Group #19136442 — subgroups

Subgroups — D₁₆×Dic₄₃ #19136442

Order 5504.

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×Dic₄₃	C₂	1	2	yes	maximal, complemented
2	#14582725	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582700	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
6	D₄×Dic₄₃	—	2	2	no	—
7	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
8	#13063259	C₂²	1	2	yes	—
9	#13063246	—	2	2	no	—
10	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
11	C₂×D₈×C₄₃	C₂²	1	2	yes	—
12	D₁₆×C₄₃	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×D₄×C₄₃	—	2	2	no	—
15	C₂²×Dic₄₃	—	4	2	no	—
16	D₈×C₄₃	—	2	2	no	—
17	D₈×C₄₃	C₂×C₄	1	4	yes	complemented
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²⋊Dic₄₃	—	4	2	no	—
20	C₄⋊Dic₄₃	—	2	2	no	—
21	C₄×Dic₄₃	D₄	1	1	yes	characteristic
22	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
23	C₁₆×C₄₃	C₂×C₄	1	2	yes	complemented
24	C₄₃⋊C₁₆	—	2	1	no	—
25	C₂³×C₄₃	—	4	2	no	—
26	D₄×C₄₃	—	2	4	no	—
27	D₄×C₄₃	—	4	2	no	—
28	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₄₃	—	4	2	no	—
30	C₂×Dic₄₃	—	8	4	no	—
31	C₂×Dic₄₃	D₈	1	1	yes	characteristic
32	C₂×Dic₄₃	D₈	1	1	yes	characteristic
33	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₄₃	#41	1	1	yes	characteristic
35	C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃	—	4	4	no	—
37	C₂²×C₄₃	—	8	2	no	—
38	C₂²×C₄₃	—	8	2	no	—
39	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
40	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
41	C₄×C₄₃	#135	1	1	yes	characteristic
42	Dic₄₃	—	2	1	no	—
43	Dic₄₃	—	8	2	no	—
44	Dic₄₃	D₁₆	1	2	yes	direct product factor
45	C₄×D₁₆	—	43	1	no	maximal, Sylow
46	C₂×C₄₃	—	8	4	no	—
47	C₂×C₄₃	C₄×D₈	1	1	yes	characteristic
48	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
49	C₂×C₄₃	#508	1	1	yes	characteristic
50	C₂×D₁₆	D₄₃	1	1	yes	characteristic
51	C₄×D₈	—	43	2	no	—
52	#366	—	43	1	no	—
53	#357	—	43	2	no	—
54	C₄×C₁₆	—	43	1	no	—
55	C₄₃	C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	C₂×D₄₃	1	2	yes	—
57	C₄×D₄	—	86	2	no	—
58	D₁₆	Dic₄₃	1	4	yes	direct product factor
59	C₂×C₁₆	—	43	1	no	—
60	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
61	#107	—	43	2	no	—
62	#102	—	86	2	no	—
63	C₄×C₈	—	43	1	no	—
64	C₂×D₄	—	2	2	no	—
65	C₂²×C₄	—	172	2	no	—
66	D₈	—	2	2	no	—
67	D₈	C₂×Dic₄₃	1	4	yes	complemented
68	C₂×C₈	—	43	1	no	—
69	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
70	C₄⋊C₄	—	86	2	no	—
71	C₂²⋊C₄	—	172	2	no	—
72	C₄²	—	43	1	no	—
73	C₁₆	—	86	1	no	—
74	C₁₆	C₂×Dic₄₃	1	2	yes	complemented
75	C₂³	—	4	2	no	—
76	D₄	—	2	4	no	—
77	D₄	—	4	2	no	—
78	C₂×C₄	—	43	1	no	—
79	C₂×C₄	—	43	1	no	—
80	C₂×C₄	—	344	4	no	—
81	C₂×C₄	—	172	2	no	—
82	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
83	C₈	—	86	1	no	—
84	C₈	#10621900	1	1	yes	characteristic
85	C₈	C₂²×Dic₄₃	1	1	yes	characteristic
86	C₂²	—	4	4	no	—
87	C₂²	—	8	2	no	—
88	C₂²	—	8	2	no	—
89	C₂²	D₈×D₄₃	1	1	yes	characteristic
90	C₄	—	43	2	no	—
91	C₄	—	86	1	no	—
92	C₄	—	344	2	no	—
93	C₄	D₄×Dic₄₃	1	1	yes	characteristic
94	C₄	#13063344	1	1	yes	characteristic
95	C₂	—	8	4	no	—
96	C₂	D₈×Dic₄₃	1	1	yes	characteristic
97	C₂	D₁₆×D₄₃	1	1	yes	characteristic
98	C₂	#14583328	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₈×Dic₄₃

C₂

yes

maximal, complemented

#14582725

C₂

yes

maximal, characteristic, complemented

#14582700

C₂

yes

maximal, complemented

C₁₆×Dic₄₃

C₂

yes

maximal, characteristic, complemented

C₂×D₁₆×C₄₃

C₂

yes

maximal, characteristic

D₄×Dic₄₃

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

—

#13063246

—

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×D₈×C₄₃

C₂²

yes

—

D₁₆×C₄₃

C₄

yes

complemented

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂²×Dic₄₃

—

D₈×C₄₃

—

D₈×C₄₃

C₂×C₄

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₁₆×C₄₃

C₂×C₄

yes

complemented

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₂×Dic₄₃

D₈

yes

characteristic

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

#135

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

D₁₆

yes

direct product factor

C₄×D₁₆

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₄×D₈

yes

characteristic

C₂×C₄₃

C₂×D₁₆

yes

characteristic

C₂×C₄₃

#508

yes

characteristic

C₂×D₁₆

D₄₃

yes

characteristic

C₄×D₈

—

#366

—

#357

—

C₄×C₁₆

—

C₄₃

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₈

C₂×D₄₃

yes

—

C₄×D₄

—

D₁₆

Dic₄₃

yes

direct product factor

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#107

—

#102

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

172

—

D₈

—

D₈

C₂×Dic₄₃

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

—

C₁₆

—

C₁₆

C₂×Dic₄₃

yes

complemented

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

—

172

—

C₂×C₄

D₄×D₄₃

yes

characteristic

C₈

—

C₈

#10621900

yes

characteristic

C₈

C₂²×Dic₄₃

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

D₈×D₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

344

—

C₄

D₄×Dic₄₃

yes

characteristic

C₄

#13063344

yes

characteristic

C₂

—

C₂

D₈×Dic₄₃

yes

characteristic

C₂

D₁₆×D₄₃

yes

characteristic

C₂

#14583328

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×D₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₂×D₁₆	D₄₃
hypocenter	C₄₃	C₄×D₁₆
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×D₁₆×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₂×D₁₆

D₄₃

hypocenter

C₄₃

C₄×D₁₆

LCS

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. D₈×Dic₄₃	C₂	semidirect
2. #14582725	C₂	semidirect
3. #14582700	C₂	semidirect
4. C₁₆×Dic₄₃	C₂	semidirect
12. D₁₆×C₄₃	C₄	semidirect
17. D₈×C₄₃	C₂×C₄	semidirect
23. C₁₆×C₄₃	C₂×C₄	semidirect
44. Dic₄₃	D₁₆	direct (N × H)
55. C₄₃	C₄×D₁₆	semidirect
58. D₁₆	Dic₄₃	direct (N × H)
67. D₈	C₂×Dic₄₃	semidirect
74. C₁₆	C₂×Dic₄₃	semidirect

H ≅ G/N

type

1. D₈×Dic₄₃

C₂

semidirect

2. #14582725

C₂

semidirect

3. #14582700

C₂

semidirect

4. C₁₆×Dic₄₃

C₂

semidirect

12. D₁₆×C₄₃

C₄

semidirect

17. D₈×C₄₃

C₂×C₄

semidirect

23. C₁₆×C₄₃

C₂×C₄

semidirect

44. Dic₄₃

D₁₆

direct (N × H)

55. C₄₃

C₄×D₁₆

semidirect

58. D₁₆

Dic₄₃

direct (N × H)

67. D₈

C₂×Dic₄₃

semidirect

74. C₁₆

C₂×Dic₄₃

semidirect

Subgroups — D₁₆×Dic₄₃ #19136442

Conjugacy classes of subgroups

Complements

Subgroups — D16×Dic43 #19136442

Conjugacy classes of subgroups

Complements

Subgroups — D₁₆×Dic₄₃ #19136442