Group #14561736 — subgroups

Subgroups — #14561736

Order 2432.

132 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 69 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×#10597269	C₂	1	1	yes	maximal, characteristic
2	#11926582	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#427	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×#117	—	2	1	no	—
6	#10597372	—	2	1	no	—
7	C₁₉×#107	—	2	1	no	—
8	C₁₉×#106	C₄	1	2	yes	complemented
9	#10597275	—	2	1	no	—
10	#10597274	C₄	1	2	yes	complemented
11	#10597269	—	2	1	no	—
12	#10597269	—	2	1	no	—
13	C₂×C₁₉⋊C₁₆	C₄	1	2	yes	complemented
14	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
21	C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂²⋊C₄×C₁₉	—	4	1	no	—
23	C₄²×C₁₉	—	4	1	no	—
24	C₂²⋊Dic₁₉	—	4	1	no	—
25	C₄⋊Dic₁₉	—	2	2	no	—
26	C₄×Dic₁₉	—	4	1	no	—
27	C₁₉⋊C₁₆	—	2	2	no	—
28	C₂³×C₁₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	4	2	no	—
30	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
35	C₂×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
36	C₂×Dic₁₉	—	4	2	no	—
37	C₈×C₁₉	C₄²	1	1	yes	characteristic
38	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	#1384	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	4	1	no	—
43	C₂²×C₁₉	#102	1	1	yes	characteristic
44	C₂²×C₁₉	#102	1	1	yes	characteristic
45	C₂²×C₁₉	#107	1	1	yes	characteristic
46	C₄×C₁₉	—	8	2	no	—
47	C₄×C₁₉	#95	1	1	yes	characteristic
48	C₄×C₁₉	#103	1	1	yes	characteristic
49	C₄×C₁₉	#103	1	1	yes	characteristic
50	C₄×C₁₉	#106	1	1	yes	characteristic
51	Dic₁₉	—	8	2	no	—
52	C₂×M₃₂	—	19	1	no	—
53	#427	—	19	1	no	—
54	#427	D₁₉	1	1	yes	characteristic
55	C₂×C₁₉	—	2	1	no	—
56	C₂×C₁₉	—	2	1	no	—
57	C₂×C₁₉	—	2	1	no	—
58	C₂×C₁₉	#340	1	1	yes	characteristic
59	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
60	#117	—	2	1	no	—
61	#117	—	38	1	no	—
62	M₃₂	—	38	1	no	—
63	M₃₂	—	38	1	no	—
64	C₂×C₁₆	—	19	2	no	—
65	#107	—	2	1	no	—
66	#107	—	38	1	no	—
67	#106	—	19	2	no	—
68	#106	Dic₁₉	1	2	yes	complemented
69	C₁₉	#1384	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
71	C₂×C₈	Dic₃₈	1	1	yes	characteristic
72	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
73	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
74	C₂×C₈	D₇₆	1	1	yes	characteristic
75	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
76	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	—	38	2	no	—
79	C₂²⋊C₄	—	4	1	no	—
80	C₂²⋊C₄	—	76	1	no	—
81	C₄²	—	4	1	no	—
82	C₄²	—	76	1	no	—
83	C₁₆	—	38	2	no	—
84	C₂³	#64525	1	1	yes	characteristic
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	—	76	2	no	—
87	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
88	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
89	C₂×C₄	#64526	1	1	yes	characteristic
90	C₂×C₄	#64527	1	1	yes	characteristic
91	C₂×C₄	#64528	1	1	yes	characteristic
92	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
93	C₈	C₄×Dic₁₉	1	1	yes	characteristic
94	C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
95	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
96	C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
97	C₂²	—	4	1	no	—
98	C₂²	#10597264	1	1	yes	characteristic
99	C₂²	#10597266	1	1	yes	characteristic
100	C₂²	#10597289	1	1	yes	characteristic
101	C₄	—	8	2	no	—
102	C₄	—	152	2	no	—
103	C₄	#10597265	1	1	yes	characteristic
104	C₄	#10597267	1	1	yes	characteristic
105	C₄	C₁₉⋊#95	1	1	yes	characteristic
106	C₄	#10597292	1	1	yes	characteristic
107	C₂	—	2	1	no	—
108	C₂	—	2	1	no	—
109	C₂	—	2	1	no	—
110	C₂	#11926306	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597269

C₂

yes

maximal, characteristic

#11926582

C₂

yes

maximal, characteristic

C₁₉×#427

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

—

#10597372

—

C₁₉×#107

—

C₁₉×#106

C₄

yes

complemented

#10597275

—

#10597274

C₄

yes

complemented

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

C₄

yes

complemented

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

Q₁₆

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

C₄²

yes

characteristic

C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

#1384

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×M₃₂

—

#427

—

#427

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#340

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

—

#117

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

—

—

—

Dic₁₉

yes

complemented

C₁₉

#1384

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₁₆

—

C₂³

#64525

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₈

C₄×Dic₁₉

yes

characteristic

C₈

Dic₁₉⋊C₄

yes

characteristic

C₈

C₄⋊Dic₁₉

yes

characteristic

C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

100

C₂²

#10597289

yes

characteristic

101

C₄

—

102

C₄

—

152

—

103

C₄

#10597265

yes

characteristic

104

C₄

#10597267

yes

characteristic

105

C₄

C₁₉⋊#95

yes

characteristic

106

C₄

#10597292

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

—

110

C₂

#11926306

yes

characteristic

	subgroup	G/H
center	C₄	#10597265
commutator	C₈×C₁₉	C₄²
Frattini	C₂²×C₈	C₂×D₁₉
Fitting	C₁₉×#427	C₂
socle	C₂×C₁₉	#340
prime radical	C₂³×C₁₉	D₈
cosocle	C₂²×C₈×C₁₉	C₂²
hypercenter	#427	D₁₉
hypocenter	C₁₉	#1384
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

subgroup

G/H

center

C₄

#10597265

commutator

C₈×C₁₉

C₄²

Frattini

C₂²×C₈

C₂×D₁₉

Fitting

C₁₉×#427

C₂

socle

C₂×C₁₉

#340

prime radical

C₂³×C₁₉

D₈

cosocle

C₂²×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

N	H ≅ G/N	type
8. C₁₉×#106	C₄	semidirect
10. #10597274	C₄	semidirect
13. C₂×C₁₉⋊C₁₆	C₄	semidirect
68. #106	Dic₁₉	semidirect
69. C₁₉	#1384	semidirect

H ≅ G/N

type

8. C₁₉×#106

C₄

semidirect

10. #10597274

C₄

semidirect

13. C₂×C₁₉⋊C₁₆

C₄

semidirect

68. #106

Dic₁₉

semidirect

69. C₁₉

#1384

semidirect

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

subgroup	index
C₂×#10597269	2
#11926582	2
C₁₉×#427	2
#1384	19

subgroup

index

C₂×#10597269

#11926582

C₁₉×#427

#1384

Subgroups — #14561736

Conjugacy classes of subgroups

Complements

Maximal subgroups