Group #18069421 — subgroups

Subgroups — #18069421

Order 4864.

222 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 119 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	C₄×#10597269	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926297	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	C₄	1	2	yes	—
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
6	#11926320	—	2	1	no	—
7	C₄×C₁₉⋊C₁₆	—	2	1	no	—
8	#11926297	—	2	1	no	—
9	#11926297	C₄	1	2	yes	—
10	C₁₉×#431	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#335	—	2	1	no	—
13	C₁₉×#334	C₄	1	2	yes	—
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	C₂²×C₁₉⋊C₈	—	4	1	no	—
18	C₁₉×C₄⋊C₈	—	2	2	no	—
19	C₁₉×C₂²⋊C₈	—	4	1	no	—
20	C₄×C₈×C₁₉	—	4	1	no	—
21	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
25	#10597269	—	2	2	no	—
26	#10597269	C₈	1	4	yes	complemented
27	C₂×C₁₉⋊C₁₆	—	2	2	no	—
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	C₂×C₁₉⋊C₈	—	8	2	no	—
47	C₁₉⋊C₁₆	—	2	4	no	—
48	#7159	—	19	1	no	maximal, Sylow
49	C₂³×C₁₉	#106	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	4	1	no	—
53	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
59	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#108	1	2	yes	—
61	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	—	8	2	no	—
64	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
65	C₈×C₁₉	#97	1	1	yes	characteristic
66	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
67	C₁₉⋊C₈	—	8	2	no	—
68	C₄×M₃₂	—	19	1	no	—
69	#1564	D₁₉	1	1	yes	characteristic
70	C₂×#335	—	19	1	no	—
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	—	2	1	no	—
73	C₂²×C₁₉	#334	1	2	yes	—
74	C₂²×C₁₉	#340	1	1	yes	characteristic
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	#335	1	2	yes	—
79	C₄×C₁₉	#336	1	1	yes	characteristic
80	C₄×C₁₉	#341	1	1	yes	characteristic
81	C₄×C₁₉	#361	1	1	yes	characteristic
82	C₄×C₁₉	#362	1	1	yes	characteristic
83	C₂×M₃₂	—	19	2	no	—
84	#431	—	2	1	no	—
85	C₂×C₄⋊C₈	—	38	1	no	—
86	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
87	#346	—	38	1	no	—
88	C₄×C₁₆	—	38	1	no	—
89	#335	—	2	1	no	—
90	#335	—	19	2	no	—
91	#335	—	38	1	no	—
92	#334	Dic₁₉	1	2	yes	—
93	C₂×C₁₉	—	2	2	no	—
94	C₂×C₁₉	#1277	1	1	yes	characteristic
95	C₂×C₁₉	#1387	1	1	yes	characteristic
96	C₂×C₁₉	#1389	1	1	yes	characteristic
97	C₂²×C₈	—	76	1	no	—
98	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
99	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
100	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
101	M₃₂	—	19	4	no	—
102	M₃₂	—	38	2	no	—
103	C₂×C₁₆	—	38	2	no	—
104	C₄⋊C₈	—	2	2	no	—
105	C₄⋊C₈	—	38	2	no	—
106	C₄⋊C₈	—	76	1	no	—
107	C₂²⋊C₈	—	4	1	no	—
108	C₄×C₈	—	4	1	no	—
109	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
110	C₄×C₈	D₇₆	1	1	yes	characteristic
111	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
112	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
113	C₁₉	#7159	1	1	yes	characteristic, complemented, Sylow
114	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
115	C₂²×C₄	#64526	1	1	yes	characteristic
116	C₂²×C₄	#64527	1	1	yes	characteristic
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	4	2	no	—
119	C₂×C₈	—	76	2	no	—
120	C₂×C₈	—	152	2	no	—
121	C₂×C₈	C₈×D₁₉	1	2	yes	—
122	C₂×C₈	#64515	1	2	yes	—
123	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
124	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
125	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
126	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
127	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
128	C₄²	#64525	1	1	yes	characteristic
129	C₄²	#64528	1	1	yes	characteristic
130	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
131	C₁₆	—	38	4	no	—
132	C₂³	#10597265	1	1	yes	characteristic
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	#10597264	1	1	yes	characteristic
137	C₂×C₄	#10597266	1	1	yes	characteristic
138	C₂×C₄	#10597267	1	1	yes	characteristic
139	C₂×C₄	Dic₁₉⋊C₈	1	2	yes	—
140	C₂×C₄	#10597279	1	2	yes	—
141	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
142	C₂×C₄	#10597289	1	1	yes	characteristic
143	C₂×C₄	#10597292	1	1	yes	characteristic
144	C₈	—	2	1	no	—
145	C₈	—	2	1	no	—
146	C₈	—	8	2	no	—
147	C₈	—	152	2	no	—
148	C₈	C₈×Dic₁₉	1	1	yes	characteristic
149	C₈	#10597272	1	1	yes	characteristic
150	C₈	(C₂×D₁₉)⋊C₈	1	2	yes	—
151	C₂²	—	2	1	no	—
152	C₂²	—	2	1	no	—
153	C₂²	#11926294	1	2	yes	—
154	C₂²	#11926306	1	1	yes	characteristic
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	—	2	1	no	—
158	C₄	#11926296	1	2	yes	—
159	C₄	#11926298	1	1	yes	characteristic
160	C₄	#11926308	1	1	yes	characteristic
161	C₄	#11926356	1	1	yes	characteristic
162	C₄	#11926359	1	1	yes	characteristic
163	C₂	—	2	2	no	—
164	C₂	#14561469	1	1	yes	characteristic
165	C₂	#14561745	1	1	yes	characteristic
166	C₂	#14561751	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597269

C₂

yes

maximal, characteristic

C₂×#11926297

C₂

yes

maximal, characteristic

C₁₉×#1564

C₂

yes

maximal, characteristic

C₂×#10597269

C₄

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

—

#11926320

—

C₄×C₁₉⋊C₁₆

—

#11926297

—

#11926297

C₄

yes

—

C₁₉×#431

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

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

#10597269

—

#10597269

C₈

yes

complemented

C₂×C₁₉⋊C₁₆

—

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

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

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

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

—

C₄×M₃₂

—

#1564

D₁₉

yes

characteristic

C₂×#335

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#334

yes

—

C₂²×C₁₉

#340

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#335

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×M₃₂

—

#431

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#346

—

C₄×C₁₆

—

—

—

—

Dic₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₄×D₁₉

yes

characteristic

100

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

101

M₃₂

—

102

M₃₂

—

103

C₂×C₁₆

—

104

C₄⋊C₈

—

105

C₄⋊C₈

—

106

C₄⋊C₈

—

107

C₂²⋊C₈

—

108

C₄×C₈

—

109

C₄×C₈

C₄×D₁₉

yes

characteristic

110

C₄×C₈

D₇₆

yes

characteristic

111

C₄×C₈

C₂×Dic₁₉

yes

characteristic

112

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

113

C₁₉

#7159

yes

characteristic, complemented, Sylow

114

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

115

C₂²×C₄

#64526

yes

characteristic

116

C₂²×C₄

#64527

yes

characteristic

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

152

—

121

C₂×C₈

C₈×D₁₉

yes

—

122

C₂×C₈

#64515

yes

—

123

C₂×C₈

C₄×Dic₁₉

yes

characteristic

124

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

125

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

126

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

127

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

128

C₄²

#64525

yes

characteristic

129

C₄²

#64528

yes

characteristic

130

C₄²

C₂²⋊Dic₁₉

yes

characteristic

131

C₁₆

—

132

C₂³

#10597265

yes

characteristic

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#10597264

yes

characteristic

137

C₂×C₄

#10597266

yes

characteristic

138

C₂×C₄

#10597267

yes

characteristic

139

C₂×C₄

Dic₁₉⋊C₈

yes

—

140

C₂×C₄

#10597279

yes

—

141

C₂×C₄

C₁₉⋊#95

yes

characteristic

142

C₂×C₄

#10597289

yes

characteristic

143

C₂×C₄

#10597292

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

—

152

—

148

C₈

C₈×Dic₁₉

yes

characteristic

149

C₈

#10597272

yes

characteristic

150

C₈

(C₂×D₁₉)⋊C₈

yes

—

151

C₂²

—

152

C₂²

—

153

C₂²

#11926294

yes

—

154

C₂²

#11926306

yes

characteristic

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

#11926296

yes

—

159

C₄

#11926298

yes

characteristic

160

C₄

#11926308

yes

characteristic

161

C₄

#11926356

yes

characteristic

162

C₄

#11926359

yes

characteristic

163

C₂

—

164

C₂

#14561469

yes

characteristic

165

C₂

#14561745

yes

characteristic

166

C₂

#14561751

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597266
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	#7159
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1564

subgroup

G/H

center

C₂×C₄

#10597266

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 ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1564

N	H ≅ G/N	type
26. #10597269	C₈	semidirect
113. C₁₉	#7159	semidirect

H ≅ G/N

type

26. #10597269

C₈

semidirect

113. C₁₉

#7159

semidirect

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

subgroup	index
C₄×#10597269	2
C₂×#11926297	2
C₁₉×#1564	2
#7159	19

subgroup

index

C₄×#10597269

C₂×#11926297

C₁₉×#1564

#7159

Subgroups — #18069421

Conjugacy classes of subgroups

Complements

Maximal subgroups