Group #18069180 — subgroups

Subgroups — #18069180

Order 4864.

156 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14563754	C₂	1	1	yes	maximal, characteristic
2	#14561575	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
5	#11926390	C₄	1	1	yes	characteristic
6	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	#11926298	—	2	1	no	—
8	#11926298	—	2	1	no	—
9	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
11	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	—	2	1	no	—
15	C₂²×C₁₉⋊C₈	—	2	1	no	—
16	C₂×C₁₆×C₁₉	—	4	1	no	—
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	C₁₉⋊#95	—	2	1	no	—
19	C₁₉⋊#95	C₈	1	1	yes	characteristic
20	C₁₉⋊#95	C₈	1	1	yes	characteristic
21	C₂×C₁₉⋊C₁₆	—	4	1	no	—
22	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
23	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	2	1	no	—
27	C₂²×Dic₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	—	4	1	no	—
31	C₂×C₈×C₁₉	—	4	1	no	—
32	C₄²×C₁₉	—	2	1	no	—
33	C₄²×C₁₉	—	2	1	no	—
34	C₄×Dic₁₉	—	4	1	no	—
35	C₄×Dic₁₉	—	4	1	no	—
36	C₂×C₁₉⋊C₈	—	4	2	no	—
37	C₂×C₁₉⋊C₈	—	4	1	no	—
38	C₁₆×C₁₉	—	8	1	no	—
39	C₁₉⋊C₁₆	—	8	1	no	—
40	#7065	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
51	C₂×Dic₁₉	—	4	1	no	—
52	C₂×Dic₁₉	—	4	1	no	—
53	C₂×Dic₁₉	—	4	1	no	—
54	C₂×Dic₁₉	—	4	1	no	—
55	C₂×Dic₁₉	—	4	1	no	—
56	C₂×Dic₁₉	—	4	1	no	—
57	C₈×C₁₉	—	4	1	no	—
58	C₈×C₁₉	—	4	1	no	—
59	C₁₉⋊C₈	—	8	1	no	—
60	#1832	—	19	1	no	—
61	#1322	—	19	1	no	—
62	#1322	D₁₉	1	1	yes	characteristic
63	C₂²×C₁₉	—	2	1	no	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	#324	1	1	yes	characteristic
66	C₂²×C₁₉	#350	1	1	yes	characteristic
67	C₂²×C₁₉	#350	1	1	yes	characteristic
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	4	1	no	—
70	C₄×C₁₉	—	4	1	no	—
71	C₄×C₁₉	#354	1	1	yes	characteristic
72	C₄×C₁₉	#355	1	1	yes	characteristic
73	Dic₁₉	—	8	1	no	—
74	Dic₁₉	—	8	1	no	—
75	C₂×C₄⋊C₈	—	19	1	no	—
76	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
77	#376	—	19	1	no	—
78	C₂²⋊C₁₆	—	2	1	no	—
79	C₂²⋊C₁₆	—	38	1	no	—
80	#336	—	38	1	no	—
81	#336	—	38	1	no	—
82	C₂×C₁₉	—	2	1	no	—
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	#1323	1	1	yes	characteristic
85	C₂×C₁₉	#1324	1	1	yes	characteristic
86	C₂×C₁₉	#1328	1	1	yes	characteristic
87	C₂²×C₈	—	38	1	no	—
88	C₂²×C₈	D₇₆	1	1	yes	characteristic
89	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
90	C₂×C₄²	—	38	1	no	—
91	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
92	C₂×C₁₆	—	4	1	no	—
93	C₂×C₁₆	—	76	1	no	—
94	C₄⋊C₈	—	4	1	no	—
95	C₄⋊C₈	—	76	1	no	—
96	#95	—	19	1	no	—
97	#95	—	19	1	no	—
98	#95	—	38	1	no	—
99	C₁₉	#7065	1	1	yes	characteristic, complemented, Sylow
100	C₂²×C₄	—	38	1	no	—
101	C₂²×C₄	—	38	1	no	—
102	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
103	C₂²×C₄	#64515	1	1	yes	characteristic
104	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	—	4	1	no	—
108	C₂×C₈	—	4	1	no	—
109	C₂×C₈	—	76	2	no	—
110	C₂×C₈	—	76	1	no	—
111	C₄²	—	2	1	no	—
112	C₄²	—	2	1	no	—
113	C₄²	—	76	1	no	—
114	C₄²	—	76	1	no	—
115	C₁₆	—	8	1	no	—
116	C₁₆	—	152	1	no	—
117	C₂³	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	76	1	no	—
126	C₂×C₄	—	76	1	no	—
127	C₂×C₄	—	76	1	no	—
128	C₂×C₄	—	76	1	no	—
129	C₂×C₄	—	76	1	no	—
130	C₂×C₄	—	76	1	no	—
131	C₂×C₄	#10597263	1	1	yes	characteristic
132	C₂×C₄	#10597281	1	1	yes	characteristic
133	C₈	—	4	1	no	—
134	C₈	—	4	1	no	—
135	C₈	—	152	1	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	#11926269	1	1	yes	characteristic
139	C₂²	#11926327	1	1	yes	characteristic
140	C₂²	#11926329	1	1	yes	characteristic
141	C₄	—	2	1	no	—
142	C₄	—	4	1	no	—
143	C₄	—	4	1	no	—
144	C₄	—	152	1	no	—
145	C₄	—	152	1	no	—
146	C₄	#11926338	1	1	yes	characteristic
147	C₄	#11926340	1	1	yes	characteristic
148	C₂	—	2	1	no	—
149	C₂	—	2	1	no	—
150	C₂	#14561576	1	1	yes	characteristic
151	C₂	#14561578	1	1	yes	characteristic
152	C₂	#14561587	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563754

C₂

yes

maximal, characteristic

#14561575

C₂

yes

maximal, characteristic

C₁₉×#1322

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₄

yes

characteristic

#11926390

C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

#11926298

—

#11926298

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₂²⋊C₁₆

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₁₉⋊#95

C₈

yes

characteristic

C₁₉⋊#95

C₈

yes

characteristic

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7065

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊C₈

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

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1832

—

#1322

—

#1322

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

#376

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

#336

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

D₇₆

yes

characteristic

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₄×D₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

—

#95

—

C₁₉

#7065

yes

characteristic, complemented, Sylow

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₈×D₁₉

yes

characteristic

103

C₂²×C₄

#64515

yes

characteristic

104

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₁₆

—

116

C₁₆

—

152

—

117

C₂³

(C₂×D₁₉)⋊C₈

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

#10597263

yes

characteristic

132

C₂×C₄

#10597281

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

—

152

—

136

C₂²

—

137

C₂²

—

138

C₂²

#11926269

yes

characteristic

139

C₂²

#11926327

yes

characteristic

140

C₂²

#11926329

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

152

—

145

C₄

—

152

—

146

C₄

#11926338

yes

characteristic

147

C₄

#11926340

yes

characteristic

148

C₂

—

149

C₂

—

150

C₂

#14561576

yes

characteristic

151

C₂

#14561578

yes

characteristic

152

C₂

#14561587

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597263
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1322	C₂
socle	C₂²×C₁₉	#324
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1322	D₁₉
hypocenter	C₁₉	#7065
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

subgroup

G/H

center

C₂×C₄

#10597263

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1322

C₂

socle

C₂²×C₁₉

#324

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₁₉×C₄⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

N	H ≅ G/N	type
99. C₁₉	#7065	semidirect

H ≅ G/N

type

99. C₁₉

#7065

semidirect

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

subgroup	index
#14563754	2
#14561575	2
C₁₉×#1322	2
#7065	19

subgroup

index

#14563754

#14561575

C₁₉×#1322

#7065

Subgroups — #18069180

Conjugacy classes of subgroups

Complements

Maximal subgroups