Group #25015067 — subgroups

Subgroups — #25015067

Order 11008.

494 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 159 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×#14583279	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582704	C₂	1	4	yes	maximal
3	C₄×#13063259	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₇₂	—	2	1	no	—
6	C₂²×Dic₁₇₂	C₂²	1	2	yes	—
7	C₂×#13063325	—	2	1	no	—
8	#14583279	—	2	2	no	—
9	#14583279	C₄	1	4	yes	complemented
10	C₂×#13063259	C₂²	1	2	yes	—
11	C₄×C₄⋊Dic₄₃	—	2	1	no	—
12	#14582704	—	2	8	no	—
13	#14582662	—	2	1	no	—
14	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×C₄⋊C₁₆	—	2	2	no	—
17	C₂²×Dic₈₆	—	2	2	no	—
18	C₂×Dic₁₇₂	—	2	4	no	—
19	C₂×Dic₁₇₂	—	2	4	no	—
20	C₂×Dic₁₇₂	—	2	4	no	—
21	C₂×Dic₁₇₂	—	2	2	no	—
22	C₂×Dic₁₇₂	—	4	4	no	—
23	C₂×Dic₁₇₂	C₂×C₄	1	4	yes	—
24	#13063325	—	2	4	no	—
25	#13063325	—	4	2	no	—
26	C₂×C₄⋊Dic₄₃	—	2	2	no	—
27	C₂×C₄⋊Dic₄₃	—	4	1	no	—
28	C₂×C₄⋊Dic₄₃	—	4	1	no	—
29	C₂×C₄×Dic₄₃	—	4	1	no	—
30	#13063259	—	2	2	no	—
31	#13063259	D₄	1	4	yes	—
32	C₄₃⋊#95	—	4	1	no	—
33	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
36	C₂×C₁₆×C₄₃	—	2	2	no	—
37	C₂×C₁₆×C₄₃	—	2	4	no	—
38	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₄₃	D₄	1	2	yes	—
40	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
41	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₄₃	—	4	2	no	—
44	C₂²×Dic₄₃	—	4	2	no	—
45	C₂×Dic₈₆	—	2	4	no	—
46	C₂×Dic₈₆	—	4	4	no	—
47	C₂×Dic₈₆	—	4	4	no	—
48	C₂×Dic₈₆	—	4	2	no	—
49	C₂×C₈×C₄₃	—	2	2	no	—
50	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₄₃	#41	1	2	yes	—
55	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
56	C₄²×C₄₃	SD₁₆	1	2	yes	—
57	C₄⋊Dic₄₃	—	2	4	no	—
58	C₄⋊Dic₄₃	—	4	4	no	—
59	C₄⋊Dic₄₃	—	4	4	no	—
60	C₄⋊Dic₄₃	—	4	2	no	—
61	C₄×Dic₄₃	—	8	2	no	—
62	Dic₁₇₂	—	2	8	no	—
63	Dic₁₇₂	—	4	8	no	—
64	Dic₁₇₂	—	4	2	no	—
65	Dic₁₇₂	—	4	2	no	—
66	C₁₆×C₄₃	—	4	2	no	—
67	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₄₃	—	2	2	no	—
69	C₂×C₄×C₄₃	#102	1	2	yes	—
70	C₂×C₄×C₄₃	#102	1	2	yes	—
71	C₂×C₄×C₄₃	SD₃₂	1	2	yes	—
72	C₂×C₄×C₄₃	Q₃₂	1	2	yes	—
73	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₄₃	#121	1	2	yes	—
75	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
77	C₂×Dic₄₃	—	4	4	no	—
78	C₂×Dic₄₃	—	4	4	no	—
79	C₂×Dic₄₃	—	8	4	no	—
80	C₂×Dic₄₃	—	8	2	no	—
81	C₂×Dic₄₃	—	8	2	no	—
82	Dic₈₆	—	4	4	no	—
83	Dic₈₆	—	4	4	no	—
84	Dic₈₆	—	8	4	no	—
85	C₈×C₄₃	—	2	2	no	—
86	C₈×C₄₃	C₄×D₄	1	2	yes	—
87	C₈×C₄₃	#124	1	1	yes	characteristic
88	C₈×C₄₃	#127	1	1	yes	characteristic
89	#13253	—	43	1	no	maximal, Sylow
90	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
91	C₂²×C₄₃	#459	1	2	yes	—
92	C₂²×C₄₃	C₂×SD₃₂	1	1	yes	characteristic
93	C₂²×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
94	C₂²×C₄₃	#510	1	2	yes	—
95	C₄×C₄₃	—	2	2	no	—
96	C₄×C₄₃	#358	1	4	yes	complemented
97	C₄×C₄₃	#390	1	1	yes	characteristic
98	C₄×C₄₃	#418	1	1	yes	characteristic
99	C₄×C₄₃	#460	1	2	yes	—
100	Dic₄₃	—	8	4	no	—
101	Dic₄₃	—	8	4	no	—
102	C₂×#494	—	43	1	no	—
103	C₂×C₄⋊C₁₆	D₄₃	1	1	yes	characteristic
104	C₂×#358	—	43	4	no	—
105	C₄×#107	—	43	1	no	—
106	C₂×C₄₃	#1982	1	1	yes	characteristic
107	C₂×C₄₃	C₂×#358	1	1	yes	characteristic
108	C₂×C₄₃	#2141	1	1	yes	characteristic
109	C₂×C₄₃	#2208	1	2	yes	—
110	C₂×C₄₃	#2209	1	2	yes	—
111	C₂²×Q₁₆	—	43	2	no	—
112	C₂²×Q₁₆	—	86	1	no	—
113	C₂×C₄⋊Q₈	—	86	1	no	—
114	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
115	#494	—	43	4	no	—
116	#494	—	86	2	no	—
117	C₂×#107	—	43	2	no	—
118	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
119	C₄×C₄⋊C₄	—	86	1	no	—
120	C₄⋊C₁₆	—	2	2	no	—
121	#358	—	86	8	no	—
122	#340	—	86	1	no	—
123	C₄₃	#13253	1	1	yes	characteristic, complemented, Sylow
124	C₂²×Q₈	—	86	2	no	—
125	C₂×Q₁₆	—	43	4	no	—
126	C₂×Q₁₆	—	86	4	no	—
127	C₂×Q₁₆	—	86	4	no	—
128	C₂×Q₁₆	—	86	4	no	—
129	C₂×Q₁₆	—	86	2	no	—
130	C₂×Q₁₆	—	172	4	no	—
131	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
132	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
133	C₄⋊Q₈	—	86	4	no	—
134	C₄⋊Q₈	—	172	2	no	—
135	C₂×C₄⋊C₄	—	86	2	no	—
136	C₂×C₄⋊C₄	—	172	1	no	—
137	C₂×C₄⋊C₄	—	172	1	no	—
138	C₂×C₄²	—	172	1	no	—
139	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
140	C₂×C₁₆	—	2	4	no	—
141	C₂×C₁₆	—	2	2	no	—
142	#107	—	43	4	no	—
143	#107	—	86	2	no	—
144	C₄×C₈	C₄×D₄₃	1	2	yes	—
145	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
146	#95	—	172	1	no	—
147	C₂×Q₈	—	86	4	no	—
148	C₂×Q₈	—	172	4	no	—
149	C₂×Q₈	—	172	4	no	—
150	C₂×Q₈	—	172	2	no	—
151	C₂²×C₄	—	172	2	no	—
152	C₂²×C₄	—	172	2	no	—
153	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
154	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
155	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
156	Q₁₆	—	86	8	no	—
157	Q₁₆	—	172	8	no	—
158	Q₁₆	—	172	2	no	—
159	Q₁₆	—	172	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
162	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
163	C₂×C₈	D₄×D₄₃	1	2	yes	—
164	C₂×C₈	#10621902	1	2	yes	—
165	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
166	C₄⋊C₄	—	86	4	no	—
167	C₄⋊C₄	—	172	4	no	—
168	C₄⋊C₄	—	172	4	no	—
169	C₄⋊C₄	—	172	2	no	—
170	C₄²	—	344	2	no	—
171	C₄²	#10621873	1	2	yes	—
172	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
173	C₁₆	—	4	2	no	—
174	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
175	Q₈	—	344	4	no	—
176	Q₈	—	172	4	no	—
177	Q₈	—	172	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	344	2	no	—
180	C₂×C₄	—	344	2	no	—
181	C₂×C₄	—	344	4	no	—
182	C₂×C₄	—	172	4	no	—
183	C₂×C₄	—	172	4	no	—
184	C₂×C₄	#13063247	1	2	yes	—
185	C₂×C₄	#13063247	1	2	yes	—
186	C₂×C₄	#13063270	1	2	yes	—
187	C₂×C₄	Dic₃₄₄	1	2	yes	—
188	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
189	C₂×C₄	#13063300	1	2	yes	—
190	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
191	C₂×C₄	#13063353	1	2	yes	—
192	C₈	—	2	2	no	—
193	C₈	#13063287	1	2	yes	—
194	C₈	#13063314	1	1	yes	characteristic
195	C₈	#13063321	1	1	yes	characteristic
196	C₂²	C₂×#13063247	1	1	yes	characteristic
197	C₂²	#14583095	1	2	yes	—
198	C₂²	C₂×#13063270	1	1	yes	characteristic
199	C₂²	C₂×Dic₃₄₄	1	1	yes	characteristic
200	C₂²	#14583342	1	2	yes	—
201	C₄	—	2	2	no	—
202	C₄	—	344	4	no	—
203	C₄	—	344	4	no	—
204	C₄	#14582704	1	4	yes	complemented
205	C₄	#14582800	1	1	yes	characteristic
206	C₄	#14582905	1	1	yes	characteristic
207	C₄	#14583100	1	2	yes	—
208	C₂	#19135521	1	1	yes	characteristic
209	C₂	C₂×#14582704	1	1	yes	characteristic
210	C₂	#19136316	1	1	yes	characteristic
211	C₂	#19136641	1	2	yes	—
212	C₂	#19136646	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583279

C₂

yes

maximal, characteristic

C₂×#14582704

C₂

yes

maximal

C₄×#13063259

C₂

yes

maximal, characteristic

C₂×C₄₃×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×Dic₁₇₂

—

C₂²×Dic₁₇₂

C₂²

yes

—

C₂×#13063325

—

#14583279

—

#14583279

C₄

yes

complemented

C₂×#13063259

C₂²

yes

—

C₄×C₄⋊Dic₄₃

—

#14582704

—

#14582662

—

C₂²×C₁₆×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

—

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

#13063325

—

#13063325

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄×Dic₄₃

—

#13063259

—

#13063259

D₄

yes

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₄²×C₄₃

C₂²⋊C₄

yes

—

C₄²×C₄₃

SD₁₆

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

SD₃₂

yes

—

C₂×C₄×C₄₃

Q₃₂

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₄×D₄

yes

—

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

C₂×SD₃₂

yes

characteristic

C₂²×C₄₃

C₂×Q₃₂

yes

characteristic

C₂²×C₄₃

#510

yes

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

100

Dic₄₃

—

101

Dic₄₃

—

102

C₂×#494

—

103

C₂×C₄⋊C₁₆

D₄₃

yes

characteristic

104

C₂×#358

—

105

C₄×#107

—

106

C₂×C₄₃

#1982

yes

characteristic

107

C₂×C₄₃

C₂×#358

yes

characteristic

108

C₂×C₄₃

#2141

yes

characteristic

109

C₂×C₄₃

#2208

yes

—

110

C₂×C₄₃

#2209

yes

—

111

C₂²×Q₁₆

—

112

C₂²×Q₁₆

—

113

C₂×C₄⋊Q₈

—

114

C₂²×C₁₆

C₂×D₄₃

yes

—

115

#494

—

116

#494

—

117

C₂×#107

—

118

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

119

C₄×C₄⋊C₄

—

120

C₄⋊C₁₆

—

121

#358

—

122

#340

—

123

C₄₃

#13253

yes

characteristic, complemented, Sylow

124

C₂²×Q₈

—

125

C₂×Q₁₆

—

126

C₂×Q₁₆

—

127

C₂×Q₁₆

—

128

C₂×Q₁₆

—

129

C₂×Q₁₆

—

130

C₂×Q₁₆

—

172

—

131

C₂²×C₈

D₁₇₂

yes

characteristic

132

C₂²×C₈

C₂²×D₄₃

yes

characteristic

133

C₄⋊Q₈

—

134

C₄⋊Q₈

—

172

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

172

—

137

C₂×C₄⋊C₄

—

172

—

138

C₂×C₄²

—

172

—

139

C₂×C₄²

D₁₇₂

yes

characteristic

140

C₂×C₁₆

—

141

C₂×C₁₆

—

142

#107

—

143

#107

—

144

C₄×C₈

C₄×D₄₃

yes

—

145

C₄×C₈

C₂²⋊D₄₃

yes

—

146

#95

—

172

—

147

C₂×Q₈

—

148

C₂×Q₈

—

172

—

149

C₂×Q₈

—

172

—

150

C₂×Q₈

—

172

—

151

C₂²×C₄

—

172

—

152

C₂²×C₄

—

172

—

153

C₂²×C₄

D₃₄₄

yes

characteristic

154

C₂²×C₄

D₃₄₄

yes

characteristic

155

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

156

Q₁₆

—

157

Q₁₆

—

172

—

158

Q₁₆

—

172

—

159

Q₁₆

—

172

—

160

C₂×C₈

—

161

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

162

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

163

C₂×C₈

D₄×D₄₃

yes

—

164

C₂×C₈

#10621902

yes

—

165

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

172

—

168

C₄⋊C₄

—

172

—

169

C₄⋊C₄

—

172

—

170

C₄²

—

344

—

171

C₄²

#10621873

yes

—

172

C₄²

(C₂×D₄₃)⋊C₄

yes

—

173

C₁₆

—

174

C₂³

C₂×D₃₄₄

yes

characteristic

175

Q₈

—

344

—

176

Q₈

—

172

—

177

Q₈

—

172

—

178

C₂×C₄

—

179

C₂×C₄

—

344

—

180

C₂×C₄

—

344

—

181

C₂×C₄

—

344

—

182

C₂×C₄

—

172

—

183

C₂×C₄

—

172

—

184

C₂×C₄

#13063247

yes

—

185

C₂×C₄

#13063247

yes

—

186

C₂×C₄

#13063270

yes

—

187

C₂×C₄

Dic₃₄₄

yes

—

188

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

189

C₂×C₄

#13063300

yes

—

190

C₂×C₄

C₂×#10621873

yes

characteristic

191

C₂×C₄

#13063353

yes

—

192

C₈

—

193

C₈

#13063287

yes

—

194

C₈

#13063314

yes

characteristic

195

C₈

#13063321

yes

characteristic

196

C₂²

C₂×#13063247

yes

characteristic

197

C₂²

#14583095

yes

—

198

C₂²

C₂×#13063270

yes

characteristic

199

C₂²

C₂×Dic₃₄₄

yes

characteristic

200

C₂²

#14583342

yes

—

201

C₄

—

202

C₄

—

344

—

203

C₄

—

344

—

204

C₄

#14582704

yes

complemented

205

C₄

#14582800

yes

characteristic

206

C₄

#14582905

yes

characteristic

207

C₄

#14583100

yes

—

208

C₂

#19135521

yes

characteristic

209

C₂

C₂×#14582704

yes

characteristic

210

C₂

#19136316

yes

characteristic

211

C₂

#19136641

yes

—

212

C₂

#19136646

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₄₃	C₂×D₈
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#13253
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center

C₂³

C₂×D₃₄₄

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×C₄⋊C₁₆

C₂

socle, prime radical

C₂³×C₄₃

C₂×D₈

cosocle

C₂²×C₈×C₄₃

C₂³

hypercenter

C₂×C₄⋊C₁₆

D₄₃

hypocenter

C₄₃

#13253

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
9. #14583279	C₄	semidirect
96. C₄×C₄₃	#358	semidirect
123. C₄₃	#13253	semidirect
204. C₄	#14582704	semidirect

H ≅ G/N

type

9. #14583279

C₄

semidirect

96. C₄×C₄₃

#358

semidirect

123. C₄₃

#13253

semidirect

204. C₄

#14582704

semidirect

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

subgroup	index
C₂×#14583279	2
C₂×#14582704	2
C₄×#13063259	2
C₂×C₄₃×C₄⋊C₁₆	2
#13253	43

subgroup

index

C₂×C₄₃×C₄⋊C₁₆

Subgroups — #25015067

Conjugacy classes of subgroups

Complements

Maximal subgroups