Group #18072987 — subgroups

Subgroups — #18072987

Order 4864.

330 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14563323	C₂	1	1	yes	maximal, characteristic
2	#14561928	C₂	1	2	yes	maximal
3	#14561466	C₂	1	1	yes	maximal, characteristic
4	#14561463	C₂	1	2	yes	maximal
5	C₁₉×#1275	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597272	C₄	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
10	#11926390	C₂²	1	1	yes	characteristic
11	#11926266	C₄	1	4	yes	complemented
12	#11926265	C₄	1	4	yes	complemented
13	C₁₉×#431	C₂²	1	2	yes	—
14	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
18	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
20	C₁₉×C₄⋊C₈	—	2	2	no	—
21	C₁₉×C₂²⋊C₈	—	2	2	no	—
22	C₁₉×#97	—	2	2	no	—
23	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
24	C₁₉⋊#95	—	2	1	no	—
25	C₁₉⋊#95	—	2	1	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	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
31	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
36	C₂²×Dic₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	—	2	2	no	—
38	C₂×C₈×C₁₉	—	2	2	no	—
39	C₂×C₈×C₁₉	—	2	4	no	—
40	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
41	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
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	C₄²	1	1	yes	characteristic
49	C₂×C₁₉⋊C₈	C₄²	1	2	yes	—
50	C₂×C₁₉⋊C₈	C₄²	1	1	yes	characteristic
51	#8139	—	19	1	no	maximal, Sylow
52	C₂³×C₁₉	#117	1	1	yes	characteristic
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#117	1	2	yes	—
57	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#117	1	2	yes	—
59	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
61	C₂×Dic₁₉	—	2	4	no	—
62	C₂×Dic₁₉	—	4	2	no	—
63	C₂×Dic₁₉	—	4	2	no	—
64	C₈×C₁₉	—	2	4	no	—
65	C₈×C₁₉	—	4	4	no	—
66	C₁₉⋊C₈	—	2	2	no	—
67	C₁₉⋊C₈	—	2	1	no	—
68	C₁₉⋊C₈	—	2	1	no	—
69	C₁₉⋊C₈	—	4	4	no	—
70	#1726	—	19	1	no	—
71	#1452	—	19	2	no	—
72	#1275	—	19	1	no	—
73	#1275	D₁₉	1	1	yes	characteristic
74	#1274	—	19	2	no	—
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	—	2	1	no	—
77	C₂²×C₁₉	#376	1	1	yes	characteristic
78	C₂²×C₁₉	#432	1	2	yes	—
79	C₄×C₁₉	—	2	2	no	—
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
82	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
83	C₄×C₁₉	#432	1	2	yes	—
84	Dic₁₉	—	4	4	no	—
85	#431	—	19	2	no	—
86	#431	C₂×D₁₉	1	2	yes	—
87	C₂×#97	—	19	2	no	—
88	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
89	C₂×C₄×C₈	—	19	1	no	—
90	C₂×C₄×C₈	—	19	2	no	—
91	#376	—	19	1	no	—
92	#322	—	19	4	no	—
93	#322	—	19	4	no	—
94	C₂×C₁₉	—	2	2	no	—
95	C₂×C₁₉	#1745	1	1	yes	characteristic
96	C₂×C₁₉	#1747	1	1	yes	characteristic
97	C₂×C₁₉	#1747	1	1	yes	characteristic
98	C₂²×C₈	—	19	1	no	—
99	C₂²×C₈	—	19	1	no	—
100	C₂²×C₈	C₄×D₁₉	1	2	yes	—
101	C₂×C₄²	—	19	2	no	—
102	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
103	C₄⋊C₈	—	2	2	no	—
104	C₄⋊C₈	—	38	2	no	—
105	C₂²⋊C₈	—	2	2	no	—
106	C₂²⋊C₈	—	38	2	no	—
107	#97	—	2	2	no	—
108	#97	—	38	4	no	—
109	C₄×C₈	—	19	2	no	—
110	C₄×C₈	—	19	2	no	—
111	C₄×C₈	—	19	4	no	—
112	C₄×C₈	—	38	4	no	—
113	C₄×C₈	C₄×D₁₉	1	4	yes	—
114	#95	—	38	1	no	—
115	#95	—	38	1	no	—
116	C₁₉	#8139	1	1	yes	characteristic, complemented, Sylow
117	C₂²×C₄	—	38	2	no	—
118	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
119	C₂²×C₄	#64543	1	1	yes	characteristic
120	C₂²×C₄	#64545	1	1	yes	characteristic
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	2	2	no	—
123	C₂×C₈	—	2	4	no	—
124	C₂×C₈	—	19	2	no	—
125	C₂×C₈	—	19	1	no	—
126	C₂×C₈	—	19	1	no	—
127	C₂×C₈	—	38	2	no	—
128	C₂×C₈	—	38	2	no	—
129	C₂×C₈	—	38	4	no	—
130	C₂×C₈	#64515	1	4	yes	—
131	C₄²	—	19	4	no	—
132	C₄²	—	38	2	no	—
133	C₄²	C₂×C₄×D₁₉	1	2	yes	—
134	C₄²	#64543	1	2	yes	—
135	C₂³	#10597338	1	1	yes	characteristic
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	—	4	1	no	—
138	C₂×C₄	—	38	4	no	—
139	C₂×C₄	—	76	2	no	—
140	C₂×C₄	—	76	2	no	—
141	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
142	C₂×C₄	#10597323	1	2	yes	—
143	C₂×C₄	#10597323	1	1	yes	characteristic
144	C₂×C₄	#10597338	1	2	yes	—
145	C₂×C₄	C₂×#64515	1	2	yes	—
146	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
147	C₈	—	2	4	no	—
148	C₈	—	4	4	no	—
149	C₈	—	38	2	no	—
150	C₈	—	38	1	no	—
151	C₈	—	38	1	no	—
152	C₈	—	76	4	no	—
153	C₂²	—	2	1	no	—
154	C₂²	—	2	1	no	—
155	C₂²	#11926389	1	1	yes	characteristic
156	C₂²	#11926600	1	2	yes	—
157	C₄	—	2	2	no	—
158	C₄	—	2	2	no	—
159	C₄	—	76	4	no	—
160	C₄	C₄×#64515	1	1	yes	characteristic
161	C₄	#11926496	1	1	yes	characteristic
162	C₄	#11926598	1	2	yes	—
163	C₂	—	2	2	no	—
164	C₂	#14563382	1	1	yes	characteristic
165	C₂	#14563389	1	1	yes	characteristic
166	C₂	#14563391	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563323

C₂

yes

maximal, characteristic

#14561928

C₂

yes

maximal

#14561466

C₂

yes

maximal, characteristic

#14561463

C₂

yes

maximal

C₁₉×#1275

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×#10597272

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₁₉

C₄

yes

—

#11926390

C₂²

yes

characteristic

#11926266

C₄

yes

complemented

#11926265

C₄

yes

complemented

C₁₉×#431

C₂²

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597272

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

M₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄²

yes

characteristic

C₂×C₁₉⋊C₈

C₄²

yes

—

C₂×C₁₉⋊C₈

C₄²

yes

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

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

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

#1274

—

C₂²×C₁₉

—

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×D₁₉

yes

characteristic

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

#322

—

#322

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

—

100

C₂²×C₈

C₄×D₁₉

yes

—

101

C₂×C₄²

—

102

C₂×C₄²

C₂²×D₁₉

yes

characteristic

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₂²⋊C₈

—

106

C₂²⋊C₈

—

107

#97

—

108

#97

—

109

C₄×C₈

—

110

C₄×C₈

—

111

C₄×C₈

—

112

C₄×C₈

—

113

C₄×C₈

C₄×D₁₉

yes

—

114

#95

—

115

#95

—

116

C₁₉

#8139

yes

characteristic, complemented, Sylow

117

C₂²×C₄

—

118

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

119

C₂²×C₄

#64543

yes

characteristic

120

C₂²×C₄

#64545

yes

characteristic

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

#64515

yes

—

131

C₄²

—

132

C₄²

—

133

C₄²

C₂×C₄×D₁₉

yes

—

134

C₄²

#64543

yes

—

135

C₂³

#10597338

yes

characteristic

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

C₄²×D₁₉

yes

characteristic

142

C₂×C₄

#10597323

yes

—

143

C₂×C₄

#10597323

yes

characteristic

144

C₂×C₄

#10597338

yes

—

145

C₂×C₄

C₂×#64515

yes

—

146

C₂×C₄

M₁₆×D₁₉

yes

—

147

C₈

—

148

C₈

—

149

C₈

—

150

C₈

—

151

C₈

—

152

C₈

—

153

C₂²

—

154

C₂²

—

155

C₂²

#11926389

yes

characteristic

156

C₂²

#11926600

yes

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

C₄×#64515

yes

characteristic

161

C₄

#11926496

yes

characteristic

162

C₄

#11926598

yes

—

163

C₂

—

164

C₂

#14563382

yes

characteristic

165

C₂

#14563389

yes

characteristic

166

C₂

#14563391

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄²×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1275	C₂
socle	C₂²×C₁₉	#376
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1275	D₁₉
hypocenter	C₁₉	#8139
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #1275

subgroup

G/H

center

C₂×C₄

C₄²×D₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1275

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #1275

N	H ≅ G/N	type
11. #11926266	C₄	semidirect
12. #11926265	C₄	semidirect
116. C₁₉	#8139	semidirect

H ≅ G/N

type

11. #11926266

C₄

semidirect

12. #11926265

C₄

semidirect

116. C₁₉

#8139

semidirect

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

subgroup	index
#14563323	2
#14561928	2
#14561466	2
#14561463	2
C₁₉×#1275	2
#8139	19

subgroup

index

C₁₉×#1275

Subgroups — #18072987

Conjugacy classes of subgroups

Complements

Maximal subgroups