Finite Group Databasebeta

← C₂×C₄₉×C₈₉ #22576563

Subgroups — C₂×C₄₉×C₈₉ #22576563

Order 8722.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₈₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₈₉	C₇	1	1	yes	maximal, characteristic
3	C₇×C₈₉	C₂×C₇	1	1	yes	characteristic
4	C₂×C₈₉	C₄₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₄₉	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₈₉	C₂×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₄₉	C₂×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₇	C₇×C₈₉	1	1	yes	characteristic
9	C₇	C₂×C₇×C₈₉	1	1	yes	characteristic
10	C₂	C₄₉×C₈₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₇	C₂×C₇×C₈₉
socle	C₂×C₇×C₈₉	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₉×C₈₉	C₂	direct (N × H)
4. C₂×C₈₉	C₄₉	direct (N × H)
5. C₂×C₄₉	C₈₉	direct (N × H)
6. C₈₉	C₂×C₄₉	direct (N × H)
7. C₄₉	C₂×C₈₉	direct (N × H)
10. C₂	C₄₉×C₈₉	direct (N × H)