Subgroups — C₃×C₁₆×C₁₇×C₂₃ #72196513

Order 18768.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₁₇×C₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₈×C₁₇×C₂₃	C₂×C₃	1	1	yes	characteristic
4	C₃×C₄×C₁₇×C₂₃	C₄	1	1	yes	characteristic
5	C₂×C₃×C₁₇×C₂₃	C₈	1	1	yes	characteristic
6	C₄×C₁₇×C₂₃	C₃×C₄	1	1	yes	characteristic
7	C₃×C₁₇×C₂₃	C₁₆	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₆×C₂₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₆×C₁₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₇×C₂₃	C₃×C₈	1	1	yes	characteristic
11	C₃×C₈×C₂₃	C₂×C₁₇	1	1	yes	characteristic
12	C₃×C₈×C₁₇	C₂×C₂₃	1	1	yes	characteristic
13	C₁₇×C₂₃	C₃×C₁₆	1	1	yes	characteristic, direct product factor, Hall
14	C₁₆×C₂₃	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₄×C₂₃	C₄×C₁₇	1	1	yes	characteristic
16	C₁₆×C₁₇	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₄×C₁₇	C₄×C₂₃	1	1	yes	characteristic
18	C₈×C₂₃	C₂×C₃×C₁₇	1	1	yes	characteristic
19	C₂×C₃×C₂₃	C₈×C₁₇	1	1	yes	characteristic
20	C₈×C₁₇	C₂×C₃×C₂₃	1	1	yes	characteristic
21	C₂×C₃×C₁₇	C₈×C₂₃	1	1	yes	characteristic
22	C₄×C₂₃	C₃×C₄×C₁₇	1	1	yes	characteristic
23	C₃×C₂₃	C₁₆×C₁₇	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₁₇	C₃×C₄×C₂₃	1	1	yes	characteristic
25	C₃×C₁₇	C₁₆×C₂₃	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₁₆	C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₂₃	C₃×C₈×C₁₇	1	1	yes	characteristic
28	C₂×C₁₇	C₃×C₈×C₂₃	1	1	yes	characteristic
29	C₃×C₈	C₂×C₁₇×C₂₃	1	1	yes	characteristic
30	C₂₃	C₃×C₁₆×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₁₇	C₃×C₁₆×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₁₆	C₃×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃×C₄	C₄×C₁₇×C₂₃	1	1	yes	characteristic
34	C₈	C₂×C₃×C₁₇×C₂₃	1	1	yes	characteristic
35	C₂×C₃	C₈×C₁₇×C₂₃	1	1	yes	characteristic
36	C₄	C₃×C₄×C₁₇×C₂₃	1	1	yes	characteristic
37	C₃	C₁₆×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂	C₃×C₈×C₁₇×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃×C₁₇×C₂₃
socle, prime radical	C₂×C₃×C₁₇×C₂₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₆×C₁₇×C₂₃	C₃	direct (N × H)
7. C₃×C₁₇×C₂₃	C₁₆	direct (N × H)
8. C₃×C₁₆×C₂₃	C₁₇	direct (N × H)
9. C₃×C₁₆×C₁₇	C₂₃	direct (N × H)
13. C₁₇×C₂₃	C₃×C₁₆	direct (N × H)
14. C₁₆×C₂₃	C₃×C₁₇	direct (N × H)
16. C₁₆×C₁₇	C₃×C₂₃	direct (N × H)
23. C₃×C₂₃	C₁₆×C₁₇	direct (N × H)
25. C₃×C₁₇	C₁₆×C₂₃	direct (N × H)
26. C₃×C₁₆	C₁₇×C₂₃	direct (N × H)
30. C₂₃	C₃×C₁₆×C₁₇	direct (N × H)
31. C₁₇	C₃×C₁₆×C₂₃	direct (N × H)
32. C₁₆	C₃×C₁₇×C₂₃	direct (N × H)
37. C₃	C₁₆×C₁₇×C₂₃	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×C₈×C₁₇×C₂₃	2
C₁₆×C₁₇×C₂₃	3
C₃×C₁₆×C₂₃	17
C₃×C₁₆×C₁₇	23

Subgroups — C3×C16×C17×C23 #72196513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₆×C₁₇×C₂₃ #72196513