Group #14564776 — subgroups

Subgroups — #14564776

Order 2432.

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

normal subgroups only

This group has 290 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	C₂×#10597315	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597292	C₂	1	2	yes	maximal
3	#11926306	C₂	1	2	yes	maximal
4	#11926299	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	—	2	1	no	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	—	2	1	no	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
13	#10597315	—	2	4	no	—
14	C₁₉×#95	—	2	1	no	—
15	C₁₉×#95	—	2	1	no	—
16	#10597292	—	2	4	no	—
17	C₂×Q₈×C₁₉	—	2	1	no	—
18	C₂×Q₈×C₁₉	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	2	no	—
20	C₂×Q₈×C₁₉	Q₈	1	2	yes	complemented
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	2	2	no	—
27	C₂×Dic₃₈	—	2	4	no	—
28	C₂×Dic₃₈	—	4	2	no	—
29	C₂×Dic₃₈	—	4	2	no	—
30	C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₄²×C₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	—	2	4	no	—
33	C₄⋊Dic₁₉	—	2	2	no	—
34	C₄⋊Dic₁₉	D₄	1	4	yes	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
39	Q₈×C₁₉	—	2	4	no	—
40	Q₈×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
52	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#41	1	2	yes	—
57	C₂×Dic₁₉	—	2	4	no	—
58	C₂×Dic₁₉	—	4	2	no	—
59	C₂×Dic₁₉	—	4	2	no	—
60	Dic₃₈	—	4	8	no	—
61	C₁₉⋊C₈	—	4	2	no	—
62	#2024	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	#120	1	1	yes	characteristic
64	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
65	C₂²×C₁₉	#124	1	1	yes	characteristic
66	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
67	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
68	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
69	C₂²×C₁₉	#137	1	1	yes	characteristic
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	—	4	2	no	—
73	C₄×C₁₉	—	8	1	no	—
74	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
75	C₄×C₁₉	#124	1	2	yes	—
76	Dic₁₉	—	4	4	no	—
77	C₂×C₄⋊Q₈	—	19	1	no	—
78	C₂×#103	—	19	2	no	—
79	#391	D₁₉	1	1	yes	characteristic
80	#340	—	19	2	no	—
81	#336	—	19	1	no	—
82	C₂×C₁₉	#393	1	1	yes	characteristic
83	C₂×C₁₉	#450	1	1	yes	characteristic
84	C₂×C₁₉	#451	1	1	yes	characteristic
85	C₂×C₁₉	#475	1	1	yes	characteristic
86	C₂×C₁₉	#477	1	1	yes	characteristic
87	C₂×C₁₉	#487	1	1	yes	characteristic
88	C₂×C₁₉	#489	1	1	yes	characteristic
89	C₂²×Q₈	—	38	1	no	—
90	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
91	C₂²×C₈	—	19	2	no	—
92	C₄⋊Q₈	—	38	4	no	—
93	C₂×C₄⋊C₄	—	19	2	no	—
94	C₂×C₄⋊C₄	—	38	1	no	—
95	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
96	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
97	#103	—	38	4	no	—
98	#95	—	2	1	no	—
99	#95	—	2	1	no	—
100	C₁₉	#2024	1	1	yes	characteristic, complemented, Sylow
101	C₂×Q₈	—	2	1	no	—
102	C₂×Q₈	—	2	2	no	—
103	C₂×Q₈	—	2	2	no	—
104	C₂×Q₈	—	38	4	no	—
105	C₂×Q₈	—	76	2	no	—
106	C₂×Q₈	—	76	2	no	—
107	C₂×Q₈	Dic₃₈	1	2	yes	complemented
108	C₂²×C₄	—	2	1	no	—
109	C₂²×C₄	—	2	1	no	—
110	C₂²×C₄	—	38	2	no	—
111	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
113	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
114	C₂×C₈	—	38	2	no	—
115	C₂×C₈	—	38	2	no	—
116	C₂×C₈	—	38	2	no	—
117	C₄⋊C₄	—	2	2	no	—
118	C₄⋊C₄	—	19	4	no	—
119	C₄⋊C₄	—	38	4	no	—
120	C₄⋊C₄	—	38	2	no	—
121	C₄²	—	2	2	no	—
122	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
123	Q₈	—	2	4	no	—
124	Q₈	—	4	2	no	—
125	Q₈	—	76	8	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	—	38	4	no	—
137	C₂×C₄	—	76	2	no	—
138	C₂×C₄	—	76	2	no	—
139	C₂×C₄	#64527	1	2	yes	—
140	C₂×C₄	#64528	1	2	yes	—
141	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
142	C₂×C₄	#64541	1	1	yes	characteristic
143	C₂×C₄	D₄×D₁₉	1	2	yes	—
144	C₂×C₄	#64543	1	2	yes	—
145	C₈	—	76	2	no	—
146	C₂²	#10597370	1	1	yes	characteristic
147	C₂²	#10597382	1	1	yes	characteristic
148	C₂²	#10597383	1	1	yes	characteristic
149	C₂²	C₂×#64527	1	1	yes	characteristic
150	C₂²	C₂×#64528	1	1	yes	characteristic
151	C₂²	#10597395	1	1	yes	characteristic
152	C₂²	#10597397	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	4	2	no	—
156	C₄	—	8	1	no	—
157	C₄	—	76	4	no	—
158	C₄	#10597324	1	2	yes	—
159	C₄	#10597331	1	2	yes	—
160	C₂	#11926456	1	1	yes	characteristic
161	C₂	#11926694	1	1	yes	characteristic
162	C₂	#11926699	1	1	yes	characteristic
163	C₂	#11926829	1	1	yes	characteristic
164	C₂	#11926839	1	1	yes	characteristic
165	C₂	#11926894	1	1	yes	characteristic
166	C₂	#11926903	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic

C₂×#10597292

C₂

yes

maximal

#11926306

C₂

yes

maximal

#11926299

C₂

yes

maximal, characteristic

C₁₉×#391

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597315

—

C₁₉×#95

—

C₁₉×#95

—

#10597292

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₈

yes

complemented

C₂²×C₄×C₁₉

—

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

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#124

yes

characteristic

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

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#124

yes

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×#103

—

#391

D₁₉

yes

characteristic

#340

—

#336

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

—

—

—

100

C₁₉

#2024

yes

characteristic, complemented, Sylow

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

Dic₃₈

yes

complemented

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

112

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

113

C₂²×C₄

C₂²×D₁₉

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄²

—

122

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

123

Q₈

—

124

Q₈

—

125

Q₈

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

#64527

yes

—

140

C₂×C₄

#64528

yes

—

141

C₂×C₄

C₂×Dic₃₈

yes

characteristic

142

C₂×C₄

#64541

yes

characteristic

143

C₂×C₄

D₄×D₁₉

yes

—

144

C₂×C₄

#64543

yes

—

145

C₈

—

146

C₂²

#10597370

yes

characteristic

147

C₂²

#10597382

yes

characteristic

148

C₂²

#10597383

yes

characteristic

149

C₂²

C₂×#64527

yes

characteristic

150

C₂²

C₂×#64528

yes

characteristic

151

C₂²

#10597395

yes

characteristic

152

C₂²

#10597397

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

#10597324

yes

—

159

C₄

#10597331

yes

—

160

C₂

#11926456

yes

characteristic

161

C₂

#11926694

yes

characteristic

162

C₂

#11926699

yes

characteristic

163

C₂

#11926829

yes

characteristic

164

C₂

#11926839

yes

characteristic

165

C₂

#11926894

yes

characteristic

166

C₂

#11926903

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#391	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2024
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#391

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
20. C₂×Q₈×C₁₉	Q₈	semidirect
100. C₁₉	#2024	semidirect
107. C₂×Q₈	Dic₃₈	semidirect

H ≅ G/N

type

20. C₂×Q₈×C₁₉

Q₈

semidirect

100. C₁₉

#2024

semidirect

107. C₂×Q₈

Dic₃₈

semidirect

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

subgroup	index
C₂×#10597315	2
C₂×#10597292	2
#11926306	2
#11926299	2
C₁₉×#391	2
#2024	19

subgroup

index

C₁₉×#391

Subgroups — #14564776

Conjugacy classes of subgroups

Complements

Maximal subgroups