Subgroups — C₄₃×ΓL(1,𝔽₈)⋊D₁₃ #37553522

Order 23478.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×ΓL(1,𝔽₈)×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×D₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃×C₄₃	—	7	1	no	maximal, Hall
5	AGL(1,𝔽₇)×C₄₃	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₄₃	—	7	1	no	Hall
7	D₁₃×C₄₃	—	7	1	no	Hall
8	ΓL(1,𝔽₈)×C₄₃	D₁₃	1	1	yes	characteristic, complemented, Hall
9	D₇×C₄₃	—	13	1	no	Hall
10	C₁₃×C₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
11	ΓL(1,𝔽₈)⋊D₁₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₄₃	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₁₃×ΓL(1,𝔽₈)	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₄₃	—	91	1	no	Hall
15	D₉₁	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄₃	—	7	1	no	Hall
17	C₇×C₁₃	C₂×C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₃	—	91	1	no	Hall
19	C₃×D₁₃	—	7	1	no	Hall
20	C₄₃	ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
21	AGL(1,𝔽₇)	—	13	1	no	Hall
22	C₃×C₁₃	—	7	1	no	Hall
23	D₁₃	—	7	1	no	Hall
24	ΓL(1,𝔽₈)	D₁₃×C₄₃	1	1	yes	characteristic, complemented, Hall
25	D₇	—	13	1	no	Hall
26	C₁₃	AGL(1,𝔽₇)×C₄₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₁₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	91	1	no	Hall
29	C₃	—	7	1	no	Sylow
30	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₃	ΓL(1,𝔽₈)⋊D₁₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₄₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×ΓL(1,𝔽₈)×C₄₃	C₂	semidirect
2. C₄₃×D₉₁	C₃	semidirect
3. C₇×C₁₃×C₄₃	C₂×C₃	semidirect
8. ΓL(1,𝔽₈)×C₄₃	D₁₃	semidirect
10. C₁₃×C₄₃	AGL(1,𝔽₇)	semidirect
11. ΓL(1,𝔽₈)⋊D₁₃	C₄₃	direct (N × H)
12. C₇×C₄₃	C₃×D₁₃	semidirect
13. C₁₃×ΓL(1,𝔽₈)	C₂×C₄₃	semidirect
15. D₉₁	C₃×C₄₃	semidirect
17. C₇×C₁₃	C₂×C₃×C₄₃	semidirect
20. C₄₃	ΓL(1,𝔽₈)⋊D₁₃	direct (N × H)
24. ΓL(1,𝔽₈)	D₁₃×C₄₃	semidirect
26. C₁₃	AGL(1,𝔽₇)×C₄₃	semidirect
27. C₇	C₃×D₁₃×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×ΓL(1,𝔽₈)×C₄₃	2
C₄₃×D₉₁	3
C₃×D₁₃×C₄₃	7
AGL(1,𝔽₇)×C₄₃	13
ΓL(1,𝔽₈)⋊D₁₃	43

Subgroups — C43×ΓL(1,𝔽8)⋊D13 #37553522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×ΓL(1,𝔽₈)⋊D₁₃ #37553522