Group #14564452 — subgroups

Subgroups — #14564452

Order 2432.

344 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 113 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×#10597292	C₂	1	2	yes	maximal, complemented
2	C₂×#10597289	C₂	1	2	yes	maximal
3	C₂×#10597260	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926414	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#124	—	2	2	no	—
9	C₁₉×#124	C₄	1	4	yes	complemented
10	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	—	2	2	no	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
15	#10597292	—	2	4	no	—
16	#10597289	—	2	4	no	—
17	#10597260	—	2	2	no	—
18	C₂⁴×C₁₉	—	2	1	no	—
19	C₂×Q₈×C₁₉	—	2	1	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	—	2	2	no	—
22	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×D₄×C₁₉	—	2	2	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	2	no	—
26	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₁₉	—	2	1	no	—
28	C₂²×C₄×C₁₉	D₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×Dic₁₉	—	2	2	no	—
31	C₂²⋊C₄×C₁₉	—	2	8	no	—
32	C₄²×C₁₉	C₂×C₄	1	2	yes	—
33	C₄²×C₁₉	D₄	1	2	yes	—
34	C₄⋊Dic₁₉	—	2	2	no	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	—	4	4	no	—
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
40	C₂³×C₁₉	—	2	2	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	C₂³×C₁₉	—	4	1	no	—
43	C₂³×C₁₉	—	4	2	no	—
44	C₂³×C₁₉	—	4	2	no	—
45	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
46	Q₈×C₁₉	—	2	4	no	—
47	Q₈×C₁₉	—	4	2	no	—
48	D₄×C₁₉	—	2	4	no	—
49	D₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
56	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#41	1	2	yes	—
60	C₂×Dic₁₉	—	4	2	no	—
61	C₂×Dic₁₉	—	4	4	no	—
62	C₁₉⋊C₈	—	2	4	no	—
63	#1959	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	4	2	no	—
65	C₂²×C₁₉	—	4	4	no	—
66	C₂²×C₁₉	—	8	2	no	—
67	C₂²×C₁₉	—	8	1	no	—
68	C₂²×C₁₉	—	8	1	no	—
69	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₁₉	#124	1	1	yes	characteristic
71	C₂²×C₁₉	#127	1	1	yes	characteristic
72	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
73	C₂²×C₁₉	#137	1	2	yes	—
74	C₄×C₁₉	—	2	4	no	—
75	C₄×C₁₉	—	4	2	no	—
76	C₄×C₁₉	C₄×D₄	1	2	yes	—
77	C₄×C₁₉	#121	1	2	yes	—
78	Dic₁₉	—	8	2	no	—
79	C₂×#124	D₁₉	1	1	yes	characteristic
80	C₂×#103	—	19	2	no	—
81	C₂×#102	—	19	2	no	—
82	C₂×#97	—	19	1	no	—
83	#384	—	19	1	no	—
84	C₂×C₁₉	—	8	2	no	—
85	C₂×C₁₉	#390	1	1	yes	characteristic
86	C₂×C₁₉	#417	1	2	yes	—
87	C₂×C₁₉	#489	1	2	yes	—
88	C₂×C₁₉	#496	1	1	yes	characteristic
89	C₂×C₁₉	#497	1	1	yes	characteristic
90	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
91	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
92	C₂²×C₈	—	19	2	no	—
93	#124	—	2	2	no	—
94	#124	Dic₁₉	1	4	yes	complemented
95	C₂×C₄⋊C₄	—	19	2	no	—
96	C₂×C₄⋊C₄	—	38	2	no	—
97	C₂×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
99	#103	—	38	4	no	—
100	#102	—	38	4	no	—
101	#97	—	38	2	no	—
102	C₁₉	#1959	1	1	yes	characteristic, complemented, Sylow
103	C₂⁴	—	2	1	no	—
104	C₂×Q₈	—	2	1	no	—
105	C₂×Q₈	—	2	2	no	—
106	C₂×Q₈	—	2	2	no	—
107	C₂×Q₈	C₂×Dic₁₉	1	2	yes	—
108	C₂×D₄	—	2	2	no	—
109	C₂×D₄	—	2	2	no	—
110	C₂×D₄	—	2	1	no	—
111	C₂×D₄	C₂×Dic₁₉	1	2	yes	—
112	C₂²×C₄	—	2	1	no	—
113	C₂²×C₄	—	38	2	no	—
114	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
115	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
116	C₂×C₈	—	19	4	no	—
117	C₂×C₈	—	38	2	no	—
118	C₂×C₈	—	38	2	no	—
119	C₄⋊C₄	—	38	2	no	—
120	C₄⋊C₄	—	38	2	no	—
121	C₄⋊C₄	—	76	4	no	—
122	C₂²⋊C₄	—	2	8	no	—
123	C₄²	C₂×Dic₁₉	1	2	yes	—
124	C₄²	C₂²⋊D₁₉	1	2	yes	—
125	C₂³	—	2	2	no	—
126	C₂³	—	4	1	no	—
127	C₂³	—	4	1	no	—
128	C₂³	—	4	2	no	—
129	C₂³	—	4	2	no	—
130	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
131	Q₈	—	2	4	no	—
132	Q₈	—	4	2	no	—
133	D₄	—	2	4	no	—
134	D₄	—	4	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	4	1	no	—
139	C₂×C₄	—	4	1	no	—
140	C₂×C₄	—	76	2	no	—
141	C₂×C₄	—	76	4	no	—
142	C₂×C₄	C₂²⋊Dic₁₉	1	4	yes	—
143	C₂×C₄	D₄×D₁₉	1	2	yes	—
144	C₂×C₄	#64543	1	2	yes	—
145	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
146	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
147	C₈	—	38	4	no	—
148	C₂²	—	4	4	no	—
149	C₂²	—	4	2	no	—
150	C₂²	—	8	2	no	—
151	C₂²	—	8	1	no	—
152	C₂²	—	8	1	no	—
153	C₂²	#10597382	1	1	yes	characteristic
154	C₂²	#10597386	1	1	yes	characteristic
155	C₂²	#10597395	1	2	yes	—
156	C₂²	#10597397	1	2	yes	—
157	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
158	C₄	—	2	4	no	—
159	C₄	—	4	2	no	—
160	C₄	—	152	2	no	—
161	C₄	D₄×Dic₁₉	1	2	yes	—
162	C₄	#10597384	1	2	yes	—
163	C₂	—	8	2	no	—
164	C₂	#11926447	1	1	yes	characteristic
165	C₂	#11926545	1	2	yes	—
166	C₂	#11926903	1	2	yes	—
167	C₂	#11926934	1	1	yes	characteristic
168	C₂	#11926939	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597292

C₂

yes

maximal, complemented

C₂×#10597289

C₂

yes

maximal

C₂×#10597260

C₂

yes

maximal, characteristic, complemented

#11926414

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#124

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#124

—

C₁₉×#124

C₄

yes

complemented

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597292

—

#10597289

—

#10597260

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1959

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

C₂×#124

D₁₉

yes

characteristic

C₂×#103

—

C₂×#102

—

C₂×#97

—

#384

—

C₂×C₁₉

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

#417

yes

—

C₂×C₁₉

#489

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

#124

—

#124

Dic₁₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#103

—

100

#102

—

101

#97

—

102

C₁₉

#1959

yes

characteristic, complemented, Sylow

103

C₂⁴

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

C₂×Dic₁₉

yes

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

C₂×Dic₁₉

yes

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

C₂²⋊D₁₉

yes

—

115

C₂²×C₄

C₂²×D₁₉

yes

characteristic

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₂²⋊C₄

—

123

C₄²

C₂×Dic₁₉

yes

—

124

C₄²

C₂²⋊D₁₉

yes

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

131

Q₈

—

132

Q₈

—

133

D₄

—

134

D₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

C₂²⋊Dic₁₉

yes

—

143

C₂×C₄

D₄×D₁₉

yes

—

144

C₂×C₄

#64543

yes

—

145

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

146

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

147

C₈

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

#10597382

yes

characteristic

154

C₂²

#10597386

yes

characteristic

155

C₂²

#10597395

yes

—

156

C₂²

#10597397

yes

—

157

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

152

—

161

C₄

D₄×Dic₁₉

yes

—

162

C₄

#10597384

yes

—

163

C₂

—

164

C₂

#11926447

yes

characteristic

165

C₂

#11926545

yes

—

166

C₂

#11926903

yes

—

167

C₂

#11926934

yes

characteristic

168

C₂

#11926939

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#124	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#124	D₁₉
hypocenter	C₁₉	#1959
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#124

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

N	H ≅ G/N	type
1. C₂×#10597292	C₂	semidirect
3. C₂×#10597260	C₂	semidirect
4. #11926414	C₂	semidirect
9. C₁₉×#124	C₄	semidirect
94. #124	Dic₁₉	semidirect
102. C₁₉	#1959	semidirect

H ≅ G/N

type

1. C₂×#10597292

C₂

semidirect

3. C₂×#10597260

C₂

semidirect

4. #11926414

C₂

semidirect

9. C₁₉×#124

C₄

semidirect

94. #124

Dic₁₉

semidirect

102. C₁₉

#1959

semidirect

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

subgroup	index
C₂×#10597292	2
C₂×#10597289	2
C₂×#10597260	2
#11926414	2
C₂×C₁₉×#124	2
#1959	19

subgroup

index

C₂×C₁₉×#124

Subgroups — #14564452

Conjugacy classes of subgroups

Complements

Maximal subgroups