Group #18087673 — subgroups

Subgroups — #18087673

Order 4864.

248 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14564358	C₂	1	1	yes	maximal, characteristic
2	#14561536	C₂	1	1	yes	maximal, characteristic
3	#14561536	C₂	1	1	yes	maximal, characteristic
4	#14561530	C₂	1	1	yes	maximal, characteristic
5	#14561530	C₂	1	1	yes	maximal, characteristic
6	#14561466	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1838	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₈	—	2	1	no	—
12	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926298	—	2	1	no	—
14	C₁₉×#423	C₂²	1	1	yes	characteristic
15	C₁₉×#423	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
17	C₁₉×#341	—	2	1	no	—
18	C₁₉×#341	—	2	1	no	—
19	C₂×M₁₆×C₁₉	—	2	1	no	—
20	C₂×M₁₆×C₁₉	—	2	1	no	—
21	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	1	no	—
25	C₂×C₄×Dic₁₉	—	2	1	no	—
26	C₂²×C₁₉⋊C₈	—	2	1	no	—
27	C₁₉×C₄⋊C₈	—	2	1	no	—
28	C₁₉×C₄⋊C₈	—	2	1	no	—
29	C₁₉×C₄⋊C₈	—	2	1	no	—
30	C₁₉×C₄⋊C₈	—	2	1	no	—
31	C₁₉×#97	—	2	1	no	—
32	C₁₉×#97	—	2	1	no	—
33	C₁₉⋊#95	Q₈	1	1	yes	characteristic
34	C₁₉⋊#95	Q₈	1	1	yes	characteristic
35	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
37	Dic₁₉⋊C₈	—	4	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
42	C₄×C₁₉⋊C₈	—	2	1	no	—
43	C₄×C₁₉⋊C₈	—	2	1	no	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₂²×Dic₁₉	—	2	1	no	—
48	C₂²×Dic₁₉	—	2	1	no	—
49	M₁₆×C₁₉	—	4	1	no	—
50	M₁₆×C₁₉	—	4	1	no	—
51	M₁₆×C₁₉	—	4	1	no	—
52	M₁₆×C₁₉	—	4	1	no	—
53	C₂×C₈×C₁₉	—	2	1	no	—
54	C₂×C₈×C₁₉	—	2	1	no	—
55	C₂×C₈×C₁₉	—	2	1	no	—
56	C₂×C₈×C₁₉	—	2	1	no	—
57	C₂×C₈×C₁₉	—	2	1	no	—
58	C₂×C₈×C₁₉	—	2	1	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	4	1	no	—
61	C₄²×C₁₉	#41	1	1	yes	characteristic
62	C₄²×C₁₉	#41	1	1	yes	characteristic
63	C₄²×C₁₉	#41	1	1	yes	characteristic
64	C₄²×C₁₉	#41	1	1	yes	characteristic
65	C₄⋊Dic₁₉	—	4	2	no	—
66	C₄×Dic₁₉	—	4	1	no	—
67	C₄×Dic₁₉	—	4	1	no	—
68	C₂×C₁₉⋊C₈	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	4	1	no	—
70	C₂×C₁₉⋊C₈	—	4	1	no	—
71	C₂×C₁₉⋊C₈	—	4	1	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	#10689	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₉	—	4	1	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
85	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
87	C₂×Dic₁₉	—	2	2	no	—
88	C₂×Dic₁₉	—	4	1	no	—
89	C₂×Dic₁₉	—	4	1	no	—
90	C₂×Dic₁₉	—	4	1	no	—
91	C₂×Dic₁₉	—	4	1	no	—
92	C₂×Dic₁₉	—	4	1	no	—
93	C₈×C₁₉	—	4	1	no	—
94	C₈×C₁₉	—	4	1	no	—
95	C₈×C₁₉	—	8	1	no	—
96	C₈×C₁₉	—	8	1	no	—
97	C₁₉⋊C₈	—	8	1	no	—
98	C₁₉⋊C₈	—	8	1	no	—
99	C₁₉⋊C₈	—	8	1	no	—
100	#1940	—	19	1	no	—
101	#1838	D₁₉	1	1	yes	characteristic
102	#1303	—	19	1	no	—
103	#1303	—	19	1	no	—
104	#1301	—	19	1	no	—
105	#1301	—	19	1	no	—
106	#1275	—	19	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	—	2	1	no	—
109	C₂²×C₁₉	#400	1	1	yes	characteristic
110	C₂²×C₁₉	#478	1	1	yes	characteristic
111	C₂²×C₁₉	#479	1	1	yes	characteristic
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	#482	1	1	yes	characteristic
117	C₄×C₁₉	#485	1	1	yes	characteristic
118	C₄×C₁₉	#488	1	1	yes	characteristic
119	C₄×C₁₉	#489	1	1	yes	characteristic
120	Dic₁₉	—	4	2	no	—
121	Dic₁₉	—	8	1	no	—
122	#431	—	19	1	no	—
123	#431	—	19	1	no	—
124	#423	C₂×D₁₉	1	1	yes	characteristic
125	#423	C₂×D₁₉	1	1	yes	characteristic
126	C₂×C₄⋊C₈	—	19	1	no	—
127	C₂×C₄⋊C₈	—	38	1	no	—
128	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
129	C₄×C₄⋊C₄	—	19	1	no	—
130	#341	—	2	1	no	—
131	#341	—	2	1	no	—
132	#336	—	38	1	no	—
133	C₂×C₁₉	—	2	1	no	—
134	C₂×C₁₉	—	2	1	no	—
135	C₂×C₁₉	#2101	1	1	yes	characteristic
136	C₂×C₁₉	#2102	1	1	yes	characteristic
137	C₂×C₁₉	#2103	1	1	yes	characteristic
138	C₂×M₁₆	—	2	1	no	—
139	C₂×M₁₆	—	2	1	no	—
140	C₂²×C₈	—	38	1	no	—
141	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
142	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
143	C₂×C₄⋊C₄	—	38	1	no	—
144	C₂×C₄²	—	38	1	no	—
145	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
146	C₄⋊C₈	—	2	1	no	—
147	C₄⋊C₈	—	2	1	no	—
148	C₄⋊C₈	—	2	1	no	—
149	C₄⋊C₈	—	2	1	no	—
150	C₄⋊C₈	—	38	1	no	—
151	C₄⋊C₈	—	38	1	no	—
152	C₄⋊C₈	—	38	1	no	—
153	C₄⋊C₈	—	38	1	no	—
154	C₄⋊C₈	—	76	2	no	—
155	C₂²⋊C₈	—	38	1	no	—
156	C₂²⋊C₈	—	38	1	no	—
157	#97	—	2	1	no	—
158	#97	—	2	1	no	—
159	C₄×C₈	—	38	1	no	—
160	C₄×C₈	—	38	1	no	—
161	#95	—	19	1	no	—
162	#95	—	19	1	no	—
163	C₁₉	#10689	1	1	yes	characteristic, complemented, Sylow
164	C₂²×C₄	—	38	1	no	—
165	C₂²×C₄	—	38	1	no	—
166	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
167	C₂²×C₄	#64545	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
169	M₁₆	—	4	1	no	—
170	M₁₆	—	4	1	no	—
171	M₁₆	—	4	1	no	—
172	M₁₆	—	4	1	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	2	1	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	—	4	1	no	—
180	C₂×C₈	—	4	1	no	—
181	C₂×C₈	—	76	1	no	—
182	C₂×C₈	—	76	1	no	—
183	C₂×C₈	—	76	1	no	—
184	C₂×C₈	—	76	1	no	—
185	C₂×C₈	—	76	1	no	—
186	C₄⋊C₄	—	76	2	no	—
187	C₄²	—	76	1	no	—
188	C₄²	—	76	1	no	—
189	C₄²	#64541	1	1	yes	characteristic
190	C₄²	#64541	1	1	yes	characteristic
191	C₄²	#64543	1	1	yes	characteristic
192	C₄²	#64543	1	1	yes	characteristic
193	C₂³	#10597392	1	1	yes	characteristic
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	38	2	no	—
197	C₂×C₄	—	76	1	no	—
198	C₂×C₄	—	76	1	no	—
199	C₂×C₄	—	76	1	no	—
200	C₂×C₄	—	76	1	no	—
201	C₂×C₄	—	76	1	no	—
202	C₂×C₄	#10597335	1	1	yes	characteristic
203	C₂×C₄	#10597335	1	1	yes	characteristic
204	C₂×C₄	#10597344	1	1	yes	characteristic
205	C₂×C₄	#10597344	1	1	yes	characteristic
206	C₂×C₄	#10597375	1	1	yes	characteristic
207	C₂×C₄	#10597382	1	1	yes	characteristic
208	C₂×C₄	#10597395	1	1	yes	characteristic
209	C₂×C₄	#10597396	1	1	yes	characteristic
210	C₂×C₄	#10597396	1	1	yes	characteristic
211	C₂×C₄	#10597397	1	1	yes	characteristic
212	C₈	—	4	1	no	—
213	C₈	—	4	1	no	—
214	C₈	—	8	1	no	—
215	C₈	—	8	1	no	—
216	C₈	—	152	1	no	—
217	C₈	—	152	1	no	—
218	C₈	—	152	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#11926482	1	1	yes	characteristic
222	C₂²	#11926841	1	1	yes	characteristic
223	C₂²	#11926848	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	76	2	no	—
229	C₄	—	152	1	no	—
230	C₄	#11926868	1	1	yes	characteristic
231	C₄	#11926885	1	1	yes	characteristic
232	C₄	#11926898	1	1	yes	characteristic
233	C₄	#11926903	1	1	yes	characteristic
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#14565202	1	1	yes	characteristic
237	C₂	#14565209	1	1	yes	characteristic
238	C₂	#14565214	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564358

C₂

yes

maximal, characteristic

#14561536

C₂

yes

maximal, characteristic

#14561536

C₂

yes

maximal, characteristic

#14561530

C₂

yes

maximal, characteristic

#14561530

C₂

yes

maximal, characteristic

#14561466

C₂

yes

maximal, characteristic

C₁₉×#1838

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₈

—

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

#11926298

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#341

—

C₁₉×#341

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₁₉×#97

—

C₁₉⋊#95

Q₈

yes

characteristic

C₁₉⋊#95

Q₈

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10689

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

#1940

—

101

#1838

D₁₉

yes

characteristic

102

#1303

—

103

#1303

—

104

#1301

—

105

#1301

—

106

#1275

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

#400

yes

characteristic

110

C₂²×C₁₉

#478

yes

characteristic

111

C₂²×C₁₉

#479

yes

characteristic

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

#482

yes

characteristic

117

C₄×C₁₉

#485

yes

characteristic

118

C₄×C₁₉

#488

yes

characteristic

119

C₄×C₁₉

#489

yes

characteristic

120

Dic₁₉

—

121

Dic₁₉

—

122

#431

—

123

#431

—

124

#423

C₂×D₁₉

yes

characteristic

125

#423

C₂×D₁₉

yes

characteristic

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

—

128

C₂×#97

C₂×D₁₉

yes

characteristic

129

C₄×C₄⋊C₄

—

130

#341

—

131

#341

—

132

#336

—

133

C₂×C₁₉

—

134

C₂×C₁₉

—

135

C₂×C₁₉

#2101

yes

characteristic

136

C₂×C₁₉

#2102

yes

characteristic

137

C₂×C₁₉

#2103

yes

characteristic

138

C₂×M₁₆

—

139

C₂×M₁₆

—

140

C₂²×C₈

—

141

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

142

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

143

C₂×C₄⋊C₄

—

144

C₂×C₄²

—

145

C₂×C₄²

C₂²×D₁₉

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₂²⋊C₈

—

156

C₂²⋊C₈

—

157

#97

—

158

#97

—

159

C₄×C₈

—

160

C₄×C₈

—

161

#95

—

162

#95

—

163

C₁₉

#10689

yes

characteristic, complemented, Sylow

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

Q₈×D₁₉

yes

characteristic

167

C₂²×C₄

#64545

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

169

M₁₆

—

170

M₁₆

—

171

M₁₆

—

172

M₁₆

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₄⋊C₄

—

187

C₄²

—

188

C₄²

—

189

C₄²

#64541

yes

characteristic

190

C₄²

#64541

yes

characteristic

191

C₄²

#64543

yes

characteristic

192

C₄²

#64543

yes

characteristic

193

C₂³

#10597392

yes

characteristic

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

#10597335

yes

characteristic

203

C₂×C₄

#10597335

yes

characteristic

204

C₂×C₄

#10597344

yes

characteristic

205

C₂×C₄

#10597344

yes

characteristic

206

C₂×C₄

#10597375

yes

characteristic

207

C₂×C₄

#10597382

yes

characteristic

208

C₂×C₄

#10597395

yes

characteristic

209

C₂×C₄

#10597396

yes

characteristic

210

C₂×C₄

#10597396

yes

characteristic

211

C₂×C₄

#10597397

yes

characteristic

212

C₈

—

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

—

152

—

217

C₈

—

152

—

218

C₈

—

152

—

219

C₂²

—

220

C₂²

—

221

C₂²

#11926482

yes

characteristic

222

C₂²

#11926841

yes

characteristic

223

C₂²

#11926848

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

152

—

230

C₄

#11926868

yes

characteristic

231

C₄

#11926885

yes

characteristic

232

C₄

#11926898

yes

characteristic

233

C₄

#11926903

yes

characteristic

234

C₂

—

235

C₂

—

236

C₂

#14565202

yes

characteristic

237

C₂

#14565209

yes

characteristic

238

C₂

#14565214

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597382
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1838	C₂
socle	C₂²×C₁₉	#400
prime radical	C₂³×C₁₉	C₂²⋊Q₈
hypercenter	#1838	D₁₉
hypocenter	C₁₉	#10689
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1838

subgroup

G/H

center

C₂×C₄

#10597382

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1838

C₂

socle

C₂²×C₁₉

#400

prime radical

C₂³×C₁₉

C₂²⋊Q₈

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1838

N	H ≅ G/N	type
163. C₁₉	#10689	semidirect

H ≅ G/N

type

163. C₁₉

#10689

semidirect

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

subgroup	index
#14564358	2
#14561536	2
#14561530	2
#14561466	2
C₁₉×#1838	2
#10689	19

subgroup

index

C₁₉×#1838

Subgroups — #18087673

Conjugacy classes of subgroups

Complements

Maximal subgroups