Subgroups — C₂×D₃₁×C₄₃⋊C₃ #30630613

Order 15996.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₁×C₄₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃₁×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×D₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃₁×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₄₃×D₃₁	C₂×C₃	1	2	yes	complemented
7	C₃₁×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₄₃⋊C₃	—	31	1	no	maximal, Hall
9	C₂×C₃×D₃₁	—	43	1	no	maximal, Hall
10	C₂×C₄₃⋊C₃	—	31	2	no	—
11	C₂×C₄₃⋊C₃	D₃₁	1	1	yes	characteristic, direct product factor
12	C₂×C₃×C₃₁	—	43	1	no	—
13	C₃×D₃₁	—	43	2	no	—
14	C₂²×C₄₃	—	31	1	no	Hall
15	C₄₃⋊C₃	C₂×D₃₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂×D₃₁	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₃₁	—	43	1	no	Hall
18	C₂×C₄₃	—	31	2	no	—
19	C₂×C₄₃	C₃×D₃₁	1	1	yes	characteristic, complemented
20	C₂×C₃₁	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
21	D₃₁	C₂×C₄₃⋊C₃	1	2	yes	direct product factor
22	C₄₃	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
23	C₃₁	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	1333	1	no	Hall
25	C₂×C₃	—	43	1	no	—
26	C₂×C₃	—	1333	2	no	—
27	C₂²	—	31	1	no	Sylow
28	C₃	—	43	1	no	Sylow
29	C₂	—	31	2	no	—
30	C₂	D₃₁×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃₁×C₄₃⋊C₃
commutator, cosocle, hypocenter	C₃₁×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃₁×C₄₃	C₂×C₃
LCS	G ▷ C₃₁×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₃₁×C₄₃⋊C₃	C₂	direct (N × H)
2. C₂×C₃₁×C₄₃⋊C₃	C₂	semidirect
3. C₂×C₄₃×D₃₁	C₃	semidirect
4. C₃₁×C₄₃⋊C₃	C₂²	semidirect
5. C₂×C₃₁×C₄₃	C₂×C₃	semidirect
6. C₄₃×D₃₁	C₂×C₃	semidirect
7. C₃₁×C₄₃	C₂²×C₃	semidirect
11. C₂×C₄₃⋊C₃	D₃₁	direct (N × H)
15. C₄₃⋊C₃	C₂×D₃₁	direct (N × H)
16. C₂×D₃₁	C₄₃⋊C₃	direct (N × H)
19. C₂×C₄₃	C₃×D₃₁	semidirect
20. C₂×C₃₁	C₂×C₄₃⋊C₃	semidirect
21. D₃₁	C₂×C₄₃⋊C₃	direct (N × H)
22. C₄₃	C₂×C₃×D₃₁	semidirect
23. C₃₁	C₂²×C₄₃⋊C₃	semidirect
30. C₂	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
D₃₁×C₄₃⋊C₃	2
C₂×C₃₁×C₄₃⋊C₃	2
C₂×C₄₃×D₃₁	3
C₂²×C₄₃⋊C₃	31
C₂×C₃×D₃₁	43

Subgroups — C2×D31×C43⋊C3 #30630613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₁×C₄₃⋊C₃ #30630613