Subgroups — C₃²×C₅×C₇²×C₁₁ #37564686

Order 24255.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₁	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₇²×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃²×C₅×C₇×C₁₁	C₇	1	8	yes	maximal, direct product factor
4	C₅×C₇²×C₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₃²×C₅×C₇²	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇²×C₁₁	C₃×C₅	1	4	yes	direct product factor
7	C₃×C₅×C₇×C₁₁	C₃×C₇	1	32	yes	direct product factor
8	C₃×C₅×C₇²	C₃×C₁₁	1	4	yes	direct product factor
9	C₃²×C₇×C₁₁	C₅×C₇	1	8	yes	direct product factor
10	C₇²×C₁₁	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃²×C₅×C₁₁	C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₃²×C₇²	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₇×C₁₁	C₃²×C₇	1	8	yes	direct product factor
14	C₃²×C₅×C₇	C₇×C₁₁	1	8	yes	direct product factor
15	C₅×C₇²	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₇×C₁₁	C₃×C₅×C₇	1	32	yes	direct product factor
17	C₃×C₅×C₁₁	C₃×C₇²	1	4	yes	direct product factor
18	C₃×C₇²	C₃×C₅×C₁₁	1	4	yes	direct product factor
19	C₃×C₅×C₇	C₃×C₇×C₁₁	1	32	yes	direct product factor
20	C₃²×C₁₁	C₅×C₇²	1	1	yes	characteristic, direct product factor, Hall
21	C₇×C₁₁	C₃²×C₅×C₇	1	8	yes	direct product factor
22	C₃²×C₇	C₅×C₇×C₁₁	1	8	yes	direct product factor
23	C₅×C₁₁	C₃²×C₇²	1	1	yes	characteristic, direct product factor, Hall
24	C₇²	C₃²×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₃²×C₅	C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
26	C₅×C₇	C₃²×C₇×C₁₁	1	8	yes	direct product factor
27	C₃×C₁₁	C₃×C₅×C₇²	1	4	yes	direct product factor
28	C₃×C₇	C₃×C₅×C₇×C₁₁	1	32	yes	direct product factor
29	C₃×C₅	C₃×C₇²×C₁₁	1	4	yes	direct product factor
30	C₁₁	C₃²×C₅×C₇²	1	1	yes	characteristic, direct product factor, Sylow
31	C₃²	C₅×C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₇	C₃²×C₅×C₇×C₁₁	1	8	yes	direct product factor
33	C₅	C₃²×C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₃	C₃×C₅×C₇²×C₁₁	1	4	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. C₃×C₅×C₇²×C₁₁	C₃	direct (N × H)
2. C₃²×C₇²×C₁₁	C₅	direct (N × H)
3. C₃²×C₅×C₇×C₁₁	C₇	direct (N × H)
4. C₅×C₇²×C₁₁	C₃²	direct (N × H)
5. C₃²×C₅×C₇²	C₁₁	direct (N × H)
6. C₃×C₇²×C₁₁	C₃×C₅	direct (N × H)
7. C₃×C₅×C₇×C₁₁	C₃×C₇	direct (N × H)
8. C₃×C₅×C₇²	C₃×C₁₁	direct (N × H)
9. C₃²×C₇×C₁₁	C₅×C₇	direct (N × H)
10. C₇²×C₁₁	C₃²×C₅	direct (N × H)
11. C₃²×C₅×C₁₁	C₇²	direct (N × H)
12. C₃²×C₇²	C₅×C₁₁	direct (N × H)
13. C₅×C₇×C₁₁	C₃²×C₇	direct (N × H)
14. C₃²×C₅×C₇	C₇×C₁₁	direct (N × H)
15. C₅×C₇²	C₃²×C₁₁	direct (N × H)
16. C₃×C₇×C₁₁	C₃×C₅×C₇	direct (N × H)
17. C₃×C₅×C₁₁	C₃×C₇²	direct (N × H)
18. C₃×C₇²	C₃×C₅×C₁₁	direct (N × H)
19. C₃×C₅×C₇	C₃×C₇×C₁₁	direct (N × H)
20. C₃²×C₁₁	C₅×C₇²	direct (N × H)
21. C₇×C₁₁	C₃²×C₅×C₇	direct (N × H)
22. C₃²×C₇	C₅×C₇×C₁₁	direct (N × H)
23. C₅×C₁₁	C₃²×C₇²	direct (N × H)
24. C₇²	C₃²×C₅×C₁₁	direct (N × H)
25. C₃²×C₅	C₇²×C₁₁	direct (N × H)
26. C₅×C₇	C₃²×C₇×C₁₁	direct (N × H)
27. C₃×C₁₁	C₃×C₅×C₇²	direct (N × H)
28. C₃×C₇	C₃×C₅×C₇×C₁₁	direct (N × H)
29. C₃×C₅	C₃×C₇²×C₁₁	direct (N × H)
30. C₁₁	C₃²×C₅×C₇²	direct (N × H)
31. C₃²	C₅×C₇²×C₁₁	direct (N × H)
32. C₇	C₃²×C₅×C₇×C₁₁	direct (N × H)
33. C₅	C₃²×C₇²×C₁₁	direct (N × H)
34. C₃	C₃×C₅×C₇²×C₁₁	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×C₅×C₇²×C₁₁	3
C₃²×C₇²×C₁₁	5
C₃²×C₅×C₇×C₁₁	7
C₃²×C₅×C₇²	11

Subgroups — C32×C5×C72×C11 #37564686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×C₇²×C₁₁ #37564686