Group #14565106 — subgroups

Subgroups — #14565106

Order 2432.

230 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10597264	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×#389	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	—	2	1	no	—
11	C₂×C₄⋊Dic₁₉	—	2	1	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
14	C₁₉×#95	—	2	1	no	—
15	#10597264	—	2	4	no	—
16	C₂²×C₄×C₁₉	—	2	1	no	—
17	C₂²×C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₁₉	—	2	2	no	—
22	C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	—	4	2	no	—
25	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
26	C₄²×C₁₉	—	2	2	no	—
27	C₄⋊Dic₁₉	—	2	2	no	—
28	C₄⋊Dic₁₉	—	2	2	no	—
29	C₄⋊Dic₁₉	—	4	2	no	—
30	C₄⋊Dic₁₉	—	4	2	no	—
31	C₂×C₁₉⋊C₈	—	2	2	no	—
32	C₂×C₁₉⋊C₈	—	2	2	no	—
33	C₂×C₁₉⋊C₈	Q₈	1	4	yes	—
34	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	2	1	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	D₈	1	2	yes	—
46	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#41	1	2	yes	—
51	C₂×Dic₁₉	—	4	2	no	—
52	C₂×Dic₁₉	—	4	2	no	—
53	C₂×Dic₁₉	—	4	2	no	—
54	C₁₉⋊C₈	—	2	4	no	—
55	#2083	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	#121	1	1	yes	characteristic
57	C₂²×C₁₉	#123	1	1	yes	characteristic
58	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
59	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
60	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
61	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
62	C₂²×C₁₉	#137	1	1	yes	characteristic
63	C₄×C₁₉	—	2	2	no	—
64	C₄×C₁₉	—	2	2	no	—
65	C₄×C₁₉	—	4	2	no	—
66	C₄×C₁₉	—	8	1	no	—
67	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
68	C₄×C₁₉	#125	1	2	yes	—
69	Dic₁₉	—	8	2	no	—
70	C₂×#107	—	19	2	no	—
71	#389	D₁₉	1	1	yes	characteristic
72	#384	—	19	1	no	—
73	#340	—	19	2	no	—
74	#336	—	19	1	no	—
75	C₂×C₁₉	#398	1	1	yes	characteristic
76	C₂×C₁₉	#459	1	1	yes	characteristic
77	C₂×C₁₉	#462	1	1	yes	characteristic
78	C₂×C₁₉	#480	1	1	yes	characteristic
79	C₂×C₁₉	#484	1	1	yes	characteristic
80	C₂×C₁₉	#500	1	1	yes	characteristic
81	C₂×C₁₉	#501	1	1	yes	characteristic
82	C₂²×C₈	—	19	2	no	—
83	C₂×C₄⋊C₄	—	2	1	no	—
84	C₂×C₄⋊C₄	—	19	2	no	—
85	C₂×C₄⋊C₄	—	38	1	no	—
86	C₂×C₄⋊C₄	—	38	1	no	—
87	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
88	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
89	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
90	#107	—	38	4	no	—
91	#95	—	2	1	no	—
92	C₁₉	#2083	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	38	2	no	—
96	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
97	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
99	C₂×C₈	—	19	4	no	—
100	C₂×C₈	—	38	2	no	—
101	C₂×C₈	—	38	2	no	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	4	2	no	—
105	C₄⋊C₄	—	38	2	no	—
106	C₄⋊C₄	—	38	2	no	—
107	C₄⋊C₄	—	76	2	no	—
108	C₄⋊C₄	—	76	2	no	—
109	C₄⋊C₄	D₇₆	1	2	yes	—
110	C₄²	—	2	2	no	—
111	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	76	2	no	—
123	C₂×C₄	—	76	2	no	—
124	C₂×C₄	—	76	2	no	—
125	C₂×C₄	#64525	1	2	yes	—
126	C₂×C₄	#64528	1	2	yes	—
127	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
128	C₂×C₄	#64541	1	1	yes	characteristic
129	C₂×C₄	#64543	1	2	yes	—
130	C₂×C₄	Q₈×D₁₉	1	2	yes	—
131	C₈	—	38	4	no	—
132	C₂²	#10597376	1	1	yes	characteristic
133	C₂²	C₂×#64525	1	1	yes	characteristic
134	C₂²	#10597381	1	1	yes	characteristic
135	C₂²	C₂×#64528	1	1	yes	characteristic
136	C₂²	#10597390	1	1	yes	characteristic
137	C₂²	#10597395	1	1	yes	characteristic
138	C₂²	#10597397	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	2	2	no	—
141	C₄	—	4	2	no	—
142	C₄	—	8	1	no	—
143	C₄	—	152	2	no	—
144	C₄	#10597335	1	2	yes	—
145	C₄	#10597343	1	2	yes	—
146	C₂	#11926474	1	1	yes	characteristic
147	C₂	#11926739	1	1	yes	characteristic
148	C₂	#11926754	1	1	yes	characteristic
149	C₂	#11926855	1	1	yes	characteristic
150	C₂	#11926877	1	1	yes	characteristic
151	C₂	#11926947	1	1	yes	characteristic
152	C₂	#11926954	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597264

C₂

yes

maximal

#11926414

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

#11926299

C₂

yes

maximal, characteristic

C₁₉×#389

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×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

—

#10597264

—

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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

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

D₈

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#125

yes

—

Dic₁₉

—

C₂×#107

—

#389

D₁₉

yes

—

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

#107

—

#95

—

C₁₉

#2083

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

D₇₆

yes

—

110

C₄²

—

111

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

#64525

yes

—

126

C₂×C₄

#64528

yes

—

127

C₂×C₄

C₂×D₇₆

yes

characteristic

128

C₂×C₄

#64541

yes

characteristic

129

C₂×C₄

#64543

yes

—

130

C₂×C₄

Q₈×D₁₉

yes

—

131

C₈

—

132

C₂²

#10597376

yes

characteristic

133

C₂²

C₂×#64525

yes

characteristic

134

C₂²

#10597381

yes

characteristic

135

C₂²

C₂×#64528

yes

characteristic

136

C₂²

#10597390

yes

characteristic

137

C₂²

#10597395

yes

characteristic

138

C₂²

#10597397

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

152

—

144

C₄

#10597335

yes

—

145

C₄

#10597343

yes

—

146

C₂

#11926474

yes

characteristic

147

C₂

#11926739

yes

characteristic

148

C₂

#11926754

yes

characteristic

149

C₂

#11926855

yes

characteristic

150

C₂

#11926877

yes

characteristic

151

C₂

#11926947

yes

characteristic

152

C₂

#11926954

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#389	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#389	D₁₉
hypocenter	C₁₉	#2083
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#389

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

N	H ≅ G/N	type
92. C₁₉	#2083	semidirect

H ≅ G/N

type

92. C₁₉

#2083

semidirect

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

subgroup	index
C₂×#10597264	2
#11926414	2
#11926306	2
#11926299	2
C₁₉×#389	2
#2083	19

subgroup

index

C₁₉×#389

Subgroups — #14565106

Conjugacy classes of subgroups

Complements

Maximal subgroups