Group #19143517 — subgroups

Subgroups — C₂×Q₈×C₄₃⋊C₈ #19143517

Order 5504.

440 conjugacy classes of subgroups; only the 333 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 333 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	Q₈×C₄₃⋊C₈	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₄⋊(C₄₃⋊C₈)	C₂	1	3	yes	maximal
3	C₂×C₄×C₄₃⋊C₈	C₂	1	3	yes	maximal
4	C₂×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₃⋊C₈	C₂²	1	3	yes	—
6	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊(C₄₃⋊C₈)	C₂²	1	12	yes	—
8	C₄×C₄₃⋊C₈	C₂²	1	12	yes	—
9	C₂²×Q₈×C₄₃	C₄	1	1	yes	characteristic
10	C₄×Q₈×C₄₃	C₄	1	4	yes	—
11	C₄×Q₈×C₄₃	C₂²	1	4	yes	—
12	C₂×C₄⋊C₄×C₄₃	C₄	1	3	yes	—
13	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
14	C₂×Q₈×C₄₃	C₈	1	8	yes	complemented
15	C₂×Q₈×C₄₃	C₂×C₄	1	4	yes	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	3	yes	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	3	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₄₃	C₂×C₄	1	12	yes	—
20	C₄²×C₄₃	C₂×C₄	1	6	yes	—
21	C₄²×C₄₃	C₂³	1	6	yes	—
22	C₂×C₄₃⋊C₈	—	2	6	no	—
23	C₂×C₄₃⋊C₈	Q₈	1	4	yes	direct product factor
24	C₂×C₄₃⋊C₈	C₂³	1	6	yes	—
25	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
26	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
27	Q₈×C₄₃	C₂×C₈	1	16	yes	complemented
28	C₂×C₄×C₄₃	—	2	6	no	—
29	C₂×C₄×C₄₃	C₂×C₈	1	12	yes	—
30	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
31	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
33	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₄₃	#41	1	2	yes	—
35	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
36	C₄₃⋊C₈	—	2	6	no	—
37	C₄₃⋊C₈	C₂×Q₈	1	4	yes	direct product factor
38	C₂²×C₄₃	C₄×Q₈	1	2	yes	—
39	C₂²×C₄₃	C₂²×C₈	1	2	yes	—
40	C₂²×C₄₃	#131	1	2	yes	—
41	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
42	C₄×C₄₃	—	2	6	no	—
43	C₄×C₄₃	C₄×Q₈	1	2	yes	—
44	C₄×C₄₃	C₂²×C₈	1	12	yes	—
45	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
46	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
47	C₂×C₈×Q₈	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	C₈×Q₈	1	4	yes	complemented
49	C₂×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
50	C₂×C₄₃	C₂³×C₈	1	1	yes	characteristic
51	C₂×C₄₃	C₂×#131	1	1	yes	characteristic
52	C₂×C₄×Q₈	D₄₃	1	1	yes	characteristic
53	C₈×Q₈	—	43	8	no	—
54	C₂×C₄⋊C₈	—	43	3	no	—
55	C₂×C₄×C₈	—	43	3	no	—
56	C₄₃	C₂×C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
57	C₂²×Q₈	Dic₄₃	1	1	yes	characteristic
58	C₂²×C₈	—	43	1	no	—
59	C₂²×C₈	—	43	3	no	—
60	C₄×Q₈	Dic₄₃	1	4	yes	—
61	C₄×Q₈	C₂×D₄₃	1	4	yes	—
62	C₂×C₄⋊C₄	Dic₄₃	1	3	yes	—
63	C₂×C₄²	C₂×D₄₃	1	3	yes	—
64	C₄⋊C₈	—	43	12	no	—
65	C₄×C₈	—	43	12	no	—
66	C₂×Q₈	C₄₃⋊C₈	1	8	yes	direct product factor
67	C₂×Q₈	C₂×Dic₄₃	1	4	yes	—
68	C₂²×C₄	C₂×Dic₄₃	1	3	yes	—
69	C₂²×C₄	C₂×Dic₄₃	1	3	yes	—
70	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
71	C₂×C₈	—	43	4	no	—
72	C₂×C₈	—	43	2	no	—
73	C₂×C₈	—	43	6	no	—
74	C₂×C₈	—	86	6	no	—
75	C₄⋊C₄	C₂×Dic₄₃	1	12	yes	—
76	C₄²	C₂×Dic₄₃	1	6	yes	—
77	C₄²	C₂²×D₄₃	1	6	yes	—
78	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
79	Q₈	C₂×C₄₃⋊C₈	1	16	yes	direct product factor
80	C₂×C₄	—	2	6	no	—
81	C₂×C₄	C₂×C₄₃⋊C₈	1	12	yes	—
82	C₂×C₄	Q₈×D₄₃	1	2	yes	—
83	C₂×C₄	#10621902	1	2	yes	—
84	C₂×C₄	C₂²×Dic₄₃	1	6	yes	—
85	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
86	C₂×C₄	C₂²×Dic₄₃	1	6	yes	—
87	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
88	C₈	—	43	4	no	—
89	C₈	—	86	6	no	—
90	C₂²	Q₈×Dic₄₃	1	2	yes	—
91	C₂²	C₂²×C₄₃⋊C₈	1	2	yes	—
92	C₂²	#13063332	1	2	yes	—
93	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
94	C₄	—	2	6	no	—
95	C₄	Q₈×Dic₄₃	1	2	yes	—
96	C₄	C₂²×C₄₃⋊C₈	1	12	yes	—
97	C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
98	C₄	C₂×#10621902	1	1	yes	characteristic
99	C₂	Q₈×C₄₃⋊C₈	1	4	yes	direct product factor
100	C₂	C₂×Q₈×Dic₄₃	1	1	yes	characteristic
101	C₂	C₂³×C₄₃⋊C₈	1	1	yes	characteristic
102	C₂	C₂×#13063332	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×C₄₃⋊C₈

C₂

yes

maximal, direct product factor

C₂×C₄⋊(C₄₃⋊C₈)

C₂

yes

maximal

C₂×C₄×C₄₃⋊C₈

C₂

yes

maximal

C₂×C₄×Q₈×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

—

C₂²×Q₈×C₄₃

C₄

yes

characteristic

C₄×Q₈×C₄₃

C₄

yes

—

C₄×Q₈×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₄

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

C₈

yes

complemented

C₂×Q₈×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂³

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

Q₈

yes

direct product factor

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

Q₈×C₄₃

C₂×C₈

yes

complemented

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

C₂×Q₈

yes

direct product factor

C₂²×C₄₃

C₄×Q₈

yes

—

C₂²×C₄₃

C₂²×C₈

yes

—

C₂²×C₄₃

#131

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄×Q₈

yes

—

C₄×C₄₃

C₂²×C₈

yes

—

C₄×C₄₃

C₂²×Q₈

yes

characteristic

C₄×C₄₃

C₂×#41

yes

characteristic

C₂×C₈×Q₈

—

maximal, Sylow

C₂×C₄₃

C₈×Q₈

yes

complemented

C₂×C₄₃

C₂×C₄×Q₈

yes

characteristic

C₂×C₄₃

C₂³×C₈

yes

characteristic

C₂×C₄₃

C₂×#131

yes

characteristic

C₂×C₄×Q₈

D₄₃

yes

characteristic

C₈×Q₈

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₄₃

C₂×C₈×Q₈

yes

characteristic, complemented, Sylow

C₂²×Q₈

Dic₄₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₄×Q₈

Dic₄₃

yes

—

C₄×Q₈

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

Dic₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

—

C₄⋊C₈

—

C₄×C₈

—

C₂×Q₈

C₄₃⋊C₈

yes

direct product factor

C₂×Q₈

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₄₃

yes

—

C₄²

C₂×Dic₄₃

yes

—

C₄²

C₂²×D₄₃

yes

—

C₂³

C₂²×Dic₄₃

yes

characteristic

Q₈

C₂×C₄₃⋊C₈

yes

direct product factor

C₂×C₄

—

C₂×C₄

C₂×C₄₃⋊C₈

yes

—

C₂×C₄

Q₈×D₄₃

yes

—

C₂×C₄

#10621902

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂³×D₄₃

yes

characteristic

C₈

—

C₈

—

C₂²

Q₈×Dic₄₃

yes

—

C₂²

C₂²×C₄₃⋊C₈

yes

—

C₂²

#13063332

yes

—

C₂²

C₂³×Dic₄₃

yes

characteristic

C₄

—

C₄

Q₈×Dic₄₃

yes

—

C₄

C₂²×C₄₃⋊C₈

yes

—

C₄

C₂×Q₈×D₄₃

yes

characteristic

C₄

C₂×#10621902

yes

characteristic

C₂

Q₈×C₄₃⋊C₈

yes

direct product factor

100

C₂

C₂×Q₈×Dic₄₃

yes

characteristic

101

C₂

C₂³×C₄₃⋊C₈

yes

characteristic

102

C₂

C₂×#13063332

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂×C₄₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×C₄×Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	C₂×C₄×Q₈	D₄₃
hypocenter	C₄₃	C₂×C₈×Q₈
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₃

commutator

C₂×C₄₃

C₂³×C₈

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×C₄×Q₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂²×C₄

hypercenter

C₂×C₄×Q₈

D₄₃

hypocenter

C₄₃

C₂×C₈×Q₈

LCS

G ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
1. Q₈×C₄₃⋊C₈	C₂	direct (N × H)
14. C₂×Q₈×C₄₃	C₈	semidirect
23. C₂×C₄₃⋊C₈	Q₈	direct (N × H)
27. Q₈×C₄₃	C₂×C₈	semidirect
37. C₄₃⋊C₈	C₂×Q₈	direct (N × H)
48. C₂×C₄₃	C₈×Q₈	semidirect
56. C₄₃	C₂×C₈×Q₈	semidirect
66. C₂×Q₈	C₄₃⋊C₈	direct (N × H)
79. Q₈	C₂×C₄₃⋊C₈	direct (N × H)
99. C₂	Q₈×C₄₃⋊C₈	direct (N × H)

H ≅ G/N

type

1. Q₈×C₄₃⋊C₈

C₂

direct (N × H)

14. C₂×Q₈×C₄₃

C₈

semidirect

23. C₂×C₄₃⋊C₈

Q₈

direct (N × H)

27. Q₈×C₄₃

C₂×C₈

semidirect

37. C₄₃⋊C₈

C₂×Q₈

direct (N × H)

48. C₂×C₄₃

C₈×Q₈

semidirect

56. C₄₃

C₂×C₈×Q₈

semidirect

66. C₂×Q₈

C₄₃⋊C₈

direct (N × H)

79. Q₈

C₂×C₄₃⋊C₈

direct (N × H)

99. C₂

Q₈×C₄₃⋊C₈

direct (N × H)

Subgroups — C₂×Q₈×C₄₃⋊C₈ #19143517

Conjugacy classes of subgroups

Complements

Subgroups — C2×Q8×C43⋊C8 #19143517

Conjugacy classes of subgroups

Complements

Subgroups — C₂×Q₈×C₄₃⋊C₈ #19143517