Group #18069410 — subgroups

Subgroups — #18069410

Order 4864.

222 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 123 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×C₄×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉⋊C₁₆	C₄	1	2	yes	—
5	#11926597	—	2	1	no	—
6	C₄×C₁₉⋊C₁₆	—	2	1	no	—
7	C₄×C₁₉⋊C₁₆	—	2	1	no	—
8	#11926297	C₄	1	2	yes	—
9	#11926295	—	2	1	no	—
10	C₁₉×#431	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#335	C₄	1	2	yes	—
13	C₁₉×#334	—	2	1	no	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	—	2	2	no	—
18	C₁₉×C₂²⋊C₈	—	4	1	no	—
19	C₄×C₈×C₁₉	—	4	1	no	—
20	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
25	C₂×C₁₉⋊C₁₆	—	2	2	no	—
26	C₂×C₁₉⋊C₁₆	—	2	2	no	—
27	C₂×C₁₉⋊C₁₆	C₈	1	4	yes	complemented
28	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
29	C₄×C₁₉⋊C₈	—	4	1	no	—
30	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₂×C₈×C₁₉	—	2	2	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	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
40	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
41	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₄²×C₁₉	D₈	1	1	yes	characteristic
44	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
45	C₂×C₁₉⋊C₈	—	4	2	no	—
46	C₁₉⋊C₁₆	—	2	4	no	—
47	#7155	—	19	1	no	maximal, Sylow
48	C₂³×C₁₉	#106	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
57	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#108	1	2	yes	—
59	C₈×C₁₉	—	2	1	no	—
60	C₈×C₁₉	—	2	1	no	—
61	C₈×C₁₉	—	8	2	no	—
62	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
63	C₈×C₁₉	#97	1	1	yes	characteristic
64	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
65	C₁₉⋊C₈	—	8	2	no	—
66	C₂×C₄×C₁₆	—	19	1	no	—
67	#1564	—	19	1	no	—
68	#1564	D₁₉	1	1	yes	characteristic
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	#334	1	2	yes	—
72	C₂²×C₁₉	#340	1	1	yes	characteristic
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	#335	1	2	yes	—
76	C₄×C₁₉	#336	1	1	yes	characteristic
77	C₄×C₁₉	#341	1	1	yes	characteristic
78	C₄×C₁₉	#359	1	2	yes	—
79	C₄×C₁₉	#359	1	2	yes	—
80	C₂²×C₁₆	—	19	2	no	—
81	#431	—	2	1	no	—
82	#431	—	38	1	no	—
83	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
84	C₄×C₁₆	—	38	1	no	—
85	C₄×C₁₆	—	38	1	no	—
86	#335	—	19	2	no	—
87	#335	Dic₁₉	1	2	yes	—
88	#334	—	2	1	no	—
89	#334	—	38	1	no	—
90	C₂×C₁₉	—	2	2	no	—
91	C₂×C₁₉	#1277	1	1	yes	characteristic
92	C₂×C₁₉	#1382	1	1	yes	characteristic
93	C₂×C₁₉	#1382	1	1	yes	characteristic
94	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
95	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
96	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
97	C₂×C₁₆	—	19	4	no	—
98	C₂×C₁₆	—	38	2	no	—
99	C₂×C₁₆	—	38	2	no	—
100	C₄⋊C₈	—	2	2	no	—
101	C₄⋊C₈	—	38	2	no	—
102	C₂²⋊C₈	—	4	1	no	—
103	C₂²⋊C₈	—	76	1	no	—
104	C₄×C₈	—	4	1	no	—
105	C₄×C₈	—	76	1	no	—
106	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
107	C₄×C₈	D₇₆	1	1	yes	characteristic
108	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
109	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₁₉	#7155	1	1	yes	characteristic, complemented, Sylow
111	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
112	C₂²×C₄	#64526	1	1	yes	characteristic
113	C₂²×C₄	#64527	1	1	yes	characteristic
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	4	2	no	—
116	C₂×C₈	—	76	2	no	—
117	C₂×C₈	C₈×D₁₉	1	2	yes	—
118	C₂×C₈	#64515	1	2	yes	—
119	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
120	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
121	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
122	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
123	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
124	C₄²	#64525	1	1	yes	characteristic
125	C₄²	#64528	1	1	yes	characteristic
126	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
127	C₁₆	—	38	4	no	—
128	C₂³	#10597265	1	1	yes	characteristic
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	#10597264	1	1	yes	characteristic
132	C₂×C₄	#10597266	1	1	yes	characteristic
133	C₂×C₄	#10597267	1	1	yes	characteristic
134	C₂×C₄	Dic₁₉⋊C₈	1	2	yes	—
135	C₂×C₄	#10597279	1	2	yes	—
136	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
137	C₂×C₄	#10597289	1	1	yes	characteristic
138	C₂×C₄	#10597292	1	1	yes	characteristic
139	C₈	—	2	1	no	—
140	C₈	—	2	1	no	—
141	C₈	—	8	2	no	—
142	C₈	—	152	2	no	—
143	C₈	C₈×Dic₁₉	1	1	yes	characteristic
144	C₈	#10597272	1	1	yes	characteristic
145	C₈	(C₂×D₁₉)⋊C₈	1	2	yes	—
146	C₂²	—	2	1	no	—
147	C₂²	—	2	1	no	—
148	C₂²	#11926294	1	2	yes	—
149	C₂²	#11926306	1	1	yes	characteristic
150	C₄	—	2	1	no	—
151	C₄	—	2	1	no	—
152	C₄	#11926296	1	2	yes	—
153	C₄	#11926298	1	1	yes	characteristic
154	C₄	#11926308	1	1	yes	characteristic
155	C₄	#11926350	1	2	yes	—
156	C₄	#11926351	1	2	yes	—
157	C₂	—	2	2	no	—
158	C₂	#14561469	1	1	yes	characteristic
159	C₂	#14561730	1	1	yes	characteristic
160	C₂	#14561732	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₁₉⋊C₁₆

C₂

yes

maximal, characteristic

#14562383

C₂

yes

maximal, characteristic

C₁₉×#1564

C₂

yes

maximal, characteristic

C₂²×C₁₉⋊C₁₆

C₄

yes

—

#11926597

—

C₄×C₁₉⋊C₁₆

—

C₄×C₁₉⋊C₁₆

—

#11926297

C₄

yes

—

#11926295

—

C₁₉×#431

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

C₄

yes

—

C₁₉×#334

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

C₈

yes

complemented

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

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

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

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

C₄⋊C₈

yes

—

C₂×C₄×C₁₉

#107

yes

characteristic

C₂×C₄×C₁₉

#108

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄×C₈

yes

characteristic

C₈×C₁₉

#97

yes

characteristic

C₈×C₁₉

C₂²⋊C₈

yes

—

C₁₉⋊C₈

—

C₂×C₄×C₁₆

—

#1564

—

#1564

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#334

yes

—

C₂²×C₁₉

#340

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#335

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

#359

yes

—

C₂²×C₁₆

—

#431

—

#431

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₁₆

—

C₄×C₁₆

—

#335

—

#335

Dic₁₉

yes

—

#334

—

#334

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₄×D₁₉

yes

characteristic

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₂²⋊C₈

—

103

C₂²⋊C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

C₄×D₁₉

yes

characteristic

107

C₄×C₈

D₇₆

yes

characteristic

108

C₄×C₈

C₂×Dic₁₉

yes

characteristic

109

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

110

C₁₉

#7155

yes

characteristic, complemented, Sylow

111

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

112

C₂²×C₄

#64526

yes

characteristic

113

C₂²×C₄

#64527

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

C₈×D₁₉

yes

—

118

C₂×C₈

#64515

yes

—

119

C₂×C₈

C₄×Dic₁₉

yes

characteristic

120

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

121

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

122

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

123

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

124

C₄²

#64525

yes

characteristic

125

C₄²

#64528

yes

characteristic

126

C₄²

C₂²⋊Dic₁₉

yes

characteristic

127

C₁₆

—

128

C₂³

#10597265

yes

characteristic

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

#10597264

yes

characteristic

132

C₂×C₄

#10597266

yes

characteristic

133

C₂×C₄

#10597267

yes

characteristic

134

C₂×C₄

Dic₁₉⋊C₈

yes

—

135

C₂×C₄

#10597279

yes

—

136

C₂×C₄

C₁₉⋊#95

yes

characteristic

137

C₂×C₄

#10597289

yes

characteristic

138

C₂×C₄

#10597292

yes

characteristic

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

152

—

143

C₈

C₈×Dic₁₉

yes

characteristic

144

C₈

#10597272

yes

characteristic

145

C₈

(C₂×D₁₉)⋊C₈

yes

—

146

C₂²

—

147

C₂²

—

148

C₂²

#11926294

yes

—

149

C₂²

#11926306

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

#11926296

yes

—

153

C₄

#11926298

yes

characteristic

154

C₄

#11926308

yes

characteristic

155

C₄

#11926350

yes

—

156

C₄

#11926351

yes

—

157

C₂

—

158

C₂

#14561469

yes

characteristic

159

C₂

#14561730

yes

characteristic

160

C₂

#14561732

yes

characteristic

	subgroup	G/H
center	C₄²	#64525
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1564	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#106
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1564	D₁₉
hypocenter	C₁₉	#7155
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1564

subgroup

G/H

center

C₄²

#64525

commutator

C₈×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#1564

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1564

N	H ≅ G/N	type
27. C₂×C₁₉⋊C₁₆	C₈	semidirect
110. C₁₉	#7155	semidirect

H ≅ G/N

type

27. C₂×C₁₉⋊C₁₆

C₈

semidirect

110. C₁₉

#7155

semidirect

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

subgroup	index
C₂×C₄×C₁₉⋊C₁₆	2
#14562383	2
C₁₉×#1564	2
#7155	19

subgroup

index

C₂×C₄×C₁₉⋊C₁₆

#14562383

C₁₉×#1564

#7155

Subgroups — #18069410

Conjugacy classes of subgroups

Complements

Maximal subgroups