Subgroups — C₃×C₄×C₉×C₁₁ #11924656

Order 1188.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×C₁₁	C₃	1	1	yes	maximal, characteristic
3	C₄×C₉×C₁₁	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₉×C₁₁	C₄	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃²×C₁₁	C₂×C₃	1	1	yes	characteristic
6	C₂×C₉×C₁₁	C₂×C₃	1	3	yes	—
7	C₃×C₄×C₁₁	C₉	1	3	yes	direct product factor
8	C₃×C₄×C₁₁	C₃²	1	1	yes	characteristic
9	C₃×C₄×C₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₁₁	C₃×C₄	1	1	yes	characteristic
11	C₉×C₁₁	C₃×C₄	1	3	yes	direct product factor
12	C₂×C₃×C₁₁	C₂×C₉	1	3	yes	—
13	C₂×C₃×C₁₁	C₂×C₃²	1	1	yes	characteristic
14	C₂×C₃×C₉	C₂×C₁₁	1	1	yes	characteristic
15	C₄×C₁₁	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃²×C₄	C₃×C₁₁	1	1	yes	characteristic
17	C₄×C₉	C₃×C₁₁	1	3	yes	direct product factor
18	C₃×C₁₁	C₄×C₉	1	3	yes	direct product factor
19	C₃×C₁₁	C₃²×C₄	1	1	yes	characteristic
20	C₃×C₉	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₁₁	C₂×C₃×C₉	1	1	yes	characteristic
22	C₂×C₃²	C₂×C₃×C₁₁	1	1	yes	characteristic
23	C₂×C₉	C₂×C₃×C₁₁	1	3	yes	—
24	C₃×C₄	C₉×C₁₁	1	3	yes	direct product factor
25	C₃×C₄	C₃²×C₁₁	1	1	yes	characteristic
26	C₁₁	C₃×C₄×C₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₃²	C₃×C₄×C₁₁	1	1	yes	characteristic
28	C₉	C₃×C₄×C₁₁	1	3	yes	direct product factor
29	C₂×C₃	C₂×C₉×C₁₁	1	3	yes	—
30	C₂×C₃	C₂×C₃²×C₁₁	1	1	yes	characteristic
31	C₄	C₃×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₃	C₄×C₉×C₁₁	1	3	yes	direct product factor
33	C₃	C₃²×C₄×C₁₁	1	1	yes	characteristic
34	C₂	C₂×C₃×C₉×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃²×C₁₁
socle, prime radical	C₂×C₃²×C₁₁	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₉×C₁₁	C₃	direct (N × H)
4. C₃×C₉×C₁₁	C₄	direct (N × H)
7. C₃×C₄×C₁₁	C₉	direct (N × H)
9. C₃×C₄×C₉	C₁₁	direct (N × H)
11. C₉×C₁₁	C₃×C₄	direct (N × H)
15. C₄×C₁₁	C₃×C₉	direct (N × H)
17. C₄×C₉	C₃×C₁₁	direct (N × H)
18. C₃×C₁₁	C₄×C₉	direct (N × H)
20. C₃×C₉	C₄×C₁₁	direct (N × H)
24. C₃×C₄	C₉×C₁₁	direct (N × H)
26. C₁₁	C₃×C₄×C₉	direct (N × H)
28. C₉	C₃×C₄×C₁₁	direct (N × H)
31. C₄	C₃×C₉×C₁₁	direct (N × H)
32. C₃	C₄×C₉×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
C₂×C₃×C₉×C₁₁	2
C₃²×C₄×C₁₁	3
C₄×C₉×C₁₁	3
C₃×C₄×C₉	11

Subgroups — C3×C4×C9×C11 #11924656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₉×C₁₁ #11924656