Group #14564878 — subgroups

Subgroups — #14564878

Order 2432.

298 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 95 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
2	C₂×#10597292	C₂	1	2	yes	maximal
3	#11926442	C₂	1	1	yes	maximal, characteristic
4	#11926299	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
7	C₁₉×C₄⋊Q₈	—	2	4	no	—
8	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
9	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₄	—	2	1	no	—
14	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
15	#10597292	—	2	4	no	—
16	#10597292	—	2	4	no	—
17	C₁₉⋊#95	—	2	1	no	—
18	C₂×Q₈×C₁₉	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	2	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	—	2	2	no	—
22	C₂×Q₈×C₁₉	—	2	2	no	—
23	C₂×Q₈×C₁₉	D₄	1	4	yes	—
24	C₂²×C₄×C₁₉	—	2	2	no	—
25	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₁₉	—	2	1	no	—
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	4	no	—
31	C₄⋊C₄×C₁₉	—	2	4	no	—
32	C₄²×C₁₉	—	2	2	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	2	no	—
35	C₄⋊Dic₁₉	D₄	1	2	yes	—
36	Dic₁₉⋊C₄	—	4	2	no	—
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
41	Q₈×C₁₉	—	2	4	no	—
42	Q₈×C₁₉	—	2	4	no	—
43	Q₈×C₁₉	—	4	2	no	—
44	Q₈×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
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	SD₁₆	1	2	yes	—
53	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₁₉	#41	1	2	yes	—
57	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
58	C₂×Dic₁₉	—	2	2	no	—
59	C₂×Dic₁₉	—	4	1	no	—
60	C₂×Dic₁₉	—	4	1	no	—
61	C₂×Dic₁₉	—	4	1	no	—
62	C₂×Dic₁₉	—	4	1	no	—
63	C₂×Dic₁₉	—	4	1	no	—
64	C₁₉⋊C₈	—	4	2	no	—
65	#2043	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	#120	1	1	yes	characteristic
67	C₂²×C₁₉	#121	1	1	yes	characteristic
68	C₂²×C₁₉	#124	1	1	yes	characteristic
69	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
70	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
71	C₂²×C₁₉	#137	1	1	yes	characteristic
72	C₂²×C₁₉	#137	1	1	yes	characteristic
73	C₄×C₁₉	—	2	2	no	—
74	C₄×C₁₉	—	2	2	no	—
75	C₄×C₁₉	—	4	4	no	—
76	C₄×C₁₉	#121	1	2	yes	—
77	C₄×C₁₉	#123	1	2	yes	—
78	Dic₁₉	—	4	2	no	—
79	Dic₁₉	—	8	1	no	—
80	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
81	C₂×#103	—	19	2	no	—
82	C₂×#103	—	19	2	no	—
83	#389	—	19	1	no	—
84	#336	—	19	1	no	—
85	C₂×C₁₉	#394	1	1	yes	characteristic
86	C₂×C₁₉	#448	1	1	yes	characteristic
87	C₂×C₁₉	#451	1	1	yes	characteristic
88	C₂×C₁₉	#461	1	1	yes	characteristic
89	C₂×C₁₉	#462	1	1	yes	characteristic
90	C₂×C₁₉	#487	1	1	yes	characteristic
91	C₂×C₁₉	#491	1	1	yes	characteristic
92	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
93	C₂²×C₈	—	19	2	no	—
94	C₄⋊Q₈	—	2	4	no	—
95	C₂×C₄⋊C₄	—	2	1	no	—
96	C₂×C₄⋊C₄	—	2	1	no	—
97	C₂×C₄⋊C₄	—	19	1	no	—
98	C₂×C₄⋊C₄	—	19	1	no	—
99	C₂×C₄⋊C₄	—	38	1	no	—
100	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
101	#103	—	38	4	no	—
102	#103	—	38	4	no	—
103	#95	—	38	1	no	—
104	C₁₉	#2043	1	1	yes	characteristic, complemented, Sylow
105	C₂×Q₈	—	2	2	no	—
106	C₂×Q₈	—	2	2	no	—
107	C₂×Q₈	—	2	2	no	—
108	C₂×Q₈	—	2	2	no	—
109	C₂×Q₈	—	2	2	no	—
110	C₂×Q₈	C₂²⋊D₁₉	1	4	yes	—
111	C₂²×C₄	—	2	2	no	—
112	C₂²×C₄	—	38	1	no	—
113	C₂²×C₄	—	38	1	no	—
114	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
115	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
116	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
117	C₂×C₈	—	38	2	no	—
118	C₂×C₈	—	38	2	no	—
119	C₂×C₈	—	38	2	no	—
120	C₄⋊C₄	—	2	4	no	—
121	C₄⋊C₄	—	2	4	no	—
122	C₄⋊C₄	—	19	2	no	—
123	C₄⋊C₄	—	38	1	no	—
124	C₄⋊C₄	—	38	2	no	—
125	C₄⋊C₄	—	76	2	no	—
126	C₄²	—	2	2	no	—
127	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
128	Q₈	—	2	4	no	—
129	Q₈	—	2	4	no	—
130	Q₈	—	4	2	no	—
131	Q₈	—	4	2	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	—	4	2	no	—
139	C₂×C₄	—	38	2	no	—
140	C₂×C₄	—	76	1	no	—
141	C₂×C₄	—	76	1	no	—
142	C₂×C₄	—	76	1	no	—
143	C₂×C₄	—	76	1	no	—
144	C₂×C₄	—	76	1	no	—
145	C₂×C₄	#64527	1	2	yes	—
146	C₂×C₄	#64528	1	2	yes	—
147	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
148	C₂×C₄	#64543	1	1	yes	characteristic
149	C₂×C₄	#64543	1	2	yes	—
150	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
151	C₈	—	76	2	no	—
152	C₂²	#10597382	1	1	yes	characteristic
153	C₂²	#10597384	1	1	yes	characteristic
154	C₂²	C₂×#64527	1	1	yes	characteristic
155	C₂²	#10597388	1	1	yes	characteristic
156	C₂²	#10597388	1	1	yes	characteristic
157	C₂²	C₂×#64528	1	1	yes	characteristic
158	C₂²	#10597399	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	2	2	no	—
161	C₄	—	4	4	no	—
162	C₄	—	76	2	no	—
163	C₄	—	152	1	no	—
164	C₄	#10597381	1	2	yes	—
165	C₄	#10597385	1	2	yes	—
166	C₂	#11926458	1	1	yes	characteristic
167	C₂	#11926683	1	1	yes	characteristic
168	C₂	#11926700	1	1	yes	characteristic
169	C₂	#11926746	1	1	yes	characteristic
170	C₂	#11926751	1	1	yes	characteristic
171	C₂	#11926894	1	1	yes	characteristic
172	C₂	#11926912	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597292

C₂

yes

maximal

C₂×#10597292

C₂

yes

maximal

#11926442

C₂

yes

maximal, characteristic

#11926299

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597292

—

#10597292

—

C₁₉⋊#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#123

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

—

—

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂×D₁₉

yes

—

C₂²×C₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

100

C₂×C₄²

C₂×D₁₉

yes

characteristic

101

#103

—

102

#103

—

103

#95

—

104

C₁₉

#2043

yes

characteristic, complemented, Sylow

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

C₂²⋊D₁₉

yes

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

115

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

116

C₂²×C₄

C₂²×D₁₉

yes

characteristic

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄²

—

127

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

128

Q₈

—

129

Q₈

—

130

Q₈

—

131

Q₈

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

#64527

yes

—

146

C₂×C₄

#64528

yes

—

147

C₂×C₄

D₄×D₁₉

yes

characteristic

148

C₂×C₄

#64543

yes

characteristic

149

C₂×C₄

#64543

yes

—

150

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

151

C₈

—

152

C₂²

#10597382

yes

characteristic

153

C₂²

#10597384

yes

characteristic

154

C₂²

C₂×#64527

yes

characteristic

155

C₂²

#10597388

yes

characteristic

156

C₂²

#10597388

yes

characteristic

157

C₂²

C₂×#64528

yes

characteristic

158

C₂²

#10597399

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

—

152

—

164

C₄

#10597381

yes

—

165

C₄

#10597385

yes

—

166

C₂

#11926458

yes

characteristic

167

C₂

#11926683

yes

characteristic

168

C₂

#11926700

yes

characteristic

169

C₂

#11926746

yes

characteristic

170

C₂

#11926751

yes

characteristic

171

C₂

#11926894

yes

characteristic

172

C₂

#11926912

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2043
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

#2043

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
104. C₁₉	#2043	semidirect

H ≅ G/N

type

104. C₁₉

#2043

semidirect

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

subgroup	index
C₂×#10597292	2
#11926442	2
#11926299	2
C₂×C₁₉×C₄⋊Q₈	2
#2043	19

subgroup

index

C₂×C₁₉×C₄⋊Q₈

Subgroups — #14564878

Conjugacy classes of subgroups

Complements

Maximal subgroups