Subgroups — C₂³×C₃³×C₉₇ #72198539

Order 20952.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×C₉₇	C₂	1	7	yes	maximal, direct product factor
2	C₂³×C₃²×C₉₇	C₃	1	13	yes	maximal, direct product factor
3	C₂×C₃³×C₉₇	C₂²	1	7	yes	direct product factor
4	C₂³×C₃×C₉₇	C₃²	1	13	yes	direct product factor
5	C₂²×C₃²×C₉₇	C₂×C₃	1	91	yes	direct product factor
6	C₃³×C₉₇	C₂³	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₉₇	C₂²×C₃	1	91	yes	direct product factor
8	C₂²×C₃×C₉₇	C₂×C₃²	1	91	yes	direct product factor
9	C₃²×C₉₇	C₂³×C₃	1	13	yes	direct product factor
10	C₂³×C₉₇	C₃³	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₉₇	C₂²×C₃²	1	91	yes	direct product factor
12	C₂²×C₉₇	C₂×C₃³	1	7	yes	direct product factor
13	C₃×C₉₇	C₂³×C₃²	1	13	yes	direct product factor
14	C₂³×C₃³	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₉₇	C₂²×C₃³	1	7	yes	direct product factor
16	C₂²×C₃³	C₂×C₉₇	1	7	yes	direct product factor
17	C₉₇	C₂³×C₃³	1	1	yes	characteristic, direct product factor, Sylow
18	C₂³×C₃²	C₃×C₉₇	1	13	yes	direct product factor
19	C₂×C₃³	C₂²×C₉₇	1	7	yes	direct product factor
20	C₂²×C₃²	C₂×C₃×C₉₇	1	91	yes	direct product factor
21	C₃³	C₂³×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂³×C₃	C₃²×C₉₇	1	13	yes	direct product factor
23	C₂×C₃²	C₂²×C₃×C₉₇	1	91	yes	direct product factor
24	C₂²×C₃	C₂×C₃²×C₉₇	1	91	yes	direct product factor
25	C₃²	C₂³×C₃×C₉₇	1	13	yes	direct product factor
26	C₂³	C₃³×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₂²×C₃²×C₉₇	1	91	yes	direct product factor
28	C₂²	C₂×C₃³×C₉₇	1	7	yes	direct product factor
29	C₃	C₂³×C₃²×C₉₇	1	13	yes	direct product factor
30	C₂	C₂²×C₃³×C₉₇	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×C₃³×C₉₇	C₂	direct (N × H)
2. C₂³×C₃²×C₉₇	C₃	direct (N × H)
3. C₂×C₃³×C₉₇	C₂²	direct (N × H)
4. C₂³×C₃×C₉₇	C₃²	direct (N × H)
5. C₂²×C₃²×C₉₇	C₂×C₃	direct (N × H)
6. C₃³×C₉₇	C₂³	direct (N × H)
7. C₂×C₃²×C₉₇	C₂²×C₃	direct (N × H)
8. C₂²×C₃×C₉₇	C₂×C₃²	direct (N × H)
9. C₃²×C₉₇	C₂³×C₃	direct (N × H)
10. C₂³×C₉₇	C₃³	direct (N × H)
11. C₂×C₃×C₉₇	C₂²×C₃²	direct (N × H)
12. C₂²×C₉₇	C₂×C₃³	direct (N × H)
13. C₃×C₉₇	C₂³×C₃²	direct (N × H)
14. C₂³×C₃³	C₉₇	direct (N × H)
15. C₂×C₉₇	C₂²×C₃³	direct (N × H)
16. C₂²×C₃³	C₂×C₉₇	direct (N × H)
17. C₉₇	C₂³×C₃³	direct (N × H)
18. C₂³×C₃²	C₃×C₉₇	direct (N × H)
19. C₂×C₃³	C₂²×C₉₇	direct (N × H)
20. C₂²×C₃²	C₂×C₃×C₉₇	direct (N × H)
21. C₃³	C₂³×C₉₇	direct (N × H)
22. C₂³×C₃	C₃²×C₉₇	direct (N × H)
23. C₂×C₃²	C₂²×C₃×C₉₇	direct (N × H)
24. C₂²×C₃	C₂×C₃²×C₉₇	direct (N × H)
25. C₃²	C₂³×C₃×C₉₇	direct (N × H)
26. C₂³	C₃³×C₉₇	direct (N × H)
27. C₂×C₃	C₂²×C₃²×C₉₇	direct (N × H)
28. C₂²	C₂×C₃³×C₉₇	direct (N × H)
29. C₃	C₂³×C₃²×C₉₇	direct (N × H)
30. C₂	C₂²×C₃³×C₉₇	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×C₃³×C₉₇	2
C₂³×C₃²×C₉₇	3
C₂³×C₃³	97

Subgroups — C23×C33×C97 #72198539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃³×C₉₇ #72198539