Group #18072986 — subgroups

Subgroups — #18072986

Order 4864.

330 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14563321	C₂	1	1	yes	maximal, characteristic
2	#14561927	C₂	1	1	yes	maximal, characteristic
3	#14561465	C₂	1	2	yes	maximal
4	#14561463	C₂	1	2	yes	maximal
5	C₁₉×#1452	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597260	C₂²	1	1	yes	characteristic
8	C₂×#10597272	C₄	1	2	yes	—
9	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
10	#11926390	C₂²	1	1	yes	characteristic
11	#11926266	C₄	1	4	yes	complemented
12	C₁₉×#431	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#322	C₄	1	4	yes	complemented
15	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
19	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
20	C₁₉×C₄⋊C₈	—	2	2	no	—
21	C₁₉×C₂²⋊C₈	—	2	2	no	—
22	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
23	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₁₉⋊#95	—	2	2	no	—
26	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
27	#10597272	—	2	4	no	—
28	C₈×Dic₁₉	—	2	4	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	#10597260	—	2	2	no	—
31	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
32	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	#41	1	2	yes	—
34	C₂²×Dic₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	—	2	4	no	—
38	C₂×C₈×C₁₉	C₄²	1	2	yes	—
39	C₂×C₈×C₁₉	C₄²	1	2	yes	—
40	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₄²×C₁₉	#41	1	2	yes	—
43	C₄×Dic₁₉	—	2	2	no	—
44	C₄×Dic₁₉	M₁₆	1	4	yes	—
45	C₂×C₁₉⋊C₈	—	2	2	no	—
46	C₂×C₁₉⋊C₈	—	2	2	no	—
47	C₂×C₁₉⋊C₈	—	2	4	no	—
48	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	—
49	#8139	—	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×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#117	1	2	yes	—
54	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#117	1	2	yes	—
56	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
58	C₂×Dic₁₉	—	2	4	no	—
59	C₂×Dic₁₉	—	4	4	no	—
60	C₈×C₁₉	—	2	2	no	—
61	C₈×C₁₉	—	2	2	no	—
62	C₈×C₁₉	—	4	4	no	—
63	C₁₉⋊C₈	—	2	4	no	—
64	C₁₉⋊C₈	—	4	4	no	—
65	#1726	—	19	1	no	—
66	#1452	—	19	1	no	—
67	#1452	D₁₉	1	1	yes	characteristic
68	#1275	—	19	2	no	—
69	#1274	—	19	2	no	—
70	C₂²×C₁₉	—	2	2	no	—
71	C₂²×C₁₉	#376	1	1	yes	characteristic
72	C₂²×C₁₉	#432	1	2	yes	—
73	C₄×C₁₉	—	2	2	no	—
74	C₄×C₁₉	—	2	2	no	—
75	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
76	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
77	C₄×C₁₉	#432	1	2	yes	—
78	Dic₁₉	—	4	4	no	—
79	#431	—	19	2	no	—
80	#431	C₂×D₁₉	1	2	yes	—
81	C₂×#97	—	19	2	no	—
82	C₂×#97	—	19	1	no	—
83	C₂×C₄×C₈	—	19	2	no	—
84	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
85	#376	—	19	1	no	—
86	#322	—	19	4	no	—
87	#322	Dic₁₉	1	4	yes	complemented
88	C₂×C₁₉	—	2	2	no	—
89	C₂×C₁₉	#1745	1	1	yes	characteristic
90	C₂×C₁₉	#1747	1	2	yes	—
91	C₂²×C₈	—	19	2	no	—
92	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
93	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
94	C₂×C₄²	—	19	2	no	—
95	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
96	C₄⋊C₈	—	2	2	no	—
97	C₄⋊C₈	—	38	2	no	—
98	C₂²⋊C₈	—	2	2	no	—
99	C₂²⋊C₈	—	38	2	no	—
100	#97	—	38	4	no	—
101	#97	—	38	2	no	—
102	C₄×C₈	—	19	4	no	—
103	C₄×C₈	—	38	4	no	—
104	C₄×C₈	C₄×D₁₉	1	2	yes	—
105	C₄×C₈	C₂×Dic₁₉	1	4	yes	—
106	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
107	#95	—	38	2	no	—
108	C₁₉	#8139	1	1	yes	characteristic, complemented, Sylow
109	C₂²×C₄	—	38	2	no	—
110	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
111	C₂²×C₄	#64541	1	2	yes	—
112	C₂×C₈	—	2	2	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	19	4	no	—
116	C₂×C₈	—	38	2	no	—
117	C₂×C₈	—	38	2	no	—
118	C₂×C₈	—	38	4	no	—
119	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
120	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
121	C₄²	—	19	4	no	—
122	C₄²	—	38	2	no	—
123	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
124	C₄²	#64541	1	2	yes	—
125	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
126	C₂³	#10597318	1	1	yes	characteristic
127	C₂×C₄	—	4	2	no	—
128	C₂×C₄	—	38	4	no	—
129	C₂×C₄	—	76	4	no	—
130	C₂×C₄	#10597318	1	2	yes	—
131	C₂×C₄	#10597318	1	1	yes	characteristic
132	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
133	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
134	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
135	C₂×C₄	#10597372	1	2	yes	—
136	C₈	—	2	2	no	—
137	C₈	—	2	2	no	—
138	C₈	—	4	4	no	—
139	C₈	—	38	4	no	—
140	C₈	—	76	4	no	—
141	C₂²	—	2	2	no	—
142	C₂²	#11926390	1	1	yes	characteristic
143	C₂²	#11926599	1	2	yes	—
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	76	4	no	—
147	C₄	M₁₆×Dic₁₉	1	1	yes	characteristic
148	C₄	M₁₆×Dic₁₉	1	1	yes	characteristic
149	C₄	#11926599	1	2	yes	—
150	C₂	—	2	2	no	—
151	C₂	#14563383	1	1	yes	characteristic
152	C₂	#14563390	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563321

C₂

yes

maximal, characteristic

#14561927

C₂

yes

maximal, characteristic

#14561465

C₂

yes

maximal

#14561463

C₂

yes

maximal

C₁₉×#1452

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×#10597260

C₂²

yes

characteristic

C₂×#10597272

C₄

yes

—

C₂×C₈×Dic₁₉

C₄

yes

—

#11926390

C₂²

yes

characteristic

#11926266

C₄

yes

complemented

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

C₄

yes

complemented

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597272

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

—

C₂×C₈×C₁₉

C₄²

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

M₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

M₁₆

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1726

—

#1452

—

#1452

D₁₉

yes

characteristic

#1275

—

#1274

—

C₂²×C₁₉

—

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

#432

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×M₁₆

yes

characteristic

C₄×C₁₉

C₄×M₁₆

yes

characteristic

C₄×C₁₉

#432

yes

—

Dic₁₉

—

#431

—

#431

C₂×D₁₉

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

Dic₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

#1745

yes

characteristic

C₂×C₁₉

#1747

yes

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₉

yes

characteristic

C₂²×C₈

C₄×D₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

100

#97

—

101

#97

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

C₄×D₁₉

yes

—

105

C₄×C₈

C₂×Dic₁₉

yes

—

106

C₄×C₈

C₂×Dic₁₉

yes

—

107

#95

—

108

C₁₉

#8139

yes

characteristic, complemented, Sylow

109

C₂²×C₄

—

110

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

111

C₂²×C₄

#64541

yes

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

C₄×Dic₁₉

yes

—

120

C₂×C₈

C₄×Dic₁₉

yes

—

121

C₄²

—

122

C₄²

—

123

C₄²

C₂×C₄×D₁₉

yes

characteristic

124

C₄²

#64541

yes

—

125

C₄²

C₂²×Dic₁₉

yes

characteristic

126

C₂³

#10597318

yes

characteristic

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

#10597318

yes

—

131

C₂×C₄

#10597318

yes

characteristic

132

C₂×C₄

M₁₆×D₁₉

yes

—

133

C₂×C₄

M₁₆×D₁₉

yes

—

134

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

135

C₂×C₄

#10597372

yes

—

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

#11926390

yes

characteristic

143

C₂²

#11926599

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

M₁₆×Dic₁₉

yes

characteristic

148

C₄

M₁₆×Dic₁₉

yes

characteristic

149

C₄

#11926599

yes

—

150

C₂

—

151

C₂

#14563383

yes

characteristic

152

C₂

#14563390

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1452	C₂
socle	C₂²×C₁₉	#376
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1452	D₁₉
hypocenter	C₁₉	#8139
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #1452

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1452

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #1452

N	H ≅ G/N	type
11. #11926266	C₄	semidirect
14. C₁₉×#322	C₄	semidirect
87. #322	Dic₁₉	semidirect
108. C₁₉	#8139	semidirect

H ≅ G/N

type

11. #11926266

C₄

semidirect

14. C₁₉×#322

C₄

semidirect

87. #322

Dic₁₉

semidirect

108. C₁₉

#8139

semidirect

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

subgroup	index
#14563321	2
#14561927	2
#14561465	2
#14561463	2
C₁₉×#1452	2
#8139	19

subgroup

index

C₁₉×#1452

Subgroups — #18072986

Conjugacy classes of subgroups

Complements

Maximal subgroups