Subgroups — C₂×C₁₉×ΓL(1,𝔽₈)×C₄₃ #46804875

Order 34314.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×ΓL(1,𝔽₈)×C₄₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₉×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₉×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₉×C₄₃	—	7	1	no	maximal, Hall
5	C₃×C₁₉×C₄₃	—	7	1	no	Hall
6	C₂×ΓL(1,𝔽₈)×C₄₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₉×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
8	ΓL(1,𝔽₈)×C₄₃	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
9	C₁₉×C₄₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₉×ΓL(1,𝔽₈)	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₇×C₄₃	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
12	C₁₉×ΓL(1,𝔽₈)	C₂×C₄₃	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₄₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₁₉	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₄₃	—	7	1	no	Hall
16	C₇×C₁₉	C₂×C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄₃	—	7	1	no	Hall
18	C₂×C₃×C₁₉	—	7	1	no	Hall
19	C₂×C₄₃	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₉	—	7	1	no	Hall
21	C₄₃	C₂×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×ΓL(1,𝔽₈)	C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₉	ΓL(1,𝔽₈)×C₄₃	1	1	yes	characteristic, direct product factor, Hall
24	ΓL(1,𝔽₈)	C₂×C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
25	C₁₉	C₂×ΓL(1,𝔽₈)×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	C₃×C₁₉×C₄₃	1	1	yes	characteristic, complemented, Hall
27	C₇	C₂×C₃×C₁₉×C₄₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	7	1	no	Hall
29	C₃	—	7	1	no	Sylow
30	C₂	C₁₉×ΓL(1,𝔽₈)×C₄₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₄₃	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₁₉×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₉×C₄₃	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₁₉×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₁₉×ΓL(1,𝔽₈)×C₄₃	C₂	direct (N × H)
2. C₂×C₇×C₁₉×C₄₃	C₃	semidirect
3. C₇×C₁₉×C₄₃	C₂×C₃	semidirect
6. C₂×ΓL(1,𝔽₈)×C₄₃	C₁₉	direct (N × H)
7. C₂×C₁₉×C₄₃	ΓL(1,𝔽₈)	direct (N × H)
8. ΓL(1,𝔽₈)×C₄₃	C₂×C₁₉	direct (N × H)
9. C₁₉×C₄₃	C₂×ΓL(1,𝔽₈)	direct (N × H)
10. C₂×C₁₉×ΓL(1,𝔽₈)	C₄₃	direct (N × H)
11. C₂×C₇×C₄₃	C₃×C₁₉	semidirect
12. C₁₉×ΓL(1,𝔽₈)	C₂×C₄₃	direct (N × H)
13. C₇×C₄₃	C₂×C₃×C₁₉	semidirect
14. C₂×C₇×C₁₉	C₃×C₄₃	semidirect
16. C₇×C₁₉	C₂×C₃×C₄₃	semidirect
19. C₂×C₄₃	C₁₉×ΓL(1,𝔽₈)	direct (N × H)
21. C₄₃	C₂×C₁₉×ΓL(1,𝔽₈)	direct (N × H)
22. C₂×ΓL(1,𝔽₈)	C₁₉×C₄₃	direct (N × H)
23. C₂×C₁₉	ΓL(1,𝔽₈)×C₄₃	direct (N × H)
24. ΓL(1,𝔽₈)	C₂×C₁₉×C₄₃	direct (N × H)
25. C₁₉	C₂×ΓL(1,𝔽₈)×C₄₃	direct (N × H)
26. C₂×C₇	C₃×C₁₉×C₄₃	semidirect
27. C₇	C₂×C₃×C₁₉×C₄₃	semidirect
30. C₂	C₁₉×ΓL(1,𝔽₈)×C₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×ΓL(1,𝔽₈)×C₄₃	2
C₂×C₇×C₁₉×C₄₃	3
C₂×C₃×C₁₉×C₄₃	7
C₂×ΓL(1,𝔽₈)×C₄₃	19
C₂×C₁₉×ΓL(1,𝔽₈)	43

Subgroups — C2×C19×ΓL(1,𝔽8)×C43 #46804875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×ΓL(1,𝔽₈)×C₄₃ #46804875