Group #18073698 — subgroups

Subgroups — #18073698

Order 4864.

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

normal subgroups only

This group has 414 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	C₄×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#14562381	C₂	1	2	yes	maximal
3	#14561918	C₂	1	1	yes	maximal, characteristic
4	#14561467	C₂	1	2	yes	maximal
5	C₁₉×#1450	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
9	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
10	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
11	#11926296	C₄	1	4	yes	complemented
12	#11926294	C₄	1	4	yes	complemented
13	#11926265	—	2	1	no	—
14	C₈×C₁₉⋊C₈	—	2	1	no	—
15	C₁₉×#431	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#322	—	2	1	no	—
18	C₈²×C₁₉	—	2	1	no	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄×Dic₁₉	—	2	2	no	—
22	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
26	C₁₉×C₂²⋊C₈	—	2	2	no	—
27	C₄×C₈×C₁₉	—	2	2	no	—
28	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
29	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
30	C₄×C₈×C₁₉	Q₈	1	2	yes	—
31	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₈×Dic₁₉	—	2	4	no	—
33	C₈×Dic₁₉	C₈	1	8	yes	complemented
34	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
35	C₄×C₁₉⋊C₈	—	2	2	no	—
36	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
37	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	#41	1	2	yes	—
40	C₂²×Dic₁₉	—	2	2	no	—
41	C₂×C₈×C₁₉	—	2	4	no	—
42	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
43	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
45	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
46	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
47	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₄×Dic₁₉	—	2	8	no	—
50	C₄×Dic₁₉	—	2	2	no	—
51	C₄×Dic₁₉	C₂×C₈	1	4	yes	—
52	C₂×C₁₉⋊C₈	—	2	2	no	—
53	C₂×C₁₉⋊C₈	—	2	4	no	—
54	C₂×C₁₉⋊C₈	C₄²	1	2	yes	—
55	C₂×C₁₉⋊C₈	C₄²	1	1	yes	characteristic
56	C₂×C₁₉⋊C₈	C₄²	1	1	yes	characteristic
57	C₂×C₁₉⋊C₈	C₂×C₈	1	4	yes	—
58	#8266	—	19	1	no	maximal, Sylow
59	C₂³×C₁₉	#117	1	1	yes	characteristic
60	C₂×C₄×C₁₉	—	2	4	no	—
61	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
64	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
65	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
66	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
67	C₂×Dic₁₉	—	2	8	no	—
68	C₂×Dic₁₉	—	2	4	no	—
69	C₈×C₁₉	—	4	4	no	—
70	C₈×C₁₉	C₄⋊C₈	1	4	yes	—
71	C₈×C₁₉	C₄⋊C₈	1	4	yes	—
72	C₁₉⋊C₈	—	2	2	no	—
73	C₁₉⋊C₈	—	4	4	no	—
74	C₁₉⋊C₈	C₄×C₈	1	2	yes	—
75	C₁₉⋊C₈	C₄×C₈	1	2	yes	—
76	C₄²×C₈	—	19	1	no	—
77	#1564	—	19	2	no	—
78	#1450	—	19	1	no	—
79	#1450	D₁₉	1	1	yes	characteristic
80	#1276	—	19	2	no	—
81	C₂²×C₁₉	—	2	2	no	—
82	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₁₉	#431	1	2	yes	—
84	C₄×C₁₉	—	2	2	no	—
85	C₄×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
86	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
87	C₄×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
88	C₄×C₁₉	#443	1	4	yes	—
89	Dic₁₉	—	2	8	no	—
90	#431	—	19	2	no	—
91	#431	C₂×D₁₉	1	2	yes	—
92	C₂×C₄×C₈	—	19	2	no	—
93	C₂×C₄×C₈	—	19	1	no	—
94	C₂×C₄×C₈	—	19	2	no	—
95	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
96	C₄³	—	19	1	no	—
97	#335	—	19	4	no	—
98	#334	—	19	4	no	—
99	#322	—	2	1	no	—
100	#322	—	38	1	no	—
101	C₈²	—	2	1	no	—
102	C₈²	—	38	1	no	—
103	C₂×C₁₉	—	2	2	no	—
104	C₂×C₁₉	C₄×C₄⋊C₈	1	1	yes	characteristic
105	C₂×C₁₉	#1772	1	2	yes	—
106	C₂²×C₈	—	19	1	no	—
107	C₂²×C₈	—	19	1	no	—
108	C₂²×C₈	C₄×D₁₉	1	2	yes	—
109	C₂×C₄²	—	19	2	no	—
110	C₂×C₄²	—	38	2	no	—
111	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
112	C₄⋊C₈	—	19	4	no	—
113	C₄⋊C₈	C₄×D₁₉	1	4	yes	—
114	C₂²⋊C₈	—	2	2	no	—
115	C₂²⋊C₈	—	38	2	no	—
116	C₄×C₈	—	2	2	no	—
117	C₄×C₈	—	19	8	no	—
118	C₄×C₈	—	19	2	no	—
119	C₄×C₈	—	19	2	no	—
120	C₄×C₈	—	38	4	no	—
121	C₄×C₈	—	38	2	no	—
122	C₄×C₈	Dic₃₈	1	2	yes	—
123	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
124	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
125	C₁₉	#8266	1	1	yes	characteristic, complemented, Sylow
126	C₂²×C₄	—	38	2	no	—
127	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
128	C₂²×C₄	#64541	1	2	yes	—
129	C₂×C₈	—	2	4	no	—
130	C₂×C₈	—	19	1	no	—
131	C₂×C₈	—	19	1	no	—
132	C₂×C₈	—	19	4	no	—
133	C₂×C₈	—	19	2	no	—
134	C₂×C₈	—	38	2	no	—
135	C₂×C₈	—	38	4	no	—
136	C₂×C₈	C₈×D₁₉	1	4	yes	—
137	C₂×C₈	#64515	1	4	yes	—
138	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
139	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
140	C₄²	—	19	4	no	—
141	C₄²	—	38	8	no	—
142	C₄²	—	38	2	no	—
143	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
144	C₄²	C₂×C₄×D₁₉	1	2	yes	—
145	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
146	C₂³	#10597318	1	1	yes	characteristic
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	38	8	no	—
149	C₂×C₄	—	38	4	no	—
150	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
151	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
152	C₂×C₄	C₂×C₈×D₁₉	1	2	yes	—
153	C₂×C₄	C₂×#64515	1	2	yes	—
154	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
155	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
156	C₈	—	4	4	no	—
157	C₈	—	19	2	no	—
158	C₈	—	19	2	no	—
159	C₈	—	38	2	no	—
160	C₈	—	76	4	no	—
161	C₈	Dic₁₉⋊C₈	1	4	yes	—
162	C₈	Dic₁₉⋊C₈	1	4	yes	—
163	C₂²	—	2	2	no	—
164	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
165	C₂²	#11926595	1	2	yes	—
166	C₄	—	2	2	no	—
167	C₄	—	38	8	no	—
168	C₄	C₄×C₈×D₁₉	1	1	yes	characteristic
169	C₄	C₄×#64515	1	1	yes	characteristic
170	C₄	C₂×Dic₁₉⋊C₈	1	2	yes	—
171	C₄	#11926659	1	4	yes	—
172	C₂	—	2	2	no	—
173	C₂	C₄×Dic₁₉⋊C₈	1	1	yes	characteristic
174	C₂	#14563515	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×Dic₁₉

C₂

yes

maximal, characteristic

#14562381

C₂

yes

maximal

#14561918

C₂

yes

maximal, characteristic

#14561467

C₂

yes

maximal

C₁₉×#1450

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₁₉

C₄

yes

—

C₂×C₈×Dic₁₉

C₄

yes

—

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926296

C₄

yes

complemented

#11926294

C₄

yes

complemented

#11926265

—

C₈×C₁₉⋊C₈

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₈²×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

C₂×C₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₈×Dic₁₉

—

C₈×Dic₁₉

C₈

yes

complemented

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂×C₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄²

yes

—

C₂×C₁₉⋊C₈

C₄²

yes

characteristic

C₂×C₁₉⋊C₈

C₄²

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₈

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₄×Q₈

yes

—

C₂×C₄×C₁₉

C₂²×C₈

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄⋊C₈

yes

—

C₈×C₁₉

C₄⋊C₈

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₄×C₈

yes

—

C₁₉⋊C₈

C₄×C₈

yes

—

C₄²×C₈

—

#1564

—

#1450

—

#1450

D₁₉

yes

characteristic

#1276

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#431

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄×C₈

yes

characteristic

C₄×C₁₉

C₄×M₁₆

yes

characteristic

C₄×C₁₉

C₂×C₄⋊C₈

yes

—

C₄×C₁₉

#443

yes

—

Dic₁₉

—

#431

—

#431

C₂×D₁₉

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄³

—

#335

—

#334

—

#322

—

100

#322

—

101

C₈²

—

102

C₈²

—

103

C₂×C₁₉

—

104

C₂×C₁₉

C₄×C₄⋊C₈

yes

characteristic

105

C₂×C₁₉

#1772

yes

—

106

C₂²×C₈

—

107

C₂²×C₈

—

108

C₂²×C₈

C₄×D₁₉

yes

—

109

C₂×C₄²

—

110

C₂×C₄²

—

111

C₂×C₄²

C₂²×D₁₉

yes

characteristic

112

C₄⋊C₈

—

113

C₄⋊C₈

C₄×D₁₉

yes

—

114

C₂²⋊C₈

—

115

C₂²⋊C₈

—

116

C₄×C₈

—

117

C₄×C₈

—

118

C₄×C₈

—

119

C₄×C₈

—

120

C₄×C₈

—

121

C₄×C₈

—

122

C₄×C₈

Dic₃₈

yes

—

123

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

124

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

125

C₁₉

#8266

yes

characteristic, complemented, Sylow

126

C₂²×C₄

—

127

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

128

C₂²×C₄

#64541

yes

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

C₈×D₁₉

yes

—

137

C₂×C₈

#64515

yes

—

138

C₂×C₈

Dic₁₉⋊C₄

yes

—

139

C₂×C₈

Dic₁₉⋊C₄

yes

—

140

C₄²

—

141

C₄²

—

142

C₄²

—

143

C₄²

C₂×Dic₃₈

yes

characteristic

144

C₄²

C₂×C₄×D₁₉

yes

—

145

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

146

C₂³

#10597318

yes

characteristic

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

C₄×Dic₃₈

yes

—

151

C₂×C₄

C₄²×D₁₉

yes

characteristic

152

C₂×C₄

C₂×C₈×D₁₉

yes

—

153

C₂×C₄

C₂×#64515

yes

—

154

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

155

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

156

C₈

—

157

C₈

—

158

C₈

—

159

C₈

—

160

C₈

—

161

C₈

Dic₁₉⋊C₈

yes

—

162

C₈

Dic₁₉⋊C₈

yes

—

163

C₂²

—

164

C₂²

C₄×Dic₁₉⋊C₄

yes

characteristic

165

C₂²

#11926595

yes

—

166

C₄

—

167

C₄

—

168

C₄

C₄×C₈×D₁₉

yes

characteristic

169

C₄

C₄×#64515

yes

characteristic

170

C₄

C₂×Dic₁₉⋊C₈

yes

—

171

C₄

#11926659

yes

—

172

C₂

—

173

C₂

C₄×Dic₁₉⋊C₈

yes

characteristic

174

C₂

#14563515

yes

—

	subgroup	G/H
center	C₄×C₈	C₂²⋊D₁₉
commutator	C₄×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1450	C₂
socle	C₂²×C₁₉	C₄×C₄⋊C₄
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1450	D₁₉
hypocenter	C₁₉	#8266
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈ ◁ #1450

subgroup

G/H

center

C₄×C₈

C₂²⋊D₁₉

commutator

C₄×C₁₉

C₂×C₄×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1450

C₂

socle

C₂²×C₁₉

C₄×C₄⋊C₄

prime radical

C₂³×C₁₉

#117

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈ ◁ #1450

N	H ≅ G/N	type
11. #11926296	C₄	semidirect
12. #11926294	C₄	semidirect
33. C₈×Dic₁₉	C₈	semidirect
125. C₁₉	#8266	semidirect

H ≅ G/N

type

11. #11926296

C₄

semidirect

12. #11926294

C₄

semidirect

33. C₈×Dic₁₉

C₈

semidirect

125. C₁₉

#8266

semidirect

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

subgroup	index
C₄×C₈×Dic₁₉	2
#14562381	2
#14561918	2
#14561467	2
C₁₉×#1450	2
#8266	19

subgroup

index

C₄×C₈×Dic₁₉

C₁₉×#1450

Subgroups — #18073698

Conjugacy classes of subgroups

Complements

Maximal subgroups