Finite Group Databasebeta

← C₄₃×C₂²⋊(C₃₇⋊C₃) #34061891

Subgroups — C₄₃×C₂²⋊(C₃₇⋊C₃) #34061891

Order 19092.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×C₃₇⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₃₇×C₄₃	—	3	1	no	—
4	C₃₇×C₄₃	A₄	1	1	yes	characteristic, complemented, Hall
5	A₄×C₄₃	—	37	1	no	maximal, Hall
6	C₂²⋊(C₃₇⋊C₃)	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₄₃	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₃₇	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₄₃	—	148	1	no	Hall
10	C₃₇⋊C₃	—	4	1	no	Hall
11	C₂×C₄₃	—	3	1	no	—
12	C₂×C₃₇	—	3	1	no	—
13	C₄₃	C₂²⋊(C₃₇⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
14	C₃₇	A₄×C₄₃	1	1	yes	characteristic, complemented, Sylow
15	A₄	—	37	1	no	Hall
16	C₂²	C₄₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃	—	148	1	no	Sylow
18	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₄₃	C₂²⋊(C₃₇⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₃₇	C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃₇×C₄₃	C₃
LCS	G ▷ C₂²×C₃₇
UCS	C₁ ◁ C₄₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₇×C₄₃	C₃	semidirect
4. C₃₇×C₄₃	A₄	semidirect
6. C₂²⋊(C₃₇⋊C₃)	C₄₃	direct (N × H)
7. C₂²×C₄₃	C₃₇⋊C₃	semidirect
8. C₂²×C₃₇	C₃×C₄₃	semidirect
13. C₄₃	C₂²⋊(C₃₇⋊C₃)	direct (N × H)
14. C₃₇	A₄×C₄₃	semidirect
16. C₂²	C₄₃×C₃₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₇×C₄₃	3
C₄₃×C₃₇⋊C₃	4
A₄×C₄₃	37
C₂²⋊(C₃₇⋊C₃)	43