Group #18072969 — subgroups

Subgroups — #18072969

Order 4864.

446 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 227 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	C₄²×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₉⋊#1273	C₂	1	4	yes	maximal
4	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₁₉⋊C₈	C₄	1	2	yes	—
6	C₂×C₄×C₁₉⋊C₈	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	C₂²	1	2	yes	—
11	C₄³×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#336	C₄	1	4	yes	—
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	4	no	—
22	C₄×C₁₉⋊C₈	—	2	4	no	—
23	C₄×C₁₉⋊C₈	—	2	4	no	—
24	C₄×C₁₉⋊C₈	—	2	4	no	—
25	C₄×C₁₉⋊C₈	C₈	1	8	yes	complemented
26	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
27	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	—	2	4	no	—
32	C₂×C₈×C₁₉	—	2	8	no	—
33	C₄²×C₁₉	—	2	4	no	—
34	C₄²×C₁₉	—	2	4	no	—
35	C₄²×C₁₉	C₂×C₈	1	4	yes	—
36	C₄²×C₁₉	M₁₆	1	4	yes	—
37	C₄²×C₁₉	#41	1	4	yes	—
38	C₂×C₁₉⋊C₈	—	2	4	no	—
39	C₂×C₁₉⋊C₈	—	2	4	no	—
40	C₂×C₁₉⋊C₈	—	2	4	no	—
41	C₂×C₁₉⋊C₈	—	2	8	no	—
42	C₂×C₁₉⋊C₈	C₂×C₈	1	8	yes	—
43	#8133	—	19	1	no	maximal, Sylow
44	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	C₄×C₈	1	4	yes	—
50	C₂×C₄×C₁₉	#97	1	4	yes	—
51	C₂×C₄×C₁₉	#117	1	2	yes	—
52	C₂×C₄×C₁₉	#117	1	2	yes	—
53	C₂×C₄×C₁₉	#117	1	2	yes	—
54	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
55	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
56	C₂×C₄×C₁₉	#131	1	4	yes	—
57	C₂×C₄×C₁₉	#131	1	4	yes	—
58	C₈×C₁₉	—	4	4	no	—
59	C₁₉⋊C₈	—	2	8	no	—
60	C₁₉⋊C₈	—	4	4	no	—
61	#1744	—	19	1	no	—
62	#1744	D₁₉	1	1	yes	characteristic
63	C₄²×C₈	—	19	1	no	—
64	#1273	—	19	4	no	—
65	C₂²×C₁₉	#376	1	1	yes	characteristic
66	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
67	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
68	C₂²×C₁₉	#405	1	2	yes	—
69	C₂²×C₁₉	#405	1	2	yes	—
70	C₄×C₁₉	—	2	4	no	—
71	C₄×C₁₉	—	2	4	no	—
72	C₄×C₁₉	#431	1	4	yes	—
73	C₄×C₁₉	#433	1	4	yes	—
74	C₄×C₁₉	#433	1	4	yes	—
75	C₂×C₄×C₈	—	19	2	no	—
76	C₂×C₄×C₈	—	19	2	no	—
77	C₂×C₄×C₈	—	19	2	no	—
78	C₂×C₄×C₈	—	19	2	no	—
79	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
80	C₄³	C₂×D₁₉	1	1	yes	characteristic
81	#336	—	19	4	no	—
82	#336	Dic₁₉	1	4	yes	—
83	C₂×C₁₉	#1450	1	2	yes	—
84	C₂×C₁₉	#1452	1	2	yes	—
85	C₂×C₁₉	#1744	1	1	yes	characteristic
86	C₂×C₁₉	#1746	1	1	yes	characteristic
87	C₂×C₁₉	#1746	1	1	yes	characteristic
88	C₂²×C₈	—	19	4	no	—
89	C₂²×C₈	—	19	4	no	—
90	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
91	C₂×C₄²	C₄×D₁₉	1	2	yes	—
92	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
93	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
94	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
95	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
96	C₄×C₈	—	2	4	no	—
97	C₄×C₈	—	19	8	no	—
98	C₄×C₈	—	38	4	no	—
99	C₄×C₈	—	38	4	no	—
100	C₄×C₈	—	38	4	no	—
101	C₁₉	#8133	1	1	yes	characteristic, complemented, Sylow
102	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
103	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
104	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
105	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
106	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
107	C₂×C₈	—	2	8	no	—
108	C₂×C₈	—	2	4	no	—
109	C₂×C₈	—	19	8	no	—
110	C₂×C₈	—	38	4	no	—
111	C₂×C₈	—	38	4	no	—
112	C₂×C₈	—	38	4	no	—
113	C₂×C₈	—	38	8	no	—
114	C₄²	—	2	4	no	—
115	C₄²	—	2	4	no	—
116	C₄²	C₈×D₁₉	1	4	yes	—
117	C₄²	#64515	1	4	yes	—
118	C₄²	#64541	1	4	yes	—
119	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	C₈×Dic₁₉	1	4	yes	—
125	C₂×C₄	#10597272	1	4	yes	—
126	C₂×C₄	#10597318	1	2	yes	—
127	C₂×C₄	#10597318	1	2	yes	—
128	C₂×C₄	C₂×C₈×D₁₉	1	2	yes	—
129	C₂×C₄	C₂×#64515	1	2	yes	—
130	C₂×C₄	#10597353	1	4	yes	—
131	C₂×C₄	#10597372	1	2	yes	—
132	C₂×C₄	#10597394	1	4	yes	—
133	C₈	—	4	4	no	—
134	C₈	—	38	8	no	—
135	C₈	—	76	4	no	—
136	C₂²	#11926390	1	1	yes	characteristic
137	C₂²	C₂×C₈×Dic₁₉	1	1	yes	characteristic
138	C₂²	C₂×#10597272	1	1	yes	characteristic
139	C₂²	#11926500	1	2	yes	—
140	C₂²	#11926502	1	2	yes	—
141	C₄	—	2	4	no	—
142	C₄	—	2	4	no	—
143	C₄	#11926595	1	4	yes	—
144	C₄	#11926605	1	4	yes	—
145	C₄	#11926606	1	4	yes	—
146	C₂	#14561919	1	2	yes	—
147	C₂	#14561928	1	2	yes	—
148	C₂	#14563380	1	1	yes	characteristic
149	C₂	#14563387	1	1	yes	characteristic
150	C₂	#14563388	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563381

C₂

yes

maximal, characteristic

C₄²×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₁₉⋊#1273

C₂

yes

maximal

C₁₉×#1744

C₂

yes

maximal, characteristic

C₂×C₄×C₁₉⋊C₈

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926299

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

C₄

yes

—

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×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₈

yes

complemented

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

—

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

—

#8133

—

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

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1744

—

#1744

D₁₉

yes

characteristic

C₄²×C₈

—

#1273

—

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

C₂×C₄×C₈

yes

characteristic

C₂²×C₁₉

C₂×#97

yes

characteristic

C₂²×C₁₉

#405

yes

—

C₂²×C₁₉

#405

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#431

yes

—

C₄×C₁₉

#433

yes

—

C₄×C₁₉

#433

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

C₂×D₁₉

yes

characteristic

#336

—

#336

Dic₁₉

yes

—

C₂×C₁₉

#1450

yes

—

C₂×C₁₉

#1452

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

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

—

101

C₁₉

#8133

yes

characteristic, complemented, Sylow

102

C₂²×C₄

C₄×Dic₁₉

yes

—

103

C₂²×C₄

C₄×Dic₁₉

yes

—

104

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

105

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

106

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄²

—

115

C₄²

—

116

C₄²

C₈×D₁₉

yes

—

117

C₄²

#64515

yes

—

118

C₄²

#64541

yes

—

119

C₂³

C₂×C₄×Dic₁₉

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

C₈×Dic₁₉

yes

—

125

C₂×C₄

#10597272

yes

—

126

C₂×C₄

#10597318

yes

—

127

C₂×C₄

#10597318

yes

—

128

C₂×C₄

C₂×C₈×D₁₉

yes

—

129

C₂×C₄

C₂×#64515

yes

—

130

C₂×C₄

#10597353

yes

—

131

C₂×C₄

#10597372

yes

—

132

C₂×C₄

#10597394

yes

—

133

C₈

—

134

C₈

—

135

C₈

—

136

C₂²

#11926390

yes

characteristic

137

C₂²

C₂×C₈×Dic₁₉

yes

characteristic

138

C₂²

C₂×#10597272

yes

characteristic

139

C₂²

#11926500

yes

—

140

C₂²

#11926502

yes

—

141

C₄

—

142

C₄

—

143

C₄

#11926595

yes

—

144

C₄

#11926605

yes

—

145

C₄

#11926606

yes

—

146

C₂

#14561919

yes

—

147

C₂

#14561928

yes

—

148

C₂

#14563380

yes

characteristic

149

C₂

#14563387

yes

characteristic

150

C₂

#14563388

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄×C₈
Fitting	C₁₉×#1744	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#8133
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ #1744

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₉

commutator

C₂²×C₁₉

C₂×C₄×C₈

Fitting

C₁₉×#1744

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄² ◁ #1744

N	H ≅ G/N	type
25. C₄×C₁₉⋊C₈	C₈	semidirect
101. C₁₉	#8133	semidirect

H ≅ G/N

type

25. C₄×C₁₉⋊C₈

C₈

semidirect

101. C₁₉

#8133

semidirect

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

subgroup	index
#14563381	2
C₄²×C₁₉⋊C₈	2
C₁₉⋊#1273	2
C₁₉×#1744	2
#8133	19

subgroup

index

#14563381

C₄²×C₁₉⋊C₈

C₁₉⋊#1273

C₁₉×#1744

#8133

Subgroups — #18072969

Conjugacy classes of subgroups

Complements

Maximal subgroups