Finite Group Databasebeta

← C₂²×C₁₇×C₃₃₇ #37523905

Subgroups — C₂²×C₁₇×C₃₃₇ #37523905

Order 22916.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₃₃₇	C₂	1	3	yes	maximal, direct product factor
2	C₁₇×C₃₃₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₃₃₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃₃₇	C₂×C₁₇	1	3	yes	direct product factor
5	C₃₃₇	C₂²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₂²×C₁₇	C₃₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₇	C₂×C₃₃₇	1	3	yes	direct product factor
8	C₁₇	C₂²×C₃₃₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²	C₁₇×C₃₃₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	C₂×C₁₇×C₃₃₇	1	3	yes	direct product factor

	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. C₂×C₁₇×C₃₃₇	C₂	direct (N × H)
2. C₁₇×C₃₃₇	C₂²	direct (N × H)
3. C₂²×C₃₃₇	C₁₇	direct (N × H)
4. C₂×C₃₃₇	C₂×C₁₇	direct (N × H)
5. C₃₃₇	C₂²×C₁₇	direct (N × H)
6. C₂²×C₁₇	C₃₃₇	direct (N × H)
7. C₂×C₁₇	C₂×C₃₃₇	direct (N × H)
8. C₁₇	C₂²×C₃₃₇	direct (N × H)
9. C₂²	C₁₇×C₃₃₇	direct (N × H)
10. C₂	C₂×C₁₇×C₃₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₇×C₃₃₇	2
C₂²×C₃₃₇	17
C₂²×C₁₇	337