Group #19132746 — subgroups

Subgroups — #19132746

Order 5504.

112 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 25 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	#14582694	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582639	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#454	C₂	1	1	yes	maximal, characteristic
4	#13063240	—	2	1	no	—
5	#13063236	—	2	1	no	—
6	2₋¹⁺⁴×C₄₃	C₄	1	1	yes	characteristic, complemented
7	AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
8	#124×C₄₃	C₂²	1	1	yes	characteristic
9	#104×C₄₃	—	2	1	no	—
10	#101×C₄₃	C₄	1	1	yes	characteristic, complemented
11	#41×C₄₃	—	2	1	no	—
12	#41×C₄₃	—	4	1	no	—
13	#41×C₄₃	—	4	1	no	—
14	C₂×Q₈×C₄₃	—	4	1	no	—
15	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
17	SD₁₆×C₄₃	—	4	1	no	—
18	D₈×C₄₃	—	4	1	no	—
19	M₁₆×C₄₃	—	2	1	no	—
20	C₂²⋊C₄×C₄₃	—	4	1	no	—
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	C₂²⋊Dic₄₃	—	4	1	no	—
23	C₂×C₄₃⋊C₈	—	4	1	no	—
24	C₂³×C₄₃	—	2	1	no	—
25	Q₈×C₄₃	—	2	1	no	—
26	Q₈×C₄₃	—	4	1	no	—
27	Q₈×C₄₃	—	4	1	no	—
28	D₄×C₄₃	—	2	1	no	—
29	D₄×C₄₃	—	4	1	no	—
30	D₄×C₄₃	—	4	1	no	—
31	D₄×C₄₃	—	4	1	no	—
32	C₂×C₄×C₄₃	—	2	1	no	—
33	C₂×C₄×C₄₃	—	2	1	no	—
34	C₂×C₄×C₄₃	—	4	1	no	—
35	C₂×C₄×C₄₃	—	4	2	no	—
36	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×Dic₄₃	—	8	1	no	—
38	C₈×C₄₃	—	4	1	no	—
39	C₄₃⋊C₈	—	4	2	no	—
40	C₂²×C₄₃	—	4	1	no	—
41	C₂²×C₄₃	—	4	1	no	—
42	C₂²×C₄₃	—	8	1	no	—
43	C₂²×C₄₃	#99	1	1	yes	characteristic
44	C₄×C₄₃	—	2	1	no	—
45	C₄×C₄₃	—	4	1	no	—
46	C₄×C₄₃	—	4	1	no	—
47	C₄×C₄₃	—	4	1	no	—
48	Dic₄₃	—	16	1	no	—
49	#1404	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	1	no	—
51	C₂×C₄₃	—	8	1	no	—
52	C₂×C₄₃	—	8	1	no	—
53	C₂×C₄₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
54	#454	D₄₃	1	1	yes	characteristic
55	#354	—	43	1	no	—
56	#329	—	43	1	no	—
57	C₄₃	#1404	1	1	yes	characteristic, complemented, Sylow
58	2₋¹⁺⁴	Dic₄₃	1	1	yes	characteristic, complemented
59	AGL(1,ℤ/8)	—	2	1	no	—
60	#124	C₂×D₄₃	1	1	yes	characteristic
61	#104	—	2	1	no	—
62	#101	Dic₄₃	1	1	yes	characteristic, complemented
63	#99	—	86	1	no	—
64	#97	—	86	1	no	—
65	#41	—	2	1	no	—
66	#41	—	4	1	no	—
67	#41	—	4	1	no	—
68	C₂×Q₈	—	4	1	no	—
69	C₂×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
70	C₂×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
71	SD₁₆	—	4	1	no	—
72	D₈	—	4	1	no	—
73	M₁₆	—	2	1	no	—
74	C₂×C₈	—	172	1	no	—
75	C₂²⋊C₄	—	4	1	no	—
76	C₂²⋊C₄	—	172	1	no	—
77	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
78	C₂³	—	2	1	no	—
79	Q₈	—	2	1	no	—
80	Q₈	—	4	1	no	—
81	Q₈	—	4	1	no	—
82	D₄	—	2	1	no	—
83	D₄	—	4	1	no	—
84	D₄	—	4	1	no	—
85	D₄	—	4	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	4	1	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	344	1	no	—
91	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
92	C₈	—	4	1	no	—
93	C₈	—	172	2	no	—
94	C₂²	—	4	1	no	—
95	C₂²	—	4	1	no	—
96	C₂²	—	8	1	no	—
97	C₂²	#13063240	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	4	1	no	—
100	C₄	—	4	1	no	—
101	C₄	—	4	1	no	—
102	C₄	—	688	1	no	—
103	C₂	—	2	1	no	—
104	C₂	—	8	1	no	—
105	C₂	—	8	1	no	—
106	C₂	#14582686	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582694

C₂

yes

maximal, characteristic, complemented

#14582639

C₂

yes

maximal, characteristic, complemented

C₄₃×#454

C₂

yes

maximal, characteristic

#13063240

—

#13063236

—

2₋¹⁺⁴×C₄₃

C₄

yes

characteristic, complemented

AGL(1,ℤ/8)×C₄₃

—

#124×C₄₃

C₂²

yes

characteristic

#104×C₄₃

—

#101×C₄₃

C₄

yes

characteristic, complemented

#41×C₄₃

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×D₄×C₄₃

D₄

yes

characteristic

SD₁₆×C₄₃

—

D₈×C₄₃

—

M₁₆×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₂²⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#99

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#1404

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

AΣL(1,𝔽₁₆)

yes

characteristic

#454

D₄₃

yes

characteristic

#354

—

#329

—

C₄₃

#1404

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

Dic₄₃

yes

characteristic, complemented

AGL(1,ℤ/8)

—

#124

C₂×D₄₃

yes

characteristic

#104

—

#101

Dic₄₃

yes

characteristic, complemented

—

—

—

—

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₄₃

yes

characteristic

C₂×D₄

C₂²⋊D₄₃

yes

characteristic

SD₁₆

—

D₈

—

M₁₆

—

C₂×C₈

—

172

—

C₂²⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₈

—

C₈

—

172

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#13063240

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

688

—

103

C₂

—

104

C₂

—

105

C₂

—

106

C₂

#14582686

yes

characteristic

	subgroup	G/H
center	C₂	#14582686
commutator	C₂×Q₈×C₄₃	C₂×C₄
Frattini	#124	C₂×D₄₃
Fitting	C₄₃×#454	C₂
socle	C₂×C₄₃	AΣL(1,𝔽₁₆)
hypercenter	#454	D₄₃
hypocenter	C₄₃	#1404
LCS	G ▷ C₂×Q₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #454

subgroup

G/H

center

C₂

#14582686

commutator

C₂×Q₈×C₄₃

C₂×C₄

Frattini

#124

C₂×D₄₃

Fitting

C₄₃×#454

C₂

socle

C₂×C₄₃

AΣL(1,𝔽₁₆)

D₄₃

C₄₃

G ▷ C₂×Q₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #454

N	H ≅ G/N	type
1. #14582694	C₂	semidirect
2. #14582639	C₂	semidirect
6. 2₋¹⁺⁴×C₄₃	C₄	semidirect
10. #101×C₄₃	C₄	semidirect
57. C₄₃	#1404	semidirect
58. 2₋¹⁺⁴	Dic₄₃	semidirect
62. #101	Dic₄₃	semidirect

H ≅ G/N

type

1. #14582694

C₂

semidirect

2. #14582639

C₂

semidirect

6. 2₋¹⁺⁴×C₄₃

C₄

semidirect

10. #101×C₄₃

C₄

semidirect

57. C₄₃

#1404

semidirect

58. 2₋¹⁺⁴

Dic₄₃

semidirect

62. #101

Dic₄₃

semidirect

Subgroups — #19132746

Conjugacy classes of subgroups

Complements