic, complemented

#14583250

—

#14583140

—

#14583140

C₂²

yes

—

C₄×Dic₁₇₂

—

C₄×Dic₁₇₂

C₄

yes

—

—

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

—

C₄₃×C₂²⋊C₁₆

C₂²

yes

—

C₄×C₁₆×C₄₃

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

—

—

—

—

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

#13063284

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

#13063259

—

#13063259

C₂×C₄

yes

—

#13063250

—

#13063250

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

SD₁₆

yes

characteristic

C₄²×C₄₃

SD₁₆

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

SD₃₂

yes

—

C₂×C₄×C₄₃

Q₃₂

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

100

#11857

—

maximal, Sylow

101

C₂²×C₄₃

—

102

C₂²×C₄₃

—

103

C₂²×C₄₃

C₂×#102

yes

characteristic

104

C₂²×C₄₃

C₂×SD₃₂

yes

characteristic

105

C₂²×C₄₃

C₂×Q₃₂

yes

characteristic

106

C₄×C₄₃

—

107

C₄×C₄₃

—

108

C₄×C₄₃

#358

yes

—

109

C₄×C₄₃

#358

yes

—

110

C₄×C₄₃

#360

yes

—

111

C₄×C₄₃

#410

yes

characteristic

112

C₄×C₄₃

#421

yes

characteristic

113

Dic₄₃

—

114

Dic₄₃

—

115

Dic₄₃

—

116

#3170

—

117

#2162

D₄₃

yes

characteristic

118

#1834

—

119

#1348

—

120

C₂×C₄₃

—

121

C₂×C₄₃

—

122

C₂×C₄₃

#1517

yes

characteristic

123

C₂×C₄₃

C₂×#358

yes

characteristic

124

C₂×C₄₃

C₂×#360

yes

characteristic

125

#533

—

126

#500

—

127

#494

—

128

#487

—

129

#467

—

130

#467

—

131

C₄×Q₁₆

—

132

C₄×Q₁₆

—

133

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

134

#384

—

135

C₄⋊C₁₆

—

136

C₂²⋊C₁₆

C₂×D₄₃

yes

—

137

C₄×C₁₆

—

138

#340

—

139

#340

—

140

C₄₃

#11857

yes

characteristic, complemented, Sylow

141

C₂×Q₁₆

—

142

C₂×Q₁₆

—

143

C₂²×C₈

D₁₇₂

yes

characteristic

144

C₂²×C₈

C₂²×D₄₃

yes

characteristic

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

#125

—

172

—

148

C₂²⋊Q₈

—

149

C₂²⋊Q₈

—

172

—

150

C₄×Q₈

—

151

C₄×Q₈

—

172

—

152

#117

—

172

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

172

—

155

C₂×C₄⋊C₄

—

172

—

156

C₂×C₄²

D₁₇₂

yes

characteristic

157

C₂×C₁₆

—

158

#107

—

159

#107

—

160

#103

—

161

#103

—

162

C₄×C₈

C₄×D₄₃

yes

characteristic

163

C₄×C₈

C₄×D₄₃

yes

characteristic

164

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

165

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

166

C₂×Q₈

—

167

C₂×Q₈

—

172

—

168

C₂²×C₄

—

172

—

169

C₂²×C₄

D₃₄₄

yes

characteristic

170

C₂²×C₄

D₃₄₄

yes

characteristic

171

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

172

Q₁₆

—

172

—

173

Q₁₆

—

172

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

177

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

178

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

179

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

180

C₄⋊C₄

—

181

C₄⋊C₄

—

344

—

182

C₄⋊C₄

—

344

—

183

C₄⋊C₄

—

172

—

184

C₄⋊C₄

—

172

—

185

C₄⋊C₄

—

172

—

186

C₄⋊C₄

—

172

—

187

C₄⋊C₄

—

172

—

188

C₄⋊C₄

—

172

—

189

C₄⋊C₄

—

172

—

190

C₂²⋊C₄

—

172

—

191

C₄²

—

172

—

192

C₄²

#10621873

yes

characteristic

193

C₄²

#10621873

yes

characteristic

194

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

195

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

196

C₁₆

—

197

C₂³

C₂×D₃₄₄

yes

characteristic

198

Q₈

—

344

—

199

Q₈

—

172

—

200

Q₈

—

172

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

344

—

205

C₂×C₄

—

344

—

206

C₂×C₄

—

344

—

207

C₂×C₄

—

172

—

208

C₂×C₄

—

172

—

209

C₂×C₄

#13063247

yes

characteristic

210

C₂×C₄

#13063247

yes

characteristic

211

C₂×C₄

#13063247

yes

characteristic

212

C₂×C₄

#13063247

yes

characteristic

213

C₂×C₄

#13063270

yes

—

214

C₂×C₄

Dic₃₄₄

yes

—

215

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

216

C₂×C₄

C₂×#10621873

yes

characteristic

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₂²

—

222

C₂²

—

223

C₂²

C₂×#13063247

yes

characteristic

224

C₂²

C₂×#13063270

yes

characteristic

225

C₂²

C₂×Dic₃₄₄

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

344

—

229

C₄

—

344

—

230

C₄

—

688

—

231

C₄

#14582704

yes

—

232

C₄

#14582704

yes

—

233

C₄

#14582710

yes

—

234

C₄

#14582872

yes

characteristic

235

C₄

#14582915

yes

characteristic

236

C₂

—

237

C₂

—

238

C₂

#19133156

yes

characteristic

239

C₂

C₂×#14582704

yes

characteristic

240

C₂

C₂×#14582710

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#13063247
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#2162	C₂
socle	C₂²×C₄₃	C₂×#102
prime radical	C₂³×C₄₃	C₂×D₈
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#2162	D₄₃
hypocenter	C₄₃	#11857
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂²

C₂×#13063247

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#2162

C₂

socle

C₂²×C₄₃

C₂×#102

prime radical

C₂³×C₄₃

C₂×D₈

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

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

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

N	H ≅ G/N	type
6. #14583304	C₄	semidirect
7. #14583279	C₄	semidirect
12. C₄×Dic₁₇₂	C₄	semidirect
140. C₄₃	#11857	semidirect

H ≅ G/N

type

6. #14583304

C₄

semidirect

7. #14583279

C₄

semidirect

12. C₄×Dic₁₇₂

C₄

semidirect

140. C₄₃

#11857

semidirect

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

subgroup	index
#19145181	2
#19134723	2
#19132608	2
C₄₃×#2162	2
#11857	43

subgroup

index

C₄₃×#2162

Subgroups — #25007544

Conjugacy classes of subgroups

Complements

Maximal subgroups