Finite Group Databasebeta

← C₂²×C₃₁×C₂₈₉ #49089367

Subgroups — C₂²×C₃₁×C₂₈₉ #49089367

Order 35836.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₂₈₉	C₂	1	3	yes	maximal, direct product factor
2	C₃₁×C₂₈₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₇×C₃₁	C₁₇	1	1	yes	maximal, characteristic
4	C₂²×C₂₈₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₇×C₃₁	C₂×C₁₇	1	3	yes	—
6	C₂×C₂₈₉	C₂×C₃₁	1	3	yes	direct product factor
7	C₁₇×C₃₁	C₂²×C₁₇	1	1	yes	characteristic
8	C₂₈₉	C₂²×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²×C₃₁	C₂₈₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂²×C₁₇	C₁₇×C₃₁	1	1	yes	characteristic
11	C₂×C₃₁	C₂×C₂₈₉	1	3	yes	direct product factor
12	C₂×C₁₇	C₂×C₁₇×C₃₁	1	3	yes	—
13	C₃₁	C₂²×C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₁₇	C₂²×C₁₇×C₃₁	1	1	yes	characteristic
15	C₂²	C₃₁×C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₃₁×C₂₈₉	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₇	C₂²×C₁₇×C₃₁
socle, prime radical	C₂²×C₁₇×C₃₁	C₁₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×C₂₈₉	C₂	direct (N × H)
2. C₃₁×C₂₈₉	C₂²	direct (N × H)
4. C₂²×C₂₈₉	C₃₁	direct (N × H)
6. C₂×C₂₈₉	C₂×C₃₁	direct (N × H)
8. C₂₈₉	C₂²×C₃₁	direct (N × H)
9. C₂²×C₃₁	C₂₈₉	direct (N × H)
11. C₂×C₃₁	C₂×C₂₈₉	direct (N × H)
13. C₃₁	C₂²×C₂₈₉	direct (N × H)
15. C₂²	C₃₁×C₂₈₉	direct (N × H)
16. C₂	C₂×C₃₁×C₂₈₉	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×C₃₁×C₂₈₉	2
C₂²×C₁₇×C₃₁	17
C₂²×C₂₈₉	31