Group #43247916 — subgroups

Subgroups — #43247916

Order 28352.

128 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 41 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	C₂×#20296776	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#20296775	C₂	1	1	yes	maximal, characteristic, complemented
3	#28381882	C₂	1	1	yes	maximal, characteristic
4	#28381851	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#28381806	C₂	1	1	yes	maximal, characteristic, complemented
7	#102×C₄₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₈₈₆	C₂²	1	1	yes	characteristic
9	C₂×D₁₇₇₂	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊D₄₄₃	—	2	1	no	—
11	C₂×C₂²⋊D₄₄₃	—	2	1	no	—
12	#20296776	—	2	2	no	—
13	#20296775	—	2	2	no	—
14	C₂×C₄₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	Dic₄₄₃⋊C₄	—	2	1	no	—
16	C₄×Dic₄₄₃	—	2	1	no	—
17	C₄×Dic₄₄₃	C₂²	1	1	yes	characteristic
18	C₂×D₄×C₄₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₄₄₃	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×C₄₄₃	C₂²	1	1	yes	characteristic
21	C₂²×D₄₄₃	—	2	1	no	—
22	Dic₈₈₆	—	2	1	no	—
23	Dic₈₈₆	D₄	1	2	yes	complemented
24	D₁₇₇₂	—	2	1	no	—
25	D₁₇₇₂	—	2	1	no	—
26	C₂²⋊D₄₄₃	—	4	2	no	—
27	C₂²⋊D₄₄₃	—	4	2	no	—
28	C₂×Dic₄₄₃	—	2	1	no	—
29	C₂×Dic₄₄₃	D₄	1	1	yes	characteristic
30	C₂×Dic₄₄₃	D₄	1	1	yes	characteristic
31	C₄₄₃⋊C₈	—	2	1	no	—
32	C₂³×C₄₄₃	—	2	1	no	—
33	D₄×C₄₄₃	—	2	1	no	—
34	D₄×C₄₄₃	—	2	1	no	—
35	C₂×C₄×C₄₄₃	—	2	1	no	—
36	C₂×C₄×C₄₄₃	C₂³	1	1	yes	characteristic
37	C₈×C₄₄₃	—	2	1	no	—
38	C₂²×C₄₄₃	—	4	1	no	—
39	C₂²×C₄₄₃	—	4	1	no	—
40	C₂²×C₄₄₃	—	4	1	no	—
41	C₂²×C₄₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×D₄₄₃	—	4	1	no	—
43	C₂×D₄₄₃	—	4	1	no	—
44	C₂×D₄₄₃	—	4	1	no	—
45	C₄×C₄₄₃	—	4	1	no	—
46	C₄×C₄₄₃	C₂×D₄	1	1	yes	characteristic
47	C₄×C₄₄₃	#41	1	1	yes	characteristic
48	Dic₄₄₃	—	2	2	no	—
49	Dic₄₄₃	—	2	1	no	—
50	Dic₄₄₃	SD₁₆	1	2	yes	complemented
51	C₂×C₄₄₃	—	8	1	no	—
52	C₂×C₄₄₃	#121	1	1	yes	characteristic
53	C₂×C₄₄₃	C₂×SD₁₆	1	1	yes	characteristic
54	C₂×C₄₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
55	D₄₄₃	—	8	1	no	—
56	C₄₄₃	#460	1	1	yes	characteristic, complemented, Sylow
57	#460	—	443	1	no	maximal, Sylow
58	C₂×SD₁₆	—	443	1	no	—
59	C₂×SD₁₆	—	443	1	no	—
60	#127	—	443	1	no	—
61	C₄×Q₈	—	443	1	no	—
62	C₄⋊C₈	—	443	1	no	—
63	#102	—	443	1	no	—
64	#102	D₄₄₃	1	1	yes	characteristic, complemented
65	C₂×Q₈	—	443	1	no	—
66	C₂×D₄	—	886	1	no	—
67	C₂×D₄	—	886	1	no	—
68	C₂×D₄	—	443	1	no	—
69	C₂×D₄	C₂×D₄₄₃	1	1	yes	characteristic
70	SD₁₆	—	886	2	no	—
71	SD₁₆	—	886	2	no	—
72	C₂×C₈	—	443	1	no	—
73	C₂×C₈	C₂×D₄₄₃	1	1	yes	characteristic
74	C₄⋊C₄	—	886	1	no	—
75	C₄⋊C₄	C₂×D₄₄₃	1	1	yes	characteristic
76	C₄²	—	886	1	no	—
77	C₄²	—	443	1	no	—
78	C₂³	—	2	1	no	—
79	C₂³	—	886	1	no	—
80	Q₈	—	886	1	no	—
81	Q₈	—	443	2	no	—
82	D₄	—	2	1	no	—
83	D₄	—	2	1	no	—
84	D₄	—	886	1	no	—
85	D₄	—	886	1	no	—
86	D₄	—	1772	2	no	—
87	D₄	—	1772	2	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	886	1	no	—
90	C₂×C₄	—	443	1	no	—
91	C₂×C₄	—	443	1	no	—
92	C₂×C₄	C₂²×D₄₄₃	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	886	1	no	—
95	C₂²	—	4	1	no	—
96	C₂²	—	4	1	no	—
97	C₂²	—	4	1	no	—
98	C₂²	—	1772	1	no	—
99	C₂²	—	1772	1	no	—
100	C₂²	—	1772	1	no	—
101	C₂²	D₄×D₄₄₃	1	1	yes	characteristic
102	C₄	—	4	1	no	—
103	C₄	—	886	2	no	—
104	C₄	—	886	1	no	—
105	C₄	—	443	2	no	—
106	C₄	D₄×D₄₄₃	1	1	yes	characteristic
107	C₄	#20296787	1	1	yes	characteristic
108	C₂	—	8	1	no	—
109	C₂	—	3544	1	no	—
110	C₂	#28381859	1	1	yes	characteristic
111	C₂	SD₁₆×D₄₄₃	1	1	yes	characteristic
112	C₂	#28381910	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#20296776

C₂

yes

maximal, characteristic, complemented

C₂×#20296775

C₂

yes

maximal, characteristic, complemented

#28381882

C₂

yes

maximal, characteristic

#28381851

C₂

yes

maximal, characteristic, complemented

Dic₄₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

#28381806

C₂

yes

maximal, characteristic, complemented

#102×C₄₄₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₈₈₆

C₂²

yes

characteristic

C₂×D₁₇₇₂

C₂²

yes

characteristic

C₂×C₂²⋊D₄₄₃

—

C₂×C₂²⋊D₄₄₃

—

#20296776

—

#20296775

—

C₂×C₄₄₃⋊C₈

C₂²

yes

characteristic

Dic₄₄₃⋊C₄

—

C₄×Dic₄₄₃

—

C₄×Dic₄₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₄₃

C₂²

yes

characteristic

C₂×C₈×C₄₄₃

C₂²

yes

characteristic

C₄⋊C₄×C₄₄₃

C₂²

yes

characteristic

C₂²×D₄₄₃

—

Dic₈₈₆

—

Dic₈₈₆

D₄

yes

complemented

D₁₇₇₂

—

D₁₇₇₂

—

C₂²⋊D₄₄₃

—

C₂²⋊D₄₄₃

—

C₂×Dic₄₄₃

—

C₂×Dic₄₄₃

D₄

yes

characteristic

C₂×Dic₄₄₃

D₄

yes

characteristic

C₄₄₃⋊C₈

—

C₂³×C₄₄₃

—

D₄×C₄₄₃

—

D₄×C₄₄₃

—

C₂×C₄×C₄₄₃

—

C₂×C₄×C₄₄₃

C₂³

yes

characteristic

C₈×C₄₄₃

—

C₂²×C₄₄₃

—

C₂²×C₄₄₃

—

C₂²×C₄₄₃

—

C₂²×C₄₄₃

C₂×D₄

yes

characteristic

C₂×D₄₄₃

—

C₂×D₄₄₃

—

C₂×D₄₄₃

—

C₄×C₄₄₃

—

C₄×C₄₄₃

C₂×D₄

yes

characteristic

C₄×C₄₄₃

#41

yes

characteristic

Dic₄₄₃

—

Dic₄₄₃

—

Dic₄₄₃

SD₁₆

yes

complemented

C₂×C₄₄₃

—

C₂×C₄₄₃

#121

yes

characteristic

C₂×C₄₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄₄₃

AGL(1,ℤ/8)

yes

characteristic

D₄₄₃

—

C₄₄₃

#460

yes

characteristic, complemented, Sylow

#460

—

443

maximal, Sylow

C₂×SD₁₆

—

443

—

C₂×SD₁₆

—

443

—

#127

—

443

—

C₄×Q₈

—

443

—

C₄⋊C₈

—

443

—

#102

—

443

—

#102

D₄₄₃

yes

characteristic, complemented

C₂×Q₈

—

443

—

C₂×D₄

—

886

—

C₂×D₄

—

886

—

C₂×D₄

—

443

—

C₂×D₄

C₂×D₄₄₃

yes

characteristic

SD₁₆

—

886

—

SD₁₆

—

886

—

C₂×C₈

—

443

—

C₂×C₈

C₂×D₄₄₃

yes

characteristic

C₄⋊C₄

—

886

—

C₄⋊C₄

C₂×D₄₄₃

yes

characteristic

C₄²

—

886

—

C₄²

—

443

—

C₂³

—

C₂³

—

886

—

Q₈

—

886

—

Q₈

—

443

—

D₄

—

D₄

—

D₄

—

886

—

D₄

—

886

—

D₄

—

1772

—

D₄

—

1772

—

C₂×C₄

—

C₂×C₄

—

886

—

C₂×C₄

—

443

—

C₂×C₄

—

443

—

C₂×C₄

C₂²×D₄₄₃

yes

characteristic

C₈

—

C₈

—

886

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

1772

—

C₂²

—

1772

—

100

C₂²

—

1772

—

101

C₂²

D₄×D₄₄₃

yes

characteristic

102

C₄

—

103

C₄

—

886

—

104

C₄

—

886

—

105

C₄

—

443

—

106

C₄

D₄×D₄₄₃

yes

characteristic

107

C₄

#20296787

yes

characteristic

108

C₂

—

109

C₂

—

3544

—

110

C₂

#28381859

yes

characteristic

111

C₂

SD₁₆×D₄₄₃

yes

characteristic

112

C₂

#28381910

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₄₃
commutator, cosocle	C₂×C₄×C₄₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₄₃
Fitting	#102×C₄₄₃	C₂
socle	C₂²×C₄₄₃	C₂×D₄
prime radical	#28381882	C₂
hypercenter	#102	D₄₄₃
hypocenter	C₄₄₃	#460
LCS	G ▷ C₂×C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

subgroup

G/H

center

C₂²

D₄×D₄₄₃

commutator, cosocle

C₂×C₄×C₄₄₃

C₂³

Frattini

C₂×C₄

C₂²×D₄₄₃

Fitting

#102×C₄₄₃

C₂

socle

C₂²×C₄₄₃

C₂×D₄

C₂

D₄₄₃

C₄₄₃

G ▷ C₂×C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

N	H ≅ G/N	type
1. C₂×#20296776	C₂	semidirect
2. C₂×#20296775	C₂	semidirect
4. #28381851	C₂	semidirect
5. Dic₄₄₃⋊C₈	C₂	semidirect
6. #28381806	C₂	semidirect
7. #102×C₄₄₃	C₂	semidirect
23. Dic₈₈₆	D₄	semidirect
50. Dic₄₄₃	SD₁₆	semidirect
56. C₄₄₃	#460	semidirect
64. #102	D₄₄₃	semidirect

H ≅ G/N

type

1. C₂×#20296776

C₂

semidirect

2. C₂×#20296775

C₂

semidirect

4. #28381851

C₂

semidirect

5. Dic₄₄₃⋊C₈

C₂

semidirect

6. #28381806

C₂

semidirect

7. #102×C₄₄₃

C₂

semidirect

23. Dic₈₈₆

D₄

semidirect

50. Dic₄₄₃

SD₁₆

semidirect

56. C₄₄₃

#460

semidirect

64. #102

D₄₄₃

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#20296776	2
C₂×#20296775	2
#28381882	2
#28381851	2
Dic₄₄₃⋊C₈	2
#28381806	2
#102×C₄₄₃	2
#460	443

subgroup

index

Dic₄₄₃⋊C₈

#102×C₄₄₃

443

Subgroups — #43247916

Conjugacy classes of subgroups

Complements

Maximal subgroups