Subgroups — D₄₃×D₁₄₁ #37564652

Order 24252.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₀₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄₇×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₃×D₄₇	—	3	1	no	maximal, Hall
5	C₃×C₄₃×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₀₂₁	—	3	1	no	—
7	C₄₃×D₄₇	—	3	1	no	—
8	C₄₇×D₄₃	D₃	1	1	yes	characteristic, complemented
9	C₄₃×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₁₄₁	—	43	1	no	maximal, Hall
11	D₃×D₄₃	—	47	1	no	maximal, Hall
12	C₂×C₃×C₄₇	—	43	1	no	—
13	D₁₄₁	—	43	1	no	—
14	D₁₄₁	D₄₃	1	1	yes	characteristic, direct product factor
15	D₁₂₉	—	47	1	no	—
16	C₃×D₄₃	D₄₇	1	1	yes	characteristic, complemented
17	D₃×C₄₃	—	47	1	no	—
18	C₂×D₄₇	—	129	1	no	Hall
19	C₂×D₄₃	—	141	1	no	Hall
20	C₃×C₄₇	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₄₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₄₇	—	43	1	no	—
23	D₄₇	—	3	1	no	—
24	D₄₇	—	129	1	no	—
25	C₂×C₄₃	—	141	1	no	—
26	D₄₃	—	141	1	no	—
27	D₄₃	D₁₄₁	1	1	yes	characteristic, direct product factor
28	C₄₇	D₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
29	C₄₃	C₂×D₁₄₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2021	1	no	Hall
31	C₂×C₃	—	43	1	no	—
32	D₃	—	47	1	no	—
33	D₃	—	2021	1	no	—
34	C₂²	—	6063	1	no	Sylow
35	C₃	D₄₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	43	1	no	—
37	C₂	—	141	1	no	—
38	C₂	—	6063	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₄₃×C₄₇	C₂²
LCS	G ▷ C₃×C₄₃×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₀₆₃	C₂	semidirect
2. C₄₃×D₁₄₁	C₂	semidirect
3. C₃×C₄₇×D₄₃	C₂	semidirect
5. C₃×C₄₃×C₄₇	C₂²	semidirect
8. C₄₇×D₄₃	D₃	semidirect
9. C₄₃×C₄₇	C₂×D₃	semidirect
14. D₁₄₁	D₄₃	direct (N × H)
16. C₃×D₄₃	D₄₇	semidirect
20. C₃×C₄₇	C₂×D₄₃	semidirect
21. C₃×C₄₃	C₂×D₄₇	semidirect
27. D₄₃	D₁₄₁	direct (N × H)
28. C₄₇	D₃×D₄₃	semidirect
29. C₄₃	C₂×D₁₄₁	semidirect
35. C₃	D₄₃×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
D₆₀₆₃	2
C₄₃×D₁₄₁	2
C₃×C₄₇×D₄₃	2
D₄₃×D₄₇	3
C₂×D₁₄₁	43
D₃×D₄₃	47

Subgroups — D43×D141 #37564652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×D₁₄₁ #37564652