Group #18082437 — subgroups

Subgroups — #18082437

Order 4864.

422 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14574221	C₂	1	1	yes	maximal, characteristic
2	#14564611	C₂	1	2	yes	maximal
3	#14563380	C₂	1	1	yes	maximal, characteristic
4	#14562089	C₂	1	2	yes	maximal
5	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	2	yes	—
7	#11926949	C₄	1	1	yes	characteristic, complemented
8	#11926924	C₄	1	1	yes	characteristic, complemented
9	#11926895	C₄	1	2	yes	complemented
10	#11926785	—	2	2	no	—
11	C₄×Dic₇₆	—	2	2	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
14	#11926305	—	2	4	no	—
15	#11926298	—	2	2	no	—
16	#11926274	—	2	4	no	—
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#335	—	2	2	no	—
20	C₂×M₁₆×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	#10597372	—	2	2	no	—
24	#10597370	—	2	2	no	—
25	#10597370	—	2	2	no	—
26	C₂×C₄×Dic₁₉	—	2	1	no	—
27	C₂×C₄×Dic₁₉	—	2	1	no	—
28	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₂×Dic₇₆	—	2	2	no	—
31	#10597316	—	2	2	no	—
32	#10597315	C₂×C₄	1	2	yes	—
33	#10597315	C₂×C₄	1	2	yes	—
34	C₄×Dic₃₈	—	2	2	no	—
35	C₄×Dic₃₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	#10597275	—	2	2	no	—
42	#10597273	—	2	4	no	—
43	C₄×C₁₉⋊C₈	—	2	1	no	—
44	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
48	C₂²×Dic₁₉	—	2	2	no	—
49	C₂×Dic₃₈	—	2	2	no	—
50	C₂×Dic₃₈	—	2	2	no	—
51	M₁₆×C₁₉	—	4	4	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	C₂²⋊Dic₁₉	—	4	2	no	—
61	C₄⋊Dic₁₉	—	2	2	no	—
62	C₄⋊Dic₁₉	—	2	2	no	—
63	C₄⋊Dic₁₉	—	2	2	no	—
64	C₄⋊Dic₁₉	—	2	2	no	—
65	Dic₁₉⋊C₄	—	4	2	no	—
66	Dic₁₉⋊C₄	—	4	2	no	—
67	C₄×Dic₁₉	—	2	2	no	—
68	C₄×Dic₁₉	—	4	2	no	—
69	C₄×Dic₁₉	—	4	2	no	—
70	C₄×Dic₁₉	—	4	2	no	—
71	C₄×Dic₁₉	Q₁₆	1	4	yes	complemented
72	C₂×C₁₉⋊C₈	—	2	2	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	Dic₇₆	—	4	4	no	—
75	#9848	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	#121	1	1	yes	characteristic
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₁₉	#135	1	2	yes	—
87	C₂×Dic₁₉	—	2	4	no	—
88	C₂×Dic₁₉	—	4	2	no	—
89	C₂×Dic₁₉	—	4	2	no	—
90	C₂×Dic₁₉	—	4	2	no	—
91	C₂×Dic₁₉	—	4	2	no	—
92	Dic₃₈	—	4	4	no	—
93	Dic₃₈	—	4	4	no	—
94	C₈×C₁₉	—	2	2	no	—
95	C₈×C₁₉	—	2	2	no	—
96	C₈×C₁₉	—	8	2	no	—
97	C₁₉⋊C₈	—	4	2	no	—
98	#3170	—	19	1	no	—
99	#1994	—	19	2	no	—
100	#1744	—	19	1	no	—
101	#1567	D₁₉	1	1	yes	characteristic
102	#1493	—	19	2	no	—
103	C₂²×C₁₉	—	2	1	no	—
104	C₂²×C₁₉	—	2	1	no	—
105	C₂²×C₁₉	#390	1	1	yes	characteristic
106	C₂²×C₁₉	#467	1	2	yes	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	#421	1	2	yes	—
110	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
111	C₄×C₁₉	#444	1	2	yes	—
112	C₄×C₁₉	#494	1	1	yes	characteristic
113	C₄×C₁₉	#495	1	1	yes	characteristic
114	Dic₁₉	—	4	4	no	—
115	Dic₁₉	—	8	2	no	—
116	Dic₁₉	—	8	2	no	—
117	#533	—	19	2	no	—
118	#500	—	19	1	no	—
119	#494	—	19	1	no	—
120	#487	—	19	2	no	—
121	#467	—	38	2	no	—
122	C₄×Q₁₆	—	38	2	no	—
123	#423	C₂×D₁₉	1	2	yes	—
124	C₂×C₄×C₈	—	19	1	no	—
125	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
126	C₄³	—	19	1	no	—
127	#339	—	38	4	no	—
128	#336	—	38	2	no	—
129	#335	—	2	2	no	—
130	Q₈⋊C₈	—	38	4	no	—
131	C₂×C₁₉	—	2	2	no	—
132	C₂×C₁₉	#1963	1	1	yes	characteristic
133	C₂×C₁₉	#1969	1	1	yes	characteristic
134	C₂×C₁₉	#1975	1	1	yes	characteristic
135	C₂×Q₁₆	—	38	2	no	—
136	C₂×M₁₆	—	2	2	no	—
137	C₂²×C₈	—	38	1	no	—
138	C₂²×C₈	D₇₆	1	2	yes	—
139	C₄⋊Q₈	—	19	2	no	—
140	C₄⋊Q₈	—	19	2	no	—
141	#125	—	38	2	no	—
142	C₂²⋊Q₈	—	38	2	no	—
143	C₂²⋊Q₈	—	38	2	no	—
144	C₄×Q₈	—	38	2	no	—
145	C₄×Q₈	—	38	2	no	—
146	#117	—	38	2	no	—
147	C₂×C₄²	—	19	2	no	—
148	C₂×C₄²	—	38	1	no	—
149	C₂×C₄²	—	38	1	no	—
150	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
151	#107	—	38	2	no	—
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	—	2	2	no	—
154	#103	—	38	4	no	—
155	C₄×C₈	—	19	2	no	—
156	C₄×C₈	—	38	1	no	—
157	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
158	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
160	C₁₉	#9848	1	1	yes	characteristic, complemented, Sylow
161	C₂×Q₈	—	38	2	no	—
162	C₂×Q₈	—	38	2	no	—
163	C₂²×C₄	—	38	2	no	—
164	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
165	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
166	C₂²×C₄	#64545	1	1	yes	characteristic
167	Q₁₆	—	76	4	no	—
168	M₁₆	—	4	4	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	38	2	no	—
172	C₂×C₈	—	76	2	no	—
173	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
174	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
175	C₄⋊C₄	—	38	2	no	—
176	C₄⋊C₄	—	38	2	no	—
177	C₄⋊C₄	—	38	2	no	—
178	C₄⋊C₄	—	38	2	no	—
179	C₄⋊C₄	—	76	2	no	—
180	C₄⋊C₄	—	76	2	no	—
181	C₂²⋊C₄	—	76	2	no	—
182	C₄²	—	19	4	no	—
183	C₄²	—	38	2	no	—
184	C₄²	—	76	2	no	—
185	C₄²	—	76	2	no	—
186	C₄²	—	76	2	no	—
187	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
188	C₄²	D₄×D₁₉	1	1	yes	characteristic
189	C₄²	#64545	1	1	yes	characteristic
190	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
191	C₂³	#10597341	1	1	yes	characteristic
192	Q₈	—	76	4	no	—
193	Q₈	—	76	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	38	4	no	—
197	C₂×C₄	—	76	2	no	—
198	C₂×C₄	—	76	2	no	—
199	C₂×C₄	—	76	2	no	—
200	C₂×C₄	—	76	2	no	—
201	C₂×C₄	#10597339	1	1	yes	characteristic
202	C₂×C₄	#10597339	1	1	yes	characteristic
203	C₂×C₄	#10597341	1	1	yes	characteristic
204	C₂×C₄	#10597358	1	2	yes	—
205	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
206	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₄	#10597386	1	1	yes	characteristic
208	C₂×C₄	#10597393	1	1	yes	characteristic
209	C₈	—	2	2	no	—
210	C₈	—	2	2	no	—
211	C₈	—	8	2	no	—
212	C₈	—	76	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#11926445	1	1	yes	characteristic
216	C₂²	#11926786	1	2	yes	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	76	4	no	—
220	C₄	—	152	2	no	—
221	C₄	—	152	2	no	—
222	C₄	#11926560	1	2	yes	—
223	C₄	#11926638	1	2	yes	—
224	C₄	#11926665	1	2	yes	—
225	C₄	#11926922	1	1	yes	characteristic
226	C₄	#11926927	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	#14564466	1	1	yes	characteristic
229	C₂	#14564494	1	1	yes	characteristic
230	C₂	#14564526	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574221

C₂

yes

maximal, characteristic

#14564611

C₂

yes

maximal

#14563380

C₂

yes

maximal, characteristic

#14562089

C₂

yes

maximal

C₁₉×#1567

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

#11926949

C₄

yes

characteristic, complemented

#11926924

C₄

yes

characteristic, complemented

#11926895

C₄

yes

complemented

#11926785

—

C₄×Dic₇₆

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₁₉

C₂²

yes

—

—

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂×Dic₇₆

—

#10597316

—

#10597315

C₂×C₄

yes

—

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

#10597275

—

#10597273

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

Q₁₆

yes

complemented

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3170

—

#1994

—

100

#1744

—

101

#1567

D₁₉

yes

characteristic

102

#1493

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#390

yes

characteristic

106

C₂²×C₁₉

#467

yes

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

#421

yes

—

110

C₄×C₁₉

C₄×Q₁₆

yes

—

111

C₄×C₁₉

#444

yes

—

112

C₄×C₁₉

#494

yes

characteristic

113

C₄×C₁₉

#495

yes

characteristic

114

Dic₁₉

—

115

Dic₁₉

—

116

Dic₁₉

—

117

#533

—

118

#500

—

119

#494

—

120

#487

—

121

#467

—

122

C₄×Q₁₆

—

123

#423

C₂×D₁₉

yes

—

124

C₂×C₄×C₈

—

125

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

126

C₄³

—

127

#339

—

128

#336

—

129

#335

—

130

Q₈⋊C₈

—

131

C₂×C₁₉

—

132

C₂×C₁₉

#1963

yes

characteristic

133

C₂×C₁₉

#1969

yes

characteristic

134

C₂×C₁₉

#1975

yes

characteristic

135

C₂×Q₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

D₇₆

yes

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

—

141

#125

—

142

C₂²⋊Q₈

—

143

C₂²⋊Q₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

146

#117

—

147

C₂×C₄²

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

C₂²×D₁₉

yes

characteristic

151

#107

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#103

—

155

C₄×C₈

—

156

C₄×C₈

—

157

C₄×C₈

C₄×D₁₉

yes

characteristic

158

C₄×C₈

C₄×D₁₉

yes

characteristic

159

C₄×C₈

C₂²⋊D₁₉

yes

—

160

C₁₉

#9848

yes

characteristic, complemented, Sylow

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₇₆

yes

characteristic

165

C₂²×C₄

D₄×D₁₉

yes

characteristic

166

C₂²×C₄

#64545

yes

characteristic

167

Q₁₆

—

168

M₁₆

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

174

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

C₂×C₄×D₁₉

yes

characteristic

188

C₄²

D₄×D₁₉

yes

characteristic

189

C₄²

#64545

yes

characteristic

190

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

191

C₂³

#10597341

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

#10597339

yes

characteristic

202

C₂×C₄

#10597339

yes

characteristic

203

C₂×C₄

#10597341

yes

characteristic

204

C₂×C₄

#10597358

yes

—

205

C₂×C₄

Q₁₆×D₁₉

yes

—

206

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

207

C₂×C₄

#10597386

yes

characteristic

208

C₂×C₄

#10597393

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

213

C₂²

—

214

C₂²

—

215

C₂²

#11926445

yes

characteristic

216

C₂²

#11926786

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

152

—

221

C₄

—

152

—

222

C₄

#11926560

yes

—

223

C₄

#11926638

yes

—

224

C₄

#11926665

yes

—

225

C₄

#11926922

yes

characteristic

226

C₄

#11926927

yes

characteristic

227

C₂

—

228

C₂

#14564466

yes

characteristic

229

C₂

#14564494

yes

characteristic

230

C₂

#14564526

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1567	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1567	D₁₉
hypocenter	C₁₉	#9848
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

subgroup

G/H

center

C₂×C₄

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1567

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

N	H ≅ G/N	type
7. #11926949	C₄	semidirect
8. #11926924	C₄	semidirect
9. #11926895	C₄	semidirect
71. C₄×Dic₁₉	Q₁₆	semidirect
160. C₁₉	#9848	semidirect

H ≅ G/N

type

7. #11926949

C₄

semidirect

8. #11926924

C₄

semidirect

9. #11926895

C₄

semidirect

71. C₄×Dic₁₉

Q₁₆

semidirect

160. C₁₉

#9848

semidirect

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

subgroup	index
#14574221	2
#14564611	2
#14563380	2
#14562089	2
C₁₉×#1567	2
#9848	19

subgroup

index

C₁₉×#1567

Subgroups — #18082437

Conjugacy classes of subgroups

Complements

Maximal subgroups