Finite Group Databasebeta

← C₃×C₃₇×C₉₇ #24924603

Subgroups — C₃×C₃₇×C₉₇ #24924603

Order 10767.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₉₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₃₇	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₉₇	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
5	C₃₇	C₃×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	C₃₇×C₉₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×C₉₇	C₃	direct (N × H)
2. C₃×C₉₇	C₃₇	direct (N × H)
3. C₃×C₃₇	C₉₇	direct (N × H)
4. C₉₇	C₃×C₃₇	direct (N × H)
5. C₃₇	C₃×C₉₇	direct (N × H)
6. C₃	C₃₇×C₉₇	direct (N × H)