Subgroups — C₃×D₃₁×C₄₃⋊C₃ #37562033

Order 23994.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃	D₃₁×C₄₃⋊C₃
commutator, cosocle, hypocenter	C₃₁×C₄₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₃₁×C₄₃	C₂×C₃
LCS	G ▷ C₃₁×C₄₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₄₃⋊C₃	C₂	semidirect
2. D₃₁×C₄₃⋊C₃	C₃	direct (N × H)
3. C₃×C₄₃×D₃₁	C₃	semidirect
4. C₃×C₃₁×C₄₃	C₂×C₃	semidirect
5. C₃₁×C₄₃⋊C₃	C₂×C₃	semidirect
6. C₄₃×D₃₁	C₃²	semidirect
7. C₃₁×C₄₃	C₂×C₃²	semidirect
10. C₃×C₄₃⋊C₃	D₃₁	direct (N × H)
15. C₃×D₃₁	C₄₃⋊C₃	direct (N × H)
16. C₃×C₄₃	C₃×D₃₁	semidirect
17. C₄₃⋊C₃	C₃×D₃₁	direct (N × H)
19. C₃×C₃₁	C₂×C₄₃⋊C₃	semidirect
21. D₃₁	C₃×C₄₃⋊C₃	direct (N × H)
22. C₄₃	C₃²×D₃₁	semidirect
23. C₃₁	C₂×C₃×C₄₃⋊C₃	semidirect
29. C₃	D₃₁×C₄₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃₁×C₄₃⋊C₃	2
D₃₁×C₄₃⋊C₃	3
C₃×C₄₃×D₃₁	3
C₂×C₃×C₄₃⋊C₃	31
C₃²×D₃₁	43

Subgroups — C3×D31×C43⋊C3 #37562033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₁×C₄₃⋊C₃ #37562033