Finite Group Databasebeta

← C₃×C₇₃×D₇₃ #44544256

Subgroups — C₃×C₇₃×D₇₃ #44544256

Order 31974.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇₃×D₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇₃²	C₂×C₃	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₃×C₇₃	—	73	1	no	maximal
5	C₃×D₇₃	C₇₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃×C₇₃	—	2	36	no	—
7	C₃×C₇₃	D₇₃	1	1	yes	characteristic, direct product factor
8	C₃×C₇₃	C₂×C₇₃	1	1	yes	characteristic, complemented
9	C₂×C₇₃	—	73	1	no	—
10	D₇₃	C₃×C₇₃	1	1	yes	characteristic, direct product factor
11	C₇₃	—	2	36	no	—
12	C₇₃	C₃×D₇₃	1	1	yes	characteristic, direct product factor
13	C₇₃	C₂×C₃×C₇₃	1	1	yes	characteristic, complemented
14	C₂×C₃	—	73	1	no	Hall
15	C₃	C₇₃×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	—	73	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇₃	D₇₃
commutator, cosocle, hypocenter	C₇₃	C₂×C₃×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₇₃²	C₂
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₃×C₇₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇₃²	C₂	semidirect
2. C₇₃×D₇₃	C₃	direct (N × H)
3. C₇₃²	C₂×C₃	semidirect
5. C₃×D₇₃	C₇₃	direct (N × H)
7. C₃×C₇₃	D₇₃	direct (N × H)
8. C₃×C₇₃	C₂×C₇₃	semidirect
10. D₇₃	C₃×C₇₃	direct (N × H)
12. C₇₃	C₃×D₇₃	direct (N × H)
13. C₇₃	C₂×C₃×C₇₃	semidirect
15. C₃	C₇₃×D₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇₃²	2
C₇₃×D₇₃	3
C₂×C₃×C₇₃	73
C₃×D₇₃	73