Finite Group Databasebeta

← C₂×C₇×C₂₃×C₇₃ #37555067

Subgroups — C₂×C₇×C₂₃×C₇₃ #37555067

Order 23506.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃×C₇₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₃×C₇₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₇₃	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₇₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₇₃	C₂×C₂₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₇×C₂₃	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₂₃	C₂×C₇₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₇₃	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
9	C₇₃	C₂×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₂₃	C₇×C₇₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂₃	C₂×C₇×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇	C₂₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
13	C₇	C₂×C₂₃×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₇×C₂₃×C₇₃	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. C₇×C₂₃×C₇₃	C₂	direct (N × H)
2. C₂×C₂₃×C₇₃	C₇	direct (N × H)
3. C₂₃×C₇₃	C₂×C₇	direct (N × H)
4. C₂×C₇×C₇₃	C₂₃	direct (N × H)
5. C₇×C₇₃	C₂×C₂₃	direct (N × H)
6. C₂×C₇×C₂₃	C₇₃	direct (N × H)
7. C₇×C₂₃	C₂×C₇₃	direct (N × H)
8. C₂×C₇₃	C₇×C₂₃	direct (N × H)
9. C₇₃	C₂×C₇×C₂₃	direct (N × H)
10. C₂×C₂₃	C₇×C₇₃	direct (N × H)
11. C₂₃	C₂×C₇×C₇₃	direct (N × H)
12. C₂×C₇	C₂₃×C₇₃	direct (N × H)
13. C₇	C₂×C₂₃×C₇₃	direct (N × H)
14. C₂	C₇×C₂₃×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
C₇×C₂₃×C₇₃	2
C₂×C₂₃×C₇₃	7
C₂×C₇×C₇₃	23
C₂×C₇×C₂₃	73