Group #16015506 — subgroups

Subgroups — #16015506

Order 3328.

910 conjugacy classes of subgroups; only the 299 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 299 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×#11718739	C₂	1	2	yes	maximal
2	C₂×#11718740	C₂	1	2	yes	maximal
3	#13123234	C₂	1	1	yes	maximal, characteristic
4	#13115005	C₂	1	8	yes	maximal
5	C₄×#88043	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2862	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×#88123	—	2	2	no	—
10	C₂×#88123	C₂²	1	2	yes	—
11	C₁₃×#391	—	2	2	no	—
12	C₁₃×#391	—	2	2	no	—
13	C₁₃×#382	C₂²	1	4	yes	—
14	C₄³×C₁₃	C₂²	1	1	yes	characteristic
15	#11718740	—	2	8	no	—
16	#11718739	—	2	8	no	—
17	C₂×#88048	C₂²	1	8	yes	—
18	C₂×#88047	C₂²	1	8	yes	—
19	#11718596	—	2	2	no	—
20	#11718596	C₂²	1	4	yes	—
21	C₂×#88043	C₂²	1	4	yes	—
22	C₂×C₄×#1055	C₂²	1	2	yes	—
23	C₂²×Q₈×C₁₃	—	2	1	no	—
24	C₂²×Q₈×C₁₃	—	2	1	no	—
25	C₂²×Dic₂₆	—	2	2	no	—
26	C₁₃×C₄⋊Q₈	—	2	4	no	—
27	C₁₃×C₄⋊Q₈	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
31	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
32	C₂×C₄²×C₁₃	D₄	1	2	yes	—
33	C₂×C₄²×C₁₃	D₄	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
36	C₂×C₄⋊Dic₁₃	—	2	8	no	—
37	C₂×C₄⋊Dic₁₃	—	2	2	no	—
38	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
39	C₂²×#1055	C₂³	1	4	yes	—
40	#88123	—	2	4	no	—
41	#88123	—	2	4	no	—
42	#88123	—	4	8	no	—
43	C₁₃×#95	—	2	8	no	—
44	#88048	—	2	16	no	—
45	#88047	—	2	16	no	—
46	#88043	Q₈	1	16	yes	complemented
47	C₄×#1055	D₄	1	8	yes	—
48	#33314	—	13	1	no	maximal, Sylow
49	C₂×Q₈×C₁₃	—	4	2	no	—
50	C₂×Q₈×C₁₃	—	4	2	no	—
51	C₂×Q₈×C₁₃	—	4	4	no	—
52	C₂×Q₈×C₁₃	—	4	4	no	—
53	C₂²×C₄×C₁₃	—	2	2	no	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
59	C₂²×Dic₁₃	—	2	4	no	—
60	C₂×Dic₂₆	—	4	4	no	—
61	C₂×Dic₂₆	—	4	8	no	—
62	C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₁₃×C₄⋊C₄	—	2	4	no	—
64	C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₄²×C₁₃	—	2	4	no	—
67	C₄²×C₁₃	—	2	4	no	—
68	C₄²×C₁₃	C₂×D₄	1	4	yes	—
69	C₄²×C₁₃	C₂×Q₈	1	8	yes	—
70	C₄⋊Dic₁₃	—	2	4	no	—
71	C₄⋊Dic₁₃	—	2	4	no	—
72	C₄⋊Dic₁₃	—	4	16	no	—
73	C₄⋊Dic₁₃	—	4	4	no	—
74	C₂×#1055	C₂×D₄	1	8	yes	—
75	C₂×#1055	C₂×Q₈	1	16	yes	—
76	C₂×#500	—	13	2	no	—
77	C₂×#498	—	13	2	no	—
78	#2868	—	13	1	no	—
79	#2862	D₁₃	1	1	yes	characteristic
80	#1847	—	13	8	no	—
81	C₄×#97	—	13	1	no	—
82	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
83	Q₈×C₁₃	—	8	4	no	—
84	Q₈×C₁₃	—	8	4	no	—
85	C₂×C₄×C₁₃	—	2	4	no	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	—	4	2	no	—
88	C₂×C₄×C₁₃	—	4	2	no	—
89	C₂×C₄×C₁₃	—	4	4	no	—
90	C₂×C₄×C₁₃	—	4	4	no	—
91	C₂×C₄×C₁₃	#127	1	2	yes	—
92	C₂×C₄×C₁₃	#127	1	2	yes	—
93	C₂×C₄×C₁₃	C₄⋊Q₈	1	8	yes	—
94	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
95	C₂×C₄×C₁₃	#137	1	4	yes	—
96	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
97	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
98	C₂×Dic₁₃	—	4	4	no	—
99	C₂×Dic₁₃	—	4	8	no	—
100	Dic₂₆	—	8	8	no	—
101	#1055	C₄⋊Q₈	1	16	yes	complemented
102	C₂×C₄⋊Q₈	—	13	2	no	—
103	C₂×C₄⋊Q₈	—	26	2	no	—
104	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
105	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
106	#500	—	26	8	no	—
107	#498	—	26	8	no	—
108	C₂×#107	—	13	8	no	—
109	C₂×#106	—	13	8	no	—
110	C₂×#97	—	13	4	no	—
111	C₂×C₄×C₈	—	13	2	no	—
112	#391	—	2	2	no	—
113	#391	—	2	2	no	—
114	#384	—	13	4	no	—
115	#384	—	26	2	no	—
116	#382	C₂×D₁₃	1	4	yes	—
117	C₄³	C₂×D₁₃	1	1	yes	characteristic
118	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
119	C₂²×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
120	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
121	C₂²×C₁₃	C₂×#137	1	2	yes	—
122	C₄×C₁₃	—	2	8	no	—
123	C₄×C₁₃	—	8	2	no	—
124	C₄×C₁₃	—	8	2	no	—
125	C₄×C₁₃	#496	1	4	yes	—
126	C₄×C₁₃	#497	1	4	yes	—
127	C₄×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
128	Dic₁₃	—	8	4	no	—
129	C₂²×Q₈	—	2	1	no	—
130	C₂²×Q₈	—	2	1	no	—
131	C₂²×Q₈	—	26	2	no	—
132	C₂²×C₈	—	13	4	no	—
133	C₄⋊Q₈	—	2	4	no	—
134	C₄⋊Q₈	—	2	4	no	—
135	C₄⋊Q₈	—	26	4	no	—
136	C₄⋊Q₈	—	26	4	no	—
137	C₄⋊Q₈	—	52	8	no	—
138	C₂×C₄⋊C₄	—	2	1	no	—
139	C₂×C₄⋊C₄	—	2	1	no	—
140	C₂×C₄⋊C₄	—	13	4	no	—
141	C₂×C₄⋊C₄	—	26	2	no	—
142	C₂×C₄⋊C₄	—	26	8	no	—
143	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
144	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
145	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
146	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
147	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
148	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
149	#107	—	26	16	no	—
150	#106	—	26	16	no	—
151	#97	—	13	16	no	—
152	C₄×C₈	—	13	8	no	—
153	#95	—	2	8	no	—
154	C₂×C₁₃	#2868	1	1	yes	characteristic
155	C₂×C₁₃	C₂×#496	1	1	yes	characteristic
156	C₂×C₁₃	C₂×#497	1	1	yes	characteristic
157	C₂×C₁₃	#3165	1	4	yes	—
158	C₂×Q₈	—	4	2	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂×Q₈	—	4	4	no	—
161	C₂×Q₈	—	4	4	no	—
162	C₂×Q₈	—	52	4	no	—
163	C₂×Q₈	—	52	8	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	26	4	no	—
167	C₂²×C₄	C₂×C₂²⋊D₁₃	1	4	yes	—
168	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
169	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
170	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
171	C₂×C₈	—	13	8	no	—
172	C₂×C₈	—	13	16	no	—
173	C₄⋊C₄	—	2	4	no	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	26	4	no	—
178	C₄⋊C₄	—	26	4	no	—
179	C₄⋊C₄	—	52	16	no	—
180	C₄⋊C₄	—	52	4	no	—
181	C₄²	—	2	4	no	—
182	C₄²	—	2	4	no	—
183	C₄²	D₄×D₁₃	1	4	yes	—
184	C₄²	Q₈×D₁₃	1	8	yes	—
185	C₁₃	#33314	1	1	yes	characteristic, complemented, Sylow
186	C₂³	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
187	Q₈	—	8	4	no	—
188	Q₈	—	8	4	no	—
189	Q₈	—	104	8	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	4	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	52	4	no	—
197	C₂×C₄	—	52	8	no	—
198	C₂×C₄	#88194	1	2	yes	—
199	C₂×C₄	#88194	1	2	yes	—
200	C₂×C₄	#88198	1	8	yes	—
201	C₂×C₄	#88203	1	4	yes	—
202	C₂×C₄	#88205	1	4	yes	—
203	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
204	C₂×C₄	C₂×Q₈×D₁₃	1	4	yes	—
205	C₈	—	13	16	no	—
206	C₂²	C₂×#88194	1	1	yes	characteristic
207	C₂²	C₂×#88198	1	2	yes	—
208	C₂²	C₂×#88203	1	2	yes	—
209	C₂²	C₂×#88205	1	2	yes	—
210	C₄	—	2	8	no	—
211	C₄	—	8	2	no	—
212	C₄	—	8	2	no	—
213	C₄	—	104	4	no	—
214	C₄	#11718719	1	4	yes	—
215	C₄	#11718721	1	4	yes	—
216	C₄	D₁₃×C₄⋊Q₈	1	4	yes	—
217	C₂	#13123232	1	1	yes	characteristic
218	C₂	C₂×#11718719	1	1	yes	characteristic
219	C₂	C₂×#11718721	1	1	yes	characteristic
220	C₂	#13125383	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718739

C₂

yes

maximal

C₂×#11718740

C₂

yes

maximal

#13123234

C₂

yes

maximal, characteristic

#13115005

C₂

yes

maximal

C₄×#88043

C₂

yes

maximal, characteristic

C₁₃×#2862

C₂

yes

maximal, characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×#88123

—

C₂×#88123

C₂²

yes

—

C₁₃×#391

—

C₁₃×#391

—

C₁₃×#382

C₂²

yes

—

C₄³×C₁₃

C₂²

yes

—

—

C₂²

yes

—

C₂×#88047

C₂²

yes

—

#11718596

—

#11718596

C₂²

yes

—

C₂×#88043

C₂²

yes

—

C₂×C₄×#1055

C₂²

yes

—

C₂²×Q₈×C₁₃

—

C₂²×Q₈×C₁₃

—

C₂²×Dic₂₆

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂³

yes

—

C₂×C₁₃×C₄⋊C₄

C₂³

yes

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

C₂³

yes

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

C₂³

yes

—

C₂²×#1055

C₂³

yes

—

#88123

—

#88123

—

#88123

—

C₁₃×#95

—

#88048

—

#88047

—

#88043

Q₈

yes

complemented

C₄×#1055

D₄

yes

—

#33314

—

maximal, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂⁴

yes

characteristic

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

C₂×Q₈

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₂×#1055

C₂×D₄

yes

—

C₂×#1055

C₂×Q₈

yes

—

—

—

—

D₁₃

yes

characteristic

#1847

—

C₄×#97

—

C₂³×C₁₃

C₂²×D₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#127

yes

—

C₂×C₄×C₁₃

#127

yes

—

C₂×C₄×C₁₃

C₄⋊Q₈

yes

—

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×C₄×C₁₃

C₂²×D₄

yes

—

C₂×C₄×C₁₃

C₂²×Q₈

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

100

Dic₂₆

—

101

#1055

C₄⋊Q₈

yes

complemented

102

C₂×C₄⋊Q₈

—

103

C₂×C₄⋊Q₈

—

104

C₂×C₄⋊Q₈

C₂×D₁₃

yes

characteristic

105

C₂×C₄⋊Q₈

C₂×D₁₃

yes

characteristic

106

#500

—

107

#498

—

108

C₂×#107

—

109

C₂×#106

—

110

C₂×#97

—

111

C₂×C₄×C₈

—

112

#391

—

113

#391

—

114

#384

—

115

#384

—

116

#382

C₂×D₁₃

yes

—

117

C₄³

C₂×D₁₃

yes

characteristic

118

C₂²×C₁₃

C₂×#127

yes

characteristic

119

C₂²×C₁₃

C₂×C₄⋊Q₈

yes

—

120

C₂²×C₁₃

C₂×AGL(1,ℤ/8)

yes

—

121

C₂²×C₁₃

C₂×#137

yes

—

122

C₄×C₁₃

—

123

C₄×C₁₃

—

124

C₄×C₁₃

—

125

C₄×C₁₃

#496

yes

—

126

C₄×C₁₃

#497

yes

—

127

C₄×C₁₃

C₂×C₄⋊Q₈

yes

—

128

Dic₁₃

—

129

C₂²×Q₈

—

130

C₂²×Q₈

—

131

C₂²×Q₈

—

132

C₂²×C₈

—

133

C₄⋊Q₈

—

134

C₄⋊Q₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

C₂²×D₁₃

yes

—

144

C₂×C₄⋊C₄

C₂²×D₁₃

yes

—

145

C₂×C₄²

C₂²⋊D₁₃

yes

—

146

C₂×C₄²

C₂²⋊D₁₃

yes

—

147

C₂×C₄²

C₂²×D₁₃

yes

characteristic

148

C₂×C₄²

C₂²×D₁₃

yes

—

149

#107

—

150

#106

—

151

#97

—

152

C₄×C₈

—

153

#95

—

154

C₂×C₁₃

#2868

yes

characteristic

155

C₂×C₁₃

C₂×#496

yes

characteristic

156

C₂×C₁₃

C₂×#497

yes

characteristic

157

C₂×C₁₃

#3165

yes

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

—

168

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

169

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

170

C₂²×C₄

C₂³×D₁₃

yes

characteristic

171

C₂×C₈

—

172

C₂×C₈

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄²

—

182

C₄²

—

183

C₄²

D₄×D₁₃

yes

—

184

C₄²

Q₈×D₁₃

yes

—

185

C₁₃

#33314

yes

characteristic, complemented, Sylow

186

C₂³

C₂²×C₂²⋊D₁₃

yes

characteristic

187

Q₈

—

188

Q₈

—

189

Q₈

—

104

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

#88194

yes

—

199

C₂×C₄

#88194

yes

—

200

C₂×C₄

#88198

yes

—

201

C₂×C₄

#88203

yes

—

202

C₂×C₄

#88205

yes

—

203

C₂×C₄

C₂×D₄×D₁₃

yes

—

204

C₂×C₄

C₂×Q₈×D₁₃

yes

—

205

C₈

—

206

C₂²

C₂×#88194

yes

characteristic

207

C₂²

C₂×#88198

yes

—

208

C₂²

C₂×#88203

yes

—

209

C₂²

C₂×#88205

yes

—

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

—

104

—

214

C₄

#11718719

yes

—

215

C₄

#11718721

yes

—

216

C₄

D₁₃×C₄⋊Q₈

yes

—

217

C₂

#13123232

yes

characteristic

218

C₂

C₂×#11718719

yes

characteristic

219

C₂

C₂×#11718721

yes

characteristic

220

C₂

#13125383

yes

—

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₁₃
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2862	C₂
socle, prime radical	C₂³×C₁₃	C₂²×D₄
hypercenter	#2862	D₁₃
hypocenter	C₁₃	#33314
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

subgroup

G/H

center

C₂³

C₂²×C₂²⋊D₁₃

commutator, cosocle

C₂²×C₄×C₁₃

C₂⁴

Frattini

C₂²×C₄

C₂³×D₁₃

Fitting

C₁₃×#2862

C₂

socle, prime radical

C₂³×C₁₃

C₂²×D₄

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

N	H ≅ G/N	type
46. #88043	Q₈	semidirect
101. #1055	C₄⋊Q₈	semidirect
185. C₁₃	#33314	semidirect

H ≅ G/N

type

46. #88043

Q₈

semidirect

101. #1055

C₄⋊Q₈

semidirect

185. C₁₃

#33314

semidirect

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

subgroup	index
C₂×#11718739	2
C₂×#11718740	2
#13123234	2
#13115005	2
C₄×#88043	2
C₁₃×#2862	2
#33314	13

subgroup

index

C₁₃×#2862

Subgroups — #16015506

Conjugacy classes of subgroups

Complements

Maximal subgroups