Group #14298897 — subgroups

Subgroups — #14298897

Order 1920.

376 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 137 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	#11752340	C₂	1	2	yes	maximal
2	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	#11746767	C₂	1	4	yes	maximal
4	#10603856	—	3	1	no	maximal, Hall
5	C₂×#6758	C₂²	1	4	yes	—
6	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
7	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
8	C₄⋊(C₃⋊#170)	—	2	2	no	—
9	C₄⋊(C₃⋊#170)	—	2	2	no	—
10	C₃×C₄×C₅×C₈	C₄	1	1	yes	characteristic
11	C₃×C₈×Dic₅	C₄	1	2	yes	—
12	C₃×C₄×#168	C₄	1	1	yes	characteristic
13	#69791	—	5	1	no	maximal, Hall
14	#65681	—	3	2	no	—
15	C₄×C₈×D₅	D₃	1	1	yes	characteristic
16	#64896	—	3	4	no	—
17	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
18	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
19	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
20	C₂×C₃⋊#170	—	2	4	no	—
21	#6758	—	2	8	no	—
22	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
23	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
24	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
25	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
26	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
27	C₂×C₃×#168	C₂×C₄	1	2	yes	—
28	C₃×C₈×D₅	—	2	4	no	—
29	C₂×C₃×C₄×C₈	—	5	1	no	—
30	#4924	—	5	2	no	—
31	#4552	—	5	4	no	—
32	C₂×#700	—	3	4	no	—
33	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
34	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
35	C₄⋊#170	—	6	2	no	—
36	C₄⋊#170	—	6	2	no	—
37	C₄×C₅×C₈	Dic₃	1	1	yes	characteristic
38	C₈×Dic₅	Dic₃	1	2	yes	—
39	C₄×#168	Dic₃	1	1	yes	characteristic
40	#1837	—	15	1	no	Sylow
41	C₂²×C₃×D₅	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
48	C₃×C₄×D₅	—	2	2	no	—
49	C₃×C₄×D₅	—	2	2	no	—
50	C₃×C₄×D₅	#41	1	4	yes	—
51	C₃⋊#170	—	4	4	no	—
52	C₃×C₅×C₈	—	2	2	no	—
53	C₃×#168	—	2	2	no	—
54	C₂²×C₃×C₈	—	5	2	no	—
55	C₂×C₃×C₄²	—	5	1	no	—
56	C₂×#208	—	5	4	no	—
57	C₃×C₄×C₈	—	5	2	no	—
58	C₃×C₄×C₈	—	5	1	no	—
59	C₃×C₄×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
60	C₄⋊(C₃⋊C₈)	—	10	2	no	—
61	C₄⋊(C₃⋊C₈)	—	10	2	no	—
62	C₂×C₄×D₅	Dic₆	1	1	yes	characteristic
63	C₂×C₄×D₅	Dic₆	1	1	yes	characteristic
64	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
65	C₂×#170	—	6	4	no	—
66	#700	—	6	8	no	—
67	C₂×C₅×C₈	C₂×Dic₃	1	2	yes	—
68	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
69	C₄×Dic₅	D₁₂	1	1	yes	characteristic
70	C₄×Dic₅	D₁₂	1	1	yes	characteristic
71	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
72	C₂×#168	C₂×Dic₃	1	2	yes	—
73	C₈×D₅	—	2	4	no	—
74	#423	—	15	2	no	—
75	C₂×C₄×C₈	—	5	1	no	—
76	#341	—	15	4	no	—
77	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₃×D₅	—	2	1	no	—
79	C₂×C₃×D₅	—	2	1	no	—
80	C₂×C₃×D₅	#125	1	2	yes	—
81	C₃×C₄×C₅	#108	1	2	yes	—
82	C₃×C₄×C₅	#108	1	2	yes	—
83	C₃×C₄×C₅	#117	1	2	yes	—
84	C₃×Dic₅	—	2	1	no	—
85	C₃×Dic₅	—	2	1	no	—
86	C₃×Dic₅	#124	1	2	yes	—
87	C₂²×C₃×C₄	—	5	1	no	—
88	C₂²×C₃×C₄	—	5	1	no	—
89	C₂²×C₃×C₄	—	5	1	no	—
90	C₂×C₃×C₈	—	5	2	no	—
91	C₂×C₃×C₈	—	10	4	no	—
92	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
93	C₃×C₄²	—	5	1	no	—
94	C₃×C₄²	—	5	1	no	—
95	C₃×C₄²	—	5	1	no	—
96	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
97	#208	—	10	8	no	—
98	C₂×C₃⋊C₈	—	10	4	no	—
99	C₂²×D₅	C₂×Dic₆	1	1	yes	characteristic
100	C₂×C₄×C₅	C₄⋊Dic₃	1	1	yes	characteristic
101	C₂×C₄×C₅	C₄⋊Dic₃	1	1	yes	characteristic
102	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
103	C₂×Dic₅	C₄⋊Dic₃	1	1	yes	characteristic
104	C₂×Dic₅	C₄⋊Dic₃	1	1	yes	characteristic
105	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
106	C₄×D₅	—	2	2	no	—
107	C₄×D₅	—	2	2	no	—
108	C₄×D₅	#235	1	4	yes	—
109	#170	—	12	4	no	—
110	C₅×C₈	—	2	2	no	—
111	#168	—	2	2	no	—
112	C₂×M₁₆	—	15	4	no	—
113	C₂²×C₈	—	5	2	no	—
114	C₂×C₄²	—	5	1	no	—
115	C₄⋊C₈	—	30	2	no	—
116	C₄⋊C₈	—	30	2	no	—
117	C₄×C₈	—	5	2	no	—
118	C₄×C₈	—	5	1	no	—
119	C₄×C₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
120	C₂×C₃×C₅	#382	1	1	yes	characteristic
121	C₂×C₃×C₅	C₂×#108	1	1	yes	characteristic
122	C₂×C₃×C₅	C₂×#108	1	1	yes	characteristic
123	C₃×D₅	—	2	2	no	—
124	C₂³×C₃	—	5	1	no	—
125	C₂×C₃×C₄	—	5	1	no	—
126	C₂×C₃×C₄	—	5	4	no	—
127	C₂×C₃×C₄	—	5	1	no	—
128	C₂×C₃×C₄	—	5	1	no	—
129	C₂×C₃×C₄	—	10	2	no	—
130	C₂×C₃×C₄	—	10	2	no	—
131	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
132	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
133	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
134	C₃×C₈	—	2	2	no	—
135	C₃×C₈	—	10	2	no	—
136	C₃⋊C₈	—	20	4	no	—
137	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
138	C₂×D₅	—	2	1	no	—
139	C₂×D₅	—	2	1	no	—
140	C₂×D₅	#870	1	2	yes	—
141	C₄×C₅	#819	1	2	yes	—
142	C₄×C₅	#819	1	2	yes	—
143	C₄×C₅	#926	1	2	yes	—
144	Dic₅	—	2	1	no	—
145	Dic₅	—	2	1	no	—
146	Dic₅	#875	1	2	yes	—
147	C₂²×C₄	—	5	1	no	—
148	C₂²×C₄	—	5	1	no	—
149	C₂²×C₄	—	5	1	no	—
150	M₁₆	—	30	8	no	—
151	C₂×C₈	—	5	2	no	—
152	C₂×C₈	—	10	4	no	—
153	C₂×C₈	—	30	4	no	—
154	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	2	yes	—
155	C₄²	—	5	1	no	—
156	C₄²	—	5	1	no	—
157	C₄²	—	5	1	no	—
158	C₄²	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
159	C₃×C₅	#1837	1	1	yes	characteristic, complemented, Hall
160	C₂²×C₃	—	5	2	no	—
161	C₂²×C₃	—	10	1	no	—
162	C₂²×C₃	—	10	1	no	—
163	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
164	C₃×C₄	—	5	2	no	—
165	C₃×C₄	—	10	1	no	—
166	C₃×C₄	—	10	1	no	—
167	C₃×C₄	#3995	1	2	yes	—
168	C₃×C₄	#3996	1	2	yes	—
169	C₃×C₄	#4130	1	2	yes	—
170	C₂×C₅	#4936	1	1	yes	characteristic
171	C₂×C₅	C₂×#819	1	1	yes	characteristic
172	C₂×C₅	C₂×#819	1	1	yes	characteristic
173	D₅	—	2	2	no	—
174	C₂³	—	5	1	no	—
175	C₂×C₄	—	5	1	no	—
176	C₂×C₄	—	5	4	no	—
177	C₂×C₄	—	5	1	no	—
178	C₂×C₄	—	5	1	no	—
179	C₂×C₄	—	10	2	no	—
180	C₂×C₄	—	10	2	no	—
181	C₂×C₄	C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
182	C₂×C₄	C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
183	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
184	C₈	—	2	2	no	—
185	C₈	—	10	2	no	—
186	C₈	—	60	4	no	—
187	C₂×C₃	—	10	2	no	—
188	C₂×C₃	#65689	1	1	yes	characteristic
189	C₂×C₃	C₂×#3995	1	1	yes	characteristic
190	C₂×C₃	C₂×#3996	1	1	yes	characteristic
191	C₅	#69791	1	1	yes	characteristic, complemented, Sylow
192	C₂²	—	5	2	no	—
193	C₂²	—	10	1	no	—
194	C₂²	—	10	1	no	—
195	C₂²	C₂×C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
196	C₄	—	5	2	no	—
197	C₄	—	10	1	no	—
198	C₄	—	10	1	no	—
199	C₄	#91224	1	2	yes	—
200	C₄	#91225	1	2	yes	—
201	C₄	#91989	1	2	yes	—
202	C₃	#10603856	1	1	yes	characteristic, complemented, Sylow
203	C₂	—	10	2	no	—
204	C₂	#11752348	1	1	yes	characteristic
205	C₂	C₂×#91224	1	1	yes	characteristic
206	C₂	C₂×#91225	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11752340

C₂

yes

maximal

C₃×C₄×C₈×D₅

C₂

yes

maximal, characteristic

#11746767

C₂

yes

—

C₂²

yes

—

C₂×C₃×C₈×D₅

C₂²

yes

—

C₃×C₄²×D₅

C₂²

yes

characteristic

C₄⋊(C₃⋊#170)

—

C₄⋊(C₃⋊#170)

—

C₃×C₄×C₅×C₈

C₄

yes

characteristic

C₃×C₈×Dic₅

C₄

yes

—

C₃×C₄×#168

C₄

yes

—

—

C₄×C₈×D₅

D₃

yes

characteristic

#64896

—

C₂×C₃×C₄×D₅

Q₈

yes

characteristic

C₂×C₃×C₄×D₅

Q₈

yes

characteristic

C₂×C₃×C₄×D₅

C₂³

yes

characteristic

C₂×C₃⋊#170

—

#6758

—

C₂×C₃×C₅×C₈

C₂×C₄

yes

—

C₃×C₄²×C₅

C₂×C₄

yes

characteristic

C₃×C₄×Dic₅

C₂×C₄

yes

characteristic

C₃×C₄×Dic₅

D₄

yes

characteristic

C₃×C₄×Dic₅

D₄

yes

characteristic

C₂×C₃×#168

C₂×C₄

yes

—

C₃×C₈×D₅

—

C₂×C₃×C₄×C₈

—

#4924

—

#4552

—

C₂×#700

—

C₂×C₈×D₅

C₂×D₃

yes

—

C₄²×D₅

C₂×D₃

yes

characteristic

C₄⋊#170

—

C₄⋊#170

—

C₄×C₅×C₈

Dic₃

yes

characteristic

C₈×Dic₅

Dic₃

yes

—

C₄×#168

Dic₃

yes

characteristic

#1837

—

Sylow

C₂²×C₃×D₅

C₂×Q₈

yes

characteristic

C₂×C₃×C₄×C₅

C₄⋊C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₄⋊C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×Dic₅

C₄⋊C₄

yes

characteristic

C₂×C₃×Dic₅

C₄⋊C₄

yes

characteristic

C₂×C₃×Dic₅

C₂×D₄

yes

characteristic

C₃×C₄×D₅

—

C₃×C₄×D₅

—

C₃×C₄×D₅

#41

yes

—

C₃⋊#170

—

C₃×C₅×C₈

—

C₃×#168

—

C₂²×C₃×C₈

—

C₂×C₃×C₄²

—

C₂×#208

—

C₃×C₄×C₈

—

C₃×C₄×C₈

—

C₃×C₄×C₈

AGL(1,𝔽₅)

yes

characteristic

C₄⋊(C₃⋊C₈)

—

C₄⋊(C₃⋊C₈)

—

C₂×C₄×D₅

Dic₆

yes

characteristic

C₂×C₄×D₅

Dic₆

yes

characteristic

C₂×C₄×D₅

C₂²×D₃

yes

characteristic

C₂×#170

—

#700

—

C₂×C₅×C₈

C₂×Dic₃

yes

—

C₄²×C₅

C₂×Dic₃

yes

characteristic

C₄×Dic₅

D₁₂

yes

characteristic

C₄×Dic₅

D₁₂

yes

characteristic

C₄×Dic₅

C₂×Dic₃

yes

characteristic

C₂×#168

C₂×Dic₃

yes

—

C₈×D₅

—

#423

—

C₂×C₄×C₈

—

#341

—

C₂²×C₃×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₃×D₅

—

C₂×C₃×D₅

—

C₂×C₃×D₅

#125

yes

—

C₃×C₄×C₅

#108

yes

—

C₃×C₄×C₅

#108

yes

—

C₃×C₄×C₅

#117

yes

—

C₃×Dic₅

—

C₃×Dic₅

—

C₃×Dic₅

#124

yes

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂×AGL(1,𝔽₅)

yes

—

C₃×C₄²

—

C₃×C₄²

—

C₃×C₄²

—

C₃×C₄²

C₂×AGL(1,𝔽₅)

yes

characteristic

#208

—

C₂×C₃⋊C₈

—

C₂²×D₅

C₂×Dic₆

yes

characteristic

100

C₂×C₄×C₅

C₄⋊Dic₃

yes

characteristic

101

C₂×C₄×C₅

C₄⋊Dic₃

yes

characteristic

102

C₂×C₄×C₅

C₂²×Dic₃

yes

characteristic

103

C₂×Dic₅

C₄⋊Dic₃

yes

characteristic

104

C₂×Dic₅

C₄⋊Dic₃

yes

characteristic

105

C₂×Dic₅

C₂×D₁₂

yes

characteristic

106

C₄×D₅

—

107

C₄×D₅

—

108

C₄×D₅

#235

yes

—

109

#170

—

110

C₅×C₈

—

111

#168

—

112

C₂×M₁₆

—

113

C₂²×C₈

—

114

C₂×C₄²

—

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

C₄×C₈

—

118

C₄×C₈

—

119

C₄×C₈

ΓL(1,𝔽₁₆)

yes

characteristic

120

C₂×C₃×C₅

#382

yes

characteristic

121

C₂×C₃×C₅

C₂×#108

yes

characteristic

122

C₂×C₃×C₅

C₂×#108

yes

characteristic

123

C₃×D₅

—

124

C₂³×C₃

—

125

C₂×C₃×C₄

—

126

C₂×C₃×C₄

—

127

C₂×C₃×C₄

—

128

C₂×C₃×C₄

—

129

C₂×C₃×C₄

—

130

C₂×C₃×C₄

—

131

C₂×C₃×C₄

C₄⋊AGL(1,𝔽₅)

yes

characteristic

132

C₂×C₃×C₄

C₄⋊AGL(1,𝔽₅)

yes

characteristic

133

C₂×C₃×C₄

C₂²×AGL(1,𝔽₅)

yes

characteristic

134

C₃×C₈

—

135

C₃×C₈

—

136

C₃⋊C₈

—

137

C₂²×C₅

C₂×C₄⋊Dic₃

yes

characteristic

138

C₂×D₅

—

139

C₂×D₅

—

140

C₂×D₅

#870

yes

—

141

C₄×C₅

#819

yes

—

142

C₄×C₅

#819

yes

—

143

C₄×C₅

#926

yes

—

144

Dic₅

—

145

Dic₅

—

146

Dic₅

#875

yes

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

M₁₆

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

C₂×ΓL(1,𝔽₁₆)

yes

—

155

C₄²

—

156

C₄²

—

157

C₄²

—

158

C₄²

C₂×ΓL(1,𝔽₁₆)

yes

characteristic

159

C₃×C₅

#1837

yes

characteristic, complemented, Hall

160

C₂²×C₃

—

161

C₂²×C₃

—

162

C₂²×C₃

—

163

C₂²×C₃

C₂×C₄⋊AGL(1,𝔽₅)

yes

characteristic

164

C₃×C₄

—

165

C₃×C₄

—

166

C₃×C₄

—

167

C₃×C₄

#3995

yes

—

168

C₃×C₄

#3996

yes

—

169

C₃×C₄

#4130

yes

—

170

C₂×C₅

#4936

yes

characteristic

171

C₂×C₅

C₂×#819

yes

characteristic

172

C₂×C₅

C₂×#819

yes

characteristic

173

D₅

—

174

C₂³

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

C₄⋊ΓL(1,𝔽₁₆)

yes

characteristic

182

C₂×C₄

C₄⋊ΓL(1,𝔽₁₆)

yes

characteristic

183

C₂×C₄

C₂²×ΓL(1,𝔽₁₆)

yes

characteristic

184

C₈

—

185

C₈

—

186

C₈

—

187

C₂×C₃

—

188

C₂×C₃

#65689

yes

characteristic

189

C₂×C₃

C₂×#3995

yes

characteristic

190

C₂×C₃

C₂×#3996

yes

characteristic

191

C₅

#69791

yes

characteristic, complemented, Sylow

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

C₂×C₄⋊ΓL(1,𝔽₁₆)

yes

characteristic

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

#91224

yes

—

200

C₄

#91225

yes

—

201

C₄

#91989

yes

—

202

C₃

#10603856

yes

characteristic, complemented, Sylow

203

C₂

—

204

C₂

#11752348

yes

characteristic

205

C₂

C₂×#91224

yes

characteristic

206

C₂

C₂×#91225

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊ΓL(1,𝔽₁₆)
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)
Fitting	C₃×C₄×C₅×C₈	C₄
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂²×C₃×D₅	C₂×Q₈
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₄×C₈	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#1837
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊ΓL(1,𝔽₁₆)

commutator

C₂×C₃×C₄×C₅

C₂²×C₄

Frattini

C₂×C₄

C₂²×ΓL(1,𝔽₁₆)

Fitting

C₃×C₄×C₅×C₈

C₄

socle

C₂²×C₃×C₅

C₂×C₄⋊C₄

prime radical

C₂²×C₃×D₅

C₂×Q₈

cosocle

C₂×C₃×C₄×D₅

C₂³

hypercenter

C₄×C₈

ΓL(1,𝔽₁₆)

hypocenter

C₃×C₅

#1837

LCS

G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
159. C₃×C₅	#1837	semidirect
191. C₅	#69791	semidirect
202. C₃	#10603856	semidirect

H ≅ G/N

type

159. C₃×C₅

#1837

semidirect

191. C₅

#69791

semidirect

202. C₃

#10603856

semidirect

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

subgroup	index
#11752340	2
C₃×C₄×C₈×D₅	2
#11746767	2
#10603856	3
#69791	5

subgroup

index

C₃×C₄×C₈×D₅

Subgroups — #14298897

Conjugacy classes of subgroups

Complements

Maximal subgroups