Group #19132749 — subgroups

Subgroups — #19132749

Order 5504.

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

normal subgroups only

This group has 106 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	#14582698	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582648	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#456	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
5	#13063244	—	2	1	no	—
6	2₋¹⁺⁴×C₄₃	C₄	1	1	yes	characteristic
7	#137×C₄₃	—	2	1	no	—
8	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
9	#104×C₄₃	—	2	1	no	—
10	#101×C₄₃	C₄	1	1	yes	characteristic
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×Q₈×C₄₃	D₄	1	1	yes	characteristic
17	Q₁₆×C₄₃	—	4	1	no	—
18	SD₁₆×C₄₃	—	4	1	no	—
19	M₁₆×C₄₃	—	2	1	no	—
20	C₄⋊C₄×C₄₃	—	4	1	no	—
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	#10621877	—	4	1	no	—
23	C₂×C₄₃⋊C₈	—	4	1	no	—
24	Q₈×C₄₃	—	2	1	no	—
25	Q₈×C₄₃	—	4	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	C₂×C₄×C₄₃	—	2	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	C₈×C₄₃	—	4	1	no	—
38	C₄₃⋊C₈	—	8	1	no	—
39	C₄₃⋊C₈	—	8	1	no	—
40	C₂²×C₄₃	—	4	1	no	—
41	C₂²×C₄₃	#99	1	1	yes	characteristic
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	—	2	1	no	—
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	#1405	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	—	2	1	no	—
50	C₂×C₄₃	—	8	1	no	—
51	C₂×C₄₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
52	#456	D₄₃	1	1	yes	characteristic
53	#356	—	43	1	no	—
54	#333	—	43	1	no	—
55	C₄₃	#1405	1	1	yes	characteristic, complemented, Sylow
56	2₋¹⁺⁴	Dic₄₃	1	1	yes	characteristic
57	#137	—	2	1	no	—
58	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
59	C₄⋊C₈	—	86	1	no	—
60	#104	—	2	1	no	—
61	#101	—	86	1	no	—
62	#101	Dic₄₃	1	1	yes	characteristic
63	#41	—	2	1	no	—
64	#41	—	4	1	no	—
65	#41	—	4	1	no	—
66	C₂×Q₈	—	4	1	no	—
67	C₂×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
68	C₂×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
69	Q₁₆	—	4	1	no	—
70	SD₁₆	—	4	1	no	—
71	M₁₆	—	2	1	no	—
72	M₁₆	—	172	1	no	—
73	C₂×C₈	—	172	1	no	—
74	C₄⋊C₄	—	4	1	no	—
75	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
76	Q₈	—	2	1	no	—
77	Q₈	—	4	1	no	—
78	Q₈	—	4	1	no	—
79	Q₈	—	4	1	no	—
80	D₄	—	2	1	no	—
81	D₄	—	4	1	no	—
82	D₄	—	4	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	—	4	2	no	—
88	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
89	C₈	—	4	1	no	—
90	C₈	—	344	1	no	—
91	C₈	—	344	1	no	—
92	C₂²	—	4	1	no	—
93	C₂²	#13063240	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	4	1	no	—
98	C₄	—	4	1	no	—
99	C₄	—	4	1	no	—
100	C₂	—	2	1	no	—
101	C₂	—	8	1	no	—
102	C₂	#14582686	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582698

C₂

yes

maximal, characteristic, complemented

#14582648

C₂

yes

maximal, characteristic, complemented

C₄₃×#456

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₈)

—

#13063244

—

2₋¹⁺⁴×C₄₃

C₄

yes

characteristic

#137×C₄₃

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

#104×C₄₃

—

#101×C₄₃

C₄

yes

characteristic

#41×C₄₃

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×Q₈×C₄₃

D₄

yes

characteristic

Q₁₆×C₄₃

—

SD₁₆×C₄₃

—

M₁₆×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

#99

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

#1405

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

AΣL(1,𝔽₁₆)

yes

characteristic

#456

D₄₃

yes

characteristic

#356

—

#333

—

C₄₃

#1405

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

Dic₄₃

yes

characteristic

#137

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

#104

—

#101

—

#101

Dic₄₃

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₄₃

yes

characteristic

C₂×Q₈

C₂²⋊D₄₃

yes

characteristic

Q₁₆

—

SD₁₆

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₄²

C₂²⋊D₄₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₈

—

C₈

—

344

—

C₈

—

344

—

C₂²

—

C₂²

#13063240

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

100

C₂

—

101

C₂

—

102

C₂

#14582686

yes

characteristic

	subgroup	G/H
center	C₂	#14582686
commutator	C₂×Q₈×C₄₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₄₃
Fitting	C₄₃×#456	C₂
socle	C₂×C₄₃	AΣL(1,𝔽₁₆)
hypercenter	#456	D₄₃
hypocenter	C₄₃	#1405
LCS	G ▷ C₂×Q₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #456

subgroup

G/H

center

C₂

#14582686

commutator

C₂×Q₈×C₄₃

C₂×C₄

Frattini

C₄⋊Q₈

C₂×D₄₃

Fitting

C₄₃×#456

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 ◁ C₄⋊Q₈ ◁ #456

N	H ≅ G/N	type
1. #14582698	C₂	semidirect
2. #14582648	C₂	semidirect
55. C₄₃	#1405	semidirect

H ≅ G/N

type

1. #14582698

C₂

semidirect

2. #14582648

C₂

semidirect

55. C₄₃

#1405

semidirect

Subgroups — #19132749

Conjugacy classes of subgroups

Complements