Finite Group Databasebeta

← C₇₃×#87704 #44415213

Subgroups — C₇₃×#87704 #44415213

Order 29127.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊C₃×C₇₃	—	7	1	no	maximal, Hall
3	ΓL(1,𝔽₈)×C₇₃	—	19	1	no	maximal, Hall
4	C₁₉×C₇₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
5	C₇×C₇₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
6	#87704	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇₃	—	133	1	no	Hall
8	C₇×C₁₉	C₃×C₇₃	1	1	yes	characteristic, complemented, Hall
9	C₇₃	#87704	1	1	yes	characteristic, direct product factor, Sylow
10	C₁₉⋊C₃	—	7	1	no	Hall
11	ΓL(1,𝔽₈)	—	19	1	no	Hall
12	C₁₉	ΓL(1,𝔽₈)×C₇₃	1	1	yes	characteristic, complemented, Sylow
13	C₇	C₁₉⋊C₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
14	C₃	—	133	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₃	#87704
commutator, cosocle, hypocenter	C₇×C₁₉	C₃×C₇₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₇₃	C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₇₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×C₇₃	C₃	semidirect
4. C₁₉×C₇₃	ΓL(1,𝔽₈)	semidirect
5. C₇×C₇₃	C₁₉⋊C₃	semidirect
6. #87704	C₇₃	direct (N × H)
8. C₇×C₁₉	C₃×C₇₃	semidirect
9. C₇₃	#87704	direct (N × H)
12. C₁₉	ΓL(1,𝔽₈)×C₇₃	semidirect
13. C₇	C₁₉⋊C₃×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₉×C₇₃	3
C₁₉⋊C₃×C₇₃	7
ΓL(1,𝔽₈)×C₇₃	19
#87704	73