Group #20241343 — subgroups

Subgroups — D₄⋊(C₄₇⋊C₁₆) #20241343

Order 6016.

110 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 53 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	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₁₆	—	2	1	no	—
5	C₂×C₄₇⋊C₁₆	—	2	1	no	—
6	C₂²×C₈×C₄₇	—	2	1	no	—
7	C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
8	C₄⋊C₈×C₄₇	C₄	1	1	yes	characteristic
9	C₂²⋊C₈×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₄₇	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	—	2	1	no	—
13	C₂×C₈×C₄₇	—	2	1	no	—
14	C₂×C₈×C₄₇	—	4	1	no	—
15	C₂×C₈×C₄₇	—	4	1	no	—
16	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₄⋊C₄×C₄₇	C₈	1	1	yes	characteristic
19	C₂²⋊C₄×C₄₇	—	2	1	no	—
20	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₄₇⋊C₁₆	—	2	2	no	—
22	C₄₇⋊C₁₆	—	4	1	no	—
23	C₂³×C₄₇	—	2	1	no	—
24	D₄×C₄₇	—	2	1	no	—
25	D₄×C₄₇	C₁₆	1	2	yes	complemented
26	C₂×C₄×C₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	—	4	1	no	—
28	C₂×C₄×C₄₇	—	4	1	no	—
29	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
32	C₈×C₄₇	—	2	1	no	—
33	C₈×C₄₇	—	4	1	no	—
34	C₈×C₄₇	D₈	1	1	yes	characteristic
35	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
36	C₂²×C₄₇	—	2	2	no	—
37	C₂²×C₄₇	—	4	1	no	—
38	C₂²×C₄₇	—	4	1	no	—
39	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₄₇	—	2	1	no	—
41	C₄×C₄₇	—	4	1	no	—
42	C₄×C₄₇	#102	1	1	yes	characteristic
43	C₄×C₄₇	#104	1	1	yes	characteristic
44	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
45	C₄×C₄₇	M₃₂	1	1	yes	characteristic
46	D₄⋊C₁₆	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	—	4	2	no	—
48	C₂×C₄₇	D₄⋊C₈	1	1	yes	characteristic
49	C₂×C₄₇	C₂²⋊C₁₆	1	1	yes	characteristic
50	C₂×C₄₇	#350	1	1	yes	characteristic
51	C₈×D₄	D₄₇	1	1	yes	characteristic
52	C₄⋊C₁₆	—	47	1	no	—
53	C₄×C₁₆	—	47	1	no	—
54	C₄₇	D₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₈	—	2	1	no	—
56	C₄×D₄	Dic₄₇	1	1	yes	characteristic
57	C₂×C₁₆	—	94	1	no	—
58	C₂×C₁₆	—	94	1	no	—
59	C₄⋊C₈	Dic₄₇	1	1	yes	characteristic
60	C₂²⋊C₈	—	2	1	no	—
61	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
62	C₂×D₄	C₄₇⋊C₈	1	1	yes	characteristic
63	C₂²×C₄	—	2	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	4	1	no	—
66	C₂×C₈	—	4	1	no	—
67	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
68	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
69	C₄⋊C₄	C₄₇⋊C₈	1	1	yes	characteristic
70	C₂²⋊C₄	—	2	1	no	—
71	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
72	C₁₆	—	94	2	no	—
73	C₁₆	—	188	1	no	—
74	C₂³	—	2	1	no	—
75	D₄	—	2	1	no	—
76	D₄	C₄₇⋊C₁₆	1	2	yes	complemented
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
81	C₂×C₄	#10625329	1	1	yes	characteristic
82	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	4	1	no	—
85	C₈	#10625334	1	1	yes	characteristic
86	C₈	#10625335	1	1	yes	characteristic
87	C₂²	—	2	2	no	—
88	C₂²	—	4	1	no	—
89	C₂²	—	4	1	no	—
90	C₂²	C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
91	C₄	—	2	1	no	—
92	C₄	—	4	1	no	—
93	C₄	#13093945	1	1	yes	characteristic
94	C₄	#13093951	1	1	yes	characteristic
95	C₄	C₂×C₄₇⋊C₁₆	1	1	yes	characteristic
96	C₄	#13093964	1	1	yes	characteristic
97	C₂	—	4	2	no	—
98	C₂	D₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
99	C₂	C₂²⋊(C₄₇⋊C₁₆)	1	1	yes	characteristic
100	C₂	#15688907	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

C₄×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₈×D₄×C₄₇

C₂

yes

maximal, characteristic

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂²×C₈×C₄₇

—

C₄×D₄×C₄₇

C₄

yes

characteristic

C₄⋊C₈×C₄₇

C₄

yes

characteristic

C₂²⋊C₈×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

C₈

yes

characteristic

C₂²×C₄×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

C₈

yes

characteristic

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

C₁₆

yes

complemented

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

characteristic

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

D₈

yes

characteristic

C₈×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊C₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

C₂×C₁₆

yes

characteristic

C₄×C₄₇

M₃₂

yes

characteristic

D₄⋊C₁₆

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

D₄⋊C₈

yes

characteristic

C₂×C₄₇

C₂²⋊C₁₆

yes

characteristic

C₂×C₄₇

#350

yes

characteristic

C₈×D₄

D₄₇

yes

characteristic

C₄⋊C₁₆

—

C₄×C₁₆

—

C₄₇

D₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₄×D₄

Dic₄₇

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

Dic₄₇

yes

characteristic

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×D₄

C₄₇⋊C₈

yes

characteristic

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

C₄₇⋊C₈

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂×Dic₄₇

yes

characteristic

C₁₆

—

C₁₆

—

188

—

C₂³

—

D₄

—

D₄

C₄₇⋊C₁₆

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄₇⋊C₈

yes

characteristic

C₂×C₄

#10625329

yes

characteristic

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂²⋊(C₄₇⋊C₈)

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₄

C₂×C₄₇⋊C₁₆

yes

characteristic

C₄

#13093964

yes

characteristic

C₂

—

C₂

D₄⋊(C₄₇⋊C₈)

yes

characteristic

C₂

C₂²⋊(C₄₇⋊C₁₆)

yes

characteristic

100

C₂

#15688907

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₈×D₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂²⋊C₈
hypercenter	C₈×D₄	D₄₇
hypocenter	C₄₇	D₄⋊C₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×D₄

subgroup

G/H

center

C₂×C₈

C₂²⋊D₄₇

commutator

C₄×C₄₇

C₂×C₁₆

Frattini

C₄×C₈

C₂×D₄₇

Fitting

C₈×D₄×C₄₇

C₂

socle

C₂²×C₄₇

C₂²⋊C₈

hypercenter

C₈×D₄

D₄₇

hypocenter

C₄₇

D₄⋊C₁₆

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×D₄

N	H ≅ G/N	type
1. C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
2. C₄×C₄₇⋊C₁₆	C₂	semidirect
25. D₄×C₄₇	C₁₆	semidirect
54. C₄₇	D₄⋊C₁₆	semidirect
76. D₄	C₄₇⋊C₁₆	semidirect

H ≅ G/N

type

1. C₄⋊(C₄₇⋊C₁₆)

C₂

semidirect

2. C₄×C₄₇⋊C₁₆

C₂

semidirect

25. D₄×C₄₇

C₁₆

semidirect

54. C₄₇

D₄⋊C₁₆

semidirect

76. D₄

C₄₇⋊C₁₆

semidirect

Subgroups — D₄⋊(C₄₇⋊C₁₆) #20241343

Conjugacy classes of subgroups

Complements

Subgroups — D4⋊(C47⋊C16) #20241343

Conjugacy classes of subgroups

Complements

Subgroups — D₄⋊(C₄₇⋊C₁₆) #20241343