Group #18075962 — subgroups

Subgroups — #18075962

Order 4864.

630 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 195 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	#14563615	C₂	1	2	yes	maximal
2	#14561518	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#384	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
5	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
6	#11926299	—	2	2	no	—
7	C₂²×C₄⋊C₄×C₁₉	—	2	2	no	—
8	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
9	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#384	—	2	2	no	—
11	C₁₉×#384	C₄	1	2	yes	—
12	C₁₉×#384	C₂²	1	2	yes	—
13	C₂³×C₄×C₁₉	—	2	2	no	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	D₄	1	2	yes	—
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
19	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
20	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
21	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₁₉	—	2	4	no	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	—	2	4	no	—
27	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
28	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
29	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	—	2	2	no	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	2	no	—
33	C₂²×C₄×C₁₉	—	2	4	no	—
34	C₂²×C₄×C₁₉	—	2	4	no	—
35	C₂²×C₄×C₁₉	—	2	4	no	—
36	C₂²×C₄×C₁₉	—	4	8	no	—
37	C₂²×C₄×C₁₉	—	4	4	no	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
41	C₂²×C₄×C₁₉	Q₁₆	1	4	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₄⋊C₄×C₁₉	—	4	4	no	—
45	C₄⋊C₄×C₁₉	—	4	4	no	—
46	C₄⋊C₄×C₁₉	—	4	8	no	—
47	C₄⋊C₄×C₁₉	—	4	8	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	—	2	4	no	—
50	C₄²×C₁₉	#41	1	4	yes	—
51	C₂×C₁₉⋊C₈	—	4	4	no	—
52	C₂×C₁₉⋊C₈	—	4	4	no	—
53	C₂×C₁₉⋊C₈	—	4	4	no	—
54	#8725	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	—	2	1	no	—
56	C₂³×C₁₉	—	2	1	no	—
57	C₂³×C₁₉	—	2	2	no	—
58	C₂³×C₁₉	#100	1	2	yes	—
59	C₂³×C₁₉	#103	1	4	yes	—
60	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	—	2	8	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	8	no	—
69	C₂×C₄×C₁₉	—	2	8	no	—
70	C₂×C₄×C₁₉	—	4	4	no	—
71	C₂×C₄×C₁₉	—	4	8	no	—
72	C₂×C₄×C₁₉	—	8	8	no	—
73	C₂×C₄×C₁₉	#101	1	2	yes	—
74	C₂×C₄×C₁₉	#103	1	4	yes	—
75	C₂×C₄×C₁₉	#117	1	2	yes	—
76	C₂×C₄×C₁₉	#123	1	4	yes	—
77	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
78	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
79	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
80	C₁₉⋊C₈	—	8	4	no	—
81	C₂×#384	D₁₉	1	1	yes	characteristic
82	#1797	—	19	2	no	—
83	#1296	—	19	4	no	—
84	C₂²×C₁₉	—	2	4	no	—
85	C₂²×C₁₉	—	2	2	no	—
86	C₂²×C₁₉	—	2	2	no	—
87	C₂²×C₁₉	—	2	4	no	—
88	C₂²×C₁₉	#333	1	4	yes	—
89	C₂²×C₁₉	#381	1	1	yes	characteristic
90	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
91	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
92	C₂²×C₁₉	C₂×#103	1	2	yes	—
93	C₂²×C₁₉	#418	1	2	yes	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	2	4	no	—
97	C₄×C₁₉	—	8	4	no	—
98	C₄×C₁₉	#481	1	4	yes	—
99	C₄×C₁₉	#484	1	4	yes	—
100	C₂²×C₄⋊C₄	—	2	2	no	—
101	C₂²×C₄⋊C₄	Dic₁₉	1	2	yes	—
102	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
103	C₂×C₄⋊C₈	—	19	4	no	—
104	C₂×C₂²⋊C₈	—	38	2	no	—
105	#384	—	2	2	no	—
106	#384	Dic₁₉	1	2	yes	—
107	#384	C₂×D₁₉	1	2	yes	—
108	#336	—	38	2	no	—
109	C₂×C₁₉	—	2	4	no	—
110	C₂×C₁₉	C₂×#333	1	1	yes	characteristic
111	C₂×C₁₉	#1549	1	2	yes	—
112	C₂×C₁₉	#1555	1	1	yes	characteristic
113	C₂×C₁₉	#1821	1	1	yes	characteristic
114	C₂×C₁₉	#1824	1	2	yes	—
115	C₂³×C₄	—	2	2	no	—
116	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
117	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
118	C₂²×C₈	—	38	4	no	—
119	C₂×C₄⋊C₄	—	2	4	no	—
120	C₂×C₄⋊C₄	—	2	2	no	—
121	C₂×C₄⋊C₄	—	2	4	no	—
122	C₂×C₄⋊C₄	—	4	4	no	—
123	C₂×C₄⋊C₄	—	4	8	no	—
124	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
125	C₂×C₄²	—	2	4	no	—
126	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
127	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
128	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
129	C₄⋊C₈	—	38	8	no	—
130	C₂²⋊C₈	—	76	4	no	—
131	C₁₉	#8725	1	1	yes	characteristic, complemented, Sylow
132	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
133	C₂²×C₄	—	2	2	no	—
134	C₂²×C₄	—	2	4	no	—
135	C₂²×C₄	—	2	2	no	—
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	—	2	4	no	—
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	—	4	8	no	—
140	C₂²×C₄	—	4	4	no	—
141	C₂²×C₄	#64527	1	4	yes	—
142	C₂²×C₄	#64528	1	4	yes	—
143	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
144	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
145	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
146	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
147	C₂×C₈	—	76	4	no	—
148	C₂×C₈	—	76	4	no	—
149	C₂×C₈	—	76	4	no	—
150	C₄⋊C₄	—	4	4	no	—
151	C₄⋊C₄	—	4	8	no	—
152	C₄⋊C₄	—	4	4	no	—
153	C₄⋊C₄	—	4	8	no	—
154	C₄²	—	2	2	no	—
155	C₄²	—	2	4	no	—
156	C₄²	#64541	1	4	yes	—
157	C₂³	—	2	2	no	—
158	C₂³	—	2	1	no	—
159	C₂³	—	2	1	no	—
160	C₂³	#10597290	1	2	yes	—
161	C₂³	#10597292	1	4	yes	—
162	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
163	C₂×C₄	—	2	8	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	8	no	—
171	C₂×C₄	—	2	8	no	—
172	C₂×C₄	—	4	8	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	—	8	8	no	—
175	C₂×C₄	#10597292	1	4	yes	—
176	C₂×C₄	#10597293	1	2	yes	—
177	C₂×C₄	#10597372	1	2	yes	—
178	C₂×C₄	#10597375	1	4	yes	—
179	C₂×C₄	#10597378	1	4	yes	—
180	C₂×C₄	C₂×#64527	1	2	yes	—
181	C₂×C₄	C₂×#64528	1	2	yes	—
182	C₈	—	152	4	no	—
183	C₂²	—	2	4	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	2	2	no	—
186	C₂²	—	2	4	no	—
187	C₂²	#11926293	1	4	yes	—
188	C₂²	#11926407	1	1	yes	characteristic
189	C₂²	C₂×#10597290	1	1	yes	characteristic
190	C₂²	C₂×#10597293	1	1	yes	characteristic
191	C₂²	C₂×#10597292	1	2	yes	—
192	C₂²	#11926549	1	2	yes	—
193	C₄	—	2	2	no	—
194	C₄	—	2	2	no	—
195	C₄	—	2	4	no	—
196	C₄	—	8	4	no	—
197	C₄	#11926862	1	4	yes	—
198	C₄	#11926879	1	4	yes	—
199	C₂	—	2	4	no	—
200	C₂	C₂×#11926293	1	1	yes	characteristic
201	C₂	#14562320	1	2	yes	—
202	C₂	#14562349	1	1	yes	characteristic
203	C₂	#14563715	1	1	yes	characteristic
204	C₂	#14563725	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563615

C₂

yes

maximal

#14561518

C₂

yes

maximal, complemented

C₂×C₁₉×#384

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926299

—

C₂²×C₄⋊C₄×C₁₉

—

C₂²×C₄⋊C₄×C₁₉

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#384

—

C₁₉×#384

C₄

yes

—

C₁₉×#384

C₂²

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8725

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#100

yes

—

C₂³×C₁₉

#103

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₁₉⋊C₈

—

C₂×#384

D₁₉

yes

characteristic

#1797

—

#1296

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#333

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#418

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#481

yes

—

C₄×C₁₉

#484

yes

—

100

C₂²×C₄⋊C₄

—

101

C₂²×C₄⋊C₄

Dic₁₉

yes

—

102

C₂²×C₄²

C₂×D₁₉

yes

characteristic

103

C₂×C₄⋊C₈

—

104

C₂×C₂²⋊C₈

—

105

#384

—

106

#384

Dic₁₉

yes

—

107

#384

C₂×D₁₉

yes

—

108

#336

—

109

C₂×C₁₉

—

110

C₂×C₁₉

C₂×#333

yes

characteristic

111

C₂×C₁₉

#1549

yes

—

112

C₂×C₁₉

#1555

yes

characteristic

113

C₂×C₁₉

#1821

yes

characteristic

114

C₂×C₁₉

#1824

yes

—

115

C₂³×C₄

—

116

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

117

C₂³×C₄

C₂²⋊D₁₉

yes

—

118

C₂²×C₈

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

125

C₂×C₄²

—

126

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

127

C₂×C₄²

C₂²⋊D₁₉

yes

—

128

C₂×C₄²

C₂²×D₁₉

yes

characteristic

129

C₄⋊C₈

—

130

C₂²⋊C₈

—

131

C₁₉

#8725

yes

characteristic, complemented, Sylow

132

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

#64527

yes

—

142

C₂²×C₄

#64528

yes

—

143

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

144

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

145

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

146

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄²

—

155

C₄²

—

156

C₄²

#64541

yes

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

#10597290

yes

—

161

C₂³

#10597292

yes

—

162

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

#10597292

yes

—

176

C₂×C₄

#10597293

yes

—

177

C₂×C₄

#10597372

yes

—

178

C₂×C₄

#10597375

yes

—

179

C₂×C₄

#10597378

yes

—

180

C₂×C₄

C₂×#64527

yes

—

181

C₂×C₄

C₂×#64528

yes

—

182

C₈

—

152

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

#11926293

yes

—

188

C₂²

#11926407

yes

characteristic

189

C₂²

C₂×#10597290

yes

characteristic

190

C₂²

C₂×#10597293

yes

characteristic

191

C₂²

C₂×#10597292

yes

—

192

C₂²

#11926549

yes

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

#11926862

yes

—

198

C₄

#11926879

yes

—

199

C₂

—

200

C₂

C₂×#11926293

yes

characteristic

201

C₂

#14562320

yes

—

202

C₂

#14562349

yes

characteristic

203

C₂

#14563715

yes

characteristic

204

C₂

#14563725

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#384	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#384	D₁₉
hypocenter	C₁₉	#8725
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#384

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#384

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#384

N	H ≅ G/N	type
2. #14561518	C₂	semidirect
131. C₁₉	#8725	semidirect

H ≅ G/N

type

2. #14561518

C₂

semidirect

131. C₁₉

#8725

semidirect

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

subgroup	index
#14563615	2
#14561518	2
C₂×C₁₉×#384	2
#8725	19

subgroup

index

#14563615

#14561518

C₂×C₁₉×#384

#8725

Subgroups — #18075962

Conjugacy classes of subgroups

Complements

Maximal subgroups