Finite Group Databasebeta

← D₃×C₄₃×C₉₇ #38736330

Subgroups — D₃×C₄₃×C₉₇ #38736330

Order 25026.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₄₃×C₉₇	—	3	1	no	maximal, Hall
3	C₄₃×C₉₇	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₉₇	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₉₇	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
6	D₃×C₄₃	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₉₇	—	3	1	no	Hall
8	C₃×C₄₃	C₂×C₉₇	1	1	yes	characteristic, complemented, Hall
9	C₉₇	D₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₄₃	—	3	1	no	Hall
11	C₄₃	D₃×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₄₃×C₉₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₄₃×C₉₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₃×C₉₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₄₃×C₉₇
Frattini	C₁	G
Fitting, socle	C₃×C₄₃×C₉₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₄₃×C₉₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₃×C₉₇	C₂	semidirect
3. C₄₃×C₉₇	D₃	direct (N × H)
4. D₃×C₉₇	C₄₃	direct (N × H)
5. C₃×C₉₇	C₂×C₄₃	semidirect
6. D₃×C₄₃	C₉₇	direct (N × H)
8. C₃×C₄₃	C₂×C₉₇	semidirect
9. C₉₇	D₃×C₄₃	direct (N × H)
11. C₄₃	D₃×C₉₇	direct (N × H)
12. D₃	C₄₃×C₉₇	direct (N × H)
13. C₃	C₂×C₄₃×C₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₃×C₉₇	2
C₂×C₄₃×C₉₇	3
D₃×C₉₇	43
D₃×C₄₃	97