Subgroups — C₄³×C₅×C₇×C₁₁ #72201962

Order 24640.

1032 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅×C₇×C₁₁	C₂	1	7	yes	maximal
2	C₂²×C₄×C₅×C₇×C₁₁	C₂²	1	7	yes	—
3	C₄²×C₅×C₇×C₁₁	C₄	1	28	yes	direct product factor
4	C₄³×C₇×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄³×C₅×C₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₅×C₇×C₁₁	C₂³	1	1	yes	characteristic
7	C₂×C₄×C₅×C₇×C₁₁	C₂×C₄	1	42	yes	—
8	C₂×C₄²×C₇×C₁₁	C₂×C₅	1	7	yes	—
9	C₄³×C₅×C₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₄²×C₅×C₁₁	C₂×C₇	1	7	yes	—
11	C₂²×C₅×C₇×C₁₁	C₂²×C₄	1	7	yes	—
12	C₄×C₅×C₇×C₁₁	C₄²	1	28	yes	direct product factor
13	C₂²×C₄×C₇×C₁₁	C₂²×C₅	1	7	yes	—
14	C₄²×C₇×C₁₁	C₄×C₅	1	28	yes	direct product factor
15	C₂×C₄²×C₅×C₇	C₂×C₁₁	1	7	yes	—
16	C₂²×C₄×C₅×C₁₁	C₂²×C₇	1	7	yes	—
17	C₄²×C₅×C₁₁	C₄×C₇	1	28	yes	direct product factor
18	C₂×C₅×C₇×C₁₁	C₂×C₄²	1	7	yes	—
19	C₄³×C₁₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂³×C₇×C₁₁	C₂³×C₅	1	1	yes	characteristic
21	C₂×C₄×C₇×C₁₁	C₂×C₄×C₅	1	42	yes	—
22	C₂²×C₄×C₅×C₇	C₂²×C₁₁	1	7	yes	—
23	C₄²×C₅×C₇	C₄×C₁₁	1	28	yes	direct product factor
24	C₄³×C₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂³×C₅×C₁₁	C₂³×C₇	1	1	yes	characteristic
26	C₂×C₄×C₅×C₁₁	C₂×C₄×C₇	1	42	yes	—
27	C₅×C₇×C₁₁	C₄³	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₄²×C₁₁	C₂×C₅×C₇	1	7	yes	—
29	C₄³×C₅	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₇×C₁₁	C₂²×C₄×C₅	1	7	yes	—
31	C₄×C₇×C₁₁	C₄²×C₅	1	28	yes	direct product factor
32	C₂³×C₅×C₇	C₂³×C₁₁	1	1	yes	characteristic
33	C₂×C₄×C₅×C₇	C₂×C₄×C₁₁	1	42	yes	—
34	C₂×C₄²×C₇	C₂×C₅×C₁₁	1	7	yes	—
35	C₂²×C₅×C₁₁	C₂²×C₄×C₇	1	7	yes	—
36	C₄×C₅×C₁₁	C₄²×C₇	1	28	yes	direct product factor
37	C₂²×C₄×C₁₁	C₂²×C₅×C₇	1	7	yes	—
38	C₄²×C₁₁	C₄×C₅×C₇	1	28	yes	direct product factor
39	C₂×C₄²×C₅	C₂×C₇×C₁₁	1	7	yes	—
40	C₂×C₇×C₁₁	C₂×C₄²×C₅	1	7	yes	—
41	C₂²×C₅×C₇	C₂²×C₄×C₁₁	1	7	yes	—
42	C₄×C₅×C₇	C₄²×C₁₁	1	28	yes	direct product factor
43	C₂²×C₄×C₇	C₂²×C₅×C₁₁	1	7	yes	—
44	C₄²×C₇	C₄×C₅×C₁₁	1	28	yes	direct product factor
45	C₂×C₅×C₁₁	C₂×C₄²×C₇	1	7	yes	—
46	C₂³×C₁₁	C₂³×C₅×C₇	1	1	yes	characteristic
47	C₂×C₄×C₁₁	C₂×C₄×C₅×C₇	1	42	yes	—
48	C₂²×C₄×C₅	C₂²×C₇×C₁₁	1	7	yes	—
49	C₄²×C₅	C₄×C₇×C₁₁	1	28	yes	direct product factor
50	C₇×C₁₁	C₄³×C₅	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₅×C₇	C₂×C₄²×C₁₁	1	7	yes	—
52	C₄³	C₅×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
53	C₂³×C₇	C₂³×C₅×C₁₁	1	1	yes	characteristic
54	C₂×C₄×C₇	C₂×C₄×C₅×C₁₁	1	42	yes	—
55	C₅×C₁₁	C₄³×C₇	1	1	yes	characteristic, direct product factor, Hall
56	C₂²×C₁₁	C₂²×C₄×C₅×C₇	1	7	yes	—
57	C₄×C₁₁	C₄²×C₅×C₇	1	28	yes	direct product factor
58	C₂³×C₅	C₂³×C₇×C₁₁	1	1	yes	characteristic
59	C₂×C₄×C₅	C₂×C₄×C₇×C₁₁	1	42	yes	—
60	C₅×C₇	C₄³×C₁₁	1	1	yes	characteristic, direct product factor, Hall
61	C₂×C₄²	C₂×C₅×C₇×C₁₁	1	7	yes	—
62	C₂²×C₇	C₂²×C₄×C₅×C₁₁	1	7	yes	—
63	C₄×C₇	C₄²×C₅×C₁₁	1	28	yes	direct product factor
64	C₂×C₁₁	C₂×C₄²×C₅×C₇	1	7	yes	—
65	C₂²×C₅	C₂²×C₄×C₇×C₁₁	1	7	yes	—
66	C₄×C₅	C₄²×C₇×C₁₁	1	28	yes	direct product factor
67	C₂²×C₄	C₂²×C₅×C₇×C₁₁	1	7	yes	—
68	C₄²	C₄×C₅×C₇×C₁₁	1	28	yes	direct product factor
69	C₂×C₇	C₂×C₄²×C₅×C₁₁	1	7	yes	—
70	C₁₁	C₄³×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₅	C₂×C₄²×C₇×C₁₁	1	7	yes	—
72	C₂³	C₂³×C₅×C₇×C₁₁	1	1	yes	characteristic
73	C₂×C₄	C₂×C₄×C₅×C₇×C₁₁	1	42	yes	—
74	C₇	C₄³×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
75	C₅	C₄³×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	C₂²×C₄×C₅×C₇×C₁₁	1	7	yes	—
77	C₄	C₄²×C₅×C₇×C₁₁	1	28	yes	direct product factor
78	C₂	C₂×C₄²×C₅×C₇×C₁₁	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂³×C₅×C₇×C₁₁
socle, prime radical	C₂³×C₅×C₇×C₁₁	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄²×C₅×C₇×C₁₁	C₄	direct (N × H)
4. C₄³×C₇×C₁₁	C₅	direct (N × H)
5. C₄³×C₅×C₁₁	C₇	direct (N × H)
9. C₄³×C₅×C₇	C₁₁	direct (N × H)
12. C₄×C₅×C₇×C₁₁	C₄²	direct (N × H)
14. C₄²×C₇×C₁₁	C₄×C₅	direct (N × H)
17. C₄²×C₅×C₁₁	C₄×C₇	direct (N × H)
19. C₄³×C₁₁	C₅×C₇	direct (N × H)
23. C₄²×C₅×C₇	C₄×C₁₁	direct (N × H)
24. C₄³×C₇	C₅×C₁₁	direct (N × H)
27. C₅×C₇×C₁₁	C₄³	direct (N × H)
29. C₄³×C₅	C₇×C₁₁	direct (N × H)
31. C₄×C₇×C₁₁	C₄²×C₅	direct (N × H)
36. C₄×C₅×C₁₁	C₄²×C₇	direct (N × H)
38. C₄²×C₁₁	C₄×C₅×C₇	direct (N × H)
42. C₄×C₅×C₇	C₄²×C₁₁	direct (N × H)
44. C₄²×C₇	C₄×C₅×C₁₁	direct (N × H)
49. C₄²×C₅	C₄×C₇×C₁₁	direct (N × H)
50. C₇×C₁₁	C₄³×C₅	direct (N × H)
52. C₄³	C₅×C₇×C₁₁	direct (N × H)
55. C₅×C₁₁	C₄³×C₇	direct (N × H)
57. C₄×C₁₁	C₄²×C₅×C₇	direct (N × H)
60. C₅×C₇	C₄³×C₁₁	direct (N × H)
63. C₄×C₇	C₄²×C₅×C₁₁	direct (N × H)
66. C₄×C₅	C₄²×C₇×C₁₁	direct (N × H)
68. C₄²	C₄×C₅×C₇×C₁₁	direct (N × H)
70. C₁₁	C₄³×C₅×C₇	direct (N × H)
74. C₇	C₄³×C₅×C₁₁	direct (N × H)
75. C₅	C₄³×C₇×C₁₁	direct (N × H)
77. C₄	C₄²×C₅×C₇×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×C₄²×C₅×C₇×C₁₁	2
C₄³×C₇×C₁₁	5
C₄³×C₅×C₁₁	7
C₄³×C₅×C₇	11

Subgroups — C43×C5×C7×C11 #72201962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×C₅×C₇×C₁₁ #72201962