Finite Group Databasebeta

← C₂×C₈×C₄₃₉ #20296294

Subgroups — C₂×C₈×C₄₃₉ #20296294

Order 7024.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄₃₉	C₂	1	1	yes	maximal, characteristic
2	C₈×C₄₃₉	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₄₃₉	C₄	1	1	yes	characteristic
4	C₄×C₄₃₉	C₄	1	1	yes	characteristic
5	C₄×C₄₃₉	C₂²	1	1	yes	characteristic
6	C₂×C₄₃₉	C₈	1	2	yes	direct product factor
7	C₂×C₄₃₉	C₂×C₄	1	1	yes	characteristic
8	C₄₃₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Sylow
9	C₂×C₈	C₄₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₄	C₂×C₄₃₉	1	1	yes	characteristic
11	C₈	C₂×C₄₃₉	1	2	yes	direct product factor
12	C₂²	C₄×C₄₃₉	1	1	yes	characteristic
13	C₄	C₄×C₄₃₉	1	1	yes	characteristic
14	C₄	C₂²×C₄₃₉	1	1	yes	characteristic
15	C₂	C₈×C₄₃₉	1	2	yes	direct product factor
16	C₂	C₂×C₄×C₄₃₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₄	C₂²×C₄₃₉
socle	C₂²×C₄₃₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₄₃₉	C₂	direct (N × H)
6. C₂×C₄₃₉	C₈	direct (N × H)
8. C₄₃₉	C₂×C₈	direct (N × H)
9. C₂×C₈	C₄₃₉	direct (N × H)
11. C₈	C₂×C₄₃₉	direct (N × H)
15. C₂	C₈×C₄₃₉	direct (N × H)