Subgroups — C₂³×C₃⁴×C₃₇ #72201262

Order 23976.

6784 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⁴×C₃₇	C₂	1	7	yes	maximal, direct product factor
2	C₂³×C₃³×C₃₇	C₃	1	40	yes	maximal, direct product factor
3	C₂×C₃⁴×C₃₇	C₂²	1	7	yes	direct product factor
4	C₂²×C₃³×C₃₇	C₂×C₃	1	280	yes	direct product factor
5	C₂³×C₃²×C₃₇	C₃²	1	130	yes	direct product factor
6	C₃⁴×C₃₇	C₂³	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃³×C₃₇	C₂²×C₃	1	280	yes	direct product factor
8	C₂²×C₃²×C₃₇	C₂×C₃²	1	910	yes	direct product factor
9	C₃³×C₃₇	C₂³×C₃	1	40	yes	direct product factor
10	C₂³×C₃×C₃₇	C₃³	1	40	yes	direct product factor
11	C₂×C₃²×C₃₇	C₂²×C₃²	1	910	yes	direct product factor
12	C₂³×C₃⁴	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₃₇	C₂×C₃³	1	280	yes	direct product factor
14	C₃²×C₃₇	C₂³×C₃²	1	130	yes	direct product factor
15	C₂²×C₃⁴	C₂×C₃₇	1	7	yes	direct product factor
16	C₂³×C₃₇	C₃⁴	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₃₇	C₂²×C₃³	1	280	yes	direct product factor
18	C₂³×C₃³	C₃×C₃₇	1	40	yes	direct product factor
19	C₂×C₃⁴	C₂²×C₃₇	1	7	yes	direct product factor
20	C₂²×C₃₇	C₂×C₃⁴	1	7	yes	direct product factor
21	C₃×C₃₇	C₂³×C₃³	1	40	yes	direct product factor
22	C₂²×C₃³	C₂×C₃×C₃₇	1	280	yes	direct product factor
23	C₃⁴	C₂³×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃₇	C₂²×C₃⁴	1	7	yes	direct product factor
25	C₂³×C₃²	C₃²×C₃₇	1	130	yes	direct product factor
26	C₂×C₃³	C₂²×C₃×C₃₇	1	280	yes	direct product factor
27	C₃₇	C₂³×C₃⁴	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²×C₃²	C₂×C₃²×C₃₇	1	910	yes	direct product factor
29	C₃³	C₂³×C₃×C₃₇	1	40	yes	direct product factor
30	C₂³×C₃	C₃³×C₃₇	1	40	yes	direct product factor
31	C₂×C₃²	C₂²×C₃²×C₃₇	1	910	yes	direct product factor
32	C₂²×C₃	C₂×C₃³×C₃₇	1	280	yes	direct product factor
33	C₃²	C₂³×C₃²×C₃₇	1	130	yes	direct product factor
34	C₂³	C₃⁴×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃	C₂²×C₃³×C₃₇	1	280	yes	direct product factor
36	C₂²	C₂×C₃⁴×C₃₇	1	7	yes	direct product factor
37	C₃	C₂³×C₃³×C₃₇	1	40	yes	direct product factor
38	C₂	C₂²×C₃⁴×C₃₇	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×C₃⁴×C₃₇	C₂	direct (N × H)
2. C₂³×C₃³×C₃₇	C₃	direct (N × H)
3. C₂×C₃⁴×C₃₇	C₂²	direct (N × H)
4. C₂²×C₃³×C₃₇	C₂×C₃	direct (N × H)
5. C₂³×C₃²×C₃₇	C₃²	direct (N × H)
6. C₃⁴×C₃₇	C₂³	direct (N × H)
7. C₂×C₃³×C₃₇	C₂²×C₃	direct (N × H)
8. C₂²×C₃²×C₃₇	C₂×C₃²	direct (N × H)
9. C₃³×C₃₇	C₂³×C₃	direct (N × H)
10. C₂³×C₃×C₃₇	C₃³	direct (N × H)
11. C₂×C₃²×C₃₇	C₂²×C₃²	direct (N × H)
12. C₂³×C₃⁴	C₃₇	direct (N × H)
13. C₂²×C₃×C₃₇	C₂×C₃³	direct (N × H)
14. C₃²×C₃₇	C₂³×C₃²	direct (N × H)
15. C₂²×C₃⁴	C₂×C₃₇	direct (N × H)
16. C₂³×C₃₇	C₃⁴	direct (N × H)
17. C₂×C₃×C₃₇	C₂²×C₃³	direct (N × H)
18. C₂³×C₃³	C₃×C₃₇	direct (N × H)
19. C₂×C₃⁴	C₂²×C₃₇	direct (N × H)
20. C₂²×C₃₇	C₂×C₃⁴	direct (N × H)
21. C₃×C₃₇	C₂³×C₃³	direct (N × H)
22. C₂²×C₃³	C₂×C₃×C₃₇	direct (N × H)
23. C₃⁴	C₂³×C₃₇	direct (N × H)
24. C₂×C₃₇	C₂²×C₃⁴	direct (N × H)
25. C₂³×C₃²	C₃²×C₃₇	direct (N × H)
26. C₂×C₃³	C₂²×C₃×C₃₇	direct (N × H)
27. C₃₇	C₂³×C₃⁴	direct (N × H)
28. C₂²×C₃²	C₂×C₃²×C₃₇	direct (N × H)
29. C₃³	C₂³×C₃×C₃₇	direct (N × H)
30. C₂³×C₃	C₃³×C₃₇	direct (N × H)
31. C₂×C₃²	C₂²×C₃²×C₃₇	direct (N × H)
32. C₂²×C₃	C₂×C₃³×C₃₇	direct (N × H)
33. C₃²	C₂³×C₃²×C₃₇	direct (N × H)
34. C₂³	C₃⁴×C₃₇	direct (N × H)
35. C₂×C₃	C₂²×C₃³×C₃₇	direct (N × H)
36. C₂²	C₂×C₃⁴×C₃₇	direct (N × H)
37. C₃	C₂³×C₃³×C₃₇	direct (N × H)
38. C₂	C₂²×C₃⁴×C₃₇	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×C₃⁴×C₃₇	2
C₂³×C₃³×C₃₇	3
C₂³×C₃⁴	37

Subgroups — C23×C34×C37 #72201262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃⁴×C₃₇ #72201262