Group #20245235 — subgroups

Subgroups — D₁₆×Dic₄₇ #20245235

Order 6016.

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×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#15688949	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688924	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
6	D₄×Dic₄₇	—	2	2	no	—
7	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
8	#13093958	C₂²	1	2	yes	—
9	#13093945	—	2	2	no	—
10	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂×D₈×C₄₇	C₂²	1	2	yes	—
12	D₁₆×C₄₇	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×D₄×C₄₇	—	2	2	no	—
15	C₂²×Dic₄₇	—	4	2	no	—
16	D₈×C₄₇	—	2	2	no	—
17	D₈×C₄₇	C₂×C₄	1	4	yes	complemented
18	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
19	C₂²⋊Dic₄₇	—	4	2	no	—
20	C₄⋊Dic₄₇	—	2	2	no	—
21	C₄×Dic₄₇	D₄	1	1	yes	characteristic
22	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
23	C₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
24	C₄₇⋊C₁₆	—	2	1	no	—
25	C₂³×C₄₇	—	4	2	no	—
26	D₄×C₄₇	—	2	4	no	—
27	D₄×C₄₇	—	4	2	no	—
28	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₄₇	—	4	2	no	—
30	C₂×Dic₄₇	—	8	4	no	—
31	C₂×Dic₄₇	D₈	1	1	yes	characteristic
32	C₂×Dic₄₇	D₈	1	1	yes	characteristic
33	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₄₇	#41	1	1	yes	characteristic
35	C₄₇⋊C₈	—	2	1	no	—
36	C₂²×C₄₇	—	4	4	no	—
37	C₂²×C₄₇	—	8	2	no	—
38	C₂²×C₄₇	—	8	2	no	—
39	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
40	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
41	C₄×C₄₇	#135	1	1	yes	characteristic
42	Dic₄₇	—	2	1	no	—
43	Dic₄₇	—	8	2	no	—
44	Dic₄₇	D₁₆	1	2	yes	direct product factor
45	C₄×D₁₆	—	47	1	no	maximal, Sylow
46	C₂×C₄₇	—	8	4	no	—
47	C₂×C₄₇	C₄×D₈	1	1	yes	characteristic
48	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
49	C₂×C₄₇	#508	1	1	yes	characteristic
50	C₂×D₁₆	D₄₇	1	1	yes	characteristic
51	C₄×D₈	—	47	2	no	—
52	#366	—	47	1	no	—
53	#357	—	47	2	no	—
54	C₄×C₁₆	—	47	1	no	—
55	C₄₇	C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	C₂×D₄₇	1	2	yes	—
57	C₄×D₄	—	94	2	no	—
58	D₁₆	Dic₄₇	1	4	yes	direct product factor
59	C₂×C₁₆	—	47	1	no	—
60	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
61	#107	—	47	2	no	—
62	#102	—	94	2	no	—
63	C₄×C₈	—	47	1	no	—
64	C₂×D₄	—	2	2	no	—
65	C₂²×C₄	—	188	2	no	—
66	D₈	—	2	2	no	—
67	D₈	C₂×Dic₄₇	1	4	yes	complemented
68	C₂×C₈	—	47	1	no	—
69	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
70	C₄⋊C₄	—	94	2	no	—
71	C₂²⋊C₄	—	188	2	no	—
72	C₄²	—	47	1	no	—
73	C₁₆	—	94	1	no	—
74	C₁₆	C₂×Dic₄₇	1	2	yes	complemented
75	C₂³	—	4	2	no	—
76	D₄	—	2	4	no	—
77	D₄	—	4	2	no	—
78	C₂×C₄	—	47	1	no	—
79	C₂×C₄	—	47	1	no	—
80	C₂×C₄	—	376	4	no	—
81	C₂×C₄	—	188	2	no	—
82	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
83	C₈	—	94	1	no	—
84	C₈	#10625352	1	1	yes	characteristic
85	C₈	C₂²×Dic₄₇	1	1	yes	characteristic
86	C₂²	—	4	4	no	—
87	C₂²	—	8	2	no	—
88	C₂²	—	8	2	no	—
89	C₂²	D₈×D₄₇	1	1	yes	characteristic
90	C₄	—	47	2	no	—
91	C₄	—	94	1	no	—
92	C₄	—	376	2	no	—
93	C₄	D₄×Dic₄₇	1	1	yes	characteristic
94	C₄	#13094043	1	1	yes	characteristic
95	C₂	—	8	4	no	—
96	C₂	D₈×Dic₄₇	1	1	yes	characteristic
97	C₂	D₁₆×D₄₇	1	1	yes	characteristic
98	C₂	#15689552	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₈×Dic₄₇

C₂

yes

maximal, complemented

#15688949

C₂

yes

maximal, characteristic, complemented

#15688924

C₂

yes

maximal, complemented

C₁₆×Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₂×D₁₆×C₄₇

C₂

yes

maximal, characteristic

D₄×Dic₄₇

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

—

#13093945

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×D₈×C₄₇

C₂²

yes

—

D₁₆×C₄₇

C₄

yes

complemented

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

—

C₂²×Dic₄₇

—

D₈×C₄₇

—

D₈×C₄₇

C₂×C₄

yes

complemented

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₁₆×C₄₇

C₂×C₄

yes

complemented

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₂×Dic₄₇

D₈

yes

characteristic

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

#135

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

D₁₆

yes

direct product factor

C₄×D₁₆

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₄×D₈

yes

characteristic

C₂×C₄₇

C₂×D₁₆

yes

characteristic

C₂×C₄₇

#508

yes

characteristic

C₂×D₁₆

D₄₇

yes

characteristic

C₄×D₈

—

#366

—

#357

—

C₄×C₁₆

—

C₄₇

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₈

C₂×D₄₇

yes

—

C₄×D₄

—

D₁₆

Dic₄₇

yes

direct product factor

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

—

#102

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

188

—

D₈

—

D₈

C₂×Dic₄₇

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

188

—

C₄²

—

C₁₆

—

C₁₆

C₂×Dic₄₇

yes

complemented

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

376

—

C₂×C₄

—

188

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₈

—

C₈

#10625352

yes

characteristic

C₈

C₂²×Dic₄₇

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

D₈×D₄₇

yes

characteristic

C₄

—

C₄

—

C₄

—

376

—

C₄

D₄×Dic₄₇

yes

characteristic

C₄

#13094043

yes

characteristic

C₂

—

C₂

D₈×Dic₄₇

yes

characteristic

C₂

D₁₆×D₄₇

yes

characteristic

C₂

#15689552

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×D₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂×D₁₆	D₄₇
hypocenter	C₄₇	C₄×D₁₆
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₈×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂×D₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₂×D₁₆

D₄₇

hypocenter

C₄₇

C₄×D₁₆

LCS

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. D₈×Dic₄₇	C₂	semidirect
2. #15688949	C₂	semidirect
3. #15688924	C₂	semidirect
4. C₁₆×Dic₄₇	C₂	semidirect
12. D₁₆×C₄₇	C₄	semidirect
17. D₈×C₄₇	C₂×C₄	semidirect
23. C₁₆×C₄₇	C₂×C₄	semidirect
44. Dic₄₇	D₁₆	direct (N × H)
55. C₄₇	C₄×D₁₆	semidirect
58. D₁₆	Dic₄₇	direct (N × H)
67. D₈	C₂×Dic₄₇	semidirect
74. C₁₆	C₂×Dic₄₇	semidirect

H ≅ G/N

type

1. D₈×Dic₄₇

C₂

semidirect

2. #15688949

C₂

semidirect

3. #15688924

C₂

semidirect

4. C₁₆×Dic₄₇

C₂

semidirect

12. D₁₆×C₄₇

C₄

semidirect

17. D₈×C₄₇

C₂×C₄

semidirect

23. C₁₆×C₄₇

C₂×C₄

semidirect

44. Dic₄₇

D₁₆

direct (N × H)

55. C₄₇

C₄×D₁₆

semidirect

58. D₁₆

Dic₄₇

direct (N × H)

67. D₈

C₂×Dic₄₇

semidirect

74. C₁₆

C₂×Dic₄₇

semidirect

Subgroups — D₁₆×Dic₄₇ #20245235

Conjugacy classes of subgroups

Complements

Subgroups — D16×Dic47 #20245235

Conjugacy classes of subgroups

Complements

Subgroups — D₁₆×Dic₄₇ #20245235