Finite Group Databasebeta

← C₃×C₁₁×C₁₇² #23750708

Subgroups — C₃×C₁₁×C₁₇² #23750708

Order 9537.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₇²	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×C₁₇	C₁₇	1	18	yes	maximal, direct product factor
4	C₁₇²	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
5	C₁₁×C₁₇	C₃×C₁₇	1	18	yes	direct product factor
6	C₃×C₁₇	C₁₁×C₁₇	1	18	yes	direct product factor
7	C₃×C₁₁	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
8	C₁₇	C₃×C₁₁×C₁₇	1	18	yes	direct product factor
9	C₁₁	C₃×C₁₇²	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₁₁×C₁₇²	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. C₁₁×C₁₇²	C₃	direct (N × H)
2. C₃×C₁₇²	C₁₁	direct (N × H)
3. C₃×C₁₁×C₁₇	C₁₇	direct (N × H)
4. C₁₇²	C₃×C₁₁	direct (N × H)
5. C₁₁×C₁₇	C₃×C₁₇	direct (N × H)
6. C₃×C₁₇	C₁₁×C₁₇	direct (N × H)
7. C₃×C₁₁	C₁₇²	direct (N × H)
8. C₁₇	C₃×C₁₁×C₁₇	direct (N × H)
9. C₁₁	C₃×C₁₇²	direct (N × H)
10. C₃	C₁₁×C₁₇²	direct (N × H)