Finite Group Databasebeta

← C₃×C₃₁×D₁₇₃ #44565641

Subgroups — C₃×C₃₁×D₁₇₃ #44565641

Order 32178.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₁₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₁₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₇₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇₃	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
6	D₁₇₃	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₃₁	—	173	1	no	maximal, Hall
8	C₁₇₃	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₃₁	D₁₇₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃₁	—	173	1	no	Hall
11	C₃₁	C₃×D₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	173	1	no	Hall
13	C₃	C₃₁×D₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	173	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₁	D₁₇₃
commutator, cosocle, hypocenter	C₁₇₃	C₂×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₃₁×C₁₇₃	C₂
LCS	G ▷ C₁₇₃
UCS	C₁ ◁ C₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₁₇₃	C₂	semidirect
2. C₃₁×D₁₇₃	C₃	direct (N × H)
3. C₃₁×C₁₇₃	C₂×C₃	semidirect
4. C₃×D₁₇₃	C₃₁	direct (N × H)
5. C₃×C₁₇₃	C₂×C₃₁	semidirect
6. D₁₇₃	C₃×C₃₁	direct (N × H)
8. C₁₇₃	C₂×C₃×C₃₁	semidirect
9. C₃×C₃₁	D₁₇₃	direct (N × H)
11. C₃₁	C₃×D₁₇₃	direct (N × H)
13. C₃	C₃₁×D₁₇₃	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×C₃₁×C₁₇₃	2
C₃₁×D₁₇₃	3
C₃×D₁₇₃	31
C₂×C₃×C₃₁	173