Group #25007933 — subgroups

Subgroups — #25007933

Order 11008.

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

normal subgroups only

This group has 310 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	#19136394	C₂	1	1	yes	maximal, characteristic
3	#19132654	C₂	1	2	yes	maximal, complemented
4	#19132643	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#335	C₂	1	1	yes	maximal, characteristic
6	#14583456	—	2	1	no	—
7	#14583304	C₂²	1	1	yes	characteristic
8	#14583279	C₂²	1	1	yes	characteristic
9	#14583250	—	2	1	no	—
10	#14583140	—	2	1	no	—
11	#14583140	C₄	1	2	yes	—
12	C₄×Dic₁₇₂	—	2	1	no	—
13	C₄×Dic₁₇₂	C₄	1	2	yes	—
14	C₄⋊(C₄₃⋊C₁₆)	C₂²	1	2	yes	—
15	C₂²⋊(C₄₃⋊C₁₆)	—	2	1	no	—
16	C₄×C₄₃⋊C₁₆	—	2	1	no	—
17	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
18	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#335	—	2	1	no	—
20	C₄₃×#335	C₂²	1	2	yes	—
21	C₂×Dic₁₇₂	—	2	1	no	—
22	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
23	#13063325	—	2	1	no	—
24	#13063325	—	2	1	no	—
25	#13063317	—	4	1	no	—
26	#13063304	—	2	2	no	—
27	#13063304	—	4	1	no	—
28	C₄×Dic₈₆	—	2	2	no	—
29	C₄×Dic₈₆	—	4	1	no	—
30	#13063284	—	4	1	no	—
31	C₂×C₄₃⋊C₁₆	—	2	2	no	—
32	#13063259	—	2	1	no	—
33	#13063259	C₂×C₄	1	2	yes	—
34	#13063250	—	2	2	no	—
35	#13063250	—	2	2	no	—
36	C₂²×C₈×C₄₃	—	4	1	no	—
37	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
40	C₄⋊C₈×C₄₃	—	2	2	no	—
41	C₄⋊C₈×C₄₃	—	4	1	no	—
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	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
49	C₂×Dic₈₆	—	2	2	no	—
50	C₂×Dic₈₆	—	4	1	no	—
51	C₂×C₈×C₄₃	—	2	2	no	—
52	C₂×C₈×C₄₃	—	4	1	no	—
53	C₂×C₈×C₄₃	—	4	2	no	—
54	C₂×C₈×C₄₃	—	8	2	no	—
55	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
60	C₄²×C₄₃	D₈	1	1	yes	characteristic
61	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
62	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
63	C₂²⋊Dic₄₃	—	4	2	no	—
64	C₄⋊Dic₄₃	—	2	2	no	—
65	C₄⋊Dic₄₃	—	4	1	no	—
66	C₄⋊Dic₄₃	—	4	1	no	—
67	C₄⋊Dic₄₃	—	4	1	no	—
68	Dic₄₃⋊C₄	—	4	2	no	—
69	Dic₄₃⋊C₄	—	4	2	no	—
70	C₄×Dic₄₃	—	4	2	no	—
71	Dic₁₇₂	—	4	2	no	—
72	Dic₁₇₂	—	4	2	no	—
73	C₄₃⋊C₁₆	—	4	2	no	—
74	C₂³×C₄₃	#102	1	1	yes	characteristic
75	C₂×C₄×C₄₃	—	2	1	no	—
76	C₂×C₄×C₄₃	—	2	1	no	—
77	C₂×C₄×C₄₃	—	4	1	no	—
78	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
79	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
80	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
81	C₂×C₄×C₄₃	SD₃₂	1	2	yes	—
82	C₂×C₄×C₄₃	Q₃₂	1	2	yes	—
83	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
86	C₂×Dic₄₃	—	4	2	no	—
87	C₂×Dic₄₃	—	4	2	no	—
88	Dic₈₆	—	4	2	no	—
89	Dic₈₆	—	4	2	no	—
90	Dic₈₆	—	8	2	no	—
91	C₈×C₄₃	—	2	1	no	—
92	C₈×C₄₃	—	2	1	no	—
93	C₈×C₄₃	—	2	1	no	—
94	C₈×C₄₃	—	8	2	no	—
95	C₈×C₄₃	#135	1	2	yes	—
96	#11949	—	43	1	no	maximal, Sylow
97	C₂²×C₄₃	—	2	1	no	—
98	C₂²×C₄₃	—	2	1	no	—
99	C₂²×C₄₃	#358	1	2	yes	—
100	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
101	C₄×C₄₃	—	2	1	no	—
102	C₄×C₄₃	—	2	1	no	—
103	C₄×C₄₃	—	2	1	no	—
104	C₄×C₄₃	#358	1	2	yes	—
105	C₄×C₄₃	#413	1	1	yes	characteristic
106	C₄×C₄₃	#416	1	1	yes	characteristic
107	C₄×C₄₃	C₂×SD₃₂	1	1	yes	characteristic
108	C₄×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
109	Dic₄₃	—	8	2	no	—
110	Dic₄₃	—	8	2	no	—
111	#3170	—	43	1	no	—
112	#2162	—	43	1	no	—
113	C₂×#335	D₄₃	1	1	yes	characteristic
114	#1365	—	43	2	no	—
115	#1362	—	43	2	no	—
116	C₂×C₄₃	—	2	2	no	—
117	C₂×C₄₃	#1540	1	1	yes	characteristic
118	C₂×C₄₃	C₂×#358	1	1	yes	characteristic
119	C₂×C₄₃	#2148	1	1	yes	characteristic
120	#533	—	86	1	no	—
121	#500	—	43	1	no	—
122	#494	—	43	1	no	—
123	#487	—	86	1	no	—
124	#467	—	43	2	no	—
125	#467	—	86	1	no	—
126	C₄×Q₁₆	—	43	2	no	—
127	C₄×Q₁₆	—	86	1	no	—
128	C₂×C₄⋊C₈	—	2	1	no	—
129	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
130	C₄⋊C₁₆	—	43	2	no	—
131	C₂²⋊C₁₆	—	86	1	no	—
132	C₄×C₁₆	—	86	1	no	—
133	#335	—	2	1	no	—
134	#335	C₂×D₄₃	1	2	yes	—
135	C₄₃	#11949	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₁₆	—	43	2	no	—
137	C₂×Q₁₆	—	86	1	no	—
138	C₂²×C₈	—	4	1	no	—
139	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
140	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
141	C₄⋊Q₈	—	86	1	no	—
142	C₄⋊Q₈	—	86	1	no	—
143	#125	—	172	1	no	—
144	C₂²⋊Q₈	—	86	2	no	—
145	C₂²⋊Q₈	—	172	1	no	—
146	C₄×Q₈	—	86	2	no	—
147	C₄×Q₈	—	172	1	no	—
148	#117	—	172	1	no	—
149	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
150	C₂×C₁₆	—	86	2	no	—
151	#107	—	43	2	no	—
152	#107	—	86	1	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	4	1	no	—
155	#103	—	86	2	no	—
156	#103	—	86	2	no	—
157	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
158	C₄×C₈	D₁₇₂	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
160	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
161	C₂×Q₈	—	86	2	no	—
162	C₂×Q₈	—	172	1	no	—
163	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
164	C₂²×C₄	#10621882	1	1	yes	characteristic
165	C₂²×C₄	#10621884	1	1	yes	characteristic
166	Q₁₆	—	172	2	no	—
167	Q₁₆	—	172	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	4	1	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	8	2	no	—
172	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
173	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
174	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
175	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
176	C₄⋊C₄	—	86	2	no	—
177	C₄⋊C₄	—	172	2	no	—
178	C₄⋊C₄	—	172	2	no	—
179	C₄⋊C₄	—	172	1	no	—
180	C₄⋊C₄	—	172	1	no	—
181	C₄⋊C₄	—	172	1	no	—
182	C₂²⋊C₄	—	172	2	no	—
183	C₄²	—	172	2	no	—
184	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
185	C₄²	#10621882	1	1	yes	characteristic
186	C₄²	#10621884	1	1	yes	characteristic
187	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
188	C₁₆	—	172	2	no	—
189	C₂³	#13063245	1	1	yes	characteristic
190	Q₈	—	344	2	no	—
191	Q₈	—	172	2	no	—
192	Q₈	—	172	2	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	172	2	no	—
197	C₂×C₄	—	172	2	no	—
198	C₂×C₄	#13063245	1	1	yes	characteristic
199	C₂×C₄	#13063245	1	1	yes	characteristic
200	C₂×C₄	#13063245	1	1	yes	characteristic
201	C₂×C₄	#13063269	1	2	yes	—
202	C₂×C₄	#13063271	1	2	yes	—
203	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
205	C₂×C₄	C₂×#10621884	1	1	yes	characteristic
206	C₈	—	2	1	no	—
207	C₈	—	2	1	no	—
208	C₈	—	2	1	no	—
209	C₈	—	8	2	no	—
210	C₈	#13063347	1	2	yes	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	#14582702	1	2	yes	—
214	C₂²	C₂×#13063245	1	1	yes	characteristic
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	344	2	no	—
219	C₄	—	344	2	no	—
220	C₄	#14582702	1	2	yes	—
221	C₄	#14582881	1	1	yes	characteristic
222	C₄	#14582896	1	1	yes	characteristic
223	C₄	C₂×#13063269	1	1	yes	characteristic
224	C₄	C₂×#13063271	1	1	yes	characteristic
225	C₂	—	2	2	no	—
226	C₂	#19133245	1	1	yes	characteristic
227	C₂	C₂×#14582702	1	1	yes	characteristic
228	C₂	#19136342	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19145181

C₂

yes

maximal, characteristic

#19136394

C₂

yes

maximal, characteristic

#19132654

C₂

yes

maximal, complemented

#19132643

C₂

yes

maximal, complemented

C₂×C₄₃×#335

C₂

yes

maximal, characteristic

#14583456

—

#14583304

C₂²

yes

characteristic

#14583279

C₂²

yes

—

—

C₄

yes

—

C₄×Dic₁₇₂

—

C₄×Dic₁₇₂

C₄

yes

—

C₄⋊(C₄₃⋊C₁₆)

C₂²

yes

—

C₂²⋊(C₄₃⋊C₁₆)

—

C₄×C₄₃⋊C₁₆

—

C₂×C₄⋊C₈×C₄₃

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#335

—

C₄₃×#335

C₂²

yes

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

—

—

—

—

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

#13063284

—

C₂×C₄₃⋊C₁₆

—

#13063259

—

#13063259

C₂×C₄

yes

—

#13063250

—

#13063250

—

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

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

D₈

yes

characteristic

C₄²×C₄₃

SD₁₆

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

#102

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

SD₃₂

yes

—

C₂×C₄×C₄₃

Q₃₂

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#135

yes

—

#11949

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#358

yes

—

100

C₂²×C₄₃

C₂×#102

yes

characteristic

101

C₄×C₄₃

—

102

C₄×C₄₃

—

103

C₄×C₄₃

—

104

C₄×C₄₃

#358

yes

—

105

C₄×C₄₃

#413

yes

characteristic

106

C₄×C₄₃

#416

yes

characteristic

107

C₄×C₄₃

C₂×SD₃₂

yes

characteristic

108

C₄×C₄₃

C₂×Q₃₂

yes

characteristic

109

Dic₄₃

—

110

Dic₄₃

—

111

#3170

—

112

#2162

—

113

C₂×#335

D₄₃

yes

characteristic

114

#1365

—

115

#1362

—

116

C₂×C₄₃

—

117

C₂×C₄₃

#1540

yes

characteristic

118

C₂×C₄₃

C₂×#358

yes

characteristic

119

C₂×C₄₃

#2148

yes

characteristic

120

#533

—

121

#500

—

122

#494

—

123

#487

—

124

#467

—

125

#467

—

126

C₄×Q₁₆

—

127

C₄×Q₁₆

—

128

C₂×C₄⋊C₈

—

129

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

130

C₄⋊C₁₆

—

131

C₂²⋊C₁₆

—

132

C₄×C₁₆

—

133

#335

—

134

#335

C₂×D₄₃

yes

—

135

C₄₃

#11949

yes

characteristic, complemented, Sylow

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂²×C₈

—

139

C₂²×C₈

C₄×D₄₃

yes

characteristic

140

C₂²×C₈

D₁₇₂

yes

characteristic

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

#125

—

172

—

144

C₂²⋊Q₈

—

145

C₂²⋊Q₈

—

172

—

146

C₄×Q₈

—

147

C₄×Q₈

—

172

—

148

#117

—

172

—

149

C₂×C₄²

C₂²⋊D₄₃

yes

characteristic

150

C₂×C₁₆

—

151

#107

—

152

#107

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

156

#103

—

157

C₄×C₈

C₄×D₄₃

yes

characteristic

158

C₄×C₈

D₁₇₂

yes

characteristic

159

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

160

C₄×C₈

C₂²×D₄₃

yes

characteristic

161

C₂×Q₈

—

162

C₂×Q₈

—

172

—

163

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

164

C₂²×C₄

#10621882

yes

characteristic

165

C₂²×C₄

#10621884

yes

characteristic

166

Q₁₆

—

172

—

167

Q₁₆

—

172

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

173

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

174

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

175

C₂×C₈

C₂×D₁₇₂

yes

characteristic

176

C₄⋊C₄

—

177

C₄⋊C₄

—

172

—

178

C₄⋊C₄

—

172

—

179

C₄⋊C₄

—

172

—

180

C₄⋊C₄

—

172

—

181

C₄⋊C₄

—

172

—

182

C₂²⋊C₄

—

172

—

183

C₄²

—

172

—

184

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

185

C₄²

#10621882

yes

characteristic

186

C₄²

#10621884

yes

characteristic

187

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

188

C₁₆

—

172

—

189

C₂³

#13063245

yes

characteristic

190

Q₈

—

344

—

191

Q₈

—

172

—

192

Q₈

—

172

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

172

—

197

C₂×C₄

—

172

—

198

C₂×C₄

#13063245

yes

characteristic

199

C₂×C₄

#13063245

yes

characteristic

200

C₂×C₄

#13063245

yes

characteristic

201

C₂×C₄

#13063269

yes

—

202

C₂×C₄

#13063271

yes

—

203

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

204

C₂×C₄

C₂×#10621882

yes

characteristic

205

C₂×C₄

C₂×#10621884

yes

characteristic

206

C₈

—

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

#13063347

yes

—

211

C₂²

—

212

C₂²

—

213

C₂²

#14582702

yes

—

214

C₂²

C₂×#13063245

yes

characteristic

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

344

—

219

C₄

—

344

—

220

C₄

#14582702

yes

—

221

C₄

#14582881

yes

characteristic

222

C₄

#14582896

yes

characteristic

223

C₄

C₂×#13063269

yes

characteristic

224

C₄

C₂×#13063271

yes

characteristic

225

C₂

—

226

C₂

#19133245

yes

characteristic

227

C₂

C₂×#14582702

yes

characteristic

228

C₂

#19136342

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063245
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#335	C₂
socle	C₂²×C₄₃	C₂×#102
prime radical	C₂³×C₄₃	#102
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	C₂×#335	D₄₃
hypocenter	C₄₃	#11949
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#335

subgroup

G/H

center

C₂×C₄

#13063245

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#335

C₂

C₂²×C₄₃

C₂³×C₄₃

C₄×C₈×C₄₃

C₂³

D₄₃

C₄₃

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

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#335

N	H ≅ G/N	type
3. #19132654	C₂	semidirect
4. #19132643	C₂	semidirect
135. C₄₃	#11949	semidirect

H ≅ G/N

type

3. #19132654

C₂

semidirect

4. #19132643

C₂

semidirect

135. C₄₃

#11949

semidirect

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

subgroup	index
#19145181	2
#19136394	2
#19132654	2
#19132643	2
C₂×C₄₃×#335	2
#11949	43

subgroup

index

C₂×C₄₃×#335

Subgroups — #25007933

Conjugacy classes of subgroups

Complements

Maximal subgroups