Group #18076242 — subgroups

Subgroups — #18076242

Order 4864.

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

normal subgroups only

This group has 270 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	#14563799	C₂	1	1	yes	maximal, characteristic
2	#14563773	C₂	1	1	yes	maximal, characteristic
3	#14561494	C₂	1	2	yes	maximal
4	#14561494	C₂	1	2	yes	maximal
5	C₁₉×#1452	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597275	—	2	1	no	—
7	C₂×#10597274	—	2	1	no	—
8	#11926568	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	#11926410	C₂²	1	2	yes	—
11	#11926309	—	2	1	no	—
12	#11926309	—	2	1	no	—
13	C₁₉×#431	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#322	C₄	1	4	yes	complemented
16	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₉	—	2	2	no	—
20	C₂×#64520	—	2	1	no	—
21	C₂×#64520	—	2	1	no	—
22	C₁₉×C₄⋊C₈	—	2	2	no	—
23	C₁₉×C₂²⋊C₈	—	2	2	no	—
24	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
25	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₁₉	Q₈	1	2	yes	—
27	C₁₉⋊#95	—	2	4	no	—
28	#10597275	—	4	2	no	—
29	#10597274	—	4	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	#41	1	2	yes	—
34	C₂²×Dic₁₉	—	4	2	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	—	2	1	no	—
39	C₂×C₈×C₁₉	—	2	4	no	—
40	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
41	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
42	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
44	C₄²×C₁₉	#41	1	2	yes	—
45	C₄⋊Dic₁₉	—	4	2	no	—
46	C₄⋊Dic₁₉	—	4	2	no	—
47	#64520	—	4	1	no	—
48	#64520	—	4	1	no	—
49	#64520	—	4	1	no	—
50	#64520	—	4	1	no	—
51	C₂×C₁₉⋊C₈	—	4	1	no	—
52	C₂×C₁₉⋊C₈	—	4	1	no	—
53	#8795	—	19	1	no	maximal, Sylow
54	C₂³×C₁₉	#124	1	1	yes	characteristic
55	C₂×C₄×C₁₉	—	4	2	no	—
56	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#117	1	2	yes	—
58	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#125	1	2	yes	—
60	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
61	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
64	C₂×Dic₁₉	—	8	4	no	—
65	C₂×Dic₁₉	—	8	2	no	—
66	C₈×C₁₉	—	2	2	no	—
67	C₈×C₁₉	—	2	2	no	—
68	C₈×C₁₉	—	4	4	no	—
69	C₁₉⋊C₈	—	8	1	no	—
70	C₁₉⋊C₈	—	8	1	no	—
71	#1846	—	19	1	no	—
72	#1837	—	19	1	no	—
73	#1452	D₁₉	1	1	yes	characteristic
74	#1286	—	19	2	no	—
75	#1286	—	19	2	no	—
76	C₂²×C₁₉	—	2	2	no	—
77	C₂²×C₁₉	#382	1	1	yes	characteristic
78	C₂²×C₁₉	#490	1	1	yes	characteristic
79	C₂²×C₁₉	#491	1	1	yes	characteristic
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	2	2	no	—
82	C₄×C₁₉	#428	1	1	yes	characteristic
83	C₄×C₁₉	#428	1	1	yes	characteristic
84	C₄×C₁₉	#489	1	1	yes	characteristic
85	C₄×C₁₉	#489	1	1	yes	characteristic
86	Dic₁₉	—	16	2	no	—
87	#431	C₂×D₁₉	1	2	yes	—
88	C₂×#107	—	38	1	no	—
89	C₂×#106	—	38	1	no	—
90	#423	—	19	1	no	—
91	#423	—	19	1	no	—
92	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
93	#382	—	19	2	no	—
94	#341	—	38	1	no	—
95	#341	—	38	1	no	—
96	#322	Dic₁₉	1	4	yes	complemented
97	C₂×C₁₉	—	2	1	no	—
98	C₂×C₁₉	—	2	1	no	—
99	C₂×C₁₉	#1833	1	2	yes	—
100	C₂×C₁₉	#1836	1	1	yes	characteristic
101	C₂×M₁₆	—	38	1	no	—
102	C₂×M₁₆	—	38	1	no	—
103	C₂²×C₈	D₇₆	1	1	yes	characteristic
104	C₂²×C₈	D₇₆	1	1	yes	characteristic
105	C₂×C₄⋊C₄	—	38	2	no	—
106	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
107	#107	—	76	2	no	—
108	#106	—	76	2	no	—
109	C₄⋊C₈	—	2	2	no	—
110	C₄⋊C₈	—	38	2	no	—
111	C₄⋊C₈	—	38	2	no	—
112	C₂²⋊C₈	—	2	2	no	—
113	C₄×C₈	Dic₃₈	1	2	yes	—
114	C₄×C₈	C₂×Dic₁₉	1	4	yes	—
115	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
116	#95	—	38	4	no	—
117	C₁₉	#8795	1	1	yes	characteristic, complemented, Sylow
118	C₂²×C₄	—	76	2	no	—
119	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
120	C₂²×C₄	#64541	1	2	yes	—
121	M₁₆	—	76	1	no	—
122	M₁₆	—	76	1	no	—
123	M₁₆	—	76	1	no	—
124	M₁₆	—	76	1	no	—
125	C₂×C₈	—	2	1	no	—
126	C₂×C₈	—	2	1	no	—
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	2	1	no	—
129	C₂×C₈	—	2	4	no	—
130	C₂×C₈	—	76	1	no	—
131	C₂×C₈	—	76	1	no	—
132	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
133	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
134	C₄⋊C₄	—	76	2	no	—
135	C₄⋊C₄	—	76	2	no	—
136	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
137	C₄²	#64541	1	2	yes	—
138	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
139	C₂³	#10597321	1	1	yes	characteristic
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	152	4	no	—
142	C₂×C₄	—	152	2	no	—
143	C₂×C₄	#10597316	1	2	yes	—
144	C₂×C₄	#10597321	1	1	yes	characteristic
145	C₂×C₄	#10597354	1	1	yes	characteristic
146	C₂×C₄	#10597354	1	1	yes	characteristic
147	C₂×C₄	#10597355	1	1	yes	characteristic
148	C₂×C₄	#10597355	1	1	yes	characteristic
149	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
150	C₂×C₄	#10597372	1	2	yes	—
151	C₈	—	2	2	no	—
152	C₈	—	2	2	no	—
153	C₈	—	4	4	no	—
154	C₈	—	152	1	no	—
155	C₈	—	152	1	no	—
156	C₂²	—	2	2	no	—
157	C₂²	#11926410	1	1	yes	characteristic
158	C₂²	#11926909	1	1	yes	characteristic
159	C₂²	#11926913	1	1	yes	characteristic
160	C₄	—	2	2	no	—
161	C₄	—	2	2	no	—
162	C₄	—	304	2	no	—
163	C₄	#11926586	1	1	yes	characteristic
164	C₄	#11926586	1	1	yes	characteristic
165	C₄	#11926904	1	1	yes	characteristic
166	C₄	#11926904	1	1	yes	characteristic
167	C₂	—	2	1	no	—
168	C₂	—	2	1	no	—
169	C₂	#14563759	1	2	yes	—
170	C₂	#14563769	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563799

C₂

yes

maximal, characteristic

#14563773

C₂

yes

maximal, characteristic

#14561494

C₂

yes

maximal

#14561494

C₂

yes

maximal

C₁₉×#1452

C₂

yes

maximal, characteristic

C₂×#10597275

—

C₂×#10597274

—

#11926568

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

#11926410

C₂²

yes

—

#11926309

—

#11926309

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

C₄

yes

complemented

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×#64520

—

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₁₉⋊#95

—

#10597275

—

#10597274

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1846

—

#1837

—

#1452

D₁₉

yes

characteristic

#1286

—

#1286

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#431

C₂×D₁₉

yes

—

—

—

—

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

Dic₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1833

yes

—

100

C₂×C₁₉

#1836

yes

characteristic

101

C₂×M₁₆

—

102

C₂×M₁₆

—

103

C₂²×C₈

D₇₆

yes

characteristic

104

C₂²×C₈

D₇₆

yes

characteristic

105

C₂×C₄⋊C₄

—

106

C₂×C₄²

C₂²×D₁₉

yes

characteristic

107

#107

—

108

#106

—

109

C₄⋊C₈

—

110

C₄⋊C₈

—

111

C₄⋊C₈

—

112

C₂²⋊C₈

—

113

C₄×C₈

Dic₃₈

yes

—

114

C₄×C₈

C₂×Dic₁₉

yes

—

115

C₄×C₈

C₂×Dic₁₉

yes

—

116

#95

—

117

C₁₉

#8795

yes

characteristic, complemented, Sylow

118

C₂²×C₄

—

119

C₂²×C₄

C₂×D₇₆

yes

characteristic

120

C₂²×C₄

#64541

yes

—

121

M₁₆

—

122

M₁₆

—

123

M₁₆

—

124

M₁₆

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

C₄⋊Dic₁₉

yes

—

133

C₂×C₈

C₄⋊Dic₁₉

yes

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄²

C₂×Dic₃₈

yes

characteristic

137

C₄²

#64541

yes

—

138

C₄²

C₂²×Dic₁₉

yes

characteristic

139

C₂³

#10597321

yes

characteristic

140

C₂×C₄

—

141

C₂×C₄

—

152

—

142

C₂×C₄

—

152

—

143

C₂×C₄

#10597316

yes

—

144

C₂×C₄

#10597321

yes

characteristic

145

C₂×C₄

#10597354

yes

characteristic

146

C₂×C₄

#10597354

yes

characteristic

147

C₂×C₄

#10597355

yes

characteristic

148

C₂×C₄

#10597355

yes

characteristic

149

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

150

C₂×C₄

#10597372

yes

—

151

C₈

—

152

C₈

—

153

C₈

—

154

C₈

—

152

—

155

C₈

—

152

—

156

C₂²

—

157

C₂²

#11926410

yes

characteristic

158

C₂²

#11926909

yes

characteristic

159

C₂²

#11926913

yes

characteristic

160

C₄

—

161

C₄

—

162

C₄

—

304

—

163

C₄

#11926586

yes

characteristic

164

C₄

#11926586

yes

characteristic

165

C₄

#11926904

yes

characteristic

166

C₄

#11926904

yes

characteristic

167

C₂

—

168

C₂

—

169

C₂

#14563759

yes

—

170

C₂

#14563769

yes

characteristic

	subgroup	G/H
center	C₂²	#11926410
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1452	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#124
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1452	D₁₉
hypocenter	C₁₉	#8795
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

subgroup

G/H

center

C₂²

#11926410

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1452

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

N	H ≅ G/N	type
15. C₁₉×#322	C₄	semidirect
96. #322	Dic₁₉	semidirect
117. C₁₉	#8795	semidirect

H ≅ G/N

type

15. C₁₉×#322

C₄

semidirect

96. #322

Dic₁₉

semidirect

117. C₁₉

#8795

semidirect

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

subgroup	index
#14563799	2
#14563773	2
#14561494	2
C₁₉×#1452	2
#8795	19

subgroup

index

C₁₉×#1452

Subgroups — #18076242

Conjugacy classes of subgroups

Complements

Maximal subgroups