Group #18076122 — subgroups

Subgroups — #18076122

Order 4864.

378 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14566600	C₂	1	1	yes	maximal, characteristic
2	#14561959	C₂	1	1	yes	maximal, characteristic
3	#14561536	C₂	1	2	yes	maximal
4	#14561495	C₂	1	2	yes	maximal
5	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926451	—	2	1	no	—
8	#11926430	—	2	2	no	—
9	#11926412	C₄	1	2	yes	—
10	#11926410	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×Dic₁₉	—	2	1	no	—
12	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926390	C₄	1	2	yes	—
14	#11926270	—	2	2	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#423	C₂²	1	2	yes	—
17	C₂×C₁₉×#101	—	2	1	no	—
18	C₁₉×#343	—	2	1	no	—
19	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×M₁₆×C₁₉	—	2	2	no	—
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	—	2	1	no	—
28	C₂×C₄⋊Dic₁₉	—	2	1	no	—
29	C₂×C₄×Dic₁₉	—	2	2	no	—
30	C₂×C₄×Dic₁₉	—	2	1	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×#101	—	4	2	no	—
34	C₁₉⋊#95	—	2	2	no	—
35	C₁₉⋊#95	—	2	2	no	—
36	C₁₉⋊#95	—	2	2	no	—
37	C₁₉⋊#95	—	2	1	no	—
38	C₁₉⋊#95	C₂×C₄	1	1	yes	characteristic
39	C₁₉⋊#95	C₂×C₄	1	2	yes	—
40	C₁₉⋊#95	C₂×C₄	1	1	yes	characteristic
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₂×Q₈×C₁₉	—	2	2	no	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	—	2	1	no	—
47	C₂×Q₈×C₁₉	—	2	1	no	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×Dic₁₉	—	2	1	no	—
54	C₂²×Dic₁₉	—	2	2	no	—
55	C₂²×Dic₁₉	—	2	1	no	—
56	M₁₆×C₁₉	—	4	2	no	—
57	M₁₆×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	#41	1	2	yes	—
64	C₄²×C₁₉	#41	1	2	yes	—
65	C₄⋊Dic₁₉	—	4	2	no	—
66	C₄⋊Dic₁₉	—	4	2	no	—
67	C₄×Dic₁₉	—	4	4	no	—
68	C₄×Dic₁₉	—	4	1	no	—
69	C₄×Dic₁₉	—	4	1	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	#8768	—	19	1	no	maximal, Sylow
72	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	Q₈×C₁₉	—	4	2	no	—
74	Q₈×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	4	1	no	—
80	C₂×C₄×C₁₉	—	4	1	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#123	1	2	yes	—
85	C₂×C₄×C₁₉	#123	1	2	yes	—
86	C₂×C₄×C₁₉	#135	1	2	yes	—
87	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
89	C₂×Dic₁₉	—	2	2	no	—
90	C₂×Dic₁₉	—	4	1	no	—
91	C₂×Dic₁₉	—	4	1	no	—
92	C₂×Dic₁₉	—	4	2	no	—
93	C₂×Dic₁₉	—	4	1	no	—
94	C₂×Dic₁₉	—	4	1	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	2	no	—
97	C₂×Dic₁₉	—	4	1	no	—
98	C₈×C₁₉	—	8	2	no	—
99	C₁₉⋊C₈	—	8	2	no	—
100	#2356	—	19	1	no	—
101	#1801	D₁₉	1	1	yes	characteristic
102	#1461	—	19	1	no	—
103	#1303	—	19	2	no	—
104	#1286	—	19	2	no	—
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	#381	1	1	yes	characteristic
108	C₂²×C₁₉	#416	1	1	yes	characteristic
109	C₂²×C₁₉	#417	1	1	yes	characteristic
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	4	2	no	—
114	C₄×C₁₉	—	4	2	no	—
115	C₄×C₁₉	#482	1	2	yes	—
116	C₄×C₁₉	#485	1	2	yes	—
117	Dic₁₉	—	4	2	no	—
118	Dic₁₉	—	8	1	no	—
119	Dic₁₉	—	8	2	no	—
120	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
121	#431	—	19	2	no	—
122	#423	C₂×D₁₉	1	2	yes	—
123	C₂×#101	—	2	1	no	—
124	#391	—	38	1	no	—
125	#387	—	38	2	no	—
126	#383	—	19	2	no	—
127	#382	—	19	1	no	—
128	C₄×C₄⋊C₄	—	19	1	no	—
129	C₄×C₄⋊C₄	—	38	1	no	—
130	#376	—	19	2	no	—
131	#343	—	2	1	no	—
132	#324	—	38	2	no	—
133	C₂×C₁₉	—	2	1	no	—
134	C₂×C₁₉	—	2	1	no	—
135	C₂×C₁₉	#1825	1	1	yes	characteristic
136	C₂×C₁₉	#1827	1	1	yes	characteristic
137	C₂×C₁₉	#1830	1	1	yes	characteristic
138	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
139	C₂×M₁₆	—	2	2	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₄×Q₈	—	2	2	no	—
142	C₂×C₄⋊C₄	—	38	1	no	—
143	C₂×C₄⋊C₄	—	38	1	no	—
144	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
145	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
146	C₂×C₄²	—	38	2	no	—
147	C₂×C₄²	—	38	1	no	—
148	C₂×C₄²	C₄×D₁₉	1	2	yes	—
149	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
150	C₄⋊C₈	—	2	2	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	38	2	no	—
153	#101	—	4	2	no	—
154	C₂²⋊C₈	—	38	2	no	—
155	C₄×C₈	—	38	2	no	—
156	#95	—	19	1	no	—
157	#95	—	19	2	no	—
158	#95	—	19	1	no	—
159	#95	—	38	2	no	—
160	#95	—	38	2	no	—
161	#95	—	38	2	no	—
162	#95	—	38	1	no	—
163	C₁₉	#8768	1	1	yes	characteristic, complemented, Sylow
164	C₂×Q₈	—	2	1	no	—
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	2	1	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂²×C₄	—	38	1	no	—
169	C₂²×C₄	—	38	2	no	—
170	C₂²×C₄	—	38	1	no	—
171	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
172	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
173	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
174	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
175	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
176	M₁₆	—	4	2	no	—
177	M₁₆	—	4	2	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	76	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	4	no	—
182	C₄⋊C₄	—	76	2	no	—
183	C₄⋊C₄	—	76	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	76	4	no	—
187	C₄²	—	76	1	no	—
188	C₄²	—	76	1	no	—
189	C₄²	#64543	1	2	yes	—
190	C₄²	#64543	1	2	yes	—
191	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
192	Q₈	—	4	2	no	—
193	Q₈	—	4	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	38	2	no	—
202	C₂×C₄	—	76	1	no	—
203	C₂×C₄	—	76	1	no	—
204	C₂×C₄	—	76	2	no	—
205	C₂×C₄	—	76	1	no	—
206	C₂×C₄	—	76	1	no	—
207	C₂×C₄	—	76	2	no	—
208	C₂×C₄	—	76	2	no	—
209	C₂×C₄	—	76	1	no	—
210	C₂×C₄	#10597323	1	1	yes	characteristic
211	C₂×C₄	#10597323	1	1	yes	characteristic
212	C₂×C₄	#10597332	1	2	yes	—
213	C₂×C₄	#10597378	1	1	yes	characteristic
214	C₂×C₄	#10597381	1	2	yes	—
215	C₂×C₄	#10597388	1	1	yes	characteristic
216	C₂×C₄	#10597396	1	2	yes	—
217	C₈	—	8	2	no	—
218	C₈	—	152	2	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#11926405	1	1	yes	characteristic
222	C₂²	#11926538	1	1	yes	characteristic
223	C₂²	#11926543	1	1	yes	characteristic
224	C₄	—	2	2	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	4	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	76	2	no	—
230	C₄	—	152	1	no	—
231	C₄	—	152	2	no	—
232	C₄	#11926865	1	2	yes	—
233	C₄	#11926882	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#14563727	1	1	yes	characteristic
237	C₂	#14563740	1	1	yes	characteristic
238	C₂	#14563747	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14566600

C₂

yes

maximal, characteristic

#14561959

C₂

yes

maximal, characteristic

#14561536

C₂

yes

maximal

#14561495

C₂

yes

maximal

C₁₉×#1801

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926451

—

#11926430

—

#11926412

C₄

yes

—

#11926410

C₂²

yes

characteristic

C₄⋊C₄×Dic₁₉

—

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

#11926390

C₄

yes

—

#11926270

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#101

—

C₁₉×#343

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂×C₄

yes

characteristic

C₁₉⋊#95

C₂×C₄

yes

—

C₁₉⋊#95

C₂×C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

#8768

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

100

#2356

—

101

#1801

D₁₉

yes

characteristic

102

#1461

—

103

#1303

—

104

#1286

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

#381

yes

characteristic

108

C₂²×C₁₉

#416

yes

characteristic

109

C₂²×C₁₉

#417

yes

characteristic

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#482

yes

—

116

C₄×C₁₉

#485

yes

—

117

Dic₁₉

—

118

Dic₁₉

—

119

Dic₁₉

—

120

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

121

#431

—

122

#423

C₂×D₁₉

yes

—

123

C₂×#101

—

124

#391

—

125

#387

—

126

#383

—

127

#382

—

128

C₄×C₄⋊C₄

—

129

C₄×C₄⋊C₄

—

130

#376

—

131

#343

—

132

#324

—

133

C₂×C₁₉

—

134

C₂×C₁₉

—

135

C₂×C₁₉

#1825

yes

characteristic

136

C₂×C₁₉

#1827

yes

characteristic

137

C₂×C₁₉

#1830

yes

characteristic

138

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

139

C₂×M₁₆

—

140

C₄×Q₈

—

141

C₄×Q₈

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

D₇₆

yes

—

145

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

146

C₂×C₄²

—

147

C₂×C₄²

—

148

C₂×C₄²

C₄×D₁₉

yes

—

149

C₂×C₄²

C₂²×D₁₉

yes

characteristic

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

#101

—

154

C₂²⋊C₈

—

155

C₄×C₈

—

156

#95

—

157

#95

—

158

#95

—

159

#95

—

160

#95

—

161

#95

—

162

#95

—

163

C₁₉

#8768

yes

characteristic, complemented, Sylow

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

172

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

173

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

174

C₂²×C₄

C₂×D₇₆

yes

characteristic

175

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

176

M₁₆

—

177

M₁₆

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

#64543

yes

—

190

C₄²

#64543

yes

—

191

C₂³

C₂×(C₂×D₁₉)⋊C₄

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

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#10597323

yes

characteristic

211

C₂×C₄

#10597323

yes

characteristic

212

C₂×C₄

#10597332

yes

—

213

C₂×C₄

#10597378

yes

characteristic

214

C₂×C₄

#10597381

yes

—

215

C₂×C₄

#10597388

yes

characteristic

216

C₂×C₄

#10597396

yes

—

217

C₈

—

218

C₈

—

152

—

219

C₂²

—

220

C₂²

—

221

C₂²

#11926405

yes

characteristic

222

C₂²

#11926538

yes

characteristic

223

C₂²

#11926543

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

152

—

231

C₄

—

152

—

232

C₄

#11926865

yes

—

233

C₄

#11926882

yes

—

234

C₂

—

235

C₂

—

236

C₂

#14563727

yes

characteristic

237

C₂

#14563740

yes

characteristic

238

C₂

#14563747

yes

characteristic

	subgroup	G/H
center	C₂²	#11926405
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1801	C₂
socle	C₂²×C₁₉	#381
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1801	D₁₉
hypocenter	C₁₉	#8768
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#11926405

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1801

C₂

socle

C₂²×C₁₉

#381

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

N	H ≅ G/N	type
163. C₁₉	#8768	semidirect

H ≅ G/N

type

163. C₁₉

#8768

semidirect

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

subgroup	index
#14566600	2
#14561959	2
#14561536	2
#14561495	2
C₁₉×#1801	2
#8768	19

subgroup

index

C₁₉×#1801

Subgroups — #18076122

Conjugacy classes of subgroups

Complements

Maximal subgroups