Group #18076190 — subgroups

Subgroups — #18076190

Order 4864.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14563388	C₂	1	1	yes	maximal, characteristic
2	#14562381	C₂	1	2	yes	maximal
3	#14561480	C₂	1	1	yes	maximal, characteristic
4	#14561463	C₂	1	2	yes	maximal
5	C₁₉×#1281	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	#11926390	C₂²	1	1	yes	characteristic
9	#11926298	C₄	1	2	yes	—
10	#11926298	C₄	1	2	yes	—
11	#11926296	—	2	2	no	—
12	#11926294	—	2	2	no	—
13	C₁₉×#431	C₂²	1	2	yes	—
14	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
20	C₁₉×C₄⋊C₈	—	2	2	no	—
21	C₁₉×C₂²⋊C₈	—	2	2	no	—
22	C₁₉×#97	—	2	2	no	—
23	C₄×C₈×C₁₉	—	2	2	no	—
24	C₁₉⋊#95	—	2	2	no	—
25	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
26	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
27	C₄×C₁₉⋊C₈	—	2	2	no	—
28	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
29	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
30	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
31	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	#41	1	2	yes	—
33	C₂²×Dic₁₉	—	2	1	no	—
34	C₂²×Dic₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	—	2	2	no	—
38	C₂×C₈×C₁₉	—	4	2	no	—
39	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₄²×C₁₉	#41	1	2	yes	—
42	C₄×Dic₁₉	—	2	2	no	—
43	C₄×Dic₁₉	—	2	2	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂×C₁₉⋊C₈	—	2	2	no	—
46	C₂×C₁₉⋊C₈	—	4	2	no	—
47	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
48	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
49	#8782	—	19	1	no	maximal, Sylow
50	C₂³×C₁₉	#117	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#124	1	2	yes	—
55	C₂×C₄×C₁₉	#125	1	2	yes	—
56	C₂×C₄×C₁₉	#131	1	2	yes	—
57	C₂×C₄×C₁₉	#131	1	2	yes	—
58	C₂×Dic₁₉	—	4	2	no	—
59	C₂×Dic₁₉	—	4	2	no	—
60	C₂×Dic₁₉	—	4	1	no	—
61	C₂×Dic₁₉	—	4	1	no	—
62	C₈×C₁₉	—	4	2	no	—
63	C₈×C₁₉	—	8	2	no	—
64	C₁₉⋊C₈	—	2	2	no	—
65	C₁₉⋊C₈	—	2	2	no	—
66	C₁₉⋊C₈	—	8	2	no	—
67	#1746	—	19	1	no	—
68	#1564	—	19	2	no	—
69	#1281	—	19	1	no	—
70	#1281	D₁₉	1	1	yes	characteristic
71	#1274	—	19	2	no	—
72	C₂²×C₁₉	—	2	2	no	—
73	C₂²×C₁₉	#382	1	1	yes	characteristic
74	C₂²×C₁₉	#433	1	1	yes	characteristic
75	C₂²×C₁₉	#433	1	1	yes	characteristic
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	2	2	no	—
78	C₄×C₁₉	#424	1	2	yes	—
79	C₄×C₁₉	#433	1	2	yes	—
80	Dic₁₉	—	8	1	no	—
81	Dic₁₉	—	8	1	no	—
82	#431	—	19	2	no	—
83	#431	C₂×D₁₉	1	2	yes	—
84	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
85	C₂×C₄×C₈	—	19	1	no	—
86	#376	—	19	1	no	—
87	#336	—	19	2	no	—
88	#336	—	19	2	no	—
89	#335	—	38	2	no	—
90	#334	—	38	2	no	—
91	C₂×C₁₉	—	2	1	no	—
92	C₂×C₁₉	—	2	1	no	—
93	C₂×C₁₉	#1832	1	1	yes	characteristic
94	C₂×C₁₉	#1833	1	2	yes	—
95	C₂²×C₈	—	19	2	no	—
96	C₂²×C₈	C₄×D₁₉	1	2	yes	—
97	C₂×C₄²	—	19	1	no	—
98	C₂×C₄²	—	19	1	no	—
99	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
100	C₄⋊C₈	—	2	2	no	—
101	C₄⋊C₈	—	38	2	no	—
102	C₂²⋊C₈	—	2	2	no	—
103	C₂²⋊C₈	—	38	2	no	—
104	#97	—	2	2	no	—
105	C₄×C₈	—	2	2	no	—
106	C₄×C₈	—	19	1	no	—
107	C₄×C₈	—	19	1	no	—
108	C₄×C₈	—	19	2	no	—
109	C₄×C₈	—	38	2	no	—
110	#95	—	38	2	no	—
111	C₁₉	#8782	1	1	yes	characteristic, complemented, Sylow
112	C₂²×C₄	—	38	1	no	—
113	C₂²×C₄	—	38	1	no	—
114	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
115	C₂²×C₄	#64541	1	2	yes	—
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	4	2	no	—
120	C₂×C₈	—	19	2	no	—
121	C₂×C₈	—	19	2	no	—
122	C₂×C₈	—	38	2	no	—
123	C₂×C₈	—	38	2	no	—
124	C₂×C₈	—	76	2	no	—
125	C₄²	—	38	2	no	—
126	C₄²	—	38	2	no	—
127	C₄²	D₄×D₁₉	1	1	yes	characteristic
128	C₄²	#64543	1	2	yes	—
129	C₄²	Q₈×D₁₉	1	1	yes	characteristic
130	C₂³	#10597318	1	1	yes	characteristic
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	76	2	no	—
133	C₂×C₄	—	76	2	no	—
134	C₂×C₄	—	76	1	no	—
135	C₂×C₄	—	76	1	no	—
136	C₂×C₄	#10597323	1	1	yes	characteristic
137	C₂×C₄	#10597331	1	2	yes	—
138	C₂×C₄	#10597335	1	2	yes	—
139	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
140	C₂×C₄	#10597347	1	2	yes	—
141	C₂×C₄	#10597353	1	2	yes	—
142	C₈	—	4	2	no	—
143	C₈	—	8	2	no	—
144	C₈	—	38	2	no	—
145	C₈	—	38	2	no	—
146	C₈	—	152	2	no	—
147	C₂²	—	2	2	no	—
148	C₂²	#11926408	1	1	yes	characteristic
149	C₂²	#11926603	1	1	yes	characteristic
150	C₂²	#11926606	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	2	2	no	—
153	C₄	—	152	1	no	—
154	C₄	—	152	1	no	—
155	C₄	#11926569	1	2	yes	—
156	C₄	#11926602	1	2	yes	—
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	#14563753	1	1	yes	characteristic
160	C₂	#14563756	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563388

C₂

yes

maximal, characteristic

#14562381

C₂

yes

maximal

#14561480

C₂

yes

maximal, characteristic

#14561463

C₂

yes

maximal

C₁₉×#1281

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926390

C₂²

yes

characteristic

#11926298

C₄

yes

—

#11926298

C₄

yes

—

#11926296

—

#11926294

—

C₁₉×#431

C₂²

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

Q₈

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

#1274

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#424

yes

—

C₄×C₁₉

#433

yes

—

Dic₁₉

—

Dic₁₉

—

#431

—

#431

C₂×D₁₉

yes

—

C₂×#97

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

—

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1832

yes

characteristic

C₂×C₁₉

#1833

yes

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₂²⋊C₈

—

103

C₂²⋊C₈

—

104

#97

—

105

C₄×C₈

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₄×C₈

—

110

#95

—

111

C₁₉

#8782

yes

characteristic, complemented, Sylow

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

115

C₂²×C₄

#64541

yes

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₄²

—

126

C₄²

—

127

C₄²

D₄×D₁₉

yes

characteristic

128

C₄²

#64543

yes

—

129

C₄²

Q₈×D₁₉

yes

characteristic

130

C₂³

#10597318

yes

characteristic

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#10597323

yes

characteristic

137

C₂×C₄

#10597331

yes

—

138

C₂×C₄

#10597335

yes

—

139

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

140

C₂×C₄

#10597347

yes

—

141

C₂×C₄

#10597353

yes

—

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

152

—

147

C₂²

—

148

C₂²

#11926408

yes

characteristic

149

C₂²

#11926603

yes

characteristic

150

C₂²

#11926606

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

—

152

—

154

C₄

—

152

—

155

C₄

#11926569

yes

—

156

C₄

#11926602

yes

—

157

C₂

—

158

C₂

—

159

C₂

#14563753

yes

characteristic

160

C₂

#14563756

yes

—

	subgroup	G/H
center	C₂×C₄	#10597323
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1281	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1281	D₁₉
hypocenter	C₁₉	#8782
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂×C₄

#10597323

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1281

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
111. C₁₉	#8782	semidirect

H ≅ G/N

type

111. C₁₉

#8782

semidirect

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

subgroup	index
#14563388	2
#14562381	2
#14561480	2
#14561463	2
C₁₉×#1281	2
#8782	19

subgroup

index

C₁₉×#1281

Subgroups — #18076190

Conjugacy classes of subgroups

Complements

Maximal subgroups