Group #14563901 — subgroups

Subgroups — #14563901

Order 2432.

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

normal subgroups only

This group has 298 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	C₂×Q₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597265	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597292	C₂	1	1	yes	maximal, characteristic
4	#11926440	C₂	1	1	yes	maximal, characteristic
5	#11926307	C₂	1	1	yes	maximal, characteristic
6	#11926298	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	Q₈×Dic₁₉	—	2	2	no	—
12	Q₈×Dic₁₉	—	2	2	no	—
13	C₂×C₄⋊Dic₁₉	—	2	1	no	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₉⋊C₄	—	2	1	no	—
17	C₂×C₄×Dic₁₉	—	2	1	no	—
18	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₁₉×#103	—	2	2	no	—
21	#10597292	C₄	1	4	yes	complemented
22	C₁₉⋊#95	—	2	1	no	—
23	#10597265	—	2	2	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	—	2	1	no	—
27	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×Q₈×C₁₉	D₄	1	2	yes	—
29	C₂×Q₈×C₁₉	Q₈	1	2	yes	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	—	2	1	no	—
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×Dic₁₉	—	2	1	no	—
34	C₂²×Dic₁₉	—	2	1	no	—
35	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
36	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	—	2	1	no	—
39	C₂×C₈×C₁₉	—	2	1	no	—
40	C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₄⋊Dic₁₉	—	2	4	no	—
43	C₄⋊Dic₁₉	—	2	1	no	—
44	C₄⋊Dic₁₉	—	2	1	no	—
45	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
46	C₄⋊Dic₁₉	D₄	1	2	yes	—
47	Dic₁₉⋊C₄	—	4	2	no	—
48	C₄×Dic₁₉	—	2	4	no	—
49	C₄×Dic₁₉	—	2	1	no	—
50	C₄×Dic₁₉	—	2	1	no	—
51	C₂×C₁₉⋊C₈	—	2	1	no	—
52	C₂×C₁₉⋊C₈	—	2	1	no	—
53	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
54	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
55	Q₈×C₁₉	—	2	2	no	—
56	Q₈×C₁₉	—	2	2	no	—
57	Q₈×C₁₉	—	2	2	no	—
58	Q₈×C₁₉	C₄⋊C₄	1	4	yes	complemented
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	4	1	no	—
63	C₂×C₄×C₁₉	—	4	1	no	—
64	C₂×C₄×C₁₉	—	4	1	no	—
65	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
71	C₂×Dic₁₉	—	2	1	no	—
72	C₂×Dic₁₉	—	2	1	no	—
73	C₂×Dic₁₉	—	2	2	no	—
74	C₂×Dic₁₉	—	2	1	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	C₂×Dic₁₉	—	2	1	no	—
77	C₂×Dic₁₉	—	2	1	no	—
78	C₂×Dic₁₉	—	4	1	no	—
79	C₂×Dic₁₉	—	4	1	no	—
80	C₂×Dic₁₉	—	4	1	no	—
81	C₂×Dic₁₉	—	4	1	no	—
82	C₂×Dic₁₉	SD₁₆	1	2	yes	—
83	C₈×C₁₉	—	4	1	no	—
84	C₁₉⋊C₈	—	2	2	no	—
85	#1865	—	19	1	no	maximal, Sylow
86	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
87	C₂²×C₁₉	#120	1	1	yes	characteristic
88	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
90	C₂²×C₁₉	#135	1	1	yes	characteristic
91	C₂²×C₁₉	#137	1	1	yes	characteristic
92	C₂²×C₁₉	#137	1	1	yes	characteristic
93	C₄×C₁₉	—	2	4	no	—
94	C₄×C₁₉	—	8	1	no	—
95	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
97	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
98	C₄×C₁₉	#123	1	1	yes	characteristic
99	Dic₁₉	—	2	2	no	—
100	Dic₁₉	—	4	2	no	—
101	Dic₁₉	—	4	1	no	—
102	Dic₁₉	—	4	2	no	—
103	C₂×C₄×Q₈	—	19	1	no	—
104	C₂×#106	—	19	1	no	—
105	C₂×#103	—	19	1	no	—
106	C₂×#103	D₁₉	1	1	yes	characteristic
107	#389	—	19	1	no	—
108	#340	—	19	1	no	—
109	#336	—	19	1	no	—
110	C₂×C₁₉	#385	1	1	yes	characteristic
111	C₂×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
112	C₂×C₁₉	#441	1	1	yes	characteristic
113	C₂×C₁₉	#448	1	1	yes	characteristic
114	C₂×C₁₉	#452	1	1	yes	characteristic
115	C₂×C₁₉	#475	1	1	yes	characteristic
116	C₂×C₁₉	#479	1	1	yes	characteristic
117	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
118	C₂²×C₈	—	19	1	no	—
119	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
120	C₄×Q₈	—	38	2	no	—
121	C₄×Q₈	—	38	2	no	—
122	C₂×C₄⋊C₄	—	19	1	no	—
123	C₂×C₄⋊C₄	—	19	1	no	—
124	C₂×C₄⋊C₄	—	38	1	no	—
125	C₂×C₄⋊C₄	—	38	1	no	—
126	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
127	C₂×C₄²	—	19	1	no	—
128	C₂×C₄²	—	38	1	no	—
129	#106	—	38	2	no	—
130	#103	—	2	2	no	—
131	#103	—	19	4	no	—
132	#95	—	38	1	no	—
133	C₁₉	#1865	1	1	yes	characteristic, complemented, Sylow
134	C₂×Q₈	—	2	1	no	—
135	C₂×Q₈	—	2	1	no	—
136	C₂×Q₈	—	2	1	no	—
137	C₂×Q₈	Dic₃₈	1	2	yes	—
138	C₂×Q₈	C₄×D₁₉	1	2	yes	—
139	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
140	C₂²×C₄	—	2	1	no	—
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	19	1	no	—
143	C₂²×C₄	—	19	1	no	—
144	C₂²×C₄	—	38	1	no	—
145	C₂²×C₄	—	38	1	no	—
146	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
147	C₂×C₈	—	2	1	no	—
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	2	1	no	—
150	C₂×C₈	—	19	2	no	—
151	C₂×C₈	—	38	1	no	—
152	C₂×C₈	—	38	1	no	—
153	C₄⋊C₄	—	2	1	no	—
154	C₄⋊C₄	—	2	1	no	—
155	C₄⋊C₄	—	19	2	no	—
156	C₄⋊C₄	—	19	2	no	—
157	C₄⋊C₄	—	38	4	no	—
158	C₄⋊C₄	—	38	1	no	—
159	C₄⋊C₄	—	38	1	no	—
160	C₄⋊C₄	—	76	2	no	—
161	C₄²	—	38	4	no	—
162	C₄²	—	38	1	no	—
163	C₄²	—	38	1	no	—
164	C₂³	D₄×D₁₉	1	1	yes	characteristic
165	Q₈	—	2	2	no	—
166	Q₈	—	2	2	no	—
167	Q₈	—	2	2	no	—
168	Q₈	Dic₁₉⋊C₄	1	4	yes	complemented
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	4	1	no	—
173	C₂×C₄	—	4	1	no	—
174	C₂×C₄	—	4	1	no	—
175	C₂×C₄	—	19	2	no	—
176	C₂×C₄	—	38	1	no	—
177	C₂×C₄	—	38	1	no	—
178	C₂×C₄	—	38	2	no	—
179	C₂×C₄	—	38	1	no	—
180	C₂×C₄	—	38	2	no	—
181	C₂×C₄	—	38	1	no	—
182	C₂×C₄	—	38	1	no	—
183	C₂×C₄	—	76	1	no	—
184	C₂×C₄	—	76	1	no	—
185	C₂×C₄	—	76	1	no	—
186	C₂×C₄	—	76	1	no	—
187	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
188	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
189	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
190	C₂×C₄	#64543	1	1	yes	characteristic
191	C₂×C₄	#64543	1	1	yes	characteristic
192	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
193	C₈	—	4	1	no	—
194	C₈	—	38	2	no	—
195	C₂²	#10597324	1	1	yes	characteristic
196	C₂²	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
197	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
198	C₂²	#10597361	1	1	yes	characteristic
199	C₂²	#10597364	1	1	yes	characteristic
200	C₂²	#10597365	1	1	yes	characteristic
201	C₂²	#10597383	1	1	yes	characteristic
202	C₄	—	2	4	no	—
203	C₄	—	8	1	no	—
204	C₄	—	38	2	no	—
205	C₄	—	76	2	no	—
206	C₄	—	76	1	no	—
207	C₄	—	76	2	no	—
208	C₄	#10597324	1	1	yes	characteristic
209	C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
210	C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
211	C₄	#10597381	1	1	yes	characteristic
212	C₂	#11926416	1	1	yes	characteristic
213	C₂	#11926629	1	1	yes	characteristic
214	C₂	#11926648	1	1	yes	characteristic
215	C₂	#11926681	1	1	yes	characteristic
216	C₂	#11926705	1	1	yes	characteristic
217	C₂	#11926827	1	1	yes	characteristic
218	C₂	#11926853	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₁₉

C₂

yes

maximal, characteristic

C₂×#10597265

C₂

yes

maximal, characteristic

C₂×#10597292

C₂

yes

maximal, characteristic

#11926440

C₂

yes

maximal, characteristic

#11926307

C₂

yes

maximal, characteristic

#11926298

C₂

yes

maximal, characteristic

C₂×C₁₉×#103

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

Q₈×Dic₁₉

—

Q₈×Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#103

—

#10597292

C₄

yes

complemented

C₁₉⋊#95

—

#10597265

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

C₄⋊C₄

yes

complemented

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

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

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

SD₁₆

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1865

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

characteristic

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#123

yes

characteristic

Dic₁₉

—

100

Dic₁₉

—

101

Dic₁₉

—

102

Dic₁₉

—

103

C₂×C₄×Q₈

—

104

C₂×#106

—

105

C₂×#103

—

106

C₂×#103

D₁₉

yes

characteristic

107

#389

—

108

#340

—

109

#336

—

110

C₂×C₁₉

#385

yes

characteristic

111

C₂×C₁₉

C₄×SD₁₆

yes

characteristic

112

C₂×C₁₉

#441

yes

characteristic

113

C₂×C₁₉

#448

yes

characteristic

114

C₂×C₁₉

#452

yes

characteristic

115

C₂×C₁₉

#475

yes

characteristic

116

C₂×C₁₉

#479

yes

characteristic

117

C₂²×Q₈

C₂×D₁₉

yes

characteristic

118

C₂²×C₈

—

119

C₂²×C₈

C₂×D₁₉

yes

characteristic

120

C₄×Q₈

—

121

C₄×Q₈

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

127

C₂×C₄²

—

128

C₂×C₄²

—

129

#106

—

130

#103

—

131

#103

—

132

#95

—

133

C₁₉

#1865

yes

characteristic, complemented, Sylow

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

Dic₃₈

yes

—

138

C₂×Q₈

C₄×D₁₉

yes

—

139

C₂×Q₈

C₂²⋊D₁₉

yes

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂²×D₁₉

yes

characteristic

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄²

—

162

C₄²

—

163

C₄²

—

164

C₂³

D₄×D₁₉

yes

characteristic

165

Q₈

—

166

Q₈

—

167

Q₈

—

168

Q₈

Dic₁₉⋊C₄

yes

complemented

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

C₂×Dic₃₈

yes

characteristic

188

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

189

C₂×C₄

D₄×D₁₉

yes

characteristic

190

C₂×C₄

#64543

yes

characteristic

191

C₂×C₄

#64543

yes

characteristic

192

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

193

C₈

—

194

C₈

—

195

C₂²

#10597324

yes

characteristic

196

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

197

C₂²

SD₁₆×D₁₉

yes

characteristic

198

C₂²

#10597361

yes

characteristic

199

C₂²

#10597364

yes

characteristic

200

C₂²

#10597365

yes

characteristic

201

C₂²

#10597383

yes

characteristic

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

#10597324

yes

characteristic

209

C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

210

C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

211

C₄

#10597381

yes

characteristic

212

C₂

#11926416

yes

characteristic

213

C₂

#11926629

yes

characteristic

214

C₂

#11926648

yes

characteristic

215

C₂

#11926681

yes

characteristic

216

C₂

#11926705

yes

characteristic

217

C₂

#11926827

yes

characteristic

218

C₂

#11926853

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#103	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#103	D₁₉
hypocenter	C₁₉	#1865
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#103

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
21. #10597292	C₄	semidirect
58. Q₈×C₁₉	C₄⋊C₄	semidirect
133. C₁₉	#1865	semidirect
168. Q₈	Dic₁₉⋊C₄	semidirect

H ≅ G/N

type

21. #10597292

C₄

semidirect

58. Q₈×C₁₉

C₄⋊C₄

semidirect

133. C₁₉

#1865

semidirect

168. Q₈

Dic₁₉⋊C₄

semidirect

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

subgroup	index
C₂×Q₈×Dic₁₉	2
C₂×#10597265	2
C₂×#10597292	2
#11926440	2
#11926307	2
#11926298	2
C₂×C₁₉×#103	2
#1865	19

subgroup

index

C₂×Q₈×Dic₁₉

C₂×C₁₉×#103

Subgroups — #14563901

Conjugacy classes of subgroups

Complements

Maximal subgroups