Finite Group Databasebeta

← C₃×C₁₇×C₂₃² #41008672

Subgroups — C₃×C₁₇×C₂₃² #41008672

Order 26979.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₂₃²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₂₃²	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×C₂₃	C₂₃	1	24	yes	maximal, direct product factor
4	C₂₃²	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
5	C₁₇×C₂₃	C₃×C₂₃	1	24	yes	direct product factor
6	C₃×C₂₃	C₁₇×C₂₃	1	24	yes	direct product factor
7	C₃×C₁₇	C₂₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₂₃	C₃×C₁₇×C₂₃	1	24	yes	direct product factor
9	C₁₇	C₃×C₂₃²	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₁₇×C₂₃²	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. C₁₇×C₂₃²	C₃	direct (N × H)
2. C₃×C₂₃²	C₁₇	direct (N × H)
3. C₃×C₁₇×C₂₃	C₂₃	direct (N × H)
4. C₂₃²	C₃×C₁₇	direct (N × H)
5. C₁₇×C₂₃	C₃×C₂₃	direct (N × H)
6. C₃×C₂₃	C₁₇×C₂₃	direct (N × H)
7. C₃×C₁₇	C₂₃²	direct (N × H)
8. C₂₃	C₃×C₁₇×C₂₃	direct (N × H)
9. C₁₇	C₃×C₂₃²	direct (N × H)
10. C₃	C₁₇×C₂₃²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₂₃²	3
C₃×C₂₃²	17
C₃×C₁₇×C₂₃	23