Subgroups — C₃×C₈×C₂₃×C₄₃ #72201054

Order 23736.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₂₃×C₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₄×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₂₃×C₄₃	C₄	1	1	yes	characteristic
4	C₄×C₂₃×C₄₃	C₂×C₃	1	1	yes	characteristic
5	C₃×C₂₃×C₄₃	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₂₃×C₄₃	C₃×C₄	1	1	yes	characteristic
7	C₃×C₈×C₄₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₃×C₄₃	C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₈×C₂₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₄×C₄₃	C₂×C₂₃	1	1	yes	characteristic
11	C₈×C₄₃	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₄×C₂₃	C₂×C₄₃	1	1	yes	characteristic
13	C₂×C₃×C₄₃	C₄×C₂₃	1	1	yes	characteristic
14	C₈×C₂₃	C₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₄₃	C₂×C₃×C₂₃	1	1	yes	characteristic
16	C₂×C₃×C₂₃	C₄×C₄₃	1	1	yes	characteristic
17	C₃×C₄₃	C₈×C₂₃	1	1	yes	characteristic, direct product factor, Hall
18	C₄×C₂₃	C₂×C₃×C₄₃	1	1	yes	characteristic
19	C₂×C₄₃	C₃×C₄×C₂₃	1	1	yes	characteristic
20	C₃×C₂₃	C₈×C₄₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₂₃	C₃×C₄×C₄₃	1	1	yes	characteristic
22	C₄₃	C₃×C₈×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₈	C₂₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂₃	C₃×C₈×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₄	C₂×C₂₃×C₄₃	1	1	yes	characteristic
26	C₈	C₃×C₂₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₄×C₂₃×C₄₃	1	1	yes	characteristic
28	C₄	C₂×C₃×C₂₃×C₄₃	1	1	yes	characteristic
29	C₃	C₈×C₂₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₄×C₂₃×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₂₃×C₄₃
socle, prime radical	C₂×C₃×C₂₃×C₄₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈×C₂₃×C₄₃	C₃	direct (N × H)
5. C₃×C₂₃×C₄₃	C₈	direct (N × H)
7. C₃×C₈×C₄₃	C₂₃	direct (N × H)
8. C₂₃×C₄₃	C₃×C₈	direct (N × H)
9. C₃×C₈×C₂₃	C₄₃	direct (N × H)
11. C₈×C₄₃	C₃×C₂₃	direct (N × H)
14. C₈×C₂₃	C₃×C₄₃	direct (N × H)
17. C₃×C₄₃	C₈×C₂₃	direct (N × H)
20. C₃×C₂₃	C₈×C₄₃	direct (N × H)
22. C₄₃	C₃×C₈×C₂₃	direct (N × H)
23. C₃×C₈	C₂₃×C₄₃	direct (N × H)
24. C₂₃	C₃×C₈×C₄₃	direct (N × H)
26. C₈	C₃×C₂₃×C₄₃	direct (N × H)
29. C₃	C₈×C₂₃×C₄₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈×C₂₃×C₄₃	3
C₃×C₄×C₂₃×C₄₃	2
C₃×C₈×C₄₃	23
C₃×C₈×C₂₃	43

Subgroups — C3×C8×C23×C43 #72201054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×C₂₃×C₄₃ #72201054