Group #18082422 — subgroups

Subgroups — #18082422

Order 4864.

478 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14564612	C₂	1	2	yes	maximal
3	#14562394	C₂	1	1	yes	maximal, characteristic
4	#14562091	C₂	1	2	yes	maximal
5	C₄²×C₈×C₁₉	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	#11926568	C₂²	1	2	yes	—
13	#11926304	—	2	4	no	—
14	#11926297	—	2	2	no	—
15	#11926276	—	2	4	no	—
16	C₂×C₄×C₈×C₁₉	—	2	2	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₄³×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	—	2	1	no	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	—	2	1	no	—
23	C₂×C₄²×C₁₉	—	2	1	no	—
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	#10597372	—	2	2	no	—
27	#10597370	—	2	2	no	—
28	#10597370	—	2	2	no	—
29	C₂×#64520	—	2	2	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	C₄×C₈×C₁₉	—	2	8	no	—
37	C₄×C₈×C₁₉	—	2	1	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	C₄×C₈×C₁₉	D₄	1	2	yes	—
42	#10597275	—	2	2	no	—
43	#10597273	—	2	4	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₂×Dic₃₈	—	2	2	no	—
51	C₂×Dic₃₈	—	2	2	no	—
52	C₂×C₈×C₁₉	—	2	4	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	—	2	4	no	—
55	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₄²×C₁₉	—	2	4	no	—
58	C₄²×C₁₉	—	2	4	no	—
59	C₄²×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	Q₁₆	1	4	yes	complemented
61	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₁₉	#41	1	1	yes	characteristic
65	C₂²⋊Dic₁₉	—	4	2	no	—
66	C₄⋊Dic₁₉	—	2	2	no	—
67	C₄⋊Dic₁₉	—	2	2	no	—
68	C₄⋊Dic₁₉	—	2	2	no	—
69	C₄⋊Dic₁₉	—	2	2	no	—
70	Dic₁₉⋊C₄	—	4	2	no	—
71	Dic₁₉⋊C₄	—	4	2	no	—
72	C₄×Dic₁₉	—	4	2	no	—
73	#64520	—	4	4	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	Dic₇₆	—	4	4	no	—
76	#9845	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	#121	1	1	yes	characteristic
78	C₂×C₄×C₁₉	—	2	4	no	—
79	C₂×C₄×C₁₉	—	2	4	no	—
80	C₂×C₄×C₁₉	—	2	4	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
90	C₂×C₄×C₁₉	#135	1	2	yes	—
91	C₂×Dic₁₉	—	4	2	no	—
92	C₂×Dic₁₉	—	4	2	no	—
93	Dic₃₈	—	4	4	no	—
94	Dic₃₈	—	4	4	no	—
95	C₈×C₁₉	—	2	4	no	—
96	C₈×C₁₉	—	2	2	no	—
97	C₈×C₁₉	#104	1	4	yes	—
98	C₁₉⋊C₈	—	8	2	no	—
99	#3170	—	19	1	no	—
100	#1994	—	19	2	no	—
101	C₄²×C₈	D₁₉	1	1	yes	characteristic
102	#1567	—	19	1	no	—
103	#1493	—	19	2	no	—
104	C₂²×C₁₉	—	2	1	no	—
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	#390	1	1	yes	characteristic
107	C₂²×C₁₉	#467	1	2	yes	—
108	C₄×C₁₉	—	2	8	no	—
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	C₂×#104	1	2	yes	—
112	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
113	C₄×C₁₉	#443	1	2	yes	—
114	C₄×C₁₉	#494	1	1	yes	characteristic
115	C₄×C₁₉	#495	1	1	yes	characteristic
116	Dic₁₉	—	8	2	no	—
117	Dic₁₉	—	8	2	no	—
118	#533	—	19	2	no	—
119	#500	—	19	1	no	—
120	#494	—	19	1	no	—
121	#487	—	19	2	no	—
122	#467	—	38	2	no	—
123	C₄×Q₁₆	—	38	2	no	—
124	#423	—	19	2	no	—
125	C₂×C₄×C₈	—	2	2	no	—
126	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
128	C₄³	C₂×D₁₉	1	1	yes	characteristic
129	#339	—	38	4	no	—
130	#335	—	38	2	no	—
131	Q₈⋊C₈	—	38	4	no	—
132	C₂×C₁₉	—	2	2	no	—
133	C₂×C₁₉	#1962	1	1	yes	characteristic
134	C₂×C₁₉	#1969	1	1	yes	characteristic
135	C₂×C₁₉	#1974	1	1	yes	characteristic
136	C₂×Q₁₆	—	38	2	no	—
137	C₂×M₁₆	—	38	2	no	—
138	C₂²×C₈	—	2	1	no	—
139	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
140	C₄⋊Q₈	—	19	2	no	—
141	C₄⋊Q₈	—	19	2	no	—
142	#125	—	38	2	no	—
143	C₂²⋊Q₈	—	38	2	no	—
144	C₂²⋊Q₈	—	38	2	no	—
145	C₄×Q₈	—	38	2	no	—
146	C₄×Q₈	—	38	2	no	—
147	#117	—	38	2	no	—
148	C₂×C₄²	—	2	1	no	—
149	C₂×C₄²	—	2	1	no	—
150	C₂×C₄²	D₇₆	1	2	yes	—
151	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
152	#107	—	38	2	no	—
153	C₄⋊C₈	—	38	2	no	—
154	C₄⋊C₈	—	38	2	no	—
155	#103	—	38	4	no	—
156	C₄×C₈	—	2	8	no	—
157	C₄×C₈	—	2	1	no	—
158	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
159	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
160	C₄×C₈	D₇₆	1	2	yes	—
161	C₄×C₈	D₇₆	1	2	yes	—
162	C₁₉	#9845	1	1	yes	characteristic, complemented, Sylow
163	C₂×Q₈	—	38	2	no	—
164	C₂×Q₈	—	38	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
167	C₂²×C₄	#64541	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
169	Q₁₆	—	76	4	no	—
170	M₁₆	—	76	4	no	—
171	C₂×C₈	—	2	4	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	76	2	no	—
175	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
176	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
177	C₄⋊C₄	—	38	2	no	—
178	C₄⋊C₄	—	38	2	no	—
179	C₄⋊C₄	—	38	2	no	—
180	C₄⋊C₄	—	38	2	no	—
181	C₄⋊C₄	—	76	2	no	—
182	C₄⋊C₄	—	76	2	no	—
183	C₂²⋊C₄	—	76	2	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	2	2	no	—
187	C₄²	—	76	2	no	—
188	C₄²	Dic₇₆	1	4	yes	complemented
189	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
190	C₄²	C₂×D₇₆	1	1	yes	characteristic
191	C₄²	C₂×D₇₆	1	1	yes	characteristic
192	C₄²	#64541	1	1	yes	characteristic
193	C₂³	#10597376	1	1	yes	characteristic
194	Q₈	—	76	4	no	—
195	Q₈	—	76	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	76	2	no	—
202	C₂×C₄	—	76	2	no	—
203	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
204	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
205	C₂×C₄	#10597320	1	1	yes	characteristic
206	C₂×C₄	#10597321	1	1	yes	characteristic
207	C₂×C₄	#10597350	1	2	yes	—
208	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
209	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
210	C₂×C₄	#10597376	1	1	yes	characteristic
211	C₈	—	2	4	no	—
212	C₈	—	2	2	no	—
213	C₈	—	152	2	no	—
214	C₈	#10597262	1	4	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	#11926446	1	1	yes	characteristic
218	C₂²	#11926785	1	2	yes	—
219	C₄	—	2	8	no	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	152	2	no	—
223	C₄	—	152	2	no	—
224	C₄	C₂×#10597262	1	2	yes	—
225	C₄	C₄×Dic₇₆	1	2	yes	—
226	C₄	#11926662	1	2	yes	—
227	C₄	#11926924	1	1	yes	characteristic
228	C₄	#11926928	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	#14564463	1	1	yes	characteristic
231	C₂	#14564496	1	1	yes	characteristic
232	C₂	#14564523	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574221

C₂

yes

maximal, characteristic

#14564612

C₂

yes

maximal

#14562394

C₂

yes

maximal, characteristic

#14562091

C₂

yes

maximal

C₄²×C₈×C₁₉

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

#11926949

C₄

yes

characteristic, complemented

#11926924

C₄

yes

characteristic, complemented

#11926895

C₄

yes

complemented

#11926785

—

C₄×Dic₇₆

—

#11926568

C₂²

yes

—

#11926304

—

#11926297

—

#11926276

—

C₂×C₄×C₈×C₁₉

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

C₂×Dic₇₆

—

#10597316

—

#10597315

C₂×C₄

yes

—

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#10597275

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

Q₁₆

yes

complemented

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

—

#64520

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#104

yes

—

C₁₉⋊C₈

—

#3170

—

100

#1994

—

101

C₄²×C₈

D₁₉

yes

characteristic

102

#1567

—

103

#1493

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

#390

yes

characteristic

107

C₂²×C₁₉

#467

yes

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

C₂×#104

yes

—

112

C₄×C₁₉

C₄×Q₁₆

yes

—

113

C₄×C₁₉

#443

yes

—

114

C₄×C₁₉

#494

yes

characteristic

115

C₄×C₁₉

#495

yes

characteristic

116

Dic₁₉

—

117

Dic₁₉

—

118

#533

—

119

#500

—

120

#494

—

121

#487

—

122

#467

—

123

C₄×Q₁₆

—

124

#423

—

125

C₂×C₄×C₈

—

126

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

127

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

128

C₄³

C₂×D₁₉

yes

characteristic

129

#339

—

130

#335

—

131

Q₈⋊C₈

—

132

C₂×C₁₉

—

133

C₂×C₁₉

#1962

yes

characteristic

134

C₂×C₁₉

#1969

yes

characteristic

135

C₂×C₁₉

#1974

yes

characteristic

136

C₂×Q₁₆

—

137

C₂×M₁₆

—

138

C₂²×C₈

—

139

C₂²×C₈

C₂²⋊D₁₉

yes

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

#125

—

143

C₂²⋊Q₈

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

#117

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

D₇₆

yes

—

151

C₂×C₄²

C₂²×D₁₉

yes

characteristic

152

#107

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

C₄×D₁₉

yes

characteristic

159

C₄×C₈

C₄×D₁₉

yes

characteristic

160

C₄×C₈

D₇₆

yes

—

161

C₄×C₈

D₇₆

yes

—

162

C₁₉

#9845

yes

characteristic, complemented, Sylow

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂²×C₄

—

166

C₂²×C₄

C₂×D₇₆

yes

characteristic

167

C₂²×C₄

#64541

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

169

Q₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

176

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

Dic₇₆

yes

complemented

189

C₄²

C₂×C₄×D₁₉

yes

characteristic

190

C₄²

C₂×D₇₆

yes

characteristic

191

C₄²

C₂×D₇₆

yes

characteristic

192

C₄²

#64541

yes

characteristic

193

C₂³

#10597376

yes

characteristic

194

Q₈

—

195

Q₈

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

C₄×D₇₆

yes

characteristic

204

C₂×C₄

C₄×D₇₆

yes

characteristic

205

C₂×C₄

#10597320

yes

characteristic

206

C₂×C₄

#10597321

yes

characteristic

207

C₂×C₄

#10597350

yes

—

208

C₂×C₄

C₂×Dic₇₆

yes

—

209

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

210

C₂×C₄

#10597376

yes

characteristic

211

C₈

—

212

C₈

—

213

C₈

—

152

—

214

C₈

#10597262

yes

—

215

C₂²

—

216

C₂²

—

217

C₂²

#11926446

yes

characteristic

218

C₂²

#11926785

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

152

—

223

C₄

—

152

—

224

C₄

C₂×#10597262

yes

—

225

C₄

C₄×Dic₇₆

yes

—

226

C₄

#11926662

yes

—

227

C₄

#11926924

yes

characteristic

228

C₄

#11926928

yes

characteristic

229

C₂

—

230

C₂

#14564463

yes

characteristic

231

C₂

#14564496

yes

characteristic

232

C₂

#14564523

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄²×C₈×C₁₉	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄²×C₈	D₁₉
hypocenter	C₁₉	#9845
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄²×C₈

subgroup

G/H

center

C₂×C₄

#10597320

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄²×C₈×C₁₉

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄²×C₈

D₁₉

hypocenter

C₁₉

#9845

LCS

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄²×C₈

N	H ≅ G/N	type
7. #11926949	C₄	semidirect
8. #11926924	C₄	semidirect
9. #11926895	C₄	semidirect
60. C₄²×C₁₉	Q₁₆	semidirect
162. C₁₉	#9845	semidirect
188. C₄²	Dic₇₆	semidirect

H ≅ G/N

type

7. #11926949

C₄

semidirect

8. #11926924

C₄

semidirect

9. #11926895

C₄

semidirect

60. C₄²×C₁₉

Q₁₆

semidirect

162. C₁₉

#9845

semidirect

188. C₄²

Dic₇₆

semidirect

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

subgroup	index
#14574221	2
#14564612	2
#14562394	2
#14562091	2
C₄²×C₈×C₁₉	2
#9845	19

subgroup

index

C₄²×C₈×C₁₉

Subgroups — #18082422

Conjugacy classes of subgroups

Complements

Maximal subgroups