Group #18069592 — subgroups

Subgroups — #18069592

Order 4864.

214 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14565438	C₂	1	1	yes	maximal, characteristic
2	#14563763	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic
4	#11926414	—	2	1	no	—
5	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
6	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	#11926320	C₄	1	2	yes	complemented
8	#11926307	—	2	1	no	—
9	#11926307	C₄	1	2	yes	—
10	C₁₉×#432	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#335	C₄	1	2	yes	complemented
13	C₁₉×#334	—	2	1	no	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₉	—	2	2	no	—
18	C₂×C₄⋊Dic₁₉	—	4	1	no	—
19	C₂×C₄⋊Dic₁₉	—	4	1	no	—
20	C₁₉×C₄⋊C₈	—	2	2	no	—
21	C₁₉×C₂²⋊C₈	—	4	1	no	—
22	C₁₉×#97	—	4	1	no	—
23	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
27	C₂×C₁₉⋊C₁₆	—	2	2	no	—
28	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	4	2	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	4	2	no	—
35	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
42	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
43	C₄⋊Dic₁₉	—	4	2	no	—
44	C₄⋊Dic₁₉	—	4	2	no	—
45	C₄⋊Dic₁₉	—	8	2	no	—
46	C₄⋊Dic₁₉	—	8	2	no	—
47	C₁₉⋊C₁₆	—	4	2	no	—
48	#7222	—	19	1	no	maximal, Sylow
49	C₂³×C₁₉	#102	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
61	C₂×Dic₁₉	—	8	2	no	—
62	C₂×Dic₁₉	—	8	2	no	—
63	C₂×Dic₁₉	—	8	2	no	—
64	C₈×C₁₉	—	2	1	no	—
65	C₈×C₁₉	—	2	1	no	—
66	C₈×C₁₉	—	2	1	no	—
67	C₈×C₁₉	—	2	1	no	—
68	C₈×C₁₉	—	8	2	no	—
69	#2163	—	19	1	no	—
70	#1834	—	19	1	no	—
71	#1568	D₁₉	1	1	yes	characteristic
72	C₂²×C₁₉	—	2	1	no	—
73	C₂²×C₁₉	—	2	1	no	—
74	C₂²×C₁₉	#340	1	1	yes	characteristic
75	C₂²×C₁₉	#361	1	1	yes	characteristic
76	C₂²×C₁₉	#362	1	1	yes	characteristic
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	2	1	no	—
79	C₄×C₁₉	—	2	1	no	—
80	C₄×C₁₉	—	2	1	no	—
81	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
82	C₄×C₁₉	#344	1	1	yes	characteristic
83	C₄×C₁₉	#360	1	2	yes	—
84	Dic₁₉	—	16	2	no	—
85	#432	—	2	1	no	—
86	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
87	#384	—	38	1	no	—
88	C₄⋊C₁₆	—	38	1	no	—
89	C₂²⋊C₁₆	—	38	1	no	—
90	#346	—	19	2	no	—
91	#340	—	19	2	no	—
92	#340	—	38	1	no	—
93	#335	Dic₁₉	1	2	yes	complemented
94	#334	—	2	1	no	—
95	C₂×C₁₉	—	2	1	no	—
96	C₂×C₁₉	—	2	1	no	—
97	C₂×C₁₉	#1286	1	1	yes	characteristic
98	C₂×C₁₉	#1386	1	1	yes	characteristic
99	C₂×C₁₉	#1387	1	1	yes	characteristic
100	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
101	C₂²×C₈	D₇₆	1	1	yes	characteristic
102	C₂×C₄⋊C₄	—	38	2	no	—
103	C₂×C₄⋊C₄	—	76	1	no	—
104	C₂×C₄⋊C₄	—	76	1	no	—
105	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
106	C₂×C₁₆	—	38	2	no	—
107	C₄⋊C₈	—	2	2	no	—
108	C₂²⋊C₈	—	4	1	no	—
109	#97	—	4	1	no	—
110	C₄×C₈	Dic₃₈	1	1	yes	characteristic
111	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
112	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
113	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
114	C₁₉	#7222	1	1	yes	characteristic, complemented, Sylow
115	C₂²×C₄	—	76	2	no	—
116	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
117	C₂²×C₄	#64525	1	1	yes	characteristic
118	C₂²×C₄	#64527	1	1	yes	characteristic
119	C₂×C₈	—	4	1	no	—
120	C₂×C₈	—	4	1	no	—
121	C₂×C₈	—	4	2	no	—
122	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
123	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
124	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
125	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
126	C₄⋊C₄	—	76	2	no	—
127	C₄⋊C₄	—	76	2	no	—
128	C₄⋊C₄	—	152	2	no	—
129	C₄⋊C₄	—	152	2	no	—
130	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
131	C₄²	#64526	1	1	yes	characteristic
132	C₄²	#64528	1	1	yes	characteristic
133	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
134	C₁₆	—	76	2	no	—
135	C₂³	#10597266	1	1	yes	characteristic
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	2	1	no	—
138	C₂×C₄	—	2	1	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	152	2	no	—
142	C₂×C₄	—	152	2	no	—
143	C₂×C₄	—	152	2	no	—
144	C₂×C₄	#10597264	1	1	yes	characteristic
145	C₂×C₄	#10597265	1	1	yes	characteristic
146	C₂×C₄	#10597267	1	1	yes	characteristic
147	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
148	C₂×C₄	#10597289	1	1	yes	characteristic
149	C₂×C₄	#10597292	1	1	yes	characteristic
150	C₈	—	2	1	no	—
151	C₈	—	2	1	no	—
152	C₈	—	2	1	no	—
153	C₈	—	2	1	no	—
154	C₈	—	8	2	no	—
155	C₂²	—	2	1	no	—
156	C₂²	—	2	1	no	—
157	C₂²	#11926306	1	1	yes	characteristic
158	C₂²	#11926356	1	1	yes	characteristic
159	C₂²	#11926359	1	1	yes	characteristic
160	C₄	—	2	1	no	—
161	C₄	—	2	1	no	—
162	C₄	—	2	1	no	—
163	C₄	—	2	1	no	—
164	C₄	—	304	2	no	—
165	C₄	#11926301	1	1	yes	characteristic
166	C₄	#11926316	1	1	yes	characteristic
167	C₄	#11926354	1	2	yes	—
168	C₂	—	2	1	no	—
169	C₂	—	2	1	no	—
170	C₂	#14561495	1	1	yes	characteristic
171	C₂	#14561740	1	1	yes	characteristic
172	C₂	#14561745	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565438

C₂

yes

maximal, characteristic

#14563763

C₂

yes

maximal, characteristic

C₁₉×#1568

C₂

yes

maximal, characteristic

#11926414

—

C₄⋊(C₁₉⋊C₁₆)

—

C₂²⋊(C₁₉⋊C₁₆)

—

#11926320

C₄

yes

complemented

#11926307

—

#11926307

C₄

yes

—

C₁₉×#432

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

C₄

yes

complemented

C₁₉×#334

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#2163

—

#1834

—

#1568

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

—

#432

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

—

—

—

Dic₁₉

yes

complemented

#334

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

100

C₂²×C₈

C₄×D₁₉

yes

characteristic

101

C₂²×C₈

D₇₆

yes

characteristic

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

106

C₂×C₁₆

—

107

C₄⋊C₈

—

108

C₂²⋊C₈

—

109

#97

—

110

C₄×C₈

Dic₃₈

yes

characteristic

111

C₄×C₈

C₄×D₁₉

yes

characteristic

112

C₄×C₈

C₂×Dic₁₉

yes

characteristic

113

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

114

C₁₉

#7222

yes

characteristic, complemented, Sylow

115

C₂²×C₄

—

116

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

117

C₂²×C₄

#64525

yes

characteristic

118

C₂²×C₄

#64527

yes

characteristic

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

C₄×Dic₁₉

yes

characteristic

123

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

124

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

125

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

152

—

129

C₄⋊C₄

—

152

—

130

C₄²

Dic₁₉⋊C₄

yes

characteristic

131

C₄²

#64526

yes

characteristic

132

C₄²

#64528

yes

characteristic

133

C₄²

C₂²⋊Dic₁₉

yes

characteristic

134

C₁₆

—

135

C₂³

#10597266

yes

characteristic

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

152

—

142

C₂×C₄

—

152

—

143

C₂×C₄

—

152

—

144

C₂×C₄

#10597264

yes

characteristic

145

C₂×C₄

#10597265

yes

characteristic

146

C₂×C₄

#10597267

yes

characteristic

147

C₂×C₄

C₁₉⋊#95

yes

characteristic

148

C₂×C₄

#10597289

yes

characteristic

149

C₂×C₄

#10597292

yes

characteristic

150

C₈

—

151

C₈

—

152

C₈

—

153

C₈

—

154

C₈

—

155

C₂²

—

156

C₂²

—

157

C₂²

#11926306

yes

characteristic

158

C₂²

#11926356

yes

characteristic

159

C₂²

#11926359

yes

characteristic

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

—

304

—

165

C₄

#11926301

yes

characteristic

166

C₄

#11926316

yes

characteristic

167

C₄

#11926354

yes

—

168

C₂

—

169

C₂

—

170

C₂

#14561495

yes

characteristic

171

C₂

#14561740

yes

characteristic

172

C₂

#14561745

yes

characteristic

	subgroup	G/H
center	C₂²	#11926306
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1568	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1568	D₁₉
hypocenter	C₁₉	#7222
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1568

subgroup

G/H

center

C₂²

#11926306

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#1568

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1568

N	H ≅ G/N	type
7. #11926320	C₄	semidirect
12. C₁₉×#335	C₄	semidirect
93. #335	Dic₁₉	semidirect
114. C₁₉	#7222	semidirect

H ≅ G/N

type

7. #11926320

C₄

semidirect

12. C₁₉×#335

C₄

semidirect

93. #335

Dic₁₉

semidirect

114. C₁₉

#7222

semidirect

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

subgroup	index
#14565438	2
#14563763	2
C₁₉×#1568	2
#7222	19

subgroup

index

#14565438

#14563763

C₁₉×#1568

#7222

Subgroups — #18069592

Conjugacy classes of subgroups

Complements

Maximal subgroups