Finite Group Databasebeta

← C₂³×C₂₃×C₁₇₃ #72208596

Subgroups — C₂³×C₂₃×C₁₇₃ #72208596

Order 31832.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×C₁₇₃	C₂	1	7	yes	maximal, direct product factor
2	C₂×C₂₃×C₁₇₃	C₂²	1	7	yes	direct product factor
3	C₂₃×C₁₇₃	C₂³	1	1	yes	characteristic, direct product factor, Hall
4	C₂³×C₁₇₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₁₇₃	C₂×C₂₃	1	7	yes	direct product factor
6	C₂×C₁₇₃	C₂²×C₂₃	1	7	yes	direct product factor
7	C₂³×C₂₃	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇₃	C₂³×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²×C₂₃	C₂×C₁₇₃	1	7	yes	direct product factor
10	C₂×C₂₃	C₂²×C₁₇₃	1	7	yes	direct product factor
11	C₂₃	C₂³×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂³	C₂₃×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²	C₂×C₂₃×C₁₇₃	1	7	yes	direct product factor
14	C₂	C₂²×C₂₃×C₁₇₃	1	7	yes	direct product factor

	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. C₂²×C₂₃×C₁₇₃	C₂	direct (N × H)
2. C₂×C₂₃×C₁₇₃	C₂²	direct (N × H)
3. C₂₃×C₁₇₃	C₂³	direct (N × H)
4. C₂³×C₁₇₃	C₂₃	direct (N × H)
5. C₂²×C₁₇₃	C₂×C₂₃	direct (N × H)
6. C₂×C₁₇₃	C₂²×C₂₃	direct (N × H)
7. C₂³×C₂₃	C₁₇₃	direct (N × H)
8. C₁₇₃	C₂³×C₂₃	direct (N × H)
9. C₂²×C₂₃	C₂×C₁₇₃	direct (N × H)
10. C₂×C₂₃	C₂²×C₁₇₃	direct (N × H)
11. C₂₃	C₂³×C₁₇₃	direct (N × H)
12. C₂³	C₂₃×C₁₇₃	direct (N × H)
13. C₂²	C₂×C₂₃×C₁₇₃	direct (N × H)
14. C₂	C₂²×C₂₃×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
C₂²×C₂₃×C₁₇₃	2
C₂³×C₁₇₃	23
C₂³×C₂₃	173