Finite Group Databasebeta

← C₂³×C₄₁×C₇₃ #72201225

Subgroups — C₂³×C₄₁×C₇₃ #72201225

Order 23944.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄₁×C₇₃	C₂	1	7	yes	maximal, direct product factor
2	C₂×C₄₁×C₇₃	C₂²	1	7	yes	direct product factor
3	C₄₁×C₇₃	C₂³	1	1	yes	characteristic, direct product factor, Hall
4	C₂³×C₇₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₄₁	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₇₃	C₂×C₄₁	1	7	yes	direct product factor
7	C₂²×C₄₁	C₂×C₇₃	1	7	yes	direct product factor
8	C₂×C₇₃	C₂²×C₄₁	1	7	yes	direct product factor
9	C₂×C₄₁	C₂²×C₇₃	1	7	yes	direct product factor
10	C₇₃	C₂³×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₄₁	C₂³×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂³	C₄₁×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²	C₂×C₄₁×C₇₃	1	7	yes	direct product factor
14	C₂	C₂²×C₄₁×C₇₃	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×C₄₁×C₇₃	C₂	direct (N × H)
2. C₂×C₄₁×C₇₃	C₂²	direct (N × H)
3. C₄₁×C₇₃	C₂³	direct (N × H)
4. C₂³×C₇₃	C₄₁	direct (N × H)
5. C₂³×C₄₁	C₇₃	direct (N × H)
6. C₂²×C₇₃	C₂×C₄₁	direct (N × H)
7. C₂²×C₄₁	C₂×C₇₃	direct (N × H)
8. C₂×C₇₃	C₂²×C₄₁	direct (N × H)
9. C₂×C₄₁	C₂²×C₇₃	direct (N × H)
10. C₇₃	C₂³×C₄₁	direct (N × H)
11. C₄₁	C₂³×C₇₃	direct (N × H)
12. C₂³	C₄₁×C₇₃	direct (N × H)
13. C₂²	C₂×C₄₁×C₇₃	direct (N × H)
14. C₂	C₂²×C₄₁×C₇₃	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×C₄₁×C₇₃	2
C₂³×C₇₃	41
C₂³×C₄₁	73