Group #14565436 — subgroups

Subgroups — #14565436

Order 2432.

152 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₄×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	(C₂×D₁₉)⋊C₁₆	C₂	1	2	yes	maximal
4	#11926320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₁₉	C₄	1	1	yes	characteristic
7	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
8	C₄²×D₁₉	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₈×Dic₁₉	C₄	1	1	yes	characteristic
12	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
14	C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
15	C₂×C₄×D₁₉	C₈	1	1	yes	characteristic
16	C₂×C₄×D₁₉	C₈	1	1	yes	characteristic
17	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
20	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₁₉	C₈	1	1	yes	characteristic
22	C₄×Dic₁₉	C₈	1	1	yes	characteristic
23	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₈×D₁₉	—	2	2	no	—
27	C₈×D₁₉	—	2	2	no	—
28	C₁₆×C₁₉	—	2	2	no	—
29	C₁₉⋊C₁₆	—	2	2	no	—
30	C₂²×D₁₉	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₁₉	C₂×C₈	1	1	yes	characteristic
35	C₂×Dic₁₉	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₁₉	C₂×C₈	1	1	yes	characteristic
37	C₄×D₁₉	—	2	2	no	—
38	C₄×D₁₉	—	2	1	no	—
39	C₄×D₁₉	—	2	1	no	—
40	C₄×D₁₉	—	2	2	no	—
41	C₈×C₁₉	M₁₆	1	2	yes	—
42	C₈×C₁₉	#41	1	2	yes	—
43	C₁₉⋊C₈	—	2	1	no	—
44	C₁₉⋊C₈	—	2	1	no	—
45	#2163	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
47	C₂×D₁₉	—	2	1	no	—
48	C₂×D₁₉	—	2	1	no	—
49	C₂×D₁₉	M₃₂	1	2	yes	—
50	C₄×C₁₉	—	2	1	no	—
51	C₄×C₁₉	—	2	1	no	—
52	C₄×C₁₉	#117	1	1	yes	characteristic
53	C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
54	Dic₁₉	—	2	1	no	—
55	Dic₁₉	—	2	1	no	—
56	Dic₁₉	M₃₂	1	2	yes	—
57	C₂×C₄×C₈	—	19	1	no	—
58	C₄⋊C₁₆	—	19	2	no	—
59	C₂²⋊C₁₆	—	19	2	no	—
60	#346	—	19	1	no	—
61	#346	D₁₉	1	1	yes	characteristic, complemented
62	C₂×C₁₉	#431	1	1	yes	characteristic
63	C₂×C₁₉	C₂×M₃₂	1	1	yes	characteristic
64	C₂×C₁₉	C₂×M₃₂	1	1	yes	characteristic
65	D₁₉	—	2	2	no	—
66	C₂²×C₈	—	19	1	no	—
67	C₂²×C₈	—	19	1	no	—
68	C₂×C₄²	—	19	1	no	—
69	C₂×C₁₆	—	19	2	no	—
70	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
71	C₄×C₈	—	19	1	no	—
72	C₄×C₈	—	19	1	no	—
73	C₄×C₈	—	19	1	no	—
74	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
75	C₁₉	#2163	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₄	—	19	1	no	—
77	C₂²×C₄	—	19	1	no	—
78	C₂²×C₄	—	19	1	no	—
79	C₂×C₈	—	19	1	no	—
80	C₂×C₈	—	19	1	no	—
81	C₂×C₈	—	38	2	no	—
82	C₂×C₈	—	38	2	no	—
83	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
85	C₄²	—	19	1	no	—
86	C₄²	—	19	1	no	—
87	C₄²	—	19	1	no	—
88	C₄²	C₄×D₁₉	1	1	yes	characteristic
89	C₁₆	—	2	2	no	—
90	C₁₆	—	38	2	no	—
91	C₂³	—	19	1	no	—
92	C₂×C₄	—	19	1	no	—
93	C₂×C₄	—	19	1	no	—
94	C₂×C₄	—	19	1	no	—
95	C₂×C₄	—	38	2	no	—
96	C₂×C₄	—	38	2	no	—
97	C₂×C₄	—	38	1	no	—
98	C₂×C₄	—	38	1	no	—
99	C₂×C₄	C₈×D₁₉	1	1	yes	characteristic
100	C₂×C₄	C₈×D₁₉	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
102	C₈	—	38	1	no	—
103	C₈	—	38	1	no	—
104	C₈	#64515	1	2	yes	—
105	C₈	#64541	1	2	yes	—
106	C₂²	—	19	2	no	—
107	C₂²	—	38	1	no	—
108	C₂²	—	38	1	no	—
109	C₂²	C₂×C₈×D₁₉	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	—	19	2	no	—
113	C₄	—	38	1	no	—
114	C₄	—	38	1	no	—
115	C₄	#10597318	1	1	yes	characteristic
116	C₄	C₂×#64515	1	1	yes	characteristic
117	C₂	—	38	2	no	—
118	C₂	#11926595	1	1	yes	characteristic
119	C₂	M₃₂×D₁₉	1	1	yes	characteristic
120	C₂	M₃₂×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×D₁₉

C₂

yes

maximal, characteristic

Dic₁₉⋊C₁₆

C₂

yes

maximal, complemented

(C₂×D₁₉)⋊C₁₆

C₂

yes

maximal

#11926320

C₂

yes

maximal, characteristic, complemented

C₁₉×#346

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₁₉

C₄

yes

characteristic

C₂×C₈×D₁₉

C₂²

yes

characteristic

C₄²×D₁₉

C₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₈×Dic₁₉

C₄

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₄×C₁₉⋊C₈

C₄

yes

characteristic

C₂×C₄×D₁₉

C₈

yes

characteristic

C₂×C₄×D₁₉

C₈

yes

characteristic

C₂×C₄×D₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄×Dic₁₉

C₈

yes

characteristic

C₄×Dic₁₉

C₈

yes

characteristic

C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₈×D₁₉

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂²×D₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×Dic₁₉

C₂×C₈

yes

characteristic

C₂×Dic₁₉

C₂×C₈

yes

characteristic

C₂×Dic₁₉

C₂×C₈

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

M₁₆

yes

—

C₈×C₁₉

#41

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2163

—

maximal, Sylow

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

M₃₂

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₂×M₁₆

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

M₃₂

yes

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#346

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#431

yes

characteristic

C₂×C₁₉

C₂×M₃₂

yes

characteristic

C₂×C₁₉

C₂×M₃₂

yes

characteristic

D₁₉

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2163

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₁₉

yes

characteristic

100

C₂×C₄

C₈×D₁₉

yes

characteristic

101

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

#64515

yes

—

105

C₈

#64541

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×C₈×D₁₉

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

#10597318

yes

characteristic

116

C₄

C₂×#64515

yes

characteristic

117

C₂

—

118

C₂

#11926595

yes

characteristic

119

C₂

M₃₂×D₁₉

yes

characteristic

120

C₂

M₃₂×D₁₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂²×C₈
Fitting	C₁₉×#346	C₂
prime radical	C₂²×D₁₉	C₂×C₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	#346	D₁₉
hypocenter	C₁₉	#2163
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₉

commutator, socle

C₂²×C₁₉

C₂²×C₈

Fitting

C₁₉×#346

C₂

prime radical

C₂²×D₁₉

C₂×C₈

cosocle

C₂×C₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
2. Dic₁₉⋊C₁₆	C₂	semidirect
4. #11926320	C₂	semidirect
5. C₁₉×#346	C₂	semidirect
61. #346	D₁₉	semidirect
75. C₁₉	#2163	semidirect

H ≅ G/N

type

2. Dic₁₉⋊C₁₆

C₂

semidirect

4. #11926320

C₂

semidirect

5. C₁₉×#346

C₂

semidirect

61. #346

D₁₉

semidirect

75. C₁₉

#2163

semidirect

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

subgroup	index
C₄×C₈×D₁₉	2
Dic₁₉⋊C₁₆	2
(C₂×D₁₉)⋊C₁₆	2
#11926320	2
C₁₉×#346	2
#2163	19

subgroup

index

C₄×C₈×D₁₉

Dic₁₉⋊C₁₆

(C₂×D₁₉)⋊C₁₆

#11926320

C₁₉×#346

#2163

Subgroups — #14565436

Conjugacy classes of subgroups

Complements

Maximal subgroups