Subgroups — C₃²×C₄²×C₅×C₁₁ #72186831

Order 7920.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄×C₅×C₁₁	C₂	1	3	yes	maximal
2	C₃×C₄²×C₅×C₁₁	C₃	1	4	yes	maximal, direct product factor
3	C₂²×C₃²×C₅×C₁₁	C₂²	1	1	yes	characteristic
4	C₃²×C₄×C₅×C₁₁	C₄	1	6	yes	direct product factor
5	C₃²×C₄²×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₄×C₅×C₁₁	C₂×C₃	1	12	yes	—
7	C₂×C₃²×C₅×C₁₁	C₂×C₄	1	3	yes	—
8	C₄²×C₅×C₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₄×C₁₁	C₂×C₅	1	3	yes	—
10	C₃²×C₄²×C₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×C₁₁	C₂²×C₃	1	4	yes	—
12	C₃×C₄×C₅×C₁₁	C₃×C₄	1	24	yes	direct product factor
13	C₃×C₄²×C₁₁	C₃×C₅	1	4	yes	direct product factor
14	C₃²×C₅×C₁₁	C₄²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₄×C₅×C₁₁	C₂×C₃²	1	3	yes	—
16	C₂²×C₃²×C₁₁	C₂²×C₅	1	1	yes	characteristic
17	C₃²×C₄×C₁₁	C₄×C₅	1	6	yes	direct product factor
18	C₂×C₃²×C₄×C₅	C₂×C₁₁	1	3	yes	—
19	C₂×C₃×C₅×C₁₁	C₂×C₃×C₄	1	12	yes	—
20	C₂×C₃×C₄×C₁₁	C₂×C₃×C₅	1	12	yes	—
21	C₃×C₄²×C₅	C₃×C₁₁	1	4	yes	direct product factor
22	C₂²×C₅×C₁₁	C₂²×C₃²	1	1	yes	characteristic
23	C₄×C₅×C₁₁	C₃²×C₄	1	6	yes	direct product factor
24	C₂×C₃²×C₁₁	C₂×C₄×C₅	1	3	yes	—
25	C₂²×C₃²×C₅	C₂²×C₁₁	1	1	yes	characteristic
26	C₃²×C₄×C₅	C₄×C₁₁	1	6	yes	direct product factor
27	C₄²×C₁₁	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅×C₁₁	C₃×C₄²	1	4	yes	direct product factor
29	C₃²×C₄²	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₃×C₁₁	C₂²×C₃×C₅	1	4	yes	—
31	C₃×C₄×C₁₁	C₃×C₄×C₅	1	24	yes	direct product factor
32	C₂×C₃×C₄×C₅	C₂×C₃×C₁₁	1	12	yes	—
33	C₂×C₅×C₁₁	C₂×C₃²×C₄	1	3	yes	—
34	C₃²×C₁₁	C₄²×C₅	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₃²×C₅	C₂×C₄×C₁₁	1	3	yes	—
36	C₂×C₄×C₁₁	C₂×C₃²×C₅	1	3	yes	—
37	C₄²×C₅	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₃²×C₄	C₂×C₅×C₁₁	1	3	yes	—
39	C₂×C₃×C₁₁	C₂×C₃×C₄×C₅	1	12	yes	—
40	C₂²×C₃×C₅	C₂²×C₃×C₁₁	1	4	yes	—
41	C₃×C₄×C₅	C₃×C₄×C₁₁	1	24	yes	direct product factor
42	C₅×C₁₁	C₃²×C₄²	1	1	yes	characteristic, direct product factor, Hall
43	C₃×C₄²	C₃×C₅×C₁₁	1	4	yes	direct product factor
44	C₃²×C₅	C₄²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
45	C₂²×C₁₁	C₂²×C₃²×C₅	1	1	yes	characteristic
46	C₄×C₁₁	C₃²×C₄×C₅	1	6	yes	direct product factor
47	C₂×C₄×C₅	C₂×C₃²×C₁₁	1	3	yes	—
48	C₂²×C₃²	C₂²×C₅×C₁₁	1	1	yes	characteristic
49	C₃²×C₄	C₄×C₅×C₁₁	1	6	yes	direct product factor
50	C₃×C₁₁	C₃×C₄²×C₅	1	4	yes	direct product factor
51	C₂×C₃×C₅	C₂×C₃×C₄×C₁₁	1	12	yes	—
52	C₂×C₃×C₄	C₂×C₃×C₅×C₁₁	1	12	yes	—
53	C₂×C₁₁	C₂×C₃²×C₄×C₅	1	3	yes	—
54	C₂²×C₅	C₂²×C₃²×C₁₁	1	1	yes	characteristic
55	C₄×C₅	C₃²×C₄×C₁₁	1	6	yes	direct product factor
56	C₂×C₃²	C₂×C₄×C₅×C₁₁	1	3	yes	—
57	C₄²	C₃²×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
58	C₃×C₅	C₃×C₄²×C₁₁	1	4	yes	direct product factor
59	C₂²×C₃	C₂²×C₃×C₅×C₁₁	1	4	yes	—
60	C₃×C₄	C₃×C₄×C₅×C₁₁	1	24	yes	direct product factor
61	C₁₁	C₃²×C₄²×C₅	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₅	C₂×C₃²×C₄×C₁₁	1	3	yes	—
63	C₃²	C₄²×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₄	C₂×C₃²×C₅×C₁₁	1	3	yes	—
65	C₂×C₃	C₂×C₃×C₄×C₅×C₁₁	1	12	yes	—
66	C₅	C₃²×C₄²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	C₂²×C₃²×C₅×C₁₁	1	1	yes	characteristic
68	C₄	C₃²×C₄×C₅×C₁₁	1	6	yes	direct product factor
69	C₃	C₃×C₄²×C₅×C₁₁	1	4	yes	direct product factor
70	C₂	C₂×C₃²×C₄×C₅×C₁₁	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃²×C₅×C₁₁
socle, prime radical	C₂²×C₃²×C₅×C₁₁	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄²×C₅×C₁₁	C₃	direct (N × H)
4. C₃²×C₄×C₅×C₁₁	C₄	direct (N × H)
5. C₃²×C₄²×C₁₁	C₅	direct (N × H)
8. C₄²×C₅×C₁₁	C₃²	direct (N × H)
10. C₃²×C₄²×C₅	C₁₁	direct (N × H)
12. C₃×C₄×C₅×C₁₁	C₃×C₄	direct (N × H)
13. C₃×C₄²×C₁₁	C₃×C₅	direct (N × H)
14. C₃²×C₅×C₁₁	C₄²	direct (N × H)
17. C₃²×C₄×C₁₁	C₄×C₅	direct (N × H)
21. C₃×C₄²×C₅	C₃×C₁₁	direct (N × H)
23. C₄×C₅×C₁₁	C₃²×C₄	direct (N × H)
26. C₃²×C₄×C₅	C₄×C₁₁	direct (N × H)
27. C₄²×C₁₁	C₃²×C₅	direct (N × H)
28. C₃×C₅×C₁₁	C₃×C₄²	direct (N × H)
29. C₃²×C₄²	C₅×C₁₁	direct (N × H)
31. C₃×C₄×C₁₁	C₃×C₄×C₅	direct (N × H)
34. C₃²×C₁₁	C₄²×C₅	direct (N × H)
37. C₄²×C₅	C₃²×C₁₁	direct (N × H)
41. C₃×C₄×C₅	C₃×C₄×C₁₁	direct (N × H)
42. C₅×C₁₁	C₃²×C₄²	direct (N × H)
43. C₃×C₄²	C₃×C₅×C₁₁	direct (N × H)
44. C₃²×C₅	C₄²×C₁₁	direct (N × H)
46. C₄×C₁₁	C₃²×C₄×C₅	direct (N × H)
49. C₃²×C₄	C₄×C₅×C₁₁	direct (N × H)
50. C₃×C₁₁	C₃×C₄²×C₅	direct (N × H)
55. C₄×C₅	C₃²×C₄×C₁₁	direct (N × H)
57. C₄²	C₃²×C₅×C₁₁	direct (N × H)
58. C₃×C₅	C₃×C₄²×C₁₁	direct (N × H)
60. C₃×C₄	C₃×C₄×C₅×C₁₁	direct (N × H)
61. C₁₁	C₃²×C₄²×C₅	direct (N × H)
63. C₃²	C₄²×C₅×C₁₁	direct (N × H)
66. C₅	C₃²×C₄²×C₁₁	direct (N × H)
68. C₄	C₃²×C₄×C₅×C₁₁	direct (N × H)
69. C₃	C₃×C₄²×C₅×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×C₃²×C₄×C₅×C₁₁	2
C₃×C₄²×C₅×C₁₁	3
C₃²×C₄²×C₁₁	5
C₃²×C₄²×C₅	11

Subgroups — C32×C42×C5×C11 #72186831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄²×C₅×C₁₁ #72186831