Group #18069578 — subgroups

Subgroups — #18069578

Order 4864.

202 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 83 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	#14565434	C₂	1	1	yes	maximal, characteristic
2	#14562398	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1835	C₂	1	1	yes	maximal, characteristic
4	#11926601	—	2	1	no	—
5	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
6	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	C₄×C₁₉⋊C₁₆	C₄	1	2	yes	complemented
8	#11926297	—	2	1	no	—
9	#11926295	C₄	1	2	yes	complemented
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#382	—	2	1	no	—
12	C₁₉×#340	—	2	1	no	—
13	C₁₉×#340	C₄	1	2	yes	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₁₉×#95	—	4	1	no	—
23	C₁₉×#95	—	4	1	no	—
24	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
25	C₂×C₁₉⋊C₁₆	—	2	2	no	—
26	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
27	#10597260	—	4	1	no	—
28	C₂²×C₄×C₁₉	—	4	2	no	—
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
38	C₄⋊C₄×C₁₉	—	4	2	no	—
39	C₄⋊C₄×C₁₉	—	4	2	no	—
40	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
43	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
44	C₂×C₁₉⋊C₈	—	4	2	no	—
45	C₁₉⋊C₁₆	—	4	2	no	—
46	#7218	—	19	1	no	maximal, Sylow
47	C₂³×C₁₉	#102	1	1	yes	characteristic
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	8	2	no	—
53	C₂×C₄×C₁₉	—	8	2	no	—
54	C₂×C₄×C₁₉	—	8	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	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	—	2	1	no	—
64	C₈×C₁₉	—	2	1	no	—
65	C₁₉⋊C₈	—	8	2	no	—
66	#2162	—	19	1	no	—
67	#1835	D₁₉	1	1	yes	characteristic
68	#1568	—	19	1	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	#340	1	1	yes	characteristic
72	C₂²×C₁₉	#359	1	2	yes	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	16	2	no	—
79	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
80	C₄×C₁₉	#344	1	1	yes	characteristic
81	#432	—	38	1	no	—
82	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
83	#382	—	2	1	no	—
84	C₄⋊C₁₆	—	38	1	no	—
85	C₂²⋊C₁₆	—	38	1	no	—
86	C₄×C₁₆	—	19	2	no	—
87	#340	—	2	1	no	—
88	#340	Dic₁₉	1	2	yes	—
89	#335	—	38	1	no	—
90	#334	—	19	2	no	—
91	C₂×C₁₉	—	2	2	no	—
92	C₂×C₁₉	#1286	1	1	yes	characteristic
93	C₂×C₁₉	#1382	1	1	yes	characteristic
94	C₂×C₁₉	#1384	1	1	yes	characteristic
95	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
96	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
97	C₂×C₄⋊C₄	—	2	2	no	—
98	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
99	C₂×C₁₆	—	38	2	no	—
100	C₄⋊C₈	—	38	2	no	—
101	C₂²⋊C₈	—	76	1	no	—
102	#97	—	76	1	no	—
103	C₄×C₈	Dic₃₈	1	1	yes	characteristic
104	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
105	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
106	C₄×C₈	D₇₆	1	1	yes	characteristic
107	#95	—	4	1	no	—
108	#95	—	4	1	no	—
109	C₁₉	#7218	1	1	yes	characteristic, complemented, Sylow
110	C₂²×C₄	—	4	2	no	—
111	C₂²×C₄	#64525	1	1	yes	characteristic
112	C₂²×C₄	#64526	1	1	yes	characteristic
113	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	4	1	no	—
116	C₂×C₈	—	76	2	no	—
117	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
118	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
119	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
120	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
121	C₄⋊C₄	—	4	2	no	—
122	C₄⋊C₄	—	4	2	no	—
123	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
124	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
125	C₄²	#64527	1	1	yes	characteristic
126	C₄²	#64528	1	1	yes	characteristic
127	C₁₆	—	76	2	no	—
128	C₂³	#10597289	1	1	yes	characteristic
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	8	2	no	—
134	C₂×C₄	—	8	2	no	—
135	C₂×C₄	—	8	2	no	—
136	C₂×C₄	#10597264	1	1	yes	characteristic
137	C₂×C₄	#10597265	1	1	yes	characteristic
138	C₂×C₄	#10597266	1	1	yes	characteristic
139	C₂×C₄	#10597267	1	1	yes	characteristic
140	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
141	C₂×C₄	#10597292	1	1	yes	characteristic
142	C₈	—	2	1	no	—
143	C₈	—	2	1	no	—
144	C₈	—	2	1	no	—
145	C₈	—	2	1	no	—
146	C₈	—	152	2	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	2	1	no	—
149	C₂²	#11926306	1	1	yes	characteristic
150	C₂²	#11926351	1	2	yes	—
151	C₄	—	2	1	no	—
152	C₄	—	2	1	no	—
153	C₄	—	2	1	no	—
154	C₄	—	2	1	no	—
155	C₄	—	2	1	no	—
156	C₄	—	16	2	no	—
157	C₄	#11926300	1	1	yes	characteristic
158	C₄	#11926314	1	1	yes	characteristic
159	C₂	—	2	2	no	—
160	C₂	#14561493	1	1	yes	characteristic
161	C₂	#14561730	1	1	yes	characteristic
162	C₂	#14561736	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565434

C₂

yes

maximal, characteristic

#14562398

C₂

yes

maximal, characteristic

C₁₉×#1835

C₂

yes

maximal, characteristic

#11926601

—

C₄⋊(C₁₉⋊C₁₆)

—

C₂²⋊(C₁₉⋊C₁₆)

—

C₄×C₁₉⋊C₁₆

C₄

yes

complemented

#11926297

—

#11926295

C₄

yes

complemented

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#382

—

C₁₉×#340

—

C₁₉×#340

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

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

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

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

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2162

—

#1835

D₁₉

yes

characteristic

#1568

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#340

yes

characteristic

C₂²×C₁₉

#359

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#382

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

#340

—

#340

Dic₁₉

yes

—

#335

—

#334

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

C₂×C₁₆

—

100

C₄⋊C₈

—

101

C₂²⋊C₈

—

102

#97

—

103

C₄×C₈

Dic₃₈

yes

characteristic

104

C₄×C₈

C₄×D₁₉

yes

characteristic

105

C₄×C₈

C₄×D₁₉

yes

characteristic

106

C₄×C₈

D₇₆

yes

characteristic

107

#95

—

108

#95

—

109

C₁₉

#7218

yes

characteristic, complemented, Sylow

110

C₂²×C₄

—

111

C₂²×C₄

#64525

yes

characteristic

112

C₂²×C₄

#64526

yes

characteristic

113

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

C₄×Dic₁₉

yes

characteristic

118

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

119

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

120

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄²

Dic₁₉⋊C₄

yes

characteristic

124

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

125

C₄²

#64527

yes

characteristic

126

C₄²

#64528

yes

characteristic

127

C₁₆

—

128

C₂³

#10597289

yes

characteristic

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#10597264

yes

characteristic

137

C₂×C₄

#10597265

yes

characteristic

138

C₂×C₄

#10597266

yes

characteristic

139

C₂×C₄

#10597267

yes

characteristic

140

C₂×C₄

C₁₉⋊#95

yes

characteristic

141

C₂×C₄

#10597292

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

152

—

147

C₂²

—

148

C₂²

—

149

C₂²

#11926306

yes

characteristic

150

C₂²

#11926351

yes

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

#11926300

yes

characteristic

158

C₄

#11926314

yes

characteristic

159

C₂

—

160

C₂

#14561493

yes

characteristic

161

C₂

#14561730

yes

characteristic

162

C₂

#14561736

yes

characteristic

	subgroup	G/H
center	C₂²	#11926306
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1835	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1835	D₁₉
hypocenter	C₁₉	#7218
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1835

subgroup

G/H

center

C₂²

#11926306

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#1835

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 ◁ #1835

N	H ≅ G/N	type
7. C₄×C₁₉⋊C₁₆	C₄	semidirect
9. #11926295	C₄	semidirect
109. C₁₉	#7218	semidirect

H ≅ G/N

type

7. C₄×C₁₉⋊C₁₆

C₄

semidirect

9. #11926295

C₄

semidirect

109. C₁₉

#7218

semidirect

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

subgroup	index
#14565434	2
#14562398	2
C₁₉×#1835	2
#7218	19

subgroup

index

#14565434

#14562398

C₁₉×#1835

#7218

Subgroups — #18069578

Conjugacy classes of subgroups

Complements

Maximal subgroups