Finite Group Databasebeta

← (C₇₉⋊C₃)⋊D₇₃ #46829499

Subgroups — (C₇₉⋊C₃)⋊D₇₃ #46829499

Order 34602.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×C₇₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₇₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₃×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₇₉⋊C₃	—	73	1	no	maximal, Hall
5	C₃×D₇₃	—	79	1	no	maximal, Hall
6	C₇₉⋊C₃	D₇₃	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇₃	—	79	1	no	Hall
8	D₇₉	—	73	1	no	Hall
9	D₇₃	—	79	1	no	Hall
10	C₇₉	C₃×D₇₃	1	1	yes	characteristic, complemented, Sylow
11	C₇₃	D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	5767	1	no	Hall
13	C₃	—	79	1	no	Sylow
14	C₂	—	5767	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇₃×C₇₉	C₂×C₃
LCS	G ▷ C₇₃×C₇₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇₃×C₇₉⋊C₃	C₂	semidirect
2. D₅₇₆₇	C₃	semidirect
3. C₇₃×C₇₉	C₂×C₃	semidirect
6. C₇₉⋊C₃	D₇₃	semidirect
10. C₇₉	C₃×D₇₃	semidirect
11. C₇₃	D₇₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×C₇₉⋊C₃	2
D₅₇₆₇	3
D₇₉⋊C₃	73
C₃×D₇₃	79