Group #14564723 — subgroups

Subgroups — #14564723

Order 2432.

474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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×#64526	C₂	1	2	yes	maximal, complemented
2	C₂×#10597289	C₂	1	2	yes	maximal, complemented
3	#11926450	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₁₉	—	2	2	no	—
7	C₂²×D₄×C₁₉	C₂²	1	2	yes	—
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₁₉×#127	—	2	4	no	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×#64526	—	2	4	no	—
12	C₂×#64526	—	2	4	no	—
13	C₂×#64526	—	2	4	no	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
16	#10597289	—	2	4	no	—
17	C₁₉⋊#95	—	2	2	no	—
18	C₂⁴×C₁₉	—	2	2	no	—
19	C₂×D₄×C₁₉	—	2	8	no	—
20	C₂×D₄×C₁₉	—	2	2	no	—
21	C₂×D₄×C₁₉	—	2	2	no	—
22	C₂×D₄×C₁₉	—	2	2	no	—
23	C₂×D₄×C₁₉	—	2	2	no	—
24	C₂×D₄×C₁₉	—	2	2	no	—
25	C₂×D₄×C₁₉	—	4	4	no	—
26	C₂×D₄×C₁₉	—	4	4	no	—
27	C₂×D₄×C₁₉	D₄	1	4	yes	—
28	C₂²×C₄×C₁₉	D₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×Dic₁₉	—	2	1	no	—
31	C₂²×Dic₁₉	—	2	1	no	—
32	C₂×Dic₃₈	—	2	2	no	—
33	C₂×Dic₃₈	—	2	2	no	—
34	C₂×Dic₃₈	—	2	1	no	—
35	C₂×Dic₃₈	D₄	1	2	yes	complemented
36	C₄²×C₁₉	—	2	2	no	—
37	#64526	—	2	16	no	—
38	C₄⋊Dic₁₉	—	2	2	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂×C₁₉⋊C₈	D₄	1	4	yes	complemented
42	C₂³×C₁₉	—	2	4	no	—
43	C₂³×C₁₉	—	4	2	no	—
44	C₂³×C₁₉	—	4	2	no	—
45	C₂³×C₁₉	—	4	4	no	—
46	C₂³×C₁₉	—	4	4	no	—
47	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
48	D₄×C₁₉	—	2	4	no	—
49	D₄×C₁₉	—	2	4	no	—
50	D₄×C₁₉	—	4	16	no	—
51	D₄×C₁₉	—	4	2	no	—
52	D₄×C₁₉	—	4	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	SD₁₆	1	4	yes	complemented
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
59	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
60	C₂×Dic₁₉	—	2	2	no	—
61	C₂×Dic₁₉	—	4	1	no	—
62	C₂×Dic₁₉	—	4	1	no	—
63	C₂×Dic₁₉	—	4	1	no	—
64	C₂×Dic₁₉	—	4	2	no	—
65	Dic₃₈	—	2	4	no	—
66	Dic₃₈	—	4	2	no	—
67	C₁₉⋊C₈	—	2	4	no	—
68	#2014	—	19	1	no	maximal, Sylow
69	C₂²×C₁₉	—	4	4	no	—
70	C₂²×C₁₉	—	4	8	no	—
71	C₂²×C₁₉	—	8	4	no	—
72	C₂²×C₁₉	—	8	2	no	—
73	C₂²×C₁₉	—	8	2	no	—
74	C₂²×C₁₉	#120	1	1	yes	characteristic
75	C₂²×C₁₉	#121	1	1	yes	characteristic
76	C₂²×C₁₉	#127	1	1	yes	characteristic
77	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
78	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
79	C₄×C₁₉	—	2	4	no	—
80	C₄×C₁₉	#120	1	2	yes	—
81	C₄×C₁₉	#121	1	2	yes	—
82	Dic₁₉	—	4	2	no	—
83	Dic₁₉	—	8	1	no	—
84	C₂²×SD₁₆	—	19	2	no	—
85	C₂×#127	D₁₉	1	1	yes	characteristic
86	C₂×#102	—	19	2	no	—
87	#391	—	19	1	no	—
88	#336	—	19	1	no	—
89	C₂×C₁₉	—	8	4	no	—
90	C₂×C₁₉	#392	1	1	yes	characteristic
91	C₂×C₁₉	#450	1	2	yes	—
92	C₂×C₁₉	#460	1	2	yes	—
93	C₂×C₁₉	#492	1	1	yes	characteristic
94	C₂×C₁₉	#496	1	1	yes	characteristic
95	C₂²×Q₈	—	19	1	no	—
96	C₂²×D₄	—	2	2	no	—
97	C₂²×D₄	C₂×D₁₉	1	2	yes	—
98	C₂×SD₁₆	—	38	4	no	—
99	C₂×SD₁₆	—	38	4	no	—
100	C₂×SD₁₆	—	38	4	no	—
101	C₂²×C₈	—	19	2	no	—
102	#127	—	2	4	no	—
103	C₂×C₄⋊C₄	—	19	1	no	—
104	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
105	#102	—	38	4	no	—
106	#95	—	38	2	no	—
107	C₁₉	#2014	1	1	yes	characteristic, complemented, Sylow
108	C₂⁴	—	2	2	no	—
109	C₂×Q₈	—	19	2	no	—
110	C₂×Q₈	—	38	1	no	—
111	C₂×Q₈	—	38	2	no	—
112	C₂×Q₈	—	38	2	no	—
113	C₂×D₄	—	2	8	no	—
114	C₂×D₄	—	2	2	no	—
115	C₂×D₄	—	2	2	no	—
116	C₂×D₄	—	2	2	no	—
117	C₂×D₄	—	2	2	no	—
118	C₂×D₄	—	2	2	no	—
119	C₂×D₄	—	4	4	no	—
120	C₂×D₄	—	4	4	no	—
121	C₂×D₄	C₂²⋊D₁₉	1	4	yes	—
122	C₂²×C₄	—	38	1	no	—
123	C₂²×C₄	—	38	1	no	—
124	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
125	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
126	SD₁₆	—	38	16	no	—
127	C₂×C₈	—	19	4	no	—
128	C₂×C₈	—	38	2	no	—
129	C₂×C₈	—	38	2	no	—
130	C₄⋊C₄	—	38	2	no	—
131	C₄²	—	2	2	no	—
132	C₂³	—	2	4	no	—
133	C₂³	—	4	4	no	—
134	C₂³	—	4	4	no	—
135	C₂³	—	4	2	no	—
136	C₂³	—	4	2	no	—
137	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
138	Q₈	—	38	4	no	—
139	Q₈	—	76	2	no	—
140	D₄	—	2	4	no	—
141	D₄	—	2	4	no	—
142	D₄	—	4	16	no	—
143	D₄	—	4	2	no	—
144	D₄	—	4	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	38	2	no	—
148	C₂×C₄	—	76	1	no	—
149	C₂×C₄	—	76	1	no	—
150	C₂×C₄	—	76	2	no	—
151	C₂×C₄	—	76	1	no	—
152	C₂×C₄	#64526	1	4	yes	complemented
153	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
154	C₂×C₄	D₄×D₁₉	1	2	yes	—
155	C₂×C₄	#64543	1	1	yes	characteristic
156	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
157	C₈	—	38	4	no	—
158	C₂²	—	4	8	no	—
159	C₂²	—	4	4	no	—
160	C₂²	—	8	2	no	—
161	C₂²	—	8	2	no	—
162	C₂²	—	8	4	no	—
163	C₂²	#10597378	1	2	yes	—
164	C₂²	C₂×#64526	1	2	yes	—
165	C₂²	#10597384	1	1	yes	characteristic
166	C₂²	#10597386	1	1	yes	characteristic
167	C₂²	#10597399	1	1	yes	characteristic
168	C₄	—	2	4	no	—
169	C₄	—	76	2	no	—
170	C₄	—	152	1	no	—
171	C₄	#10597383	1	2	yes	—
172	C₄	#10597385	1	2	yes	—
173	C₂	—	8	4	no	—
174	C₂	#11926452	1	1	yes	characteristic
175	C₂	#11926695	1	2	yes	—
176	C₂	#11926741	1	2	yes	—
177	C₂	#11926916	1	1	yes	characteristic
178	C₂	#11926931	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64526

C₂

yes

maximal, complemented

C₂×#10597289

C₂

yes

maximal, complemented

#11926450

C₂

yes

maximal, characteristic, complemented

#11926299

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#127

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

characteristic

C₁₉×#127

—

C₂×C₄²×C₁₉

C₂²

yes

—

—

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597289

—

C₁₉⋊#95

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

complemented

C₄²×C₁₉

—

#64526

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

complemented

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

complemented

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

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

#2014

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

Dic₁₉

—

C₂²×SD₁₆

—

C₂×#127

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#392

yes

characteristic

C₂×C₁₉

#450

yes

—

C₂×C₁₉

#460

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂²×D₄

—

C₂²×D₄

C₂×D₁₉

yes

—

C₂×SD₁₆

—

C₂×SD₁₆

—

100

C₂×SD₁₆

—

101

C₂²×C₈

—

102

#127

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄²

C₂×D₁₉

yes

characteristic

105

#102

—

106

#95

—

107

C₁₉

#2014

yes

characteristic, complemented, Sylow

108

C₂⁴

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

—

118

C₂×D₄

—

119

C₂×D₄

—

120

C₂×D₄

—

121

C₂×D₄

C₂²⋊D₁₉

yes

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₂²⋊D₁₉

yes

—

125

C₂²×C₄

C₂²×D₁₉

yes

characteristic

126

SD₁₆

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₄⋊C₄

—

131

C₄²

—

132

C₂³

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

138

Q₈

—

139

Q₈

—

140

D₄

—

141

D₄

—

142

D₄

—

143

D₄

—

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

#64526

yes

complemented

153

C₂×C₄

D₄×D₁₉

yes

characteristic

154

C₂×C₄

D₄×D₁₉

yes

—

155

C₂×C₄

#64543

yes

characteristic

156

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

157

C₈

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

#10597378

yes

—

164

C₂²

C₂×#64526

yes

—

165

C₂²

#10597384

yes

characteristic

166

C₂²

#10597386

yes

characteristic

167

C₂²

#10597399

yes

characteristic

168

C₄

—

169

C₄

—

170

C₄

—

152

—

171

C₄

#10597383

yes

—

172

C₄

#10597385

yes

—

173

C₂

—

174

C₂

#11926452

yes

characteristic

175

C₂

#11926695

yes

—

176

C₂

#11926741

yes

—

177

C₂

#11926916

yes

characteristic

178

C₂

#11926931

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#127	C₂
socle	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#127	D₁₉
hypocenter	C₁₉	#2014
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting, prime radical

C₂×C₁₉×#127

C₂

socle

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. C₂²×#64526	C₂	semidirect
2. C₂×#10597289	C₂	semidirect
3. #11926450	C₂	semidirect
4. #11926299	C₂	semidirect
35. C₂×Dic₃₈	D₄	semidirect
41. C₂×C₁₉⋊C₈	D₄	semidirect
55. C₂×C₄×C₁₉	SD₁₆	semidirect
107. C₁₉	#2014	semidirect
152. C₂×C₄	#64526	semidirect

H ≅ G/N

type

1. C₂²×#64526

C₂

semidirect

2. C₂×#10597289

C₂

semidirect

3. #11926450

C₂

semidirect

4. #11926299

C₂

semidirect

35. C₂×Dic₃₈

D₄

semidirect

41. C₂×C₁₉⋊C₈

D₄

semidirect

55. C₂×C₄×C₁₉

SD₁₆

semidirect

107. C₁₉

#2014

semidirect

152. C₂×C₄

#64526

semidirect

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

subgroup	index
C₂²×#64526	2
C₂×#10597289	2
#11926450	2
#11926299	2
C₂×C₁₉×#127	2
#2014	19

subgroup

index

C₂²×#64526

C₂×C₁₉×#127

Subgroups — #14564723

Conjugacy classes of subgroups

Complements

Maximal subgroups