Group #14563975 — subgroups

Subgroups — #14563975

Order 2432.

338 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 103 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	C₂²×Dic₇₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597273	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597273	C₂	1	1	yes	maximal, characteristic
5	#11926450	C₂	1	1	yes	maximal, characteristic
6	#11926307	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#336	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₉⋊C₄	—	2	1	no	—
16	C₂×C₄×Dic₁₉	—	2	1	no	—
17	C₂×Dic₇₆	—	2	2	no	—
18	C₂×Dic₇₆	—	2	2	no	—
19	C₂×Dic₇₆	C₄	1	4	yes	complemented
20	C₄×Dic₃₈	—	2	2	no	—
21	C₄×Dic₃₈	—	2	2	no	—
22	C₁₉⋊#95	—	2	1	no	—
23	C₁₉⋊#95	—	2	1	no	—
24	#10597273	—	2	2	no	—
25	#10597273	—	2	2	no	—
26	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₂²×Dic₁₉	—	2	1	no	—
31	C₂²×Dic₁₉	—	2	1	no	—
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂×Dic₃₈	—	2	1	no	—
34	C₂×Dic₃₈	—	2	1	no	—
35	C₂×Dic₃₈	—	2	1	no	—
36	C₂×Dic₃₈	—	2	1	no	—
37	C₂×Dic₃₈	—	2	1	no	—
38	C₂×Dic₃₈	—	2	1	no	—
39	C₂×Dic₃₈	—	2	1	no	—
40	C₂×Dic₃₈	—	2	1	no	—
41	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
42	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
43	C₂×Dic₃₈	D₄	1	2	yes	—
44	C₂×Dic₃₈	D₄	1	2	yes	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	—	2	1	no	—
47	C₂×C₈×C₁₉	—	2	1	no	—
48	C₂×C₈×C₁₉	—	2	1	no	—
49	C₂×C₈×C₁₉	—	2	1	no	—
50	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
51	C₄²×C₁₉	—	2	1	no	—
52	C₄²×C₁₉	—	2	1	no	—
53	C₄⋊Dic₁₉	—	2	1	no	—
54	C₄⋊Dic₁₉	—	2	1	no	—
55	C₄⋊Dic₁₉	—	2	1	no	—
56	C₄⋊Dic₁₉	D₄	1	2	yes	—
57	Dic₁₉⋊C₄	—	2	4	no	—
58	C₄×Dic₁₉	—	2	4	no	—
59	Dic₇₆	—	2	8	no	—
60	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	Q₁₆	1	2	yes	complemented
67	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
73	C₂×Dic₁₉	—	2	2	no	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	C₂×Dic₁₉	—	2	2	no	—
77	C₂×Dic₁₉	—	2	2	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	—	4	1	no	—
83	C₂×Dic₁₉	—	4	1	no	—
84	C₂×Dic₁₉	—	4	1	no	—
85	Dic₃₈	—	2	2	no	—
86	Dic₃₈	—	2	2	no	—
87	Dic₃₈	—	2	2	no	—
88	Dic₃₈	—	2	2	no	—
89	Dic₃₈	—	2	2	no	—
90	Dic₃₈	—	4	1	no	—
91	Dic₃₈	—	4	1	no	—
92	Dic₃₈	C₂²⋊C₄	1	4	yes	—
93	C₈×C₁₉	—	2	2	no	—
94	C₈×C₁₉	—	4	1	no	—
95	#1878	—	19	1	no	maximal, Sylow
96	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
97	C₂²×C₁₉	#120	1	1	yes	characteristic
98	C₂²×C₁₉	#121	1	1	yes	characteristic
99	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
100	C₂²×C₁₉	#135	1	1	yes	characteristic
101	C₂²×C₁₉	#137	1	1	yes	characteristic
102	C₂²×C₁₉	#137	1	1	yes	characteristic
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	4	1	no	—
105	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
107	C₄×C₁₉	#121	1	1	yes	characteristic
108	C₄×C₁₉	#123	1	1	yes	characteristic
109	Dic₁₉	—	2	4	no	—
110	Dic₁₉	—	4	2	no	—
111	Dic₁₉	—	4	2	no	—
112	Dic₁₉	—	8	1	no	—
113	C₂²×Q₁₆	—	19	1	no	—
114	C₂×C₄×Q₈	—	19	1	no	—
115	C₂×#103	—	19	1	no	—
116	C₂×#103	—	19	1	no	—
117	#391	—	19	1	no	—
118	#340	—	19	1	no	—
119	#336	D₁₉	1	1	yes	characteristic
120	C₂×C₁₉	#386	1	1	yes	characteristic
121	C₂×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
122	C₂×C₁₉	#441	1	1	yes	characteristic
123	C₂×C₁₉	#451	1	1	yes	characteristic
124	C₂×C₁₉	#452	1	1	yes	characteristic
125	C₂×C₁₉	#462	1	1	yes	characteristic
126	C₂×C₁₉	#464	1	1	yes	characteristic
127	C₂²×Q₈	—	19	1	no	—
128	C₂²×Q₈	—	19	1	no	—
129	C₂×Q₁₆	—	19	4	no	—
130	C₂×Q₁₆	—	38	2	no	—
131	C₂×Q₁₆	—	38	2	no	—
132	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
133	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
134	C₄×Q₈	—	38	2	no	—
135	C₄×Q₈	—	38	2	no	—
136	C₂×C₄⋊C₄	—	19	1	no	—
137	C₂×C₄⋊C₄	—	19	1	no	—
138	C₂×C₄⋊C₄	—	38	1	no	—
139	C₂×C₄²	—	38	1	no	—
140	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
141	#103	—	38	2	no	—
142	#103	—	38	2	no	—
143	#95	—	38	1	no	—
144	#95	—	38	1	no	—
145	C₁₉	#1878	1	1	yes	characteristic, complemented, Sylow
146	C₂×Q₈	—	19	2	no	—
147	C₂×Q₈	—	19	2	no	—
148	C₂×Q₈	—	19	2	no	—
149	C₂×Q₈	—	19	2	no	—
150	C₂×Q₈	—	38	1	no	—
151	C₂×Q₈	—	38	1	no	—
152	C₂×Q₈	—	38	1	no	—
153	C₂×Q₈	—	38	1	no	—
154	C₂×Q₈	—	38	1	no	—
155	C₂×Q₈	—	38	1	no	—
156	C₂×Q₈	—	38	1	no	—
157	C₂×Q₈	—	38	1	no	—
158	C₂²×C₄	—	38	1	no	—
159	C₂²×C₄	—	38	1	no	—
160	C₂²×C₄	—	38	1	no	—
161	C₂²×C₄	—	38	1	no	—
162	C₂²×C₄	D₇₆	1	1	yes	characteristic
163	C₂²×C₄	D₇₆	1	1	yes	characteristic
164	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
165	Q₁₆	—	38	8	no	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	2	1	no	—
168	C₂×C₈	—	2	1	no	—
169	C₂×C₈	—	2	1	no	—
170	C₂×C₈	—	2	1	no	—
171	C₂×C₈	C₄×D₁₉	1	2	yes	—
172	C₄⋊C₄	—	19	2	no	—
173	C₄⋊C₄	—	38	4	no	—
174	C₄⋊C₄	—	38	1	no	—
175	C₄⋊C₄	—	38	1	no	—
176	C₄⋊C₄	—	38	1	no	—
177	C₄²	—	2	1	no	—
178	C₄²	—	2	1	no	—
179	C₄²	—	38	4	no	—
180	C₂³	C₂×D₇₆	1	1	yes	characteristic
181	Q₈	—	19	4	no	—
182	Q₈	—	38	2	no	—
183	Q₈	—	38	2	no	—
184	Q₈	—	38	2	no	—
185	Q₈	—	38	2	no	—
186	Q₈	—	38	2	no	—
187	Q₈	—	76	1	no	—
188	Q₈	—	76	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	38	2	no	—
195	C₂×C₄	—	38	2	no	—
196	C₂×C₄	—	38	2	no	—
197	C₂×C₄	—	38	2	no	—
198	C₂×C₄	—	38	2	no	—
199	C₂×C₄	—	76	1	no	—
200	C₂×C₄	—	76	1	no	—
201	C₂×C₄	—	76	1	no	—
202	C₂×C₄	—	76	1	no	—
203	C₂×C₄	—	76	1	no	—
204	C₂×C₄	—	76	1	no	—
205	C₂×C₄	—	76	1	no	—
206	C₂×C₄	Dic₇₆	1	2	yes	complemented
207	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
208	C₂×C₄	#64541	1	1	yes	characteristic
209	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
210	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
211	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
212	C₂×C₄	#64545	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	—	4	1	no	—
215	C₂²	C₄×D₇₆	1	1	yes	characteristic
216	C₂²	#10597328	1	1	yes	characteristic
217	C₂²	#10597341	1	1	yes	characteristic
218	C₂²	#10597350	1	1	yes	characteristic
219	C₂²	C₂×Dic₇₆	1	1	yes	characteristic
220	C₂²	#10597355	1	1	yes	characteristic
221	C₂²	#10597355	1	1	yes	characteristic
222	C₄	—	2	2	no	—
223	C₄	—	4	1	no	—
224	C₄	—	38	4	no	—
225	C₄	—	76	2	no	—
226	C₄	—	76	2	no	—
227	C₄	—	152	1	no	—
228	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
229	C₄	#10597330	1	1	yes	characteristic
230	C₄	#10597339	1	1	yes	characteristic
231	C₄	#10597340	1	1	yes	characteristic
232	C₂	#11926422	1	1	yes	characteristic
233	C₂	C₄×Dic₇₆	1	1	yes	characteristic
234	C₂	#11926652	1	1	yes	characteristic
235	C₂	#11926702	1	1	yes	characteristic
236	C₂	#11926708	1	1	yes	characteristic
237	C₂	#11926755	1	1	yes	characteristic
238	C₂	#11926767	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₆

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal, characteristic

#11926450

C₂

yes

maximal, characteristic

#11926307

C₂

yes

maximal, characteristic

C₁₉×#336

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₂×Dic₇₆

C₄

yes

complemented

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597273

—

#10597273

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×Dic₃₈

D₄

yes

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

Q₁₆

yes

complemented

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×D₄

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

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

C₂²⋊C₄

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#1878

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×Q₁₆

yes

characteristic

100

C₂²×C₁₉

#135

yes

characteristic

101

C₂²×C₁₉

#137

yes

characteristic

102

C₂²×C₁₉

#137

yes

characteristic

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

106

C₄×C₁₉

C₄×D₄

yes

characteristic

107

C₄×C₁₉

#121

yes

characteristic

108

C₄×C₁₉

#123

yes

characteristic

109

Dic₁₉

—

110

Dic₁₉

—

111

Dic₁₉

—

112

Dic₁₉

—

113

C₂²×Q₁₆

—

114

C₂×C₄×Q₈

—

115

C₂×#103

—

116

C₂×#103

—

117

#391

—

118

#340

—

119

#336

D₁₉

yes

characteristic

120

C₂×C₁₉

#386

yes

characteristic

121

C₂×C₁₉

C₄×Q₁₆

yes

characteristic

122

C₂×C₁₉

#441

yes

characteristic

123

C₂×C₁₉

#451

yes

characteristic

124

C₂×C₁₉

#452

yes

characteristic

125

C₂×C₁₉

#462

yes

characteristic

126

C₂×C₁₉

#464

yes

characteristic

127

C₂²×Q₈

—

128

C₂²×Q₈

—

129

C₂×Q₁₆

—

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

132

C₂²×C₈

C₂×D₁₉

yes

characteristic

133

C₂²×C₈

C₂×D₁₉

yes

characteristic

134

C₄×Q₈

—

135

C₄×Q₈

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄²

—

140

C₂×C₄²

C₂×D₁₉

yes

characteristic

141

#103

—

142

#103

—

143

#95

—

144

#95

—

145

C₁₉

#1878

yes

characteristic, complemented, Sylow

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

D₇₆

yes

characteristic

163

C₂²×C₄

D₇₆

yes

characteristic

164

C₂²×C₄

C₂²×D₁₉

yes

characteristic

165

Q₁₆

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

C₄×D₁₉

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄²

—

178

C₄²

—

179

C₄²

—

180

C₂³

C₂×D₇₆

yes

characteristic

181

Q₈

—

182

Q₈

—

183

Q₈

—

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

188

Q₈

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

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

Dic₇₆

yes

complemented

207

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

208

C₂×C₄

#64541

yes

characteristic

209

C₂×C₄

D₄×D₁₉

yes

characteristic

210

C₂×C₄

D₄×D₁₉

yes

characteristic

211

C₂×C₄

D₄×D₁₉

yes

characteristic

212

C₂×C₄

#64545

yes

characteristic

213

C₈

—

214

C₈

—

215

C₂²

C₄×D₇₆

yes

characteristic

216

C₂²

#10597328

yes

characteristic

217

C₂²

#10597341

yes

characteristic

218

C₂²

#10597350

yes

characteristic

219

C₂²

C₂×Dic₇₆

yes

characteristic

220

C₂²

#10597355

yes

characteristic

221

C₂²

#10597355

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

152

—

228

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

229

C₄

#10597330

yes

characteristic

230

C₄

#10597339

yes

characteristic

231

C₄

#10597340

yes

characteristic

232

C₂

#11926422

yes

characteristic

233

C₂

C₄×Dic₇₆

yes

characteristic

234

C₂

#11926652

yes

characteristic

235

C₂

#11926702

yes

characteristic

236

C₂

#11926708

yes

characteristic

237

C₂

#11926755

yes

characteristic

238

C₂

#11926767

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#336	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#336	D₁₉
hypocenter	C₁₉	#1878
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#336

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 ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
19. C₂×Dic₇₆	C₄	semidirect
66. C₂×C₄×C₁₉	Q₁₆	semidirect
145. C₁₉	#1878	semidirect
206. C₂×C₄	Dic₇₆	semidirect

H ≅ G/N

type

19. C₂×Dic₇₆

C₄

semidirect

66. C₂×C₄×C₁₉

Q₁₆

semidirect

145. C₁₉

#1878

semidirect

206. C₂×C₄

Dic₇₆

semidirect

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

subgroup	index
C₂²×Dic₇₆	2
C₂×C₄×Dic₃₈	2
C₂×#10597273	2
#11926450	2
#11926307	2
C₁₉×#336	2
#1878	19

subgroup

index

C₂²×Dic₇₆

C₂×C₄×Dic₃₈

C₁₉×#336

Subgroups — #14563975

Conjugacy classes of subgroups

Complements

Maximal subgroups