Group #18076007 — subgroups

Subgroups — #18076007

Order 4864.

418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₂×#11926270	C₂	1	2	yes	maximal
2	#14561483	C₂	1	4	yes	maximal
3	C₁₉×#2313	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
5	#11926270	—	2	4	no	—
6	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#387	—	2	4	no	—
8	C₁₉×#381	C₄	1	2	yes	—
9	C₁₉×#380	C₄	1	2	yes	—
10	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
16	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
17	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
18	C₂×C₄²×C₁₉	—	2	2	no	—
19	C₂²×C₁₉⋊C₈	—	2	4	no	—
20	C₁₉×#95	—	2	2	no	—
21	C₁₉×#95	—	2	4	no	—
22	C₁₉×#95	—	2	2	no	—
23	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
24	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
25	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	—	2	2	no	—
27	C₂²×C₄×C₁₉	—	2	4	no	—
28	C₂²×C₄×C₁₉	—	2	2	no	—
29	C₂²×C₄×C₁₉	—	2	4	no	—
30	C₂²×C₄×C₁₉	—	8	1	no	—
31	C₂²×C₄×C₁₉	—	8	1	no	—
32	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂²×C₄×C₁₉	#41	1	4	yes	—
36	C₄⋊C₄×C₁₉	—	2	8	no	—
37	C₄⋊C₄×C₁₉	—	8	2	no	—
38	C₂²⋊C₄×C₁₉	—	2	8	no	—
39	C₄²×C₁₉	—	8	2	no	—
40	C₂×C₁₉⋊C₈	—	4	4	no	—
41	C₂×C₁₉⋊C₈	—	8	4	no	—
42	#8737	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	—	4	1	no	—
44	C₂³×C₁₉	—	4	1	no	—
45	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂³×C₁₉	#117	1	2	yes	—
47	C₂³×C₁₉	#131	1	4	yes	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	4	no	—
51	C₂×C₄×C₁₉	—	4	4	no	—
52	C₂×C₄×C₁₉	—	4	2	no	—
53	C₂×C₄×C₁₉	—	4	4	no	—
54	C₂×C₄×C₁₉	—	4	2	no	—
55	C₂×C₄×C₁₉	—	4	4	no	—
56	C₂×C₄×C₁₉	—	4	4	no	—
57	C₂×C₄×C₁₉	—	4	4	no	—
58	C₂×C₄×C₁₉	—	8	2	no	—
59	C₂×C₄×C₁₉	#123	1	4	yes	—
60	C₁₉⋊C₈	—	8	4	no	—
61	#2313	D₁₉	1	1	yes	characteristic
62	C₂×#324	—	19	2	no	—
63	#1282	—	19	4	no	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	2	2	no	—
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	2	2	no	—
68	C₂²×C₁₉	—	4	4	no	—
69	C₂²×C₁₉	#381	1	1	yes	characteristic
70	C₂²×C₁₉	#408	1	2	yes	—
71	C₂²×C₁₉	#433	1	4	yes	—
72	C₄×C₁₉	—	2	4	no	—
73	C₄×C₁₉	—	4	2	no	—
74	C₄×C₁₉	—	4	2	no	—
75	C₄×C₁₉	—	8	4	no	—
76	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
77	C₂×C₂²⋊C₈	—	19	4	no	—
78	#387	—	2	4	no	—
79	#381	Dic₁₉	1	2	yes	—
80	#380	Dic₁₉	1	2	yes	—
81	C₄×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
82	#324	—	38	4	no	—
83	C₂×C₁₉	—	2	2	no	—
84	C₂×C₁₉	—	2	4	no	—
85	C₂×C₁₉	#1818	1	1	yes	characteristic
86	C₂×C₁₉	#1828	1	1	yes	characteristic
87	C₂×C₁₉	#1830	1	1	yes	characteristic
88	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
89	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
90	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
91	C₂²×C₈	—	38	4	no	—
92	C₂×C₄⋊C₄	—	2	4	no	—
93	C₂×C₄⋊C₄	—	2	2	no	—
94	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	4	yes	—
95	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	4	yes	—
96	C₂×C₄²	—	2	2	no	—
97	C₂²⋊C₈	—	38	4	no	—
98	C₂²⋊C₈	—	38	4	no	—
99	#95	—	2	2	no	—
100	#95	—	2	4	no	—
101	#95	—	2	2	no	—
102	C₁₉	#8737	1	1	yes	characteristic, complemented, Sylow
103	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
104	C₂²×C₄	—	2	4	no	—
105	C₂²×C₄	—	2	2	no	—
106	C₂²×C₄	—	2	2	no	—
107	C₂²×C₄	—	2	4	no	—
108	C₂²×C₄	—	8	1	no	—
109	C₂²×C₄	—	8	1	no	—
110	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
111	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
112	C₂²×C₄	#64541	1	4	yes	—
113	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
114	C₂×C₈	—	76	4	no	—
115	C₂×C₈	—	152	4	no	—
116	C₄⋊C₄	—	2	8	no	—
117	C₄⋊C₄	—	8	2	no	—
118	C₂²⋊C₄	—	2	8	no	—
119	C₄²	—	8	2	no	—
120	C₂³	—	4	1	no	—
121	C₂³	—	4	1	no	—
122	C₂³	#10597372	1	2	yes	—
123	C₂³	#10597394	1	4	yes	—
124	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	4	4	no	—
133	C₂×C₄	—	4	4	no	—
134	C₂×C₄	—	4	4	no	—
135	C₂×C₄	—	8	2	no	—
136	C₂×C₄	#10597375	1	4	yes	—
137	C₈	—	152	4	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	2	no	—
140	C₂²	—	2	1	no	—
141	C₂²	—	2	2	no	—
142	C₂²	—	4	4	no	—
143	C₂²	#11926407	1	1	yes	characteristic
144	C₂²	#11926511	1	2	yes	—
145	C₂²	#11926605	1	4	yes	—
146	C₄	—	2	4	no	—
147	C₄	—	4	2	no	—
148	C₄	—	4	2	no	—
149	C₄	—	8	4	no	—
150	C₂	—	2	2	no	—
151	C₂	—	2	4	no	—
152	C₂	#14563706	1	1	yes	characteristic
153	C₂	#14563743	1	1	yes	characteristic
154	C₂	#14563749	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926270

C₂

yes

maximal

#14561483

C₂

yes

maximal

C₁₉×#2313

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926270

—

C₂²×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₁₉×#387

—

C₁₉×#381

C₄

yes

—

C₁₉×#380

C₄

yes

—

C₄×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8737

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

C₂³×C₁₉

#131

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#123

yes

—

C₁₉⋊C₈

—

#2313

D₁₉

yes

characteristic

C₂×#324

—

#1282

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#381

yes

characteristic

C₂²×C₁₉

#408

yes

—

C₂²×C₁₉

#433

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂²×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₈

—

#387

—

#381

Dic₁₉

yes

—

#380

Dic₁₉

yes

—

C₄×C₂²⋊C₄

C₂×D₁₉

yes

—

#324

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂³×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

C₂×C₄²

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#95

—

100

#95

—

101

#95

—

102

C₁₉

#8737

yes

characteristic, complemented, Sylow

103

C₂⁴

C₂²×Dic₁₉

yes

characteristic

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

111

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

112

C₂²×C₄

#64541

yes

—

113

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

114

C₂×C₈

—

115

C₂×C₈

—

152

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

119

C₄²

—

120

C₂³

—

121

C₂³

—

122

C₂³

#10597372

yes

—

123

C₂³

#10597394

yes

—

124

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#10597375

yes

—

137

C₈

—

152

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#11926407

yes

characteristic

144

C₂²

#11926511

yes

—

145

C₂²

#11926605

yes

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₂

—

151

C₂

—

152

C₂

#14563706

yes

characteristic

153

C₂

#14563743

yes

characteristic

154

C₂

#14563749

yes

characteristic

	subgroup	G/H
center	C₂²	#11926407
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2313	C₂
socle	C₂²×C₁₉	#381
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2313	D₁₉
hypocenter	C₁₉	#8737
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2313

subgroup

G/H

center

C₂²

#11926407

commutator, prime radical

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₁₉×#2313

C₂

socle

C₂²×C₁₉

#381

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2313

N	H ≅ G/N	type
102. C₁₉	#8737	semidirect

H ≅ G/N

type

102. C₁₉

#8737

semidirect

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

subgroup	index
C₂×#11926270	2
#14561483	2
C₁₉×#2313	2
#8737	19

subgroup

index

C₂×#11926270

#14561483

C₁₉×#2313

#8737

Subgroups — #18076007

Conjugacy classes of subgroups

Complements

Maximal subgroups