Group #14565482 — subgroups

Subgroups — D₁₆×Dic₁₉ #14565482

Order 2432.

174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 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	D₈×Dic₁₉	C₂	1	2	yes	maximal, complemented
2	#11926370	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926345	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×D₈×C₁₉	C₂²	1	2	yes	—
7	D₄×Dic₁₉	—	2	2	no	—
8	C₁₉×D₁₆	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	#10597289	—	2	2	no	—
11	#10597275	C₂²	1	2	yes	—
12	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₂×D₄×C₁₉	—	2	2	no	—
15	C₂²×Dic₁₉	—	4	2	no	—
16	D₈×C₁₉	—	2	2	no	—
17	D₈×C₁₉	C₂×C₄	1	4	yes	complemented
18	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²⋊Dic₁₉	—	4	2	no	—
20	C₄⋊Dic₁₉	—	2	2	no	—
21	C₄×Dic₁₉	D₄	1	1	yes	characteristic
22	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
23	C₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
24	C₁₉⋊C₁₆	—	2	1	no	—
25	C₂³×C₁₉	—	4	2	no	—
26	D₄×C₁₉	—	2	4	no	—
27	D₄×C₁₉	—	4	2	no	—
28	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₁₉	—	4	2	no	—
30	C₂×Dic₁₉	—	8	4	no	—
31	C₂×Dic₁₉	D₈	1	1	yes	characteristic
32	C₂×Dic₁₉	D₈	1	1	yes	characteristic
33	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₉	#41	1	1	yes	characteristic
35	C₁₉⋊C₈	—	2	1	no	—
36	C₄×D₁₆	—	19	1	no	maximal, Sylow
37	C₂²×C₁₉	—	4	4	no	—
38	C₂²×C₁₉	—	8	2	no	—
39	C₂²×C₁₉	—	8	2	no	—
40	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
41	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
42	C₄×C₁₉	#135	1	1	yes	characteristic
43	Dic₁₉	—	2	1	no	—
44	Dic₁₉	—	8	2	no	—
45	Dic₁₉	D₁₆	1	2	yes	direct product factor
46	C₂×D₁₆	D₁₉	1	1	yes	characteristic
47	C₄×D₈	—	19	2	no	—
48	#366	—	19	1	no	—
49	#357	—	19	2	no	—
50	C₄×C₁₆	—	19	1	no	—
51	C₂×C₁₉	—	8	4	no	—
52	C₂×C₁₉	C₄×D₈	1	1	yes	characteristic
53	C₂×C₁₉	C₂×D₁₆	1	1	yes	characteristic
54	C₂×C₁₉	#508	1	1	yes	characteristic
55	C₂×D₈	C₂×D₁₉	1	2	yes	—
56	C₄×D₄	—	38	2	no	—
57	D₁₆	Dic₁₉	1	4	yes	direct product factor
58	C₂×C₁₆	—	19	1	no	—
59	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
60	#107	—	19	2	no	—
61	#102	—	38	2	no	—
62	C₄×C₈	—	19	1	no	—
63	C₁₉	C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
64	C₂×D₄	—	2	2	no	—
65	C₂²×C₄	—	76	2	no	—
66	D₈	—	2	2	no	—
67	D₈	C₂×Dic₁₉	1	4	yes	complemented
68	C₂×C₈	—	19	1	no	—
69	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
70	C₄⋊C₄	—	38	2	no	—
71	C₂²⋊C₄	—	76	2	no	—
72	C₄²	—	19	1	no	—
73	C₁₆	—	38	1	no	—
74	C₁₆	C₂×Dic₁₉	1	2	yes	complemented
75	C₂³	—	4	2	no	—
76	D₄	—	2	4	no	—
77	D₄	—	4	2	no	—
78	C₂×C₄	—	19	1	no	—
79	C₂×C₄	—	19	1	no	—
80	C₂×C₄	—	76	2	no	—
81	C₂×C₄	—	152	4	no	—
82	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
83	C₈	—	38	1	no	—
84	C₈	#64543	1	1	yes	characteristic
85	C₈	C₂²×Dic₁₉	1	1	yes	characteristic
86	C₂²	—	4	4	no	—
87	C₂²	—	8	2	no	—
88	C₂²	—	8	2	no	—
89	C₂²	D₈×D₁₉	1	1	yes	characteristic
90	C₄	—	19	2	no	—
91	C₄	—	38	1	no	—
92	C₄	—	152	2	no	—
93	C₄	#10597358	1	1	yes	characteristic
94	C₄	D₄×Dic₁₉	1	1	yes	characteristic
95	C₂	—	8	4	no	—
96	C₂	D₈×Dic₁₉	1	1	yes	characteristic
97	C₂	D₁₆×D₁₉	1	1	yes	characteristic
98	C₂	#11926973	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₈×Dic₁₉

C₂

yes

maximal, complemented

#11926370

C₂

yes

maximal, characteristic, complemented

#11926345

C₂

yes

maximal, complemented

C₁₆×Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

C₂²

yes

—

D₄×Dic₁₉

—

C₁₉×D₁₆

C₄

yes

complemented

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597289

—

#10597275

C₂²

yes

—

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

C₂×D₄×C₁₉

—

C₂²×Dic₁₉

—

D₈×C₁₉

—

D₈×C₁₉

C₂×C₄

yes

complemented

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₁₆×C₁₉

C₂×C₄

yes

complemented

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

C₂×Dic₁₉

D₈

yes

characteristic

C₈×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

C₄×D₁₆

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

#135

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

D₁₆

yes

direct product factor

C₂×D₁₆

D₁₉

yes

characteristic

C₄×D₈

—

#366

—

#357

—

C₄×C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

C₄×D₈

yes

characteristic

C₂×C₁₉

C₂×D₁₆

yes

characteristic

C₂×C₁₉

#508

yes

characteristic

C₂×D₈

C₂×D₁₉

yes

—

C₄×D₄

—

D₁₆

Dic₁₉

yes

direct product factor

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

#107

—

#102

—

C₄×C₈

—

C₁₉

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

C₂×Dic₁₉

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

C₂×Dic₁₉

yes

complemented

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

152

—

C₂×C₄

D₄×D₁₉

yes

characteristic

C₈

—

C₈

#64543

yes

characteristic

C₈

C₂²×Dic₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

D₈×D₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

152

—

C₄

#10597358

yes

characteristic

C₄

D₄×Dic₁₉

yes

characteristic

C₂

—

C₂

D₈×Dic₁₉

yes

characteristic

C₂

D₁₆×D₁₉

yes

characteristic

C₂

#11926973

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×D₁₆	C₂
socle	C₂²×C₁₉	C₂×D₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂×D₁₆	D₁₉
hypocenter	C₁₉	C₄×D₁₆
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator

C₈×C₁₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₁₉

Fitting, prime radical

C₂×C₁₉×D₁₆

C₂

socle

C₂²×C₁₉

C₂×D₈

cosocle

C₂×C₈×C₁₉

C₂³

hypercenter

C₂×D₁₆

D₁₉

hypocenter

C₁₉

C₄×D₁₆

LCS

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. D₈×Dic₁₉	C₂	semidirect
2. #11926370	C₂	semidirect
3. #11926345	C₂	semidirect
4. C₁₆×Dic₁₉	C₂	semidirect
8. C₁₉×D₁₆	C₄	semidirect
17. D₈×C₁₉	C₂×C₄	semidirect
23. C₁₆×C₁₉	C₂×C₄	semidirect
45. Dic₁₉	D₁₆	direct (N × H)
57. D₁₆	Dic₁₉	direct (N × H)
63. C₁₉	C₄×D₁₆	semidirect
67. D₈	C₂×Dic₁₉	semidirect
74. C₁₆	C₂×Dic₁₉	semidirect

H ≅ G/N

type

1. D₈×Dic₁₉

C₂

semidirect

2. #11926370

C₂

semidirect

3. #11926345

C₂

semidirect

4. C₁₆×Dic₁₉

C₂

semidirect

8. C₁₉×D₁₆

C₄

semidirect

17. D₈×C₁₉

C₂×C₄

semidirect

23. C₁₆×C₁₉

C₂×C₄

semidirect

45. Dic₁₉

D₁₆

direct (N × H)

57. D₁₆

Dic₁₉

direct (N × H)

63. C₁₉

C₄×D₁₆

semidirect

67. D₈

C₂×Dic₁₉

semidirect

74. C₁₆

C₂×Dic₁₉

semidirect

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

subgroup	index
D₈×Dic₁₉	2
#11926370	2
#11926345	2
C₁₆×Dic₁₉	2
C₂×C₁₉×D₁₆	2
C₄×D₁₆	19

subgroup

index

D₈×Dic₁₉

#11926370

#11926345

C₁₆×Dic₁₉

C₂×C₁₉×D₁₆

C₄×D₁₆

Subgroups — D₁₆×Dic₁₉ #14565482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D16×Dic19 #14565482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₆×Dic₁₉ #14565482