Subgroups — C₃×C₇×C₁₆×C₇₃ #72201780

Order 24528.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₆×C₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₈×C₇₃	C₂×C₃	1	1	yes	characteristic
4	C₃×C₁₆×C₇₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄×C₇×C₇₃	C₄	1	1	yes	characteristic
6	C₂×C₃×C₇×C₇₃	C₈	1	1	yes	characteristic
7	C₄×C₇×C₇₃	C₃×C₄	1	1	yes	characteristic
8	C₃×C₈×C₇₃	C₂×C₇	1	1	yes	characteristic
9	C₃×C₇×C₇₃	C₁₆	1	1	yes	characteristic, direct product factor, Hall
10	C₁₆×C₇₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₇×C₇₃	C₃×C₈	1	1	yes	characteristic
12	C₃×C₄×C₇₃	C₄×C₇	1	1	yes	characteristic
13	C₈×C₇₃	C₂×C₃×C₇	1	1	yes	characteristic
14	C₇×C₇₃	C₃×C₁₆	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₇₃	C₇×C₈	1	1	yes	characteristic
16	C₃×C₇×C₁₆	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₄×C₇₃	C₃×C₄×C₇	1	1	yes	characteristic
18	C₃×C₇₃	C₇×C₁₆	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₇×C₈	C₂×C₇₃	1	1	yes	characteristic
20	C₂×C₇₃	C₃×C₇×C₈	1	1	yes	characteristic
21	C₇×C₁₆	C₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₄×C₇	C₄×C₇₃	1	1	yes	characteristic
23	C₇₃	C₃×C₇×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
24	C₇×C₈	C₂×C₃×C₇₃	1	1	yes	characteristic
25	C₃×C₁₆	C₇×C₇₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₃×C₇	C₈×C₇₃	1	1	yes	characteristic
27	C₄×C₇	C₃×C₄×C₇₃	1	1	yes	characteristic
28	C₃×C₈	C₂×C₇×C₇₃	1	1	yes	characteristic
29	C₃×C₇	C₁₆×C₇₃	1	1	yes	characteristic, direct product factor, Hall
30	C₁₆	C₃×C₇×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₇	C₃×C₈×C₇₃	1	1	yes	characteristic
32	C₃×C₄	C₄×C₇×C₇₃	1	1	yes	characteristic
33	C₈	C₂×C₃×C₇×C₇₃	1	1	yes	characteristic
34	C₇	C₃×C₁₆×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃	C₇×C₈×C₇₃	1	1	yes	characteristic
36	C₄	C₃×C₄×C₇×C₇₃	1	1	yes	characteristic
37	C₃	C₇×C₁₆×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂	C₃×C₇×C₈×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃×C₇×C₇₃
socle, prime radical	C₂×C₃×C₇×C₇₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₆×C₇₃	C₃	direct (N × H)
4. C₃×C₁₆×C₇₃	C₇	direct (N × H)
9. C₃×C₇×C₇₃	C₁₆	direct (N × H)
10. C₁₆×C₇₃	C₃×C₇	direct (N × H)
14. C₇×C₇₃	C₃×C₁₆	direct (N × H)
16. C₃×C₇×C₁₆	C₇₃	direct (N × H)
18. C₃×C₇₃	C₇×C₁₆	direct (N × H)
21. C₇×C₁₆	C₃×C₇₃	direct (N × H)
23. C₇₃	C₃×C₇×C₁₆	direct (N × H)
25. C₃×C₁₆	C₇×C₇₃	direct (N × H)
29. C₃×C₇	C₁₆×C₇₃	direct (N × H)
30. C₁₆	C₃×C₇×C₇₃	direct (N × H)
34. C₇	C₃×C₁₆×C₇₃	direct (N × H)
37. C₃	C₇×C₁₆×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
C₃×C₇×C₈×C₇₃	2
C₇×C₁₆×C₇₃	3
C₃×C₁₆×C₇₃	7
C₃×C₇×C₁₆	73

Subgroups — C3×C7×C16×C73 #72201780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₆×C₇₃ #72201780