Group #14569356 — subgroups

Subgroups — #14569356

Order 2432.

782 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 165 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	C₂³×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597381	C₂	1	2	yes	maximal
3	#11926464	C₂	1	4	yes	maximal, complemented
4	#11926456	C₂	1	4	yes	maximal, complemented
5	#11926407	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926405	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#123	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×Dic₁₉	C₂²	1	2	yes	—
11	C₂²×Dic₃₈	—	2	4	no	—
12	C₂²×Dic₃₈	—	2	8	no	—
13	C₂²×Dic₃₈	C₂²	1	4	yes	—
14	C₁₉×#123	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
20	#10597381	—	2	8	no	—
21	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
22	C₁₉⋊#95	C₂²	1	8	yes	—
23	C₁₉⋊#95	C₂²	1	4	yes	—
24	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
25	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×D₄×C₁₉	—	2	4	no	—
27	C₂×D₄×C₁₉	—	2	2	no	—
28	C₂²×C₄×C₁₉	—	2	4	no	—
29	C₂²×C₄×C₁₉	D₄	1	4	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
33	C₂²×Dic₁₉	—	2	4	no	—
34	C₂²×Dic₁₉	—	2	4	no	—
35	C₂²×Dic₁₉	D₄	1	8	yes	—
36	C₂²×Dic₁₉	C₂³	1	4	yes	—
37	C₂²×Dic₁₉	C₂³	1	4	yes	—
38	C₂×Dic₃₈	—	2	32	no	—
39	C₂×Dic₃₈	—	2	8	no	—
40	C₂×Dic₃₈	—	2	16	no	—
41	C₄⋊C₄×C₁₉	—	2	4	no	—
42	C₂²⋊C₄×C₁₉	—	2	2	no	—
43	C₂²⋊C₄×C₁₉	—	2	4	no	—
44	C₂²⋊Dic₁₉	—	2	4	no	—
45	C₂²⋊Dic₁₉	—	2	8	no	—
46	Dic₁₉⋊C₄	—	2	8	no	—
47	C₂³×C₁₉	—	2	4	no	—
48	C₂³×C₁₉	—	2	2	no	—
49	C₂³×C₁₉	—	2	1	no	—
50	C₂³×C₁₉	—	2	4	no	—
51	C₂³×C₁₉	C₂×D₄	1	4	yes	—
52	C₂³×C₁₉	C₂×D₄	1	2	yes	—
53	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
54	D₄×C₁₉	—	4	4	no	—
55	C₂×C₄×C₁₉	—	2	8	no	—
56	C₂×C₄×C₁₉	—	2	4	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	4	no	—
61	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
62	C₂×Dic₁₉	—	2	16	no	—
63	C₂×Dic₁₉	—	2	4	no	—
64	C₂×Dic₁₉	—	2	4	no	—
65	C₂×Dic₁₉	—	2	4	no	—
66	C₂×Dic₁₉	—	2	8	no	—
67	C₂×Dic₁₉	C₂×D₄	1	8	yes	—
68	Dic₃₈	—	2	32	no	—
69	#2614	—	19	1	no	maximal, Sylow
70	C₂²×C₁₉	—	2	4	no	—
71	C₂²×C₁₉	—	2	8	no	—
72	C₂²×C₁₉	—	4	1	no	—
73	C₂²×C₁₉	—	4	2	no	—
74	C₂²×C₁₉	—	4	4	no	—
75	C₂²×C₁₉	#120	1	4	yes	—
76	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
77	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
78	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
79	C₄×C₁₉	—	2	4	no	—
80	C₄×C₁₉	—	4	1	no	—
81	C₄×C₁₉	—	4	2	no	—
82	Dic₁₉	—	2	8	no	—
83	Dic₁₉	—	4	4	no	—
84	C₂³×Q₈	—	19	1	no	—
85	C₂×#123	—	19	2	no	—
86	C₂×#123	D₁₉	1	1	yes	characteristic
87	#395	—	19	4	no	—
88	#393	—	19	4	no	—
89	#381	—	19	1	no	—
90	#381	—	19	2	no	—
91	C₂×C₁₉	—	2	4	no	—
92	C₂×C₁₉	—	8	1	no	—
93	C₂×C₁₉	C₂×#120	1	1	yes	characteristic
94	C₂×C₁₉	#536	1	2	yes	—
95	C₂×C₁₉	#536	1	4	yes	—
96	C₂²×Q₈	—	19	4	no	—
97	C₂²×Q₈	—	38	8	no	—
98	C₂²×Q₈	—	38	4	no	—
99	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
100	C₂³×C₄	—	19	2	no	—
101	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
102	#123	—	2	4	no	—
103	#123	—	38	8	no	—
104	C₂×C₄⋊C₄	—	19	4	no	—
105	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
106	C₂×C₂²⋊C₄	—	19	2	no	—
107	C₂×C₂²⋊C₄	—	19	4	no	—
108	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
109	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
110	#95	—	19	8	no	—
111	#95	—	19	4	no	—
112	C₁₉	#2614	1	1	yes	characteristic, complemented, Sylow
113	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
114	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
115	C₂×Q₈	—	38	16	no	—
116	C₂×Q₈	—	38	32	no	—
117	C₂×Q₈	—	38	8	no	—
118	C₂×D₄	—	2	4	no	—
119	C₂×D₄	—	2	2	no	—
120	C₂²×C₄	—	2	4	no	—
121	C₂²×C₄	—	19	8	no	—
122	C₂²×C₄	—	19	4	no	—
123	C₂²×C₄	—	19	4	no	—
124	C₂²×C₄	—	38	4	no	—
125	C₂²×C₄	—	38	4	no	—
126	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
127	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
128	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
129	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
130	C₄⋊C₄	—	2	4	no	—
131	C₄⋊C₄	—	38	8	no	—
132	C₂²⋊C₄	—	2	2	no	—
133	C₂²⋊C₄	—	2	4	no	—
134	C₂²⋊C₄	—	38	8	no	—
135	C₂²⋊C₄	—	38	4	no	—
136	C₂³	—	2	4	no	—
137	C₂³	—	2	2	no	—
138	C₂³	—	2	4	no	—
139	C₂³	—	2	1	no	—
140	C₂³	D₄×D₁₉	1	4	yes	—
141	C₂³	C₂×C₂²⋊D₁₉	1	2	yes	—
142	C₂³	C₂³×D₁₉	1	1	yes	characteristic
143	Q₈	—	38	32	no	—
144	D₄	—	4	4	no	—
145	C₂×C₄	—	2	8	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	19	8	no	—
152	C₂×C₄	—	38	16	no	—
153	C₂×C₄	—	38	4	no	—
154	C₂×C₄	—	38	4	no	—
155	C₂×C₄	—	38	4	no	—
156	C₂×C₄	—	38	8	no	—
157	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
158	C₂²	—	2	4	no	—
159	C₂²	—	2	8	no	—
160	C₂²	—	4	2	no	—
161	C₂²	—	4	4	no	—
162	C₂²	—	4	1	no	—
163	C₂²	#10597383	1	4	yes	—
164	C₂²	C₂×D₄×D₁₉	1	2	yes	—
165	C₂²	#10597436	1	4	yes	—
166	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
167	C₄	—	2	4	no	—
168	C₄	—	4	2	no	—
169	C₄	—	4	1	no	—
170	C₄	—	38	8	no	—
171	C₄	—	76	4	no	—
172	C₂	—	2	4	no	—
173	C₂	—	8	1	no	—
174	C₂	C₂×#10597383	1	1	yes	characteristic
175	C₂	#11927115	1	2	yes	—
176	C₂	#11927116	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×Dic₃₈

C₂

yes

maximal, characteristic, complemented

C₂×#10597381

C₂

yes

maximal

#11926464

C₂

yes

maximal, complemented

#11926456

C₂

yes

maximal, complemented

#11926407

C₂

yes

maximal, characteristic, complemented

#11926405

C₂

yes

maximal, complemented

C₂×C₁₉×#123

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

C₂²

yes

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

C₂²

yes

—

C₁₉×#123

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597381

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

#2614

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

—

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂³×Q₈

—

C₂×#123

—

C₂×#123

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#120

yes

characteristic

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#536

yes

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×D₄

C₂×D₁₉

yes

characteristic

100

C₂³×C₄

—

101

C₂³×C₄

C₂×D₁₉

yes

characteristic

102

#123

—

103

#123

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

106

C₂×C₂²⋊C₄

—

107

C₂×C₂²⋊C₄

—

108

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

109

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

110

#95

—

111

#95

—

112

C₁₉

#2614

yes

characteristic, complemented, Sylow

113

C₂⁴

C₂²×D₁₉

yes

characteristic

114

C₂⁴

C₂²×D₁₉

yes

characteristic

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×D₄

—

119

C₂×D₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

C₂²⋊D₁₉

yes

—

127

C₂²×C₄

C₂²×D₁₉

yes

—

128

C₂²×C₄

C₂²×D₁₉

yes

characteristic

129

C₂²×C₄

C₂²×D₁₉

yes

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₂²⋊C₄

—

133

C₂²⋊C₄

—

134

C₂²⋊C₄

—

135

C₂²⋊C₄

—

136

C₂³

—

137

C₂³

—

138

C₂³

—

139

C₂³

—

140

C₂³

D₄×D₁₉

yes

—

141

C₂³

C₂×C₂²⋊D₁₉

yes

—

142

C₂³

C₂³×D₁₉

yes

characteristic

143

Q₈

—

144

D₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

#10597383

yes

—

164

C₂²

C₂×D₄×D₁₉

yes

—

165

C₂²

#10597436

yes

—

166

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

167

C₄

—

168

C₄

—

169

C₄

—

170

C₄

—

171

C₄

—

172

C₂

—

173

C₂

—

174

C₂

C₂×#10597383

yes

characteristic

175

C₂

#11927115

yes

—

176

C₂

#11927116

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#123	C₂
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	C₂×#123	D₁₉
hypocenter	C₁₉	#2614
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#123

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#123

C₂

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#123

N	H ≅ G/N	type
1. C₂³×Dic₃₈	C₂	semidirect
3. #11926464	C₂	semidirect
4. #11926456	C₂	semidirect
5. #11926407	C₂	semidirect
6. #11926405	C₂	semidirect
112. C₁₉	#2614	semidirect

H ≅ G/N

type

1. C₂³×Dic₃₈

C₂

semidirect

3. #11926464

C₂

semidirect

4. #11926456

C₂

semidirect

5. #11926407

C₂

semidirect

6. #11926405

C₂

semidirect

112. C₁₉

#2614

semidirect

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

subgroup	index
C₂³×Dic₃₈	2
C₂×#10597381	2
#11926464	2
#11926456	2
#11926407	2
#11926405	2
C₂×C₁₉×#123	2
#2614	19

subgroup

index

C₂³×Dic₃₈

C₂×C₁₉×#123

Subgroups — #14569356

Conjugacy classes of subgroups

Complements

Maximal subgroups