Group #18072965 — subgroups

Subgroups — #18072965

Order 4864.

478 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 243 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	#14563381	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597260	C₂	1	1	yes	maximal, characteristic
3	C₁₉⋊#1273	C₂	1	4	yes	maximal
4	C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597260	C₄	1	2	yes	—
6	C₂×#10597260	C₄	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
9	#11926299	C₄	1	4	yes	—
10	C₂×C₄×C₈×C₁₉	C₄	1	4	yes	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
12	C₄³×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
14	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
20	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
21	C₄×C₈×C₁₉	—	2	8	no	—
22	C₄×C₈×C₁₉	—	2	4	no	—
23	#10597260	—	2	4	no	—
24	#10597260	C₈	1	8	yes	complemented
25	C₄×C₁₉⋊C₈	—	2	4	no	—
26	C₄×C₁₉⋊C₈	—	2	4	no	—
27	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
28	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	—	2	4	no	—
33	C₂×C₈×C₁₉	—	2	4	no	—
34	C₂×C₈×C₁₉	M₁₆	1	8	yes	—
35	C₄²×C₁₉	—	2	4	no	—
36	C₄²×C₁₉	—	2	4	no	—
37	C₄²×C₁₉	C₂×C₈	1	4	yes	—
38	C₄²×C₁₉	M₁₆	1	4	yes	—
39	C₄²×C₁₉	#41	1	4	yes	—
40	C₂×C₁₉⋊C₈	—	2	4	no	—
41	C₂×C₁₉⋊C₈	—	2	4	no	—
42	C₂×C₁₉⋊C₈	—	2	4	no	—
43	C₂×C₁₉⋊C₈	—	2	8	no	—
44	C₂×C₁₉⋊C₈	C₂×C₈	1	8	yes	—
45	#8132	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	C₄×C₈	1	4	yes	—
52	C₂×C₄×C₁₉	#97	1	4	yes	—
53	C₂×C₄×C₁₉	#117	1	2	yes	—
54	C₂×C₄×C₁₉	#117	1	2	yes	—
55	C₂×C₄×C₁₉	#117	1	2	yes	—
56	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
58	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
59	C₂×C₄×C₁₉	#131	1	4	yes	—
60	C₈×C₁₉	—	2	8	no	—
61	C₁₉⋊C₈	—	2	8	no	—
62	C₁₉⋊C₈	—	4	4	no	—
63	#1744	—	19	1	no	—
64	C₄×#97	—	19	1	no	—
65	C₄²×C₈	D₁₉	1	1	yes	characteristic
66	#1273	—	19	4	no	—
67	C₂²×C₁₉	#376	1	1	yes	characteristic
68	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
69	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
70	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
71	C₂²×C₁₉	#405	1	2	yes	—
72	C₄×C₁₉	—	2	4	no	—
73	C₄×C₁₉	—	2	4	no	—
74	C₄×C₁₉	#431	1	4	yes	—
75	C₄×C₁₉	#432	1	4	yes	—
76	C₄×C₁₉	#433	1	4	yes	—
77	C₂×#97	—	19	2	no	—
78	C₂×#97	—	19	2	no	—
79	C₂×C₄×C₈	—	19	2	no	—
80	C₂×C₄×C₈	—	19	2	no	—
81	C₂×C₄×C₈	Dic₁₉	1	4	yes	—
82	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
83	C₄³	C₂×D₁₉	1	1	yes	characteristic
84	#336	—	19	4	no	—
85	C₂×C₁₉	C₈×M₁₆	1	2	yes	—
86	C₂×C₁₉	#1451	1	2	yes	—
87	C₂×C₁₉	#1744	1	1	yes	characteristic
88	C₂×C₁₉	#1745	1	1	yes	characteristic
89	C₂×C₁₉	#1746	1	1	yes	characteristic
90	C₂²×C₈	—	19	4	no	—
91	C₂²×C₈	—	19	4	no	—
92	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
93	C₂×C₄²	C₄×D₁₉	1	2	yes	—
94	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
95	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
96	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
97	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
98	#97	—	19	8	no	—
99	#97	—	38	4	no	—
100	C₄×C₈	—	2	8	no	—
101	C₄×C₈	—	2	4	no	—
102	C₄×C₈	—	38	4	no	—
103	C₄×C₈	—	38	4	no	—
104	C₁₉	#8132	1	1	yes	characteristic, complemented, Sylow
105	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
106	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
107	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
108	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
109	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
110	C₂×C₈	—	2	4	no	—
111	C₂×C₈	—	2	4	no	—
112	C₂×C₈	—	19	8	no	—
113	C₂×C₈	—	38	4	no	—
114	C₂×C₈	—	38	4	no	—
115	C₂×C₈	—	38	4	no	—
116	C₂×C₈	—	38	8	no	—
117	C₂×C₈	#64520	1	8	yes	—
118	C₄²	—	2	4	no	—
119	C₄²	—	2	4	no	—
120	C₄²	C₈×D₁₉	1	4	yes	—
121	C₄²	#64515	1	4	yes	—
122	C₄²	#64541	1	4	yes	—
123	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	C₈×Dic₁₉	1	4	yes	—
129	C₂×C₄	#10597272	1	4	yes	—
130	C₂×C₄	#10597318	1	2	yes	—
131	C₂×C₄	#10597318	1	2	yes	—
132	C₂×C₄	C₂×C₈×D₁₉	1	2	yes	—
133	C₂×C₄	C₂×#64515	1	2	yes	—
134	C₂×C₄	#10597347	1	4	yes	—
135	C₂×C₄	C₂×#64520	1	4	yes	—
136	C₂×C₄	#10597372	1	2	yes	—
137	C₈	—	2	8	no	—
138	C₈	—	38	8	no	—
139	C₈	—	76	4	no	—
140	C₂²	#11926390	1	1	yes	characteristic
141	C₂²	C₂×C₈×Dic₁₉	1	1	yes	characteristic
142	C₂²	C₂×#10597272	1	1	yes	characteristic
143	C₂²	C₄×#64520	1	2	yes	—
144	C₂²	#11926499	1	2	yes	—
145	C₄	—	2	4	no	—
146	C₄	—	2	4	no	—
147	C₄	#11926595	1	4	yes	—
148	C₄	#11926601	1	4	yes	—
149	C₄	#11926603	1	4	yes	—
150	C₂	C₈×#64520	1	2	yes	—
151	C₂	#14561924	1	2	yes	—
152	C₂	#14563380	1	1	yes	characteristic
153	C₂	#14563384	1	1	yes	characteristic
154	C₂	#14563386	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563381

C₂

yes

maximal, characteristic

C₄×#10597260

C₂

yes

maximal, characteristic

C₁₉⋊#1273

C₂

yes

maximal

C₄²×C₈×C₁₉

C₂

yes

maximal, characteristic

C₂×#10597260

C₄

yes

—

C₂×#10597260

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926299

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

#10597260

—

#10597260

C₈

yes

complemented

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₄²

yes

—

C₂²×C₄×C₁₉

C₄²

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

—

C₄²×C₁₉

M₁₆

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₈

yes

—

#8132

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄×C₈

yes

—

C₂×C₄×C₁₉

#97

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

C₂²×C₈

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1744

—

C₄×#97

—

C₄²×C₈

D₁₉

yes

characteristic

#1273

—

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

C₂×C₄×C₈

yes

characteristic

C₂²×C₁₉

C₂×#97

yes

characteristic

C₂²×C₁₉

C₄×M₁₆

yes

—

C₂²×C₁₉

#405

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#431

yes

—

C₄×C₁₉

#432

yes

—

C₄×C₁₉

#433

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

Dic₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

C₂×D₁₉

yes

characteristic

#336

—

C₂×C₁₉

C₈×M₁₆

yes

—

C₂×C₁₉

#1451

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

C₄×D₁₉

yes

characteristic

C₂×C₄²

C₄×D₁₉

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#97

—

#97

—

100

C₄×C₈

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₁₉

#8132

yes

characteristic, complemented, Sylow

105

C₂²×C₄

C₄×Dic₁₉

yes

—

106

C₂²×C₄

C₄×Dic₁₉

yes

—

107

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

108

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

109

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

#64520

yes

—

118

C₄²

—

119

C₄²

—

120

C₄²

C₈×D₁₉

yes

—

121

C₄²

#64515

yes

—

122

C₄²

#64541

yes

—

123

C₂³

C₂×C₄×Dic₁₉

yes

characteristic

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₈×Dic₁₉

yes

—

129

C₂×C₄

#10597272

yes

—

130

C₂×C₄

#10597318

yes

—

131

C₂×C₄

#10597318

yes

—

132

C₂×C₄

C₂×C₈×D₁₉

yes

—

133

C₂×C₄

C₂×#64515

yes

—

134

C₂×C₄

#10597347

yes

—

135

C₂×C₄

C₂×#64520

yes

—

136

C₂×C₄

#10597372

yes

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₂²

#11926390

yes

characteristic

141

C₂²

C₂×C₈×Dic₁₉

yes

characteristic

142

C₂²

C₂×#10597272

yes

characteristic

143

C₂²

C₄×#64520

yes

—

144

C₂²

#11926499

yes

—

145

C₄

—

146

C₄

—

147

C₄

#11926595

yes

—

148

C₄

#11926601

yes

—

149

C₄

#11926603

yes

—

150

C₂

C₈×#64520

yes

—

151

C₂

#14561924

yes

—

152

C₂

#14563380

yes

characteristic

153

C₂

#14563384

yes

characteristic

154

C₂

#14563386

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄×C₈
Fitting	C₄²×C₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄²×C₈	D₁₉
hypocenter	C₁₉	#8132
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₄²×C₈

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₉

commutator

C₂²×C₁₉

C₂×C₄×C₈

Fitting

C₄²×C₈×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄²

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄²×C₈

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄² ◁ C₄²×C₈

N	H ≅ G/N	type
24. #10597260	C₈	semidirect
104. C₁₉	#8132	semidirect

H ≅ G/N

type

24. #10597260

C₈

semidirect

104. C₁₉

#8132

semidirect

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

subgroup	index
#14563381	2
C₄×#10597260	2
C₁₉⋊#1273	2
C₄²×C₈×C₁₉	2
#8132	19

subgroup

index

#14563381

C₄×#10597260

C₁₉⋊#1273

C₄²×C₈×C₁₉

#8132

Subgroups — #18072965

Conjugacy classes of subgroups

Complements

Maximal subgroups