Group #18070139 — subgroups

Subgroups — #18070139

Order 4864.

182 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 39 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	#14561571	C₂	1	1	yes	maximal, characteristic
2	#14561522	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2091	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
5	#11926326	—	2	1	no	—
6	C₁₉×#430	—	2	1	no	—
7	C₁₉×#430	C₄	1	1	yes	characteristic
8	C₁₉×#407	—	2	1	no	—
9	C₁₉×#407	C₂²	1	1	yes	characteristic
10	C₁₉×#338	C₄	1	1	yes	characteristic
11	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	—	2	1	no	—
13	C₂×M₁₆×C₁₉	—	2	1	no	—
14	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	—	4	1	no	—
17	C₁₉×#108	—	4	2	no	—
18	C₁₉×#108	—	4	1	no	—
19	C₁₉×C₂²⋊C₈	—	4	1	no	—
20	C₁₉×C₂²⋊C₈	—	4	2	no	—
21	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
23	#10597269	—	4	1	no	—
24	C₂⁴×C₁₉	Q₁₆	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄×C₁₉	—	4	1	no	—
28	C₂²×C₄×C₁₉	—	4	1	no	—
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
31	M₁₆×C₁₉	—	4	1	no	—
32	M₁₆×C₁₉	—	4	1	no	—
33	M₁₆×C₁₉	—	4	1	no	—
34	M₁₆×C₁₉	—	4	1	no	—
35	M₁₆×C₁₉	—	4	1	no	—
36	M₁₆×C₁₉	—	4	1	no	—
37	C₂×C₈×C₁₉	—	2	2	no	—
38	C₂×C₈×C₁₉	—	2	1	no	—
39	C₂×C₈×C₁₉	—	2	1	no	—
40	C₂×C₈×C₁₉	—	4	1	no	—
41	C₂×C₁₉⋊C₈	—	4	2	no	—
42	C₂×C₁₉⋊C₈	—	8	1	no	—
43	C₂×C₁₉⋊C₈	—	8	1	no	—
44	C₁₉⋊C₁₆	—	8	1	no	—
45	#7433	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	—	2	1	no	—
47	C₂³×C₁₉	—	4	1	no	—
48	C₂³×C₁₉	—	4	2	no	—
49	C₂³×C₁₉	#103	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	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	8	1	no	—
57	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
59	C₈×C₁₉	—	4	2	no	—
60	C₈×C₁₉	—	4	1	no	—
61	C₈×C₁₉	—	4	1	no	—
62	C₈×C₁₉	—	8	1	no	—
63	C₁₉⋊C₈	—	8	2	no	—
64	#2091	D₁₉	1	1	yes	characteristic
65	#1320	—	19	1	no	—
66	#1298	—	19	1	no	—
67	C₂²×C₁₉	—	2	2	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	4	1	no	—
70	C₂²×C₁₉	—	4	1	no	—
71	C₂²×C₁₉	—	4	2	no	—
72	C₂²×C₁₉	—	4	1	no	—
73	C₂²×C₁₉	—	8	1	no	—
74	C₂²×C₁₉	#328	1	1	yes	characteristic
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	4	1	no	—
77	C₄×C₁₉	#352	1	1	yes	characteristic
78	C₄×C₁₉	#353	1	1	yes	characteristic
79	#430	—	2	1	no	—
80	#430	Dic₁₉	1	1	yes	characteristic
81	#407	—	2	1	no	—
82	#407	C₂×D₁₉	1	1	yes	characteristic
83	C₂×C₂²⋊C₈	—	38	1	no	—
84	#349	—	38	1	no	—
85	#338	Dic₁₉	1	1	yes	characteristic
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	—	4	2	no	—
88	C₂×C₁₉	—	4	1	no	—
89	C₂×C₁₉	#1352	1	1	yes	characteristic
90	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
91	C₂×M₁₆	—	2	1	no	—
92	C₂×M₁₆	—	2	1	no	—
93	C₂×M₁₆	C₂×Dic₁₉	1	1	yes	characteristic
94	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
95	C₂²×C₈	—	76	1	no	—
96	M₃₂	—	76	1	no	—
97	#108	—	4	1	no	—
98	#108	—	4	2	no	—
99	C₂²⋊C₈	—	4	1	no	—
100	C₂²⋊C₈	—	4	2	no	—
101	C₂²⋊C₈	—	38	2	no	—
102	C₂²⋊C₈	—	76	1	no	—
103	C₁₉	#7433	1	1	yes	characteristic, complemented, Sylow
104	C₂⁴	#64528	1	1	yes	characteristic
105	C₂²×C₄	—	2	1	no	—
106	C₂²×C₄	—	2	1	no	—
107	C₂²×C₄	—	4	1	no	—
108	C₂²×C₄	—	4	1	no	—
109	C₂²×C₄	#64527	1	1	yes	characteristic
110	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
111	M₁₆	—	4	1	no	—
112	M₁₆	—	4	1	no	—
113	M₁₆	—	4	1	no	—
114	M₁₆	—	4	1	no	—
115	M₁₆	—	4	1	no	—
116	M₁₆	—	4	1	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	2	1	no	—
119	C₂×C₈	—	2	1	no	—
120	C₂×C₈	—	4	1	no	—
121	C₂×C₈	—	76	2	no	—
122	C₂×C₈	—	152	1	no	—
123	C₂×C₈	—	152	1	no	—
124	C₁₆	—	152	1	no	—
125	C₂³	—	2	1	no	—
126	C₂³	—	4	1	no	—
127	C₂³	—	4	2	no	—
128	C₂³	#10597292	1	1	yes	characteristic
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	8	1	no	—
136	C₂×C₄	#10597291	1	1	yes	characteristic
137	C₂×C₄	#10597294	1	1	yes	characteristic
138	C₈	—	4	2	no	—
139	C₈	—	4	1	no	—
140	C₈	—	4	1	no	—
141	C₈	—	8	1	no	—
142	C₈	—	152	2	no	—
143	C₂²	—	2	2	no	—
144	C₂²	—	2	1	no	—
145	C₂²	—	4	1	no	—
146	C₂²	—	4	1	no	—
147	C₂²	—	4	2	no	—
148	C₂²	—	4	1	no	—
149	C₂²	—	8	1	no	—
150	C₂²	#11926281	1	1	yes	characteristic
151	C₄	—	2	1	no	—
152	C₄	—	4	1	no	—
153	C₄	#11926334	1	1	yes	characteristic
154	C₄	#11926337	1	1	yes	characteristic
155	C₂	—	2	1	no	—
156	C₂	—	4	2	no	—
157	C₂	—	4	1	no	—
158	C₂	#14561659	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561571

C₂

yes

maximal, characteristic

#14561522

C₂

yes

maximal, characteristic

C₁₉×#2091

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926326

—

C₁₉×#430

—

C₁₉×#430

C₄

yes

characteristic

C₁₉×#407

—

C₁₉×#407

C₂²

yes

characteristic

C₁₉×#338

C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#108

—

C₁₉×#108

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597269

—

C₂⁴×C₁₉

Q₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

#7433

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#103

yes

characteristic

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

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2091

D₁₉

yes

characteristic

#1320

—

#1298

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#328

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

yes

characteristic

#407

—

#407

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₈

—

#349

—

#338

Dic₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1352

yes

characteristic

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×Dic₁₉

yes

characteristic

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

C₂²×C₈

—

M₃₂

—

#108

—

#108

—

C₂²⋊C₈

—

100

C₂²⋊C₈

—

101

C₂²⋊C₈

—

102

C₂²⋊C₈

—

103

C₁₉

#7433

yes

characteristic, complemented, Sylow

104

C₂⁴

#64528

yes

characteristic

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

#64527

yes

characteristic

110

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

M₁₆

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

152

—

123

C₂×C₈

—

152

—

124

C₁₆

—

152

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

#10597292

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

#10597291

yes

characteristic

137

C₂×C₄

#10597294

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

152

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

#11926281

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

#11926334

yes

characteristic

154

C₄

#11926337

yes

characteristic

155

C₂

—

156

C₂

—

157

C₂

—

158

C₂

#14561659

yes

characteristic

	subgroup	G/H
center	C₄	#11926337
commutator	C₂×M₁₆×C₁₉	C₂×C₄
Frattini	#407	C₂×D₁₉
Fitting	C₁₉×#2091	C₂
socle	C₂×C₁₉	#1352
prime radical	C₂⁴×C₁₉	Q₁₆
cosocle	C₁₉×#407	C₂²
hypercenter	#2091	D₁₉
hypocenter	C₁₉	#7433
LCS	G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #2091

subgroup

G/H

center

C₄

#11926337

commutator

C₂×M₁₆×C₁₉

C₂×C₄

Frattini

#407

C₂×D₁₉

Fitting

C₁₉×#2091

C₂

socle

C₂×C₁₉

#1352

prime radical

C₂⁴×C₁₉

Q₁₆

cosocle

C₁₉×#407

C₂²

D₁₉

C₁₉

G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #2091

N	H ≅ G/N	type
103. C₁₉	#7433	semidirect

H ≅ G/N

type

103. C₁₉

#7433

semidirect

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

subgroup	index
#14561571	2
#14561522	2
C₁₉×#2091	2
#7433	19

subgroup

index

#14561571

#14561522

C₁₉×#2091

#7433

Subgroups — #18070139

Conjugacy classes of subgroups

Complements

Maximal subgroups