Group #14583714 — subgroups

Subgroups — #14583714

Order 2752.

248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 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	#13063372	C₂	1	1	yes	maximal, characteristic, complemented
2	#13063356	C₂	1	3	yes	maximal, complemented
3	#13063355	C₂	1	3	yes	maximal, complemented
4	#13063345	C₂	1	3	yes	maximal, complemented
5	C₂×#10621885	C₂	1	3	yes	maximal, complemented
6	#13063332	C₂	1	1	yes	maximal, characteristic, complemented
7	2₋¹⁺⁴×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#41×C₄₃	—	2	3	no	—
9	#41×C₄₃	C₂²	1	3	yes	—
10	#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₄₃	—	2	1	no	—
12	C₂×Q₈×C₄₃	C₂²	1	3	yes	—
13	Q₈×D₄₃	—	2	1	no	—
14	#10621900	—	2	3	no	—
15	#10621898	C₂²	1	3	yes	—
16	C₂×Dic₈₆	C₂²	1	3	yes	—
17	#10621885	C₂²	1	3	yes	—
18	#10621885	C₂²	1	6	yes	—
19	#10621884	C₂²	1	3	yes	—
20	#10621883	C₂²	1	3	yes	—
21	#10621882	C₂²	1	1	yes	characteristic
22	#10621877	C₂²	1	3	yes	—
23	C₂×C₄₃⋊C₈	C₂²	1	3	yes	—
24	Q₈×C₄₃	—	2	3	no	—
25	Q₈×C₄₃	D₄	1	1	yes	characteristic
26	Q₈×C₄₃	C₂³	1	3	yes	—
27	D₄×C₄₃	—	2	3	no	—
28	D₄×C₄₃	D₄	1	3	yes	—
29	D₄×C₄₃	C₂³	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	2	3	no	—
31	C₂×C₄×C₄₃	—	2	3	no	—
32	C₂×C₄×C₄₃	C₂³	1	3	yes	—
33	C₂²⋊D₄₃	—	2	3	no	—
34	C₂×Dic₄₃	—	2	3	no	—
35	D₁₇₂	C₂³	1	1	yes	characteristic
36	C₄×D₄₃	—	2	3	no	—
37	Dic₈₆	—	2	3	no	—
38	Dic₈₆	C₂³	1	3	yes	—
39	C₄₃⋊C₈	C₂³	1	1	yes	characteristic
40	C₄₃⋊C₈	C₂³	1	3	yes	—
41	C₂²×C₄₃	—	2	1	no	—
42	C₂²×C₄₃	C₂×D₄	1	3	yes	—
43	C₂×D₄₃	—	2	1	no	—
44	C₄×C₄₃	—	2	3	no	—
45	C₄×C₄₃	C₂×D₄	1	3	yes	—
46	C₄×C₄₃	C₂⁴	1	1	yes	characteristic
47	Dic₄₃	—	2	3	no	—
48	C₂×C₄₃	—	2	3	no	—
49	C₂×C₄₃	—	4	1	no	—
50	C₂×C₄₃	C₂²×D₄	1	1	yes	characteristic
51	D₄₃	—	4	1	no	—
52	#578	—	43	1	no	maximal, Sylow
53	C₄₃	#578	1	1	yes	characteristic, complemented, Sylow
54	2₋¹⁺⁴	—	43	1	no	—
55	2₋¹⁺⁴	D₄₃	1	1	yes	characteristic, complemented
56	#137	—	43	3	no	—
57	#137	—	43	3	no	—
58	#135	—	43	3	no	—
59	C₂×Q₁₆	—	43	3	no	—
60	#131	—	43	1	no	—
61	#41	—	2	3	no	—
62	#41	—	43	3	no	—
63	#41	—	86	3	no	—
64	#41	C₂×D₄₃	1	3	yes	—
65	#41	C₂×D₄₃	1	1	yes	characteristic
66	C₂×Q₈	—	2	1	no	—
67	C₂×Q₈	—	43	3	no	—
68	C₂×Q₈	—	86	1	no	—
69	C₂×Q₈	C₂×D₄₃	1	3	yes	—
70	Q₁₆	—	43	3	no	—
71	Q₁₆	—	43	6	no	—
72	SD₁₆	—	43	3	no	—
73	SD₁₆	—	43	3	no	—
74	D₈	—	43	1	no	—
75	M₁₆	—	43	3	no	—
76	C₂×C₈	—	43	3	no	—
77	Q₈	—	2	3	no	—
78	Q₈	—	43	3	no	—
79	Q₈	—	86	3	no	—
80	Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
81	Q₈	C₂²×D₄₃	1	3	yes	—
82	D₄	—	2	3	no	—
83	D₄	—	43	1	no	—
84	D₄	—	86	3	no	—
85	D₄	C₂²⋊D₄₃	1	3	yes	—
86	D₄	C₂²×D₄₃	1	1	yes	characteristic
87	C₂×C₄	—	2	3	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	86	3	no	—
90	C₂×C₄	—	86	3	no	—
91	C₂×C₄	C₂²×D₄₃	1	3	yes	—
92	C₈	—	43	1	no	—
93	C₈	—	43	3	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	86	1	no	—
96	C₂²	C₂×C₂²⋊D₄₃	1	3	yes	—
97	C₄	—	2	3	no	—
98	C₄	—	86	3	no	—
99	C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
100	C₄	C₂³×D₄₃	1	1	yes	characteristic
101	C₂	—	2	3	no	—
102	C₂	—	4	1	no	—
103	C₂	—	172	1	no	—
104	C₂	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13063372

C₂

yes

maximal, characteristic, complemented

#13063356

C₂

yes

maximal, complemented

#13063355

C₂

yes

maximal, complemented

#13063345

C₂

yes

maximal, complemented

C₂×#10621885

C₂

yes

maximal, complemented

#13063332

C₂

yes

maximal, characteristic, complemented

2₋¹⁺⁴×C₄₃

C₂

yes

maximal, characteristic, complemented

#41×C₄₃

—

#41×C₄₃

C₂²

yes

—

#41×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂²

yes

—

Q₈×D₄₃

—

#10621900

—

#10621898

C₂²

yes

—

C₂×Dic₈₆

C₂²

yes

—

#10621885

C₂²

yes

—

#10621885

C₂²

yes

—

#10621884

C₂²

yes

—

#10621883

C₂²

yes

—

#10621882

C₂²

yes

characteristic

#10621877

C₂²

yes

—

C₂×C₄₃⋊C₈

C₂²

yes

—

Q₈×C₄₃

—

Q₈×C₄₃

D₄

yes

characteristic

Q₈×C₄₃

C₂³

yes

—

D₄×C₄₃

—

D₄×C₄₃

D₄

yes

—

D₄×C₄₃

C₂³

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂³

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

C₂³

yes

characteristic

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

C₂³

yes

—

C₄₃⋊C₈

C₂³

yes

characteristic

C₄₃⋊C₈

C₂³

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₄

yes

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×D₄

yes

—

C₄×C₄₃

C₂⁴

yes

characteristic

Dic₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₂²×D₄

yes

characteristic

D₄₃

—

#578

—

maximal, Sylow

C₄₃

#578

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

—

2₋¹⁺⁴

D₄₃

yes

characteristic, complemented

#137

—

#137

—

#135

—

C₂×Q₁₆

—

—

—

—

—

C₂×D₄₃

yes

—

#41

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×D₄₃

yes

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

C₂×C₈

—

Q₈

—

Q₈

—

Q₈

—

Q₈

C₂²⋊D₄₃

yes

characteristic

Q₈

C₂²×D₄₃

yes

—

D₄

—

D₄

—

D₄

—

D₄

C₂²⋊D₄₃

yes

—

D₄

C₂²×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×D₄₃

yes

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊D₄₃

yes

—

C₄

—

C₄

—

C₄

C₂×C₂²⋊D₄₃

yes

—

100

C₄

C₂³×D₄₃

yes

characteristic

101

C₂

—

102

C₂

—

103

C₂

—

172

—

104

C₂

C₂²×C₂²⋊D₄₃

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₄×C₄₃	C₂⁴
Frattini	C₄	C₂³×D₄₃
Fitting	2₋¹⁺⁴×C₄₃	C₂
socle	C₂×C₄₃	C₂²×D₄
hypercenter	2₋¹⁺⁴	D₄₃
hypocenter	C₄₃	#578
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ 2₋¹⁺⁴

subgroup

G/H

center

C₂

C₂²×C₂²⋊D₄₃

commutator, cosocle

C₄×C₄₃

C₂⁴

Frattini

C₄

C₂³×D₄₃

Fitting

2₋¹⁺⁴×C₄₃

C₂

socle

C₂×C₄₃

C₂²×D₄

hypercenter

2₋¹⁺⁴

D₄₃

hypocenter

C₄₃

#578

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ #41 ◁ 2₋¹⁺⁴

N	H ≅ G/N	type
1. #13063372	C₂	semidirect
2. #13063356	C₂	semidirect
3. #13063355	C₂	semidirect
4. #13063345	C₂	semidirect
5. C₂×#10621885	C₂	semidirect
6. #13063332	C₂	semidirect
7. 2₋¹⁺⁴×C₄₃	C₂	semidirect
53. C₄₃	#578	semidirect
55. 2₋¹⁺⁴	D₄₃	semidirect

H ≅ G/N

type

1. #13063372

C₂

semidirect

2. #13063356

C₂

semidirect

3. #13063355

C₂

semidirect

4. #13063345

C₂

semidirect

5. C₂×#10621885

C₂

semidirect

6. #13063332

C₂

semidirect

7. 2₋¹⁺⁴×C₄₃

C₂

semidirect

53. C₄₃

#578

semidirect

55. 2₋¹⁺⁴

D₄₃

semidirect

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

subgroup	index
#13063372	2
#13063356	2
#13063355	2
#13063345	2
C₂×#10621885	2
#13063332	2
2₋¹⁺⁴×C₄₃	2
#578	43

subgroup

index

2₋¹⁺⁴×C₄₃

Subgroups — #14583714

Conjugacy classes of subgroups

Complements

Maximal subgroups