Group #14563785 — subgroups

Subgroups — #14563785

Order 2432.

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

normal subgroups only

This group has 162 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	M₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#11926316	C₂	1	2	yes	maximal
3	#11926305	C₂	1	2	yes	maximal
4	#11926301	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#338	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	#10597372	C₂²	1	2	yes	—
9	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂×#64520	C₂²	1	1	yes	characteristic
11	#10597272	C₄	1	2	yes	complemented
12	C₈×Dic₁₉	C₄	1	2	yes	complemented
13	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
14	C₂²×Dic₁₉	—	2	1	no	—
15	M₁₆×C₁₉	—	2	2	no	—
16	M₁₆×C₁₉	—	2	2	no	—
17	M₁₆×C₁₉	—	2	2	no	—
18	C₂×C₈×C₁₉	—	2	2	no	—
19	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²⋊Dic₁₉	—	2	2	no	—
21	C₄⋊Dic₁₉	—	2	2	no	—
22	C₄×Dic₁₉	—	2	1	no	—
23	C₄×Dic₁₉	—	2	2	no	—
24	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
26	#64520	—	2	2	no	—
27	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
28	C₂³×C₁₉	#41	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₉	#41	1	2	yes	—
31	C₂×C₄×C₁₉	#41	1	2	yes	—
32	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
33	C₂×Dic₁₉	—	2	1	no	—
34	C₂×Dic₁₉	—	2	1	no	—
35	C₂×Dic₁₉	—	4	2	no	—
36	C₂×Dic₁₉	—	4	2	no	—
37	C₈×C₁₉	—	2	2	no	—
38	C₈×C₁₉	—	4	2	no	—
39	C₁₉⋊C₈	—	2	2	no	—
40	#1841	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	—	4	1	no	—
42	C₂²×C₁₉	#117	1	1	yes	characteristic
43	C₂²×C₁₉	#126	1	2	yes	—
44	C₄×C₁₉	#117	1	1	yes	characteristic
45	C₄×C₁₉	#117	1	1	yes	characteristic
46	C₄×C₁₉	#126	1	2	yes	—
47	Dic₁₉	—	2	2	no	—
48	Dic₁₉	—	4	1	no	—
49	Dic₁₉	—	8	2	no	—
50	C₄×M₁₆	—	19	1	no	—
51	#344	—	19	2	no	—
52	#339	—	19	2	no	—
53	#338	D₁₉	1	1	yes	characteristic
54	H(3,ℤ/4)	—	19	1	no	—
55	C₂×C₁₉	—	2	1	no	—
56	C₂×C₁₉	—	2	2	no	—
57	C₂×C₁₉	#383	1	1	yes	characteristic
58	C₂×M₁₆	—	19	1	no	—
59	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
60	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
61	#117	—	19	2	no	—
62	C₂×C₄²	—	19	1	no	—
63	#97	—	19	2	no	—
64	C₄×C₈	—	19	2	no	—
65	C₁₉	#1841	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	38	1	no	—
67	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	38	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	19	2	no	—
74	C₂×C₈	C₄×D₁₉	1	2	yes	—
75	C₄⋊C₄	—	38	2	no	—
76	C₂²⋊C₄	—	38	2	no	—
77	C₄²	—	19	1	no	—
78	C₄²	—	19	1	no	—
79	C₄²	—	38	1	no	—
80	C₄²	—	38	2	no	—
81	C₂³	#64545	1	1	yes	characteristic
82	C₂×C₄	—	38	1	no	—
83	C₂×C₄	—	38	1	no	—
84	C₂×C₄	—	76	2	no	—
85	C₂×C₄	—	76	2	no	—
86	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
87	C₂×C₄	#64541	1	2	yes	—
88	C₂×C₄	#64543	1	2	yes	—
89	C₂×C₄	#64543	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	4	2	no	—
92	C₈	—	38	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#10597338	1	1	yes	characteristic
95	C₂²	#10597344	1	2	yes	—
96	C₄	—	38	2	no	—
97	C₄	—	76	1	no	—
98	C₄	—	152	2	no	—
99	C₄	#10597318	1	1	yes	characteristic
100	C₄	#10597323	1	1	yes	characteristic
101	C₄	#10597325	1	2	yes	—
102	C₂	—	2	1	no	—
103	C₂	—	2	2	no	—
104	C₂	#11926411	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₁₆×Dic₁₉

C₂

yes

maximal, characteristic

#11926316

C₂

yes

maximal

#11926305

C₂

yes

maximal

#11926301

C₂

yes

maximal, characteristic

C₁₉×#338

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

#10597272

C₄

yes

complemented

C₈×Dic₁₉

C₄

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₄×Dic₁₉

C₂×C₄

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1841

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#117

yes

characteristic

C₂²×C₁₉

#126

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₄×M₁₆

—

#344

—

#339

—

#338

D₁₉

yes

characteristic

H(3,ℤ/4)

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#383

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

#117

—

C₂×C₄²

—

#97

—

C₄×C₈

—

C₁₉

#1841

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

#64545

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

C₂×C₄

#64541

yes

—

C₂×C₄

#64543

yes

—

C₂×C₄

#64543

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#10597338

yes

characteristic

C₂²

#10597344

yes

—

C₄

—

C₄

—

C₄

—

152

—

C₄

#10597318

yes

characteristic

100

C₄

#10597323

yes

characteristic

101

C₄

#10597325

yes

—

102

C₂

—

103

C₂

—

104

C₂

#11926411

yes

characteristic

	subgroup	G/H
center	C₄	#10597318
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#338	C₂
socle	C₂×C₁₉	#383
prime radical	C₂³×C₁₉	#41
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#338	D₁₉
hypocenter	C₁₉	#1841
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

subgroup

G/H

center

C₄

#10597318

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#338

C₂

C₂×C₁₉

C₂³×C₁₉

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

N	H ≅ G/N	type
11. #10597272	C₄	semidirect
12. C₈×Dic₁₉	C₄	semidirect
65. C₁₉	#1841	semidirect

H ≅ G/N

type

11. #10597272

C₄

semidirect

12. C₈×Dic₁₉

C₄

semidirect

65. C₁₉

#1841

semidirect

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

subgroup	index
M₁₆×Dic₁₉	2
#11926316	2
#11926305	2
#11926301	2
C₁₉×#338	2
#1841	19

subgroup

index

M₁₆×Dic₁₉

C₁₉×#338

Subgroups — #14563785

Conjugacy classes of subgroups

Complements

Maximal subgroups