Group #14562506 — subgroups

Subgroups — #14562506

Order 2432.

152 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 65 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	#11926674	C₂	1	1	yes	maximal, characteristic
2	C₄×#64528	C₂	1	1	yes	maximal, characteristic
3	#11926294	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	#11926274	C₂	1	1	yes	maximal, characteristic
6	#11926266	C₂	1	1	yes	maximal, characteristic
7	C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×#64528	C₄	1	1	yes	characteristic
10	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₁₉×C₄⋊C₈	—	2	1	no	—
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₁₉	—	2	1	no	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	#10597292	C₄	1	1	yes	characteristic
16	#10597272	—	2	1	no	—
17	Dic₁₉⋊C₈	—	2	1	no	—
18	#10597267	C₄	1	1	yes	characteristic
19	#10597264	C₄	1	1	yes	characteristic
20	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₁₉	—	2	1	no	—
31	C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	#64528	—	2	2	no	—
33	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
34	Dic₁₉⋊C₄	—	2	1	no	—
35	C₄×Dic₁₉	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	1	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
40	Q₈×C₁₉	—	2	1	no	—
41	Q₈×C₁₉	M₁₆	1	2	yes	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₂×Dic₁₉	—	2	1	no	—
48	C₂×Dic₁₉	—	2	1	no	—
49	Dic₃₈	—	2	1	no	—
50	Dic₃₈	—	2	1	no	—
51	C₈×C₁₉	—	2	1	no	—
52	C₈×C₁₉	—	2	1	no	—
53	C₈×C₁₉	—	4	1	no	—
54	C₁₉⋊C₈	—	2	2	no	—
55	C₁₉⋊C₈	—	2	1	no	—
56	C₁₉⋊C₈	—	2	1	no	—
57	C₁₉⋊C₈	—	4	1	no	—
58	#1587	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
60	C₄×C₁₉	—	2	2	no	—
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	4	1	no	—
63	C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
64	C₄×C₁₉	#131	1	1	yes	characteristic
65	C₄×C₁₉	#137	1	1	yes	characteristic
66	C₄×C₁₉	#137	1	1	yes	characteristic
67	Dic₁₉	—	4	1	no	—
68	Dic₁₉	—	4	1	no	—
69	#446	—	19	1	no	—
70	C₈×Q₈	D₁₉	1	1	yes	characteristic
71	C₄×Q₁₆	—	19	1	no	—
72	#334	—	19	1	no	—
73	Q₈⋊C₈	—	19	1	no	—
74	Q₈⋊C₈	—	19	1	no	—
75	#322	—	19	1	no	—
76	C₂×C₁₉	#435	1	1	yes	characteristic
77	C₂×C₁₉	#441	1	1	yes	characteristic
78	C₂×C₁₉	#443	1	1	yes	characteristic
79	C₂×Q₁₆	—	19	1	no	—
80	C₄×Q₈	—	19	1	no	—
81	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
82	#107	—	19	1	no	—
83	C₄⋊C₈	—	2	1	no	—
84	C₄⋊C₈	—	19	1	no	—
85	C₄⋊C₈	—	38	1	no	—
86	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
87	#103	—	19	1	no	—
88	#103	—	19	1	no	—
89	#97	—	38	1	no	—
90	C₄×C₈	—	2	1	no	—
91	C₄×C₈	—	19	1	no	—
92	C₄×C₈	—	19	1	no	—
93	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
94	C₁₉	#1587	1	1	yes	characteristic, complemented, Sylow
95	C₂×Q₈	—	19	1	no	—
96	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
97	Q₁₆	—	38	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	19	1	no	—
100	C₂×C₈	—	19	1	no	—
101	C₂×C₈	—	38	1	no	—
102	C₂×C₈	—	38	1	no	—
103	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
104	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	19	1	no	—
107	C₄⋊C₄	—	38	1	no	—
108	C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
109	C₄²	—	2	1	no	—
110	C₄²	—	38	1	no	—
111	C₄²	C₂²×D₁₉	1	1	yes	characteristic
112	Q₈	—	2	1	no	—
113	Q₈	—	38	1	no	—
114	Q₈	—	38	1	no	—
115	Q₈	#64515	1	2	yes	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	38	1	no	—
119	C₂×C₄	—	38	1	no	—
120	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
121	C₂×C₄	#64541	1	1	yes	characteristic
122	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	2	1	no	—
125	C₈	—	4	1	no	—
126	C₈	—	38	2	no	—
127	C₈	—	38	1	no	—
128	C₈	—	38	1	no	—
129	C₈	—	76	1	no	—
130	C₂²	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	2	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	76	1	no	—
135	C₄	—	76	1	no	—
136	C₄	C₂×#64515	1	1	yes	characteristic
137	C₄	#10597347	1	1	yes	characteristic
138	C₄	#10597388	1	1	yes	characteristic
139	C₄	#10597397	1	1	yes	characteristic
140	C₂	#11926615	1	1	yes	characteristic
141	C₂	#11926649	1	1	yes	characteristic
142	C₂	#11926659	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926674

C₂

yes

maximal, characteristic

C₄×#64528

C₂

yes

maximal, characteristic

#11926294

C₂

yes

maximal, characteristic

Q₈⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

#11926274

C₂

yes

maximal, characteristic

#11926266

C₂

yes

maximal, characteristic

C₈×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×#64528

C₄

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597292

C₄

yes

characteristic

#10597272

—

Dic₁₉⋊C₈

—

#10597267

C₄

yes

characteristic

#10597264

C₄

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×Dic₃₈

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

C₄⋊Dic₁₉

C₂×C₄

yes

characteristic

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1587

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×M₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

#446

—

C₈×Q₈

D₁₉

yes

characteristic

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

Q₈⋊C₈

—

#322

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄×Q₈

—

C₄×Q₈

C₂×D₁₉

yes

characteristic

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1587

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₄×D₁₉

yes

characteristic

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

104

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

C₄×D₁₉

yes

characteristic

109

C₄²

—

110

C₄²

—

111

C₄²

C₂²×D₁₉

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

#64515

yes

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

121

C₂×C₄

#64541

yes

characteristic

122

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₂²

C₄×C₂²⋊D₁₉

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

C₂×#64515

yes

characteristic

137

C₄

#10597347

yes

characteristic

138

C₄

#10597388

yes

characteristic

139

C₄

#10597397

yes

characteristic

140

C₂

#11926615

yes

characteristic

141

C₂

#11926649

yes

characteristic

142

C₂

#11926659

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting	C₈×Q₈×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₄×D₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	C₈×Q₈	D₁₉
hypocenter	C₁₉	#1587
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₈

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting

C₈×Q₈×C₁₉

C₂

socle, prime radical

C₂²×C₁₉

C₄×D₄

cosocle

C₄²×C₁₉

C₂³

hypercenter

C₈×Q₈

D₁₉

hypocenter

C₁₉

#1587

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₈

N	H ≅ G/N	type
94. C₁₉	#1587	semidirect

H ≅ G/N

type

94. C₁₉

#1587

semidirect

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

subgroup	index
#11926674	2
C₄×#64528	2
#11926294	2
Q₈⋊(C₁₉⋊C₈)	2
#11926274	2
#11926266	2
C₈×Q₈×C₁₉	2
#1587	19

subgroup

index

Q₈⋊(C₁₉⋊C₈)

C₈×Q₈×C₁₉

Subgroups — #14562506

Conjugacy classes of subgroups

Complements

Maximal subgroups