Subgroups — C₂×C₄×C₉×C₁₁×C₃₁ #72201794

Order 24552.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₁₁×C₃₁	C₃	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁×C₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
3	C₂×C₄×C₉×C₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₉×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₄×C₉×C₁₁×C₃₁	C₂	1	2	yes	maximal, direct product factor
6	C₂×C₉×C₁₁×C₃₁	C₄	1	2	yes	direct product factor
7	C₂×C₉×C₁₁×C₃₁	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₁₁×C₃₁	C₂×C₃	1	1	yes	characteristic
9	C₃×C₄×C₁₁×C₃₁	C₂×C₃	1	2	yes	—
10	C₉×C₁₁×C₃₁	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₁₁×C₃₁	C₃×C₄	1	2	yes	—
12	C₂×C₃×C₁₁×C₃₁	C₂²×C₃	1	1	yes	characteristic
13	C₂²×C₁₁×C₃₁	C₂×C₉	1	1	yes	characteristic
14	C₄×C₁₁×C₃₁	C₂×C₉	1	2	yes	direct product factor
15	C₂²×C₉×C₃₁	C₂×C₁₁	1	1	yes	characteristic
16	C₄×C₉×C₃₁	C₂×C₁₁	1	2	yes	direct product factor
17	C₃×C₁₁×C₃₁	C₂×C₃×C₄	1	1	yes	characteristic
18	C₂×C₄×C₉×C₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₄×C₃₁	C₃×C₁₁	1	1	yes	characteristic
20	C₂×C₁₁×C₃₁	C₄×C₉	1	2	yes	direct product factor
21	C₂×C₁₁×C₃₁	C₂²×C₉	1	1	yes	characteristic
22	C₂×C₉×C₃₁	C₄×C₁₁	1	2	yes	direct product factor
23	C₂×C₉×C₃₁	C₂²×C₁₁	1	1	yes	characteristic
24	C₂²×C₉×C₁₁	C₂×C₃₁	1	1	yes	characteristic
25	C₄×C₉×C₁₁	C₂×C₃₁	1	2	yes	direct product factor
26	C₂²×C₃×C₃₁	C₂×C₃×C₁₁	1	1	yes	characteristic
27	C₃×C₄×C₃₁	C₂×C₃×C₁₁	1	2	yes	—
28	C₁₁×C₃₁	C₂×C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
29	C₉×C₃₁	C₂×C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₄×C₁₁	C₃×C₃₁	1	1	yes	characteristic
31	C₂×C₄×C₃₁	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₉×C₁₁	C₄×C₃₁	1	2	yes	direct product factor
33	C₂×C₉×C₁₁	C₂²×C₃₁	1	1	yes	characteristic
34	C₂×C₃×C₃₁	C₃×C₄×C₁₁	1	2	yes	—
35	C₂×C₃×C₃₁	C₂²×C₃×C₁₁	1	1	yes	characteristic
36	C₂²×C₃×C₁₁	C₂×C₃×C₃₁	1	1	yes	characteristic
37	C₃×C₄×C₁₁	C₂×C₃×C₃₁	1	2	yes	—
38	C₂²×C₃₁	C₂×C₉×C₁₁	1	1	yes	characteristic
39	C₄×C₃₁	C₂×C₉×C₁₁	1	2	yes	direct product factor
40	C₉×C₁₁	C₂×C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
41	C₃×C₃₁	C₂×C₃×C₄×C₁₁	1	1	yes	characteristic
42	C₂×C₄×C₁₁	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₄×C₉	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₃×C₁₁	C₃×C₄×C₃₁	1	2	yes	—
45	C₂×C₃×C₁₁	C₂²×C₃×C₃₁	1	1	yes	characteristic
46	C₂×C₃₁	C₄×C₉×C₁₁	1	2	yes	direct product factor
47	C₂×C₃₁	C₂²×C₉×C₁₁	1	1	yes	characteristic
48	C₂²×C₁₁	C₂×C₉×C₃₁	1	1	yes	characteristic
49	C₄×C₁₁	C₂×C₉×C₃₁	1	2	yes	direct product factor
50	C₂²×C₉	C₂×C₁₁×C₃₁	1	1	yes	characteristic
51	C₄×C₉	C₂×C₁₁×C₃₁	1	2	yes	direct product factor
52	C₃×C₁₁	C₂×C₃×C₄×C₃₁	1	1	yes	characteristic
53	C₃₁	C₂×C₄×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₃×C₄	C₃×C₁₁×C₃₁	1	1	yes	characteristic
55	C₂×C₁₁	C₄×C₉×C₃₁	1	2	yes	direct product factor
56	C₂×C₁₁	C₂²×C₉×C₃₁	1	1	yes	characteristic
57	C₂×C₉	C₄×C₁₁×C₃₁	1	2	yes	direct product factor
58	C₂×C₉	C₂²×C₁₁×C₃₁	1	1	yes	characteristic
59	C₂²×C₃	C₂×C₃×C₁₁×C₃₁	1	1	yes	characteristic
60	C₃×C₄	C₂×C₃×C₁₁×C₃₁	1	2	yes	—
61	C₁₁	C₂×C₄×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
62	C₉	C₂×C₄×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₄	C₉×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	C₃×C₄×C₁₁×C₃₁	1	2	yes	—
65	C₂×C₃	C₂²×C₃×C₁₁×C₃₁	1	1	yes	characteristic
66	C₂²	C₂×C₉×C₁₁×C₃₁	1	1	yes	characteristic
67	C₄	C₂×C₉×C₁₁×C₃₁	1	2	yes	direct product factor
68	C₃	C₂×C₃×C₄×C₁₁×C₃₁	1	1	yes	characteristic
69	C₂	C₄×C₉×C₁₁×C₃₁	1	2	yes	direct product factor
70	C₂	C₂²×C₉×C₁₁×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₁₁×C₃₁
socle, prime radical	C₂²×C₃×C₁₁×C₃₁	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₁×C₃₁	C₉	direct (N × H)
3. C₂×C₄×C₉×C₃₁	C₁₁	direct (N × H)
5. C₄×C₉×C₁₁×C₃₁	C₂	direct (N × H)
6. C₂×C₉×C₁₁×C₃₁	C₄	direct (N × H)
10. C₉×C₁₁×C₃₁	C₂×C₄	direct (N × H)
14. C₄×C₁₁×C₃₁	C₂×C₉	direct (N × H)
16. C₄×C₉×C₃₁	C₂×C₁₁	direct (N × H)
18. C₂×C₄×C₉×C₁₁	C₃₁	direct (N × H)
20. C₂×C₁₁×C₃₁	C₄×C₉	direct (N × H)
22. C₂×C₉×C₃₁	C₄×C₁₁	direct (N × H)
25. C₄×C₉×C₁₁	C₂×C₃₁	direct (N × H)
28. C₁₁×C₃₁	C₂×C₄×C₉	direct (N × H)
29. C₉×C₃₁	C₂×C₄×C₁₁	direct (N × H)
31. C₂×C₄×C₃₁	C₉×C₁₁	direct (N × H)
32. C₂×C₉×C₁₁	C₄×C₃₁	direct (N × H)
39. C₄×C₃₁	C₂×C₉×C₁₁	direct (N × H)
40. C₉×C₁₁	C₂×C₄×C₃₁	direct (N × H)
42. C₂×C₄×C₁₁	C₉×C₃₁	direct (N × H)
43. C₂×C₄×C₉	C₁₁×C₃₁	direct (N × H)
46. C₂×C₃₁	C₄×C₉×C₁₁	direct (N × H)
49. C₄×C₁₁	C₂×C₉×C₃₁	direct (N × H)
51. C₄×C₉	C₂×C₁₁×C₃₁	direct (N × H)
53. C₃₁	C₂×C₄×C₉×C₁₁	direct (N × H)
55. C₂×C₁₁	C₄×C₉×C₃₁	direct (N × H)
57. C₂×C₉	C₄×C₁₁×C₃₁	direct (N × H)
61. C₁₁	C₂×C₄×C₉×C₃₁	direct (N × H)
62. C₉	C₂×C₄×C₁₁×C₃₁	direct (N × H)
63. C₂×C₄	C₉×C₁₁×C₃₁	direct (N × H)
67. C₄	C₂×C₉×C₁₁×C₃₁	direct (N × H)
69. C₂	C₄×C₉×C₁₁×C₃₁	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×C₄×C₁₁×C₃₁	3
C₂×C₄×C₉×C₃₁	11
C₂²×C₉×C₁₁×C₃₁	2
C₄×C₉×C₁₁×C₃₁	2
C₂×C₄×C₉×C₁₁	31

Subgroups — C2×C4×C9×C11×C31 #72201794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₉×C₁₁×C₃₁ #72201794