Finite Group Databasebeta

← D₃×C₄₁×C₉₇ #37558787

Subgroups — D₃×C₄₁×C₉₇ #37558787

Order 23862.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₄₁×C₉₇	—	3	1	no	maximal, Hall
3	C₄₁×C₉₇	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₉₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₉₇	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
6	D₃×C₄₁	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₉₇	—	3	1	no	Hall
8	C₃×C₄₁	C₂×C₉₇	1	1	yes	characteristic, complemented, Hall
9	C₉₇	D₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₄₁	—	3	1	no	Hall
11	C₄₁	D₃×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₄₁×C₉₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₄₁×C₉₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁×C₉₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₄₁×C₉₇
Frattini	C₁	G
Fitting, socle	C₃×C₄₁×C₉₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₄₁×C₉₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₁×C₉₇	C₂	semidirect
3. C₄₁×C₉₇	D₃	direct (N × H)
4. D₃×C₉₇	C₄₁	direct (N × H)
5. C₃×C₉₇	C₂×C₄₁	semidirect
6. D₃×C₄₁	C₉₇	direct (N × H)
8. C₃×C₄₁	C₂×C₉₇	semidirect
9. C₉₇	D₃×C₄₁	direct (N × H)
11. C₄₁	D₃×C₉₇	direct (N × H)
12. D₃	C₄₁×C₉₇	direct (N × H)
13. C₃	C₂×C₄₁×C₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₁×C₉₇	2
C₂×C₄₁×C₉₇	3
D₃×C₉₇	41
D₃×C₄₁	97