Finite Group Databasebeta

← C₂×C₃×C₃₁×C₁₇₃ #44565639

Subgroups — C₂×C₃×C₃₁×C₁₇₃ #44565639

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, direct product factor, Hall
2	C₂×C₃₁×C₁₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₁₇₃	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₇₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇₃	C₂×C₃₁	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₇₃	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₃₁	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇₃	C₂×C₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×C₃₁	C₂×C₁₇₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃₁	C₃×C₁₇₃	1	1	yes	characteristic, direct product factor, Hall
11	C₃₁	C₂×C₃×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	C₃₁×C₁₇₃	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₃₁×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₃×C₃₁×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

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