Finite Group Databasebeta

← C₂×C₁₇²×C₄₁ #37557111

Subgroups — C₂×C₁₇²×C₄₁ #37557111

Order 23698.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₄₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₇×C₄₁	C₁₇	1	18	yes	maximal, direct product factor
3	C₁₇×C₄₁	C₂×C₁₇	1	18	yes	direct product factor
4	C₂×C₁₇²	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇²	C₂×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₂×C₄₁	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
7	C₄₁	C₂×C₁₇²	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₁₇	C₁₇×C₄₁	1	18	yes	direct product factor
9	C₁₇	C₂×C₁₇×C₄₁	1	18	yes	direct product factor
10	C₂	C₁₇²×C₄₁	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. C₁₇²×C₄₁	C₂	direct (N × H)
2. C₂×C₁₇×C₄₁	C₁₇	direct (N × H)
3. C₁₇×C₄₁	C₂×C₁₇	direct (N × H)
4. C₂×C₁₇²	C₄₁	direct (N × H)
5. C₁₇²	C₂×C₄₁	direct (N × H)
6. C₂×C₄₁	C₁₇²	direct (N × H)
7. C₄₁	C₂×C₁₇²	direct (N × H)
8. C₂×C₁₇	C₁₇×C₄₁	direct (N × H)
9. C₁₇	C₂×C₁₇×C₄₁	direct (N × H)
10. C₂	C₁₇²×C₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇²×C₄₁	2
C₂×C₁₇×C₄₁	17
C₂×C₁₇²	41