Group #19142995 — subgroups

Subgroups — C₂²×C₈×Dic₄₃ #19142995

Order 5504.

760 conjugacy classes of subgroups; only the 549 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 549 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	C₂³×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×Dic₄₃	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₄₃	C₄	1	2	yes	—
6	C₂²×C₄₃⋊C₈	C₄	1	8	yes	complemented
7	C₂²×C₄₃⋊C₈	C₂²	1	6	yes	—
8	C₂×C₄×Dic₄₃	C₄	1	6	yes	—
9	C₂×C₄×Dic₄₃	C₂²	1	6	yes	—
10	C₈×Dic₄₃	C₂²	1	16	yes	direct product factor
11	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₄₃	C₄	1	8	yes	complemented
13	C₂²×C₈×C₄₃	C₂²	1	6	yes	—
14	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	3	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
19	C₂²×Dic₄₃	C₈	1	16	yes	direct product factor
20	C₂²×Dic₄₃	C₂×C₄	1	12	yes	—
21	C₂×C₈×C₄₃	C₂×C₄	1	24	yes	complemented
22	C₂×C₈×C₄₃	C₂³	1	4	yes	—
23	C₄×Dic₄₃	C₂×C₄	1	12	yes	—
24	C₄×Dic₄₃	C₂³	1	4	yes	—
25	C₂×C₄₃⋊C₈	C₂×C₄	1	24	yes	complemented
26	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
27	C₂³×C₄₃	C₄²	1	4	yes	—
28	C₂³×C₄₃	C₂×C₈	1	8	yes	—
29	C₂³×C₄₃	C₂²×C₄	1	3	yes	—
30	C₂×C₄×C₄₃	C₄²	1	12	yes	—
31	C₂×C₄×C₄₃	C₂²×C₄	1	3	yes	—
32	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
33	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
34	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
35	C₂×Dic₄₃	C₂×C₈	1	48	yes	direct product factor
36	C₂×Dic₄₃	C₂²×C₄	1	8	yes	—
37	C₈×C₄₃	C₂²×C₄	1	8	yes	complemented
38	C₄₃⋊C₈	C₂²×C₄	1	8	yes	complemented
39	C₂²×C₄₃	C₄×C₈	1	16	yes	complemented
40	C₂²×C₄₃	C₂×C₄²	1	6	yes	—
41	C₂²×C₄₃	C₂²×C₈	1	12	yes	—
42	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
43	C₄×C₄₃	C₂×C₄²	1	6	yes	—
44	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
45	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
46	Dic₄₃	C₂²×C₈	1	16	yes	direct product factor
47	C₂²×C₄×C₈	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	C₂×C₄×C₈	1	12	yes	complemented
49	C₂×C₄₃	C₂²×C₄²	1	1	yes	characteristic
50	C₂×C₄₃	C₂³×C₈	1	2	yes	—
51	C₂³×C₈	—	43	1	no	—
52	C₂³×C₈	D₄₃	1	1	yes	characteristic
53	C₂²×C₄²	—	43	1	no	—
54	C₂×C₄×C₈	—	43	12	no	—
55	C₄₃	C₂²×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
56	C₂³×C₄	—	43	2	no	—
57	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
58	C₂²×C₈	—	43	6	no	—
59	C₂²×C₈	—	43	8	no	—
60	C₂²×C₈	Dic₄₃	1	8	yes	direct product factor
61	C₂²×C₈	C₂×D₄₃	1	6	yes	—
62	C₂×C₄²	—	43	6	no	—
63	C₂×C₄²	—	43	6	no	—
64	C₄×C₈	—	43	16	no	—
65	C₂⁴	C₄×D₄₃	1	1	yes	characteristic
66	C₂²×C₄	—	43	16	no	—
67	C₂²×C₄	—	43	12	no	—
68	C₂²×C₄	C₄×D₄₃	1	3	yes	—
69	C₂²×C₄	C₄×D₄₃	1	4	yes	—
70	C₂²×C₄	C₂×Dic₄₃	1	4	yes	—
71	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
72	C₂×C₈	—	43	24	no	—
73	C₂×C₈	—	43	4	no	—
74	C₂×C₈	C₂×Dic₄₃	1	24	yes	direct product factor
75	C₂×C₈	C₂²×D₄₃	1	4	yes	—
76	C₄²	—	43	12	no	—
77	C₄²	—	43	4	no	—
78	C₂³	C₈×D₄₃	1	8	yes	—
79	C₂³	C₄×Dic₄₃	1	4	yes	—
80	C₂³	C₂×C₄×D₄₃	1	3	yes	—
81	C₂×C₄	—	43	48	no	—
82	C₂×C₄	—	43	8	no	—
83	C₂×C₄	C₄×Dic₄₃	1	12	yes	—
84	C₂×C₄	C₂×C₄×D₄₃	1	3	yes	—
85	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
86	C₂×C₄	C₂²×Dic₄₃	1	6	yes	—
87	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
88	C₈	—	43	8	no	—
89	C₈	C₂²×Dic₄₃	1	8	yes	direct product factor
90	C₂²	C₈×Dic₄₃	1	16	yes	direct product factor
91	C₂²	C₂×C₄×Dic₄₃	1	6	yes	—
92	C₂²	C₂×C₈×D₄₃	1	12	yes	—
93	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
94	C₄	—	43	16	no	—
95	C₄	C₂×C₄×Dic₄₃	1	6	yes	—
96	C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
97	C₄	C₂³×Dic₄₃	1	1	yes	characteristic
98	C₂	C₂×C₈×Dic₄₃	1	12	yes	direct product factor
99	C₂	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
100	C₂	C₂²×C₈×D₄₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₂²×C₄×Dic₄₃

C₂

yes

maximal, characteristic

C₂×C₈×Dic₄₃

C₂

yes

maximal, direct product factor

C₂³×C₈×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₄

yes

—

C₂²×C₄₃⋊C₈

C₄

yes

complemented

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₈×Dic₄₃

C₂²

yes

direct product factor

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₄

yes

complemented

C₂²×C₈×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₈

yes

direct product factor

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

complemented

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₄²

yes

—

C₂³×C₄₃

C₂×C₈

yes

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

C₂×C₈

yes

direct product factor

C₂×Dic₄₃

C₂²×C₄

yes

—

C₈×C₄₃

C₂²×C₄

yes

complemented

C₄₃⋊C₈

C₂²×C₄

yes

complemented

C₂²×C₄₃

C₄×C₈

yes

complemented

C₂²×C₄₃

C₂×C₄²

yes

—

C₂²×C₄₃

C₂²×C₈

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

C₂×C₄²

yes

—

C₄×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

C₂³×C₄

yes

characteristic

Dic₄₃

C₂²×C₈

yes

direct product factor

C₂²×C₄×C₈

—

maximal, Sylow

C₂×C₄₃

C₂×C₄×C₈

yes

complemented

C₂×C₄₃

C₂²×C₄²

yes

characteristic

C₂×C₄₃

C₂³×C₈

yes

—

C₂³×C₈

—

C₂³×C₈

D₄₃

yes

characteristic

C₂²×C₄²

—

C₂×C₄×C₈

—

C₄₃

C₂²×C₄×C₈

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

Dic₄₃

yes

direct product factor

C₂²×C₈

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₄×C₈

—

C₂⁴

C₄×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

direct product factor

C₂×C₈

C₂²×D₄₃

yes

—

C₄²

—

C₄²

—

C₂³

C₈×D₄₃

yes

—

C₂³

C₄×Dic₄₃

yes

—

C₂³

C₂×C₄×D₄₃

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₄₃

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂³×D₄₃

yes

characteristic

C₈

—

C₈

C₂²×Dic₄₃

yes

direct product factor

C₂²

C₈×Dic₄₃

yes

direct product factor

C₂²

C₂×C₄×Dic₄₃

yes

—

C₂²

C₂×C₈×D₄₃

yes

—

C₂²

C₂²×C₄×D₄₃

yes

characteristic

C₄

—

C₄

C₂×C₄×Dic₄₃

yes

—

C₄

C₂²×C₄×D₄₃

yes

characteristic

C₄

C₂³×Dic₄₃

yes

characteristic

C₂

C₂×C₈×Dic₄₃

yes

direct product factor

C₂

C₂²×C₄×Dic₄₃

yes

characteristic

100

C₂

C₂²×C₈×D₄₃

yes

—

	subgroup	G/H
center, hypercenter	C₂³×C₈	D₄₃
commutator, hypocenter	C₄₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂³×C₈×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂×C₄
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂³×C₈

subgroup

G/H

center, hypercenter

C₂³×C₈

D₄₃

commutator, hypocenter

C₄₃

C₂²×C₄×C₈

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂³×C₈×C₄₃

C₂

socle

C₂⁴×C₄₃

C₂×C₄

LCS

G ▷ C₄₃

UCS

C₁ ◁ C₂³×C₈

N	H ≅ G/N	type
3. C₂×C₈×Dic₄₃	C₂	direct (N × H)
6. C₂²×C₄₃⋊C₈	C₄	semidirect
10. C₈×Dic₄₃	C₂²	direct (N × H)
12. C₂²×C₈×C₄₃	C₄	semidirect
19. C₂²×Dic₄₃	C₈	direct (N × H)
21. C₂×C₈×C₄₃	C₂×C₄	semidirect
25. C₂×C₄₃⋊C₈	C₂×C₄	semidirect
35. C₂×Dic₄₃	C₂×C₈	direct (N × H)
37. C₈×C₄₃	C₂²×C₄	semidirect
38. C₄₃⋊C₈	C₂²×C₄	semidirect
39. C₂²×C₄₃	C₄×C₈	semidirect
46. Dic₄₃	C₂²×C₈	direct (N × H)
48. C₂×C₄₃	C₂×C₄×C₈	semidirect
55. C₄₃	C₂²×C₄×C₈	semidirect
60. C₂²×C₈	Dic₄₃	direct (N × H)
74. C₂×C₈	C₂×Dic₄₃	direct (N × H)
89. C₈	C₂²×Dic₄₃	direct (N × H)
90. C₂²	C₈×Dic₄₃	direct (N × H)
98. C₂	C₂×C₈×Dic₄₃	direct (N × H)

H ≅ G/N

type

3. C₂×C₈×Dic₄₃

C₂

direct (N × H)

6. C₂²×C₄₃⋊C₈

C₄

semidirect

10. C₈×Dic₄₃

C₂²

direct (N × H)

12. C₂²×C₈×C₄₃

C₄

semidirect

19. C₂²×Dic₄₃

C₈

direct (N × H)

21. C₂×C₈×C₄₃

C₂×C₄

semidirect

25. C₂×C₄₃⋊C₈

C₂×C₄

semidirect

35. C₂×Dic₄₃

C₂×C₈

direct (N × H)

37. C₈×C₄₃

C₂²×C₄

semidirect

38. C₄₃⋊C₈

C₂²×C₄

semidirect

39. C₂²×C₄₃

C₄×C₈

semidirect

46. Dic₄₃

C₂²×C₈

direct (N × H)

48. C₂×C₄₃

C₂×C₄×C₈

semidirect

55. C₄₃

C₂²×C₄×C₈

semidirect

60. C₂²×C₈

Dic₄₃

direct (N × H)

74. C₂×C₈

C₂×Dic₄₃

direct (N × H)

89. C₈

C₂²×Dic₄₃

direct (N × H)

90. C₂²

C₈×Dic₄₃

direct (N × H)

98. C₂

C₂×C₈×Dic₄₃

direct (N × H)

Subgroups — C₂²×C₈×Dic₄₃ #19142995

Conjugacy classes of subgroups

Complements

Subgroups — C22×C8×Dic43 #19142995

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₈×Dic₄₃ #19142995