Group #14565043 — subgroups

Subgroups — #14565043

Order 2432.

238 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 89 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	C₂×#10597292	C₂	1	2	yes	maximal
2	#11926414	C₂	1	1	yes	maximal, characteristic
3	#11926306	C₂	1	2	yes	maximal
4	#11926299	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	—	2	1	no	—
10	C₂×C₄⋊Dic₁₉	—	2	1	no	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
13	C₁₉×#95	—	2	1	no	—
14	C₁₉×#95	—	2	1	no	—
15	#10597292	—	2	4	no	—
16	C₂×Q₈×C₁₉	—	2	1	no	—
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	—	2	2	no	—
19	C₂×Q₈×C₁₉	D₄	1	2	yes	—
20	C₂²×C₄×C₁₉	—	2	1	no	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄²×C₁₉	—	2	2	no	—
28	C₄⋊Dic₁₉	—	2	2	no	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	C₄⋊Dic₁₉	—	4	2	no	—
31	C₄⋊Dic₁₉	—	4	2	no	—
32	C₂×C₁₉⋊C₈	—	2	2	no	—
33	C₂×C₁₉⋊C₈	—	2	2	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
36	Q₈×C₁₉	—	2	4	no	—
37	Q₈×C₁₉	—	4	2	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
49	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#41	1	2	yes	—
53	C₂×C₄×C₁₉	#41	1	2	yes	—
54	C₂×Dic₁₉	—	4	2	no	—
55	C₂×Dic₁₉	—	4	2	no	—
56	C₂×Dic₁₉	—	4	2	no	—
57	C₁₉⋊C₈	—	4	2	no	—
58	#2072	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	#121	1	1	yes	characteristic
60	C₂²×C₁₉	#123	1	1	yes	characteristic
61	C₂²×C₁₉	#124	1	1	yes	characteristic
62	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
63	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
64	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂²×C₁₉	#137	1	1	yes	characteristic
66	C₄×C₁₉	—	2	2	no	—
67	C₄×C₁₉	—	2	2	no	—
68	C₄×C₁₉	—	4	2	no	—
69	C₄×C₁₉	—	8	1	no	—
70	C₄×C₁₉	#123	1	2	yes	—
71	C₄×C₁₉	#126	1	2	yes	—
72	Dic₁₉	—	8	2	no	—
73	C₂×#103	—	19	2	no	—
74	#391	D₁₉	1	1	yes	characteristic
75	#384	—	19	1	no	—
76	#340	—	19	2	no	—
77	#336	—	19	1	no	—
78	C₂×C₁₉	#397	1	1	yes	characteristic
79	C₂×C₁₉	#460	1	1	yes	characteristic
80	C₂×C₁₉	#462	1	1	yes	characteristic
81	C₂×C₁₉	#483	1	1	yes	characteristic
82	C₂×C₁₉	#484	1	1	yes	characteristic
83	C₂×C₁₉	#487	1	1	yes	characteristic
84	C₂×C₁₉	#489	1	1	yes	characteristic
85	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
86	C₂²×C₈	—	19	2	no	—
87	C₂×C₄⋊C₄	—	19	2	no	—
88	C₂×C₄⋊C₄	—	38	1	no	—
89	C₂×C₄⋊C₄	—	38	1	no	—
90	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
91	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
92	#103	—	38	4	no	—
93	#95	—	2	1	no	—
94	#95	—	2	1	no	—
95	C₁₉	#2072	1	1	yes	characteristic, complemented, Sylow
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	2	2	no	—
98	C₂×Q₈	—	2	2	no	—
99	C₂×Q₈	D₇₆	1	2	yes	—
100	C₂²×C₄	—	2	1	no	—
101	C₂²×C₄	—	2	1	no	—
102	C₂²×C₄	—	38	2	no	—
103	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
104	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
106	C₂×C₈	—	38	2	no	—
107	C₂×C₈	—	38	2	no	—
108	C₂×C₈	—	38	2	no	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	38	2	no	—
111	C₄⋊C₄	—	38	2	no	—
112	C₄⋊C₄	—	76	2	no	—
113	C₄⋊C₄	—	76	2	no	—
114	C₄²	—	2	2	no	—
115	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
116	Q₈	—	2	4	no	—
117	Q₈	—	4	2	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	76	2	no	—
129	C₂×C₄	—	76	2	no	—
130	C₂×C₄	—	76	2	no	—
131	C₂×C₄	#64527	1	2	yes	—
132	C₂×C₄	#64528	1	2	yes	—
133	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
134	C₂×C₄	#64541	1	1	yes	characteristic
135	C₂×C₄	#64543	1	2	yes	—
136	C₂×C₄	#64543	1	2	yes	—
137	C₈	—	76	2	no	—
138	C₂²	#10597376	1	1	yes	characteristic
139	C₂²	#10597381	1	1	yes	characteristic
140	C₂²	#10597382	1	1	yes	characteristic
141	C₂²	C₂×#64527	1	1	yes	characteristic
142	C₂²	C₂×#64528	1	1	yes	characteristic
143	C₂²	#10597395	1	1	yes	characteristic
144	C₂²	#10597397	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	4	2	no	—
148	C₄	—	8	1	no	—
149	C₄	—	152	2	no	—
150	C₄	#10597325	1	2	yes	—
151	C₄	#10597332	1	2	yes	—
152	C₂	#11926469	1	1	yes	characteristic
153	C₂	#11926744	1	1	yes	characteristic
154	C₂	#11926754	1	1	yes	characteristic
155	C₂	#11926872	1	1	yes	characteristic
156	C₂	#11926877	1	1	yes	characteristic
157	C₂	#11926894	1	1	yes	characteristic
158	C₂	#11926903	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597292

C₂

yes

maximal

#11926414

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

#11926299

C₂

yes

maximal, characteristic

C₁₉×#391

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉×#95

—

C₁₉×#95

—

#10597292

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#123

yes

—

C₄×C₁₉

#126

yes

—

Dic₁₉

—

C₂×#103

—

#391

D₁₉

yes

—

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#2072

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₇₆

yes

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

104

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

105

C₂²×C₄

C₂²×D₁₉

yes

characteristic

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄²

—

115

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

116

Q₈

—

117

Q₈

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

#64527

yes

—

132

C₂×C₄

#64528

yes

—

133

C₂×C₄

C₂×D₇₆

yes

characteristic

134

C₂×C₄

#64541

yes

characteristic

135

C₂×C₄

#64543

yes

—

136

C₂×C₄

#64543

yes

—

137

C₈

—

138

C₂²

#10597376

yes

characteristic

139

C₂²

#10597381

yes

characteristic

140

C₂²

#10597382

yes

characteristic

141

C₂²

C₂×#64527

yes

characteristic

142

C₂²

C₂×#64528

yes

characteristic

143

C₂²

#10597395

yes

characteristic

144

C₂²

#10597397

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

152

—

150

C₄

#10597325

yes

—

151

C₄

#10597332

yes

—

152

C₂

#11926469

yes

characteristic

153

C₂

#11926744

yes

characteristic

154

C₂

#11926754

yes

characteristic

155

C₂

#11926872

yes

characteristic

156

C₂

#11926877

yes

characteristic

157

C₂

#11926894

yes

characteristic

158

C₂

#11926903

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#391	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2072
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#391

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
95. C₁₉	#2072	semidirect

H ≅ G/N

type

95. C₁₉

#2072

semidirect

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

subgroup	index
C₂×#10597292	2
#11926414	2
#11926306	2
#11926299	2
C₁₉×#391	2
#2072	19

subgroup

index

C₁₉×#391

Subgroups — #14565043

Conjugacy classes of subgroups

Complements

Maximal subgroups