Subgroups — C₃×D₃₉₉₉ #37562060

Order 23994.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉₉₉	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₃₃₃	—	3	1	no	maximal
4	C₃×C₃₁×C₄₃	—	2	1	no	—
5	C₃×C₃₁×C₄₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₃₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₃₃₃	—	3	1	no	Hall
8	C₃₁×C₄₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₁₂₉	—	31	1	no	maximal, Hall
10	C₃×D₉₃	—	43	1	no	maximal, Hall
11	C₃²×C₄₃	D₃₁	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₃₁	D₄₃	1	1	yes	characteristic, complemented, Hall
13	D₁₂₉	—	31	1	no	—
14	C₃×D₄₃	—	93	1	no	—
15	D₉₃	—	43	1	no	—
16	C₃×D₃₁	—	129	1	no	—
17	C₃×C₄₃	—	2	1	no	—
18	C₃×C₄₃	C₃×D₃₁	1	1	yes	characteristic, complemented
19	C₃×C₄₃	D₉₃	1	1	yes	characteristic, complemented
20	C₃×C₃₁	—	2	1	no	—
21	C₃×C₃₁	C₃×D₄₃	1	1	yes	characteristic, complemented
22	C₃×C₃₁	D₁₂₉	1	1	yes	characteristic, complemented
23	D₄₃	—	93	1	no	Hall
24	D₃₁	—	129	1	no	Hall
25	C₄₃	C₃×D₉₃	1	1	yes	characteristic, complemented, Sylow
26	C₃₁	C₃×D₁₂₉	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1333	1	no	Hall
28	C₃²	D₁₃₃₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3999	1	no	—
30	D₃	—	1333	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₃₃₃	1	1	yes	characteristic, complemented
33	C₃	D₃₉₉₉	1	1	yes	characteristic, direct product factor
34	C₂	—	3999	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃₉₉₉
commutator, cosocle, hypocenter	C₃×C₃₁×C₄₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₃₁×C₄₃	C₂
LCS	G ▷ C₃×C₃₁×C₄₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃₁×C₄₃	C₂	semidirect
2. D₃₉₉₉	C₃	direct (N × H)
5. C₃×C₃₁×C₄₃	D₃	semidirect
6. C₃×C₃₁×C₄₃	C₂×C₃	semidirect
8. C₃₁×C₄₃	C₃×D₃	semidirect
11. C₃²×C₄₃	D₃₁	semidirect
12. C₃²×C₃₁	D₄₃	semidirect
18. C₃×C₄₃	C₃×D₃₁	semidirect
19. C₃×C₄₃	D₉₃	semidirect
21. C₃×C₃₁	C₃×D₄₃	semidirect
22. C₃×C₃₁	D₁₂₉	semidirect
25. C₄₃	C₃×D₉₃	semidirect
26. C₃₁	C₃×D₁₂₉	semidirect
28. C₃²	D₁₃₃₃	semidirect
32. C₃	C₃×D₁₃₃₃	semidirect
33. C₃	D₃₉₉₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₃₁×C₄₃	2
D₃₉₉₉	3
C₃×D₁₃₃₃	3
C₃×D₁₂₉	31
C₃×D₉₃	43

Subgroups — C3×D3999 #37562060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₉₉₉ #37562060