Finite Group Databasebeta

← C₂×C₇₉×C₇₃⋊C₃ #46829481

Subgroups — C₂×C₇₉×C₇₃⋊C₃ #46829481

Order 34602.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₇₉×C₇₃⋊C₃	C₂	direct (N × H)
2. C₂×C₇₃×C₇₉	C₃	semidirect
3. C₇₃×C₇₉	C₂×C₃	semidirect
5. C₂×C₇₃⋊C₃	C₇₉	direct (N × H)
7. C₇₃⋊C₃	C₂×C₇₉	direct (N × H)
8. C₂×C₇₉	C₇₃⋊C₃	direct (N × H)
9. C₂×C₇₃	C₃×C₇₉	semidirect
10. C₇₉	C₂×C₇₃⋊C₃	direct (N × H)
11. C₇₃	C₂×C₃×C₇₉	semidirect
14. C₂	C₇₉×C₇₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₉×C₇₃⋊C₃	2
C₂×C₇₃×C₇₉	3
C₂×C₃×C₇₉	73
C₂×C₇₃⋊C₃	79