Finite Group Databasebeta

← C₇₃×D₂₁₉ #44544259

Subgroups — C₇₃×D₂₁₉ #44544259

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	—	3	1	no	maximal, Hall
3	C₇₃²	D₃	1	1	yes	characteristic, complemented, Sylow
4	D₂₁₉	C₇₃	1	1	yes	maximal, characteristic, direct product factor
5	D₃×C₇₃	—	73	1	no	maximal
6	C₃×C₇₃	—	2	36	no	—
7	C₃×C₇₃	D₇₃	1	1	yes	characteristic, complemented
8	C₃×C₇₃	C₂×C₇₃	1	1	yes	characteristic, complemented
9	C₂×C₇₃	—	219	1	no	—
10	D₇₃	—	3	1	no	—
11	C₇₃	—	2	36	no	—
12	C₇₃	D₃×C₇₃	1	1	yes	characteristic, complemented
13	C₇₃	D₂₁₉	1	1	yes	characteristic, direct product factor
14	D₃	—	73	1	no	Hall
15	C₃	C₇₃×D₇₃	1	1	yes	characteristic, complemented, Sylow
16	C₂	—	219	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₃	D₂₁₉
commutator, cosocle, hypocenter	C₃×C₇₃	C₂×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₇₃²	C₂
LCS	G ▷ C₃×C₇₃
UCS	C₁ ◁ C₇₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇₃²	C₂	semidirect
3. C₇₃²	D₃	semidirect
4. D₂₁₉	C₇₃	direct (N × H)
7. C₃×C₇₃	D₇₃	semidirect
8. C₃×C₇₃	C₂×C₇₃	semidirect
12. C₇₃	D₃×C₇₃	semidirect
13. C₇₃	D₂₁₉	direct (N × H)
15. C₃	C₇₃×D₇₃	semidirect

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
D₂₁₉	73
D₃×C₇₃	73