Subgroups — C₃⋊D₃×C₄₃×D₂₃ #49085259

Order 35604.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₃×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₃×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×C₃⋊D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₄₃×D₂₃	—	3	4	no	maximal
5	C₃²×C₂₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₄₃×D₆₉	—	3	4	no	—
7	D₃×C₂₃×C₄₃	—	3	4	no	—
8	C₃×C₄₃×D₂₃	D₃	1	4	yes	complemented
9	C₂×C₄₃×D₂₃	—	9	1	no	Hall
10	C₃×C₂₃×C₄₃	C₂×D₃	1	4	yes	complemented
11	C₂×C₂₃×C₄₃	—	9	1	no	—
12	C₄₃×D₂₃	—	9	1	no	—
13	C₄₃×D₂₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
14	C₂×C₃⋊D₃×C₄₃	—	23	1	no	maximal, Hall
15	C₂₃×C₄₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
16	C₃⋊D₃×D₂₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃²×C₄₃	—	23	1	no	—
18	C₃⋊D₃×C₄₃	—	23	1	no	—
19	C₃⋊D₃×C₄₃	D₂₃	1	1	yes	characteristic, direct product factor
20	C₂×D₃×C₄₃	—	69	4	no	—
21	C₃⋊D₆₉	C₂×C₄₃	1	1	yes	characteristic, complemented
22	C₃⋊D₃×C₂₃	C₂×C₄₃	1	1	yes	characteristic, complemented
23	C₃²×D₂₃	C₂×C₄₃	1	1	yes	characteristic, complemented
24	C₃²×C₄₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
25	D₃×D₂₃	—	3	4	no	—
26	C₂×C₃×C₄₃	—	23	4	no	—
27	D₃×C₄₃	—	3	4	no	—
28	D₃×C₄₃	—	69	4	no	—
29	C₃²×C₂₃	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₄₃	—	207	1	no	Hall
31	D₆₉	—	3	4	no	—
32	C₃×D₂₃	D₃×C₄₃	1	4	yes	complemented
33	D₃×C₂₃	—	3	4	no	—
34	C₃×C₄₃	D₃×D₂₃	1	4	yes	complemented
35	C₂×D₂₃	—	9	1	no	Hall
36	C₂×C₄₃	—	9	1	no	—
37	C₂×C₄₃	—	23	1	no	—
38	C₂×C₄₃	—	207	1	no	—
39	C₃×C₂₃	C₂×D₃×C₄₃	1	4	yes	complemented
40	C₂×C₂₃	—	9	1	no	—
41	D₂₃	—	9	1	no	—
42	D₂₃	C₃⋊D₃×C₄₃	1	1	yes	characteristic, direct product factor
43	C₄₃	C₃⋊D₃×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃⋊D₃	—	23	1	no	Hall
45	C₂₃	C₂×C₃⋊D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃²	—	23	1	no	—
47	C₃⋊D₃	—	23	1	no	—
48	C₃⋊D₃	C₄₃×D₂₃	1	1	yes	characteristic, direct product factor
49	C₂×D₃	—	69	4	no	—
50	C₃²	C₂×C₄₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	23	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	69	4	no	—
54	C₂²	—	207	1	no	Sylow
55	C₃	D₃×C₄₃×D₂₃	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	23	1	no	—
58	C₂	—	207	1	no	—

	subgroup	G/H
center, hypercenter	C₄₃	C₃⋊D₃×D₂₃
commutator, cosocle, hypocenter	C₃²×C₂₃	C₂²×C₄₃
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃×C₄₃	C₂²
LCS	G ▷ C₃²×C₂₃
UCS	C₁ ◁ C₄₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×C₄₃×D₂₃	C₂	semidirect
2. C₃⋊D₃×C₂₃×C₄₃	C₂	semidirect
3. C₄₃×C₃⋊D₆₉	C₂	semidirect
5. C₃²×C₂₃×C₄₃	C₂²	semidirect
8. C₃×C₄₃×D₂₃	D₃	semidirect
10. C₃×C₂₃×C₄₃	C₂×D₃	semidirect
13. C₄₃×D₂₃	C₃⋊D₃	direct (N × H)
15. C₂₃×C₄₃	C₂×C₃⋊D₃	semidirect
16. C₃⋊D₃×D₂₃	C₄₃	direct (N × H)
19. C₃⋊D₃×C₄₃	D₂₃	direct (N × H)
21. C₃⋊D₆₉	C₂×C₄₃	semidirect
22. C₃⋊D₃×C₂₃	C₂×C₄₃	semidirect
23. C₃²×D₂₃	C₂×C₄₃	semidirect
24. C₃²×C₄₃	C₂×D₂₃	semidirect
29. C₃²×C₂₃	C₂²×C₄₃	semidirect
32. C₃×D₂₃	D₃×C₄₃	semidirect
34. C₃×C₄₃	D₃×D₂₃	semidirect
39. C₃×C₂₃	C₂×D₃×C₄₃	semidirect
42. D₂₃	C₃⋊D₃×C₄₃	direct (N × H)
43. C₄₃	C₃⋊D₃×D₂₃	direct (N × H)
45. C₂₃	C₂×C₃⋊D₃×C₄₃	semidirect
48. C₃⋊D₃	C₄₃×D₂₃	direct (N × H)
50. C₃²	C₂×C₄₃×D₂₃	semidirect
55. C₃	D₃×C₄₃×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄₃×D₂₃	2
C₃⋊D₃×C₂₃×C₄₃	2
C₄₃×C₃⋊D₆₉	2
D₃×C₄₃×D₂₃	3
C₂×C₃⋊D₃×C₄₃	23
C₃⋊D₃×D₂₃	43

Subgroups — C3⋊D3×C43×D23 #49085259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×C₄₃×D₂₃ #49085259