Group #14564646 — subgroups

Subgroups — #14564646

Order 2432.

392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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	C₂²×Dic₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597343	C₂	1	2	yes	maximal
3	C₂×#10597267	C₂	1	2	yes	maximal, complemented
4	C₂×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
11	C₂×C₄⋊Dic₁₉	—	2	2	no	—
12	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×Dic₇₆	—	2	4	no	—
14	C₂×Dic₇₆	—	2	2	no	—
15	#10597343	—	2	4	no	—
16	#10597343	—	2	4	no	—
17	(C₂×D₁₉)⋊C₈	—	2	2	no	—
18	#10597267	—	2	4	no	—
19	C₂³×D₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₁₉	—	2	2	no	—
23	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄×D₁₉	—	2	1	no	—
25	C₂×C₄×D₁₉	—	2	2	no	—
26	C₂×C₄×D₁₉	—	2	2	no	—
27	C₂×C₄×D₁₉	—	2	1	no	—
28	C₂×Dic₃₈	—	2	2	no	—
29	C₂×Dic₃₈	—	2	2	no	—
30	C₂×Dic₃₈	—	2	2	no	—
31	C₂×Dic₃₈	—	2	2	no	—
32	C₂×Dic₃₈	—	2	2	no	—
33	C₂×Dic₃₈	D₄	1	4	yes	—
34	C₂×C₈×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	D₄	1	2	yes	—
36	C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₄⋊C₄×C₁₉	D₄	1	4	yes	—
38	(C₂×D₁₉)⋊C₄	—	2	8	no	—
39	C₄⋊Dic₁₉	—	2	8	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂×C₁₉⋊C₈	—	2	1	no	—
42	Dic₇₆	—	2	8	no	—
43	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×D₁₉	—	2	2	no	—
45	C₂²×D₁₉	—	2	1	no	—
46	C₂²×D₁₉	—	2	1	no	—
47	C₂²×D₁₉	—	2	2	no	—
48	C₂²×D₁₉	Q₁₆	1	2	yes	complemented
49	C₂×C₄×C₁₉	—	2	4	no	—
50	C₂×C₄×C₁₉	—	4	2	no	—
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
56	C₂×Dic₁₉	—	2	2	no	—
57	C₂×Dic₁₉	—	2	4	no	—
58	C₂×Dic₁₉	—	2	1	no	—
59	C₂×Dic₁₉	—	4	2	no	—
60	C₂×Dic₁₉	—	4	2	no	—
61	C₄×D₁₉	—	4	1	no	—
62	C₄×D₁₉	—	4	2	no	—
63	C₄×D₁₉	—	4	1	no	—
64	Dic₃₈	—	2	4	no	—
65	Dic₃₈	—	2	4	no	—
66	Dic₃₈	—	4	2	no	—
67	Dic₃₈	—	4	2	no	—
68	C₈×C₁₉	—	2	2	no	—
69	C₁₉⋊C₈	—	4	1	no	—
70	#2001	—	19	1	no	maximal, Sylow
71	C₂²×C₁₉	#120	1	2	yes	—
72	C₂²×C₁₉	#121	1	1	yes	characteristic
73	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
74	C₂²×C₁₉	#135	1	1	yes	characteristic
75	C₂²×C₁₉	#137	1	2	yes	—
76	C₂×D₁₉	—	2	4	no	—
77	C₂×D₁₉	—	2	2	no	—
78	C₂×D₁₉	—	4	1	no	—
79	C₂×D₁₉	—	4	2	no	—
80	C₂×D₁₉	—	4	1	no	—
81	C₄×C₁₉	—	4	4	no	—
82	C₄×C₁₉	#120	1	1	yes	characteristic
83	C₄×C₁₉	#121	1	2	yes	—
84	C₄×C₁₉	#127	1	1	yes	characteristic
85	Dic₁₉	—	4	4	no	—
86	Dic₁₉	—	4	1	no	—
87	C₂²×Q₁₆	—	19	1	no	—
88	C₂×C₂²⋊Q₈	—	19	2	no	—
89	C₂×#103	—	19	2	no	—
90	C₂×C₂²⋊C₈	—	19	1	no	—
91	#340	D₁₉	1	1	yes	characteristic, complemented
92	C₂×C₁₉	#392	1	1	yes	characteristic
93	C₂×C₁₉	#451	1	2	yes	—
94	C₂×C₁₉	#452	1	2	yes	—
95	C₂×C₁₉	#467	1	1	yes	characteristic
96	C₂×C₁₉	#470	1	1	yes	characteristic
97	D₁₉	—	4	2	no	—
98	C₂²×Q₈	—	19	2	no	—
99	C₂³×C₄	—	19	1	no	—
100	C₂×Q₁₆	—	38	4	no	—
101	C₂×Q₁₆	—	38	2	no	—
102	C₂²×C₈	—	19	1	no	—
103	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
104	C₂²⋊Q₈	—	38	4	no	—
105	C₂²⋊Q₈	—	38	4	no	—
106	C₂×C₄⋊C₄	—	38	2	no	—
107	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
108	C₂×C₂²⋊C₄	—	38	2	no	—
109	#103	—	38	4	no	—
110	C₂²⋊C₈	—	38	2	no	—
111	C₁₉	#2001	1	1	yes	characteristic, complemented, Sylow
112	C₂⁴	—	19	1	no	—
113	C₂×Q₈	—	19	4	no	—
114	C₂×Q₈	—	38	2	no	—
115	C₂×Q₈	—	38	2	no	—
116	C₂×Q₈	—	38	2	no	—
117	C₂×Q₈	—	38	2	no	—
118	C₂×Q₈	—	38	2	no	—
119	C₂²×C₄	—	2	2	no	—
120	C₂²×C₄	—	19	1	no	—
121	C₂²×C₄	—	38	2	no	—
122	C₂²×C₄	—	38	1	no	—
123	C₂²×C₄	—	38	2	no	—
124	C₂²×C₄	—	38	2	no	—
125	C₂²×C₄	—	38	1	no	—
126	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
127	Q₁₆	—	38	8	no	—
128	C₂×C₈	—	2	2	no	—
129	C₂×C₈	—	38	1	no	—
130	C₂×C₈	—	38	2	no	—
131	C₂×C₈	D₇₆	1	2	yes	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	—	38	8	no	—
134	C₄⋊C₄	D₇₆	1	4	yes	—
135	C₂²⋊C₄	—	38	8	no	—
136	C₂³	—	19	2	no	—
137	C₂³	—	38	2	no	—
138	C₂³	—	38	1	no	—
139	C₂³	—	38	1	no	—
140	C₂³	—	38	2	no	—
141	C₂³	D₄×D₁₉	1	1	yes	characteristic
142	Q₈	—	38	4	no	—
143	Q₈	—	38	4	no	—
144	Q₈	—	76	2	no	—
145	Q₈	—	76	2	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	—	38	4	no	—
150	C₂×C₄	—	38	2	no	—
151	C₂×C₄	—	38	1	no	—
152	C₂×C₄	—	76	2	no	—
153	C₂×C₄	—	76	2	no	—
154	C₂×C₄	—	76	1	no	—
155	C₂×C₄	—	76	1	no	—
156	C₂×C₄	—	76	2	no	—
157	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
158	C₂×C₄	C₂×D₇₆	1	2	yes	—
159	C₂×C₄	D₄×D₁₉	1	2	yes	—
160	C₂×C₄	#64545	1	1	yes	characteristic
161	C₈	—	2	2	no	—
162	C₈	—	76	1	no	—
163	C₂²	—	38	2	no	—
164	C₂²	—	38	4	no	—
165	C₂²	—	76	1	no	—
166	C₂²	—	76	2	no	—
167	C₂²	—	76	1	no	—
168	C₂²	#10597328	1	2	yes	—
169	C₂²	#10597341	1	1	yes	characteristic
170	C₂²	#10597358	1	1	yes	characteristic
171	C₂²	#10597361	1	2	yes	—
172	C₂²	Q₁₆×D₁₉	1	1	yes	characteristic
173	C₄	—	4	4	no	—
174	C₄	—	76	1	no	—
175	C₄	—	76	4	no	—
176	C₄	#10597320	1	1	yes	characteristic
177	C₄	#10597328	1	1	yes	characteristic
178	C₄	#10597341	1	2	yes	—
179	C₂	—	76	2	no	—
180	C₂	#11926454	1	1	yes	characteristic
181	C₂	#11926701	1	2	yes	—
182	C₂	#11926707	1	2	yes	—
183	C₂	#11926786	1	1	yes	characteristic
184	C₂	#11926803	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₆

C₂

yes

maximal, characteristic, complemented

C₂×#10597343

C₂

yes

maximal

C₂×#10597267

C₂

yes

maximal, complemented

C₂×(C₂×D₁₉)⋊C₈

C₂

yes

maximal, characteristic

C₁₉×#340

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Dic₇₆

—

C₂×Dic₇₆

—

#10597343

—

#10597343

—

(C₂×D₁₉)⋊C₈

—

#10597267

—

C₂³×D₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

Q₁₆

yes

complemented

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2001

—

maximal, Sylow

C₂²×C₁₉

#120

yes

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#127

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂²×Q₁₆

—

C₂×C₂²⋊Q₈

—

C₂×#103

—

C₂×C₂²⋊C₈

—

#340

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#392

yes

characteristic

C₂×C₁₉

#451

yes

—

C₂×C₁₉

#452

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂²×Q₈

—

C₂³×C₄

—

100

C₂×Q₁₆

—

101

C₂×Q₁₆

—

102

C₂²×C₈

—

103

C₂²×C₈

C₂×D₁₉

yes

characteristic

104

C₂²⋊Q₈

—

105

C₂²⋊Q₈

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

108

C₂×C₂²⋊C₄

—

109

#103

—

110

C₂²⋊C₈

—

111

C₁₉

#2001

yes

characteristic, complemented, Sylow

112

C₂⁴

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

C₂²×D₁₉

yes

characteristic

127

Q₁₆

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

D₇₆

yes

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

D₇₆

yes

—

135

C₂²⋊C₄

—

136

C₂³

—

137

C₂³

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

D₄×D₁₉

yes

characteristic

142

Q₈

—

143

Q₈

—

144

Q₈

—

145

Q₈

—

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×D₇₆

yes

characteristic

158

C₂×C₄

C₂×D₇₆

yes

—

159

C₂×C₄

D₄×D₁₉

yes

—

160

C₂×C₄

#64545

yes

characteristic

161

C₈

—

162

C₈

—

163

C₂²

—

164

C₂²

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

#10597328

yes

—

169

C₂²

#10597341

yes

characteristic

170

C₂²

#10597358

yes

characteristic

171

C₂²

#10597361

yes

—

172

C₂²

Q₁₆×D₁₉

yes

characteristic

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

#10597320

yes

characteristic

177

C₄

#10597328

yes

characteristic

178

C₄

#10597341

yes

—

179

C₂

—

180

C₂

#11926454

yes

characteristic

181

C₂

#11926701

yes

—

182

C₂

#11926707

yes

—

183

C₂

#11926786

yes

characteristic

184

C₂

#11926803

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#340	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂³×D₁₉	D₄
hypercenter	#340	D₁₉
hypocenter	C₁₉	#2001
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#340

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂³×D₁₉

D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
1. C₂²×Dic₇₆	C₂	semidirect
3. C₂×#10597267	C₂	semidirect
5. C₁₉×#340	C₂	semidirect
48. C₂²×D₁₉	Q₁₆	semidirect
91. #340	D₁₉	semidirect
111. C₁₉	#2001	semidirect

H ≅ G/N

type

1. C₂²×Dic₇₆

C₂

semidirect

3. C₂×#10597267

C₂

semidirect

5. C₁₉×#340

C₂

semidirect

48. C₂²×D₁₉

Q₁₆

semidirect

91. #340

D₁₉

semidirect

111. C₁₉

#2001

semidirect

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

subgroup	index
C₂²×Dic₇₆	2
C₂×#10597343	2
C₂×#10597267	2
C₂×(C₂×D₁₉)⋊C₈	2
C₁₉×#340	2
#2001	19

subgroup

index

C₂²×Dic₇₆

C₂×#10597343

C₂×#10597267

C₂×(C₂×D₁₉)⋊C₈

C₁₉×#340

#2001

Subgroups — #14564646

Conjugacy classes of subgroups

Complements

Maximal subgroups