Group #18069300 — subgroups

Subgroups — #18069300

Order 4864.

270 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 71 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	#14561719	C₂	1	1	yes	maximal, characteristic, complemented
2	#14561466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1972	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	#11926597	—	2	1	no	—
6	C₂²×D₈×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₁₉×#106	C₄	1	1	yes	characteristic
8	C₂×C₁₉×#102	—	2	1	no	—
9	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
10	C₁₉×#390	—	2	1	no	—
11	C₂²×D₄×C₁₉	—	2	1	no	—
12	C₂×D₈×C₁₉	—	2	1	no	—
13	C₂×D₈×C₁₉	—	4	1	no	—
14	C₂×D₈×C₁₉	—	4	1	no	—
15	C₂×D₈×C₁₉	C₈	1	2	yes	complemented
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
19	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
20	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
21	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
22	C₁₉×#106	—	4	1	no	—
23	C₁₉×#102	—	4	1	no	—
24	C₁₉×#102	—	4	1	no	—
25	C₁₉×#97	—	4	1	no	—
26	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
27	#10597269	—	2	2	no	—
28	#10597269	—	4	1	no	—
29	C₂×C₁₉⋊C₁₆	—	4	1	no	—
30	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
31	C₄×C₁₉⋊C₈	—	2	2	no	—
32	C₂⁴×C₁₉	—	4	1	no	—
33	C₂×D₄×C₁₉	—	2	2	no	—
34	C₂×D₄×C₁₉	—	4	1	no	—
35	C₂×D₄×C₁₉	—	4	1	no	—
36	C₂×D₄×C₁₉	—	4	1	no	—
37	C₂×D₄×C₁₉	—	4	1	no	—
38	C₂×D₄×C₁₉	—	4	1	no	—
39	C₂²×C₄×C₁₉	—	4	1	no	—
40	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
43	D₈×C₁₉	—	4	2	no	—
44	D₈×C₁₉	—	4	2	no	—
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	C₂×C₈	1	1	yes	characteristic
50	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
51	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
52	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
53	C₄⋊C₄×C₁₉	—	4	1	no	—
54	C₄⋊C₄×C₁₉	—	4	1	no	—
55	C₂²⋊C₄×C₁₉	—	8	2	no	—
56	C₂²⋊C₄×C₁₉	—	8	2	no	—
57	C₄²×C₁₉	—	2	1	no	—
58	C₄²×C₁₉	—	2	1	no	—
59	C₂×C₁₉⋊C₈	—	4	2	no	—
60	C₁₉⋊C₁₆	—	4	2	no	—
61	#7110	—	19	1	no	maximal, Sylow
62	C₂³×C₁₉	—	4	2	no	—
63	C₂³×C₁₉	—	8	1	no	—
64	C₂³×C₁₉	—	8	1	no	—
65	C₂³×C₁₉	—	8	1	no	—
66	C₂³×C₁₉	—	8	1	no	—
67	C₂³×C₁₉	—	8	1	no	—
68	C₂³×C₁₉	—	8	1	no	—
69	C₂³×C₁₉	#102	1	1	yes	characteristic
70	D₄×C₁₉	—	4	2	no	—
71	D₄×C₁₉	—	4	2	no	—
72	D₄×C₁₉	—	8	1	no	—
73	D₄×C₁₉	—	8	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	—	4	1	no	—
78	C₂×C₄×C₁₉	—	8	1	no	—
79	C₂×C₄×C₁₉	—	8	1	no	—
80	C₂×C₄×C₁₉	—	8	1	no	—
81	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
87	C₈×C₁₉	—	2	1	no	—
88	C₈×C₁₉	—	2	1	no	—
89	C₈×C₁₉	—	2	1	no	—
90	C₈×C₁₉	—	2	1	no	—
91	C₁₉⋊C₈	—	8	2	no	—
92	#1972	D₁₉	1	1	yes	characteristic
93	#1377	—	19	1	no	—
94	#1275	—	19	1	no	—
95	C₂²×C₁₉	—	2	1	no	—
96	C₂²×C₁₉	—	2	1	no	—
97	C₂²×C₁₉	—	8	2	no	—
98	C₂²×C₁₉	—	8	2	no	—
99	C₂²×C₁₉	—	8	2	no	—
100	C₂²×C₁₉	—	16	1	no	—
101	C₂²×C₁₉	—	16	1	no	—
102	C₂²×C₁₉	—	16	1	no	—
103	C₂²×C₁₉	—	16	1	no	—
104	C₂²×C₁₉	D₄⋊C₈	1	1	yes	characteristic
105	C₂²×C₁₉	#327	1	1	yes	characteristic
106	C₂²×C₁₉	#331	1	1	yes	characteristic
107	C₄×C₁₉	—	4	1	no	—
108	C₄×C₁₉	—	4	1	no	—
109	C₄×C₁₉	—	16	1	no	—
110	C₄×C₁₉	#323	1	1	yes	characteristic
111	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
112	C₄×C₁₉	#327	1	1	yes	characteristic
113	C₄×C₁₉	#329	1	1	yes	characteristic
114	C₂²×D₈	Dic₁₉	1	1	yes	characteristic
115	C₂×M₃₂	—	38	1	no	—
116	#431	—	38	1	no	—
117	C₂×#106	Dic₁₉	1	1	yes	characteristic
118	C₂×#102	—	2	1	no	—
119	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
120	#390	—	2	1	no	—
121	C₂×C₁₉	—	2	1	no	—
122	C₂×C₁₉	—	2	1	no	—
123	C₂×C₁₉	—	16	2	no	—
124	C₂×C₁₉	#1270	1	1	yes	characteristic
125	C₂×C₁₉	#1339	1	1	yes	characteristic
126	C₂×C₁₉	#1341	1	1	yes	characteristic
127	C₂²×D₄	—	2	1	no	—
128	C₂×D₈	—	2	1	no	—
129	C₂×D₈	—	4	1	no	—
130	C₂×D₈	—	4	1	no	—
131	C₂×D₈	C₁₉⋊C₈	1	2	yes	complemented
132	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
133	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
134	C₂×C₄⋊C₄	—	2	1	no	—
135	C₂×C₂²⋊C₄	—	4	1	no	—
136	C₂×C₂²⋊C₄	—	4	1	no	—
137	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
138	M₃₂	—	38	2	no	—
139	M₃₂	—	76	1	no	—
140	C₂×C₁₆	—	76	1	no	—
141	#106	—	4	1	no	—
142	C₄⋊C₈	—	76	1	no	—
143	#102	—	4	1	no	—
144	#102	—	4	1	no	—
145	C₂²⋊C₈	—	76	1	no	—
146	#97	—	4	1	no	—
147	C₄×C₈	—	38	2	no	—
148	C₁₉	#7110	1	1	yes	characteristic, complemented, Sylow
149	C₂⁴	—	4	1	no	—
150	C₂×D₄	—	2	2	no	—
151	C₂×D₄	—	4	1	no	—
152	C₂×D₄	—	4	1	no	—
153	C₂×D₄	—	4	1	no	—
154	C₂×D₄	—	4	1	no	—
155	C₂×D₄	—	4	1	no	—
156	C₂²×C₄	—	4	1	no	—
157	C₂²×C₄	#64525	1	1	yes	characteristic
158	C₂²×C₄	#64526	1	1	yes	characteristic
159	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
160	D₈	—	4	2	no	—
161	D₈	—	4	2	no	—
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	2	1	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	76	2	no	—
167	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
168	C₂×C₈	#64520	1	1	yes	characteristic
169	C₂×C₈	#64525	1	1	yes	characteristic
170	C₂×C₈	#64526	1	1	yes	characteristic
171	C₄⋊C₄	—	4	1	no	—
172	C₄⋊C₄	—	4	1	no	—
173	C₂²⋊C₄	—	8	2	no	—
174	C₂²⋊C₄	—	8	2	no	—
175	C₄²	—	2	1	no	—
176	C₄²	—	2	1	no	—
177	C₁₆	—	76	2	no	—
178	C₂³	—	4	2	no	—
179	C₂³	—	8	1	no	—
180	C₂³	—	8	1	no	—
181	C₂³	—	8	1	no	—
182	C₂³	—	8	1	no	—
183	C₂³	—	8	1	no	—
184	C₂³	—	8	1	no	—
185	C₂³	#10597289	1	1	yes	characteristic
186	D₄	—	4	2	no	—
187	D₄	—	4	2	no	—
188	D₄	—	8	1	no	—
189	D₄	—	8	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	8	1	no	—
195	C₂×C₄	—	8	1	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
198	C₂×C₄	#10597289	1	1	yes	characteristic
199	C₂×C₄	#10597290	1	1	yes	characteristic
200	C₂×C₄	#10597291	1	1	yes	characteristic
201	C₂×C₄	#10597294	1	1	yes	characteristic
202	C₂×C₄	#10597294	1	1	yes	characteristic
203	C₈	—	2	1	no	—
204	C₈	—	2	1	no	—
205	C₈	—	2	1	no	—
206	C₈	—	2	1	no	—
207	C₈	—	152	2	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	8	2	no	—
211	C₂²	—	8	2	no	—
212	C₂²	—	8	2	no	—
213	C₂²	—	16	1	no	—
214	C₂²	—	16	1	no	—
215	C₂²	—	16	1	no	—
216	C₂²	—	16	1	no	—
217	C₂²	D₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
218	C₂²	#11926278	1	1	yes	characteristic
219	C₂²	#11926288	1	1	yes	characteristic
220	C₄	—	4	1	no	—
221	C₄	—	4	1	no	—
222	C₄	—	16	1	no	—
223	C₄	#11926268	1	1	yes	characteristic
224	C₄	D₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
225	C₄	#11926278	1	1	yes	characteristic
226	C₄	#11926284	1	1	yes	characteristic
227	C₂	—	2	1	no	—
228	C₂	—	2	1	no	—
229	C₂	—	16	2	no	—
230	C₂	#14561456	1	1	yes	characteristic
231	C₂	#14561620	1	1	yes	characteristic
232	C₂	#14561626	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561719

C₂

yes

maximal, characteristic, complemented

#14561466

C₂

yes

maximal, characteristic, complemented

C₁₉×#1972

C₂

yes

maximal, characteristic

C₂×#10597269

—

#11926597

—

C₂²×D₈×C₁₉

C₄

yes

characteristic

C₂×C₁₉×#106

C₄

yes

characteristic

C₂×C₁₉×#102

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#390

—

C₂²×D₄×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

C₈

yes

complemented

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×#106

—

C₁₉×#102

—

C₁₉×#102

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

#7110

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#102

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1972

D₁₉

yes

characteristic

#1377

—

#1275

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

D₄⋊C₈

yes

characteristic

105

C₂²×C₁₉

#327

yes

characteristic

106

C₂²×C₁₉

#331

yes

characteristic

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

#323

yes

characteristic

111

C₄×C₁₉

D₄⋊C₈

yes

characteristic

112

C₄×C₁₉

#327

yes

characteristic

113

C₄×C₁₉

#329

yes

characteristic

114

C₂²×D₈

Dic₁₉

yes

characteristic

115

C₂×M₃₂

—

116

#431

—

117

C₂×#106

Dic₁₉

yes

characteristic

118

C₂×#102

—

119

C₂×#97

C₂×D₁₉

yes

characteristic

120

#390

—

121

C₂×C₁₉

—

122

C₂×C₁₉

—

123

C₂×C₁₉

—

124

C₂×C₁₉

#1270

yes

characteristic

125

C₂×C₁₉

#1339

yes

characteristic

126

C₂×C₁₉

#1341

yes

characteristic

127

C₂²×D₄

—

128

C₂×D₈

—

129

C₂×D₈

—

130

C₂×D₈

—

131

C₂×D₈

C₁₉⋊C₈

yes

complemented

132

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

133

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

134

C₂×C₄⋊C₄

—

135

C₂×C₂²⋊C₄

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

138

M₃₂

—

139

M₃₂

—

140

C₂×C₁₆

—

141

#106

—

142

C₄⋊C₈

—

143

#102

—

144

#102

—

145

C₂²⋊C₈

—

146

#97

—

147

C₄×C₈

—

148

C₁₉

#7110

yes

characteristic, complemented, Sylow

149

C₂⁴

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂²×C₄

—

157

C₂²×C₄

#64525

yes

characteristic

158

C₂²×C₄

#64526

yes

characteristic

159

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

160

D₈

—

161

D₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

C₂×C₁₉⋊C₈

yes

characteristic

168

C₂×C₈

#64520

yes

characteristic

169

C₂×C₈

#64525

yes

characteristic

170

C₂×C₈

#64526

yes

characteristic

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₄²

—

176

C₄²

—

177

C₁₆

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

#10597289

yes

characteristic

186

D₄

—

187

D₄

—

188

D₄

—

189

D₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

198

C₂×C₄

#10597289

yes

characteristic

199

C₂×C₄

#10597290

yes

characteristic

200

C₂×C₄

#10597291

yes

characteristic

201

C₂×C₄

#10597294

yes

characteristic

202

C₂×C₄

#10597294

yes

characteristic

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

207

C₈

—

152

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

D₄⋊(C₁₉⋊C₈)

yes

characteristic

218

C₂²

#11926278

yes

characteristic

219

C₂²

#11926288

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

#11926268

yes

characteristic

224

C₄

D₄⋊(C₁₉⋊C₈)

yes

characteristic

225

C₄

#11926278

yes

characteristic

226

C₄

#11926284

yes

characteristic

227

C₂

—

228

C₂

—

229

C₂

—

230

C₂

#14561456

yes

characteristic

231

C₂

#14561620

yes

characteristic

232

C₂

#14561626

yes

characteristic

	subgroup	G/H
center	C₂²	#11926278
commutator	C₂×C₈×C₁₉	C₂×C₈
Frattini	C₂×#97	C₂×D₁₉
Fitting	C₁₉×#1972	C₂
socle	C₂²×C₁₉	#327
prime radical	C₂²×D₈×C₁₉	C₄
cosocle	C₂×C₁₉×#97	C₂²
hypercenter	#1972	D₁₉
hypocenter	C₁₉	#7110
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1972

subgroup

G/H

center

C₂²

#11926278

commutator

C₂×C₈×C₁₉

C₂×C₈

Frattini

C₂×#97

C₂×D₁₉

Fitting

C₁₉×#1972

C₂

socle

C₂²×C₁₉

#327

prime radical

C₂²×D₈×C₁₉

C₄

cosocle

C₂×C₁₉×#97

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1972

N	H ≅ G/N	type
1. #14561719	C₂	semidirect
2. #14561466	C₂	semidirect
15. C₂×D₈×C₁₉	C₈	semidirect
131. C₂×D₈	C₁₉⋊C₈	semidirect
148. C₁₉	#7110	semidirect

H ≅ G/N

type

1. #14561719

C₂

semidirect

2. #14561466

C₂

semidirect

15. C₂×D₈×C₁₉

C₈

semidirect

131. C₂×D₈

C₁₉⋊C₈

semidirect

148. C₁₉

#7110

semidirect

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

subgroup	index
#14561719	2
#14561466	2
C₁₉×#1972	2
#7110	19

subgroup

index

#14561719

#14561466

C₁₉×#1972

#7110

Subgroups — #18069300

Conjugacy classes of subgroups

Complements

Maximal subgroups