Group #14573963 — subgroups

Subgroups — C₂×#11926903 #14573963

Order 2432.

436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597315	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926903	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10597292	C₂	1	2	yes	maximal, complemented
4	C₂×#10597289	C₂	1	2	yes	maximal
5	C₂×#10597260	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	—	2	1	no	—
10	C₁₉×#124	—	2	2	no	—
11	C₁₉×#124	C₂²	1	4	yes	—
12	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
13	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₉	—	2	1	no	—
16	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
17	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
18	#10597315	—	2	2	no	—
19	#10597315	C₂²	1	4	yes	complemented
20	#10597292	C₂²	1	8	yes	complemented
21	#10597289	C₂²	1	8	yes	—
22	#10597260	C₂²	1	4	yes	complemented
23	C₂⁴×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	4	no	—
26	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
27	C₂×D₄×C₁₉	—	2	1	no	—
28	C₂×D₄×C₁₉	—	2	4	no	—
29	C₂×D₄×C₁₉	C₂³	1	2	yes	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×Dic₁₉	—	2	2	no	—
35	C₂×Dic₃₈	—	2	4	no	—
36	C₂×Dic₃₈	—	4	4	no	—
37	C₂²⋊C₄×C₁₉	—	2	4	no	—
38	C₂²⋊C₄×C₁₉	—	2	4	no	—
39	C₄²×C₁₉	D₄	1	2	yes	—
40	C₄²×C₁₉	C₂³	1	2	yes	—
41	C₄⋊Dic₁₉	—	2	2	no	—
42	C₄⋊Dic₁₉	—	2	4	no	—
43	C₄⋊Dic₁₉	C₂³	1	4	yes	—
44	C₂×C₁₉⋊C₈	—	2	4	no	—
45	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
46	C₂³×C₁₉	—	2	2	no	—
47	C₂³×C₁₉	—	4	2	no	—
48	C₂³×C₁₉	—	4	2	no	—
49	C₂³×C₁₉	—	4	2	no	—
50	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
51	Q₈×C₁₉	—	2	4	no	—
52	Q₈×C₁₉	—	4	2	no	—
53	D₄×C₁₉	—	2	4	no	—
54	D₄×C₁₉	—	4	2	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	4	2	no	—
59	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#41	1	4	yes	—
63	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
64	C₂×Dic₁₉	—	2	4	no	—
65	C₂×Dic₁₉	—	4	4	no	—
66	Dic₃₈	—	4	8	no	—
67	C₁₉⋊C₈	—	2	4	no	—
68	C₂×#489	—	19	1	no	maximal, Sylow
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	—	4	2	no	—
71	C₂²×C₁₉	—	4	2	no	—
72	C₂²×C₁₉	—	8	4	no	—
73	C₂²×C₁₉	#124	1	2	yes	—
74	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
75	C₂²×C₁₉	#137	1	2	yes	—
76	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
77	C₄×C₁₉	—	2	2	no	—
78	C₄×C₁₉	—	2	2	no	—
79	C₄×C₁₉	—	4	2	no	—
80	C₄×C₁₉	#124	1	2	yes	—
81	C₄×C₁₉	C₂×#41	1	2	yes	—
82	Dic₁₉	—	4	4	no	—
83	C₂×C₄⋊Q₈	—	19	1	no	—
84	C₂×#124	D₁₉	1	1	yes	characteristic
85	#489	—	19	8	no	—
86	C₂×#103	—	19	2	no	—
87	C₂×#102	—	19	2	no	—
88	C₂×#97	—	19	1	no	—
89	C₂×C₁₉	—	8	2	no	—
90	C₂×C₁₉	#489	1	4	yes	complemented
91	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
92	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
94	C₂²×Q₈	—	38	1	no	—
95	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
96	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
97	C₂²×C₈	—	19	2	no	—
98	C₄⋊Q₈	—	19	4	no	—
99	C₄⋊Q₈	—	38	2	no	—
100	#124	—	2	2	no	—
101	#124	C₂×D₁₉	1	4	yes	—
102	C₂×C₄⋊C₄	—	19	2	no	—
103	C₂×C₄⋊C₄	—	38	1	no	—
104	C₂×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
107	#103	—	19	8	no	—
108	#102	—	19	8	no	—
109	#97	—	19	4	no	—
110	C₁₉	C₂×#489	1	1	yes	characteristic, complemented, Sylow
111	C₂⁴	—	2	1	no	—
112	C₂×Q₈	—	2	1	no	—
113	C₂×Q₈	—	2	4	no	—
114	C₂×Q₈	—	38	4	no	—
115	C₂×Q₈	—	76	4	no	—
116	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
117	C₂×D₄	—	2	4	no	—
118	C₂×D₄	—	2	1	no	—
119	C₂×D₄	C₂²×D₁₉	1	2	yes	—
120	C₂²×C₄	—	2	1	no	—
121	C₂²×C₄	—	38	2	no	—
122	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
123	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
124	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
125	C₂×C₈	—	19	4	no	—
126	C₂×C₈	—	38	4	no	—
127	C₄⋊C₄	—	19	4	no	—
128	C₄⋊C₄	—	38	2	no	—
129	C₄⋊C₄	—	38	4	no	—
130	C₂²⋊C₄	—	2	4	no	—
131	C₂²⋊C₄	—	2	4	no	—
132	C₄²	C₂²⋊D₁₉	1	2	yes	—
133	C₄²	C₂²×D₁₉	1	2	yes	—
134	C₂³	—	2	2	no	—
135	C₂³	—	4	2	no	—
136	C₂³	—	4	2	no	—
137	C₂³	—	4	2	no	—
138	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
139	Q₈	—	2	4	no	—
140	Q₈	—	4	2	no	—
141	Q₈	—	76	8	no	—
142	D₄	—	2	4	no	—
143	D₄	—	4	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	—	38	4	no	—
149	C₂×C₄	—	76	4	no	—
150	C₂×C₄	#64543	1	4	yes	—
151	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
152	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
153	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
154	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
155	C₈	—	38	4	no	—
156	C₂²	—	4	2	no	—
157	C₂²	—	4	2	no	—
158	C₂²	—	4	2	no	—
159	C₂²	—	8	4	no	—
160	C₂²	#10597382	1	2	yes	—
161	C₂²	#10597395	1	2	yes	—
162	C₂²	#10597397	1	2	yes	—
163	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
164	C₄	—	2	2	no	—
165	C₄	—	2	2	no	—
166	C₄	—	4	2	no	—
167	C₄	—	76	4	no	—
168	C₄	#10597382	1	2	yes	—
169	C₄	C₂×#64543	1	2	yes	—
170	C₂	—	8	2	no	—
171	C₂	#11926903	1	4	yes	direct product factor
172	C₂	C₂×#10597382	1	1	yes	characteristic
173	C₂	C₂×#10597395	1	1	yes	characteristic
174	C₂	C₂×#10597397	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic, complemented

#11926903

C₂

yes

maximal, direct product factor

C₂×#10597292

C₂

yes

maximal, complemented

C₂×#10597289

C₂

yes

maximal

C₂×#10597260

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#124

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₁₉×#124

—

C₁₉×#124

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597315

—

#10597315

C₂²

yes

complemented

#10597292

C₂²

yes

complemented

#10597289

C₂²

yes

—

#10597260

C₂²

yes

complemented

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

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×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

C₂×#489

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#124

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²×C₁₉

#137

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×#124

D₁₉

yes

—

—

—

C₂×#97

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

100

#124

—

101

#124

C₂×D₁₉

yes

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₂²⋊C₄

—

105

C₂×C₂²⋊C₄

—

106

C₂×C₄²

C₂×D₁₉

yes

characteristic

107

#103

—

108

#102

—

109

#97

—

110

C₁₉

C₂×#489

yes

characteristic, complemented, Sylow

111

C₂⁴

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

C₂²×D₁₉

yes

—

117

C₂×D₄

—

118

C₂×D₄

—

119

C₂×D₄

C₂²×D₁₉

yes

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

123

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

124

C₂²×C₄

C₂²×D₁₉

yes

characteristic

125

C₂×C₈

—

126

C₂×C₈

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₂²⋊C₄

—

131

C₂²⋊C₄

—

132

C₄²

C₂²⋊D₁₉

yes

—

133

C₄²

C₂²×D₁₉

yes

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

—

138

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

139

Q₈

—

140

Q₈

—

141

Q₈

—

142

D₄

—

143

D₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

#64543

yes

—

151

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

152

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

153

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

154

C₂×C₄

C₂³×D₁₉

yes

characteristic

155

C₈

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

#10597382

yes

—

161

C₂²

#10597395

yes

—

162

C₂²

#10597397

yes

—

163

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

—

168

C₄

#10597382

yes

—

169

C₄

C₂×#64543

yes

—

170

C₂

—

171

C₂

#11926903

yes

direct product factor

172

C₂

C₂×#10597382

yes

characteristic

173

C₂

C₂×#10597395

yes

characteristic

174

C₂

C₂×#10597397

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#124	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	C₂×#124	D₁₉
hypocenter	C₁₉	C₂×#489
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#124

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

N	H ≅ G/N	type
1. C₂×#10597315	C₂	semidirect
2. #11926903	C₂	direct (N × H)
3. C₂×#10597292	C₂	semidirect
5. C₂×#10597260	C₂	semidirect
19. #10597315	C₂²	semidirect
20. #10597292	C₂²	semidirect
22. #10597260	C₂²	semidirect
90. C₂×C₁₉	#489	semidirect
110. C₁₉	C₂×#489	semidirect
171. C₂	#11926903	direct (N × H)

H ≅ G/N

type

1. C₂×#10597315

C₂

semidirect

2. #11926903

C₂

direct (N × H)

3. C₂×#10597292

C₂

semidirect

5. C₂×#10597260

C₂

semidirect

19. #10597315

C₂²

semidirect

20. #10597292

C₂²

semidirect

22. #10597260

C₂²

semidirect

90. C₂×C₁₉

#489

semidirect

110. C₁₉

C₂×#489

semidirect

171. C₂

#11926903

direct (N × H)

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

subgroup	index
C₂×#10597315	2
#11926903	2
C₂×#10597292	2
C₂×#10597289	2
C₂×#10597260	2
C₂×C₁₉×#124	2
C₂×#489	19

subgroup

index

C₂×C₁₉×#124

Subgroups — C₂×#11926903 #14573963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926903 #14573963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926903 #14573963