Subgroups — C₄³×C₈×C₄₇ #72201365

Order 24064.

6660 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₈×C₄₇	C₂	1	14	yes	maximal
2	C₄⁴×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈×C₄₇	C₂²	1	28	yes	—
4	C₂×C₄³×C₄₇	C₄	1	8	yes	—
5	C₂×C₄³×C₄₇	C₂²	1	7	yes	—
6	C₄²×C₈×C₄₇	C₄	1	112	yes	direct product factor
7	C₂³×C₈×C₄₇	C₂³	1	8	yes	—
8	C₂²×C₄²×C₄₇	C₂×C₄	1	28	yes	—
9	C₂²×C₄²×C₄₇	C₂³	1	7	yes	—
10	C₂×C₄×C₈×C₄₇	C₂×C₄	1	336	yes	—
11	C₄³×C₄₇	C₈	1	64	yes	direct product factor
12	C₄³×C₄₇	C₂×C₄	1	56	yes	—
13	C₂³×C₄×C₄₇	C₂²×C₄	1	14	yes	—
14	C₂³×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
15	C₂²×C₈×C₄₇	C₂²×C₄	1	112	yes	—
16	C₂×C₄²×C₄₇	C₄²	1	112	yes	—
17	C₂×C₄²×C₄₇	C₂×C₈	1	224	yes	—
18	C₂×C₄²×C₄₇	C₂²×C₄	1	84	yes	—
19	C₄×C₈×C₄₇	C₄²	1	448	yes	direct product factor
20	C₂⁴×C₄₇	C₂³×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	C₂×C₄²	1	84	yes	—
22	C₂²×C₄×C₄₇	C₂²×C₈	1	112	yes	—
23	C₂²×C₄×C₄₇	C₂³×C₄	1	14	yes	—
24	C₂×C₈×C₄₇	C₂×C₄²	1	224	yes	—
25	C₄²×C₄₇	C₄×C₈	1	448	yes	direct product factor
26	C₄²×C₄₇	C₂×C₄²	1	112	yes	—
27	C₄³×C₈	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄₇	C₂²×C₄²	1	7	yes	—
29	C₂³×C₄₇	C₂³×C₈	1	8	yes	—
30	C₂×C₄×C₄₇	C₄³	1	56	yes	—
31	C₂×C₄×C₄₇	C₂×C₄×C₈	1	336	yes	—
32	C₂×C₄×C₄₇	C₂²×C₄²	1	28	yes	—
33	C₈×C₄₇	C₄³	1	64	yes	direct product factor
34	C₂×C₄²×C₈	C₂×C₄₇	1	14	yes	—
35	C₄⁴	C₂×C₄₇	1	1	yes	characteristic
36	C₂²×C₄₇	C₂×C₄³	1	7	yes	—
37	C₂²×C₄₇	C₂²×C₄×C₈	1	28	yes	—
38	C₄×C₄₇	C₄²×C₈	1	112	yes	direct product factor
39	C₄×C₄₇	C₂×C₄³	1	8	yes	—
40	C₂²×C₄×C₈	C₂²×C₄₇	1	28	yes	—
41	C₂×C₄³	C₄×C₄₇	1	8	yes	—
42	C₂×C₄³	C₂²×C₄₇	1	7	yes	—
43	C₄²×C₈	C₄×C₄₇	1	112	yes	direct product factor
44	C₂×C₄₇	C₄⁴	1	1	yes	characteristic
45	C₂×C₄₇	C₂×C₄²×C₈	1	14	yes	—
46	C₂³×C₈	C₂³×C₄₇	1	8	yes	—
47	C₂²×C₄²	C₂×C₄×C₄₇	1	28	yes	—
48	C₂²×C₄²	C₂³×C₄₇	1	7	yes	—
49	C₂×C₄×C₈	C₂×C₄×C₄₇	1	336	yes	—
50	C₄³	C₈×C₄₇	1	64	yes	direct product factor
51	C₄³	C₂×C₄×C₄₇	1	56	yes	—
52	C₄₇	C₄³×C₈	1	1	yes	characteristic, direct product factor, Sylow
53	C₂³×C₄	C₂²×C₄×C₄₇	1	14	yes	—
54	C₂³×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
55	C₂²×C₈	C₂²×C₄×C₄₇	1	112	yes	—
56	C₂×C₄²	C₄²×C₄₇	1	112	yes	—
57	C₂×C₄²	C₂×C₈×C₄₇	1	224	yes	—
58	C₂×C₄²	C₂²×C₄×C₄₇	1	84	yes	—
59	C₄×C₈	C₄²×C₄₇	1	448	yes	direct product factor
60	C₂⁴	C₂³×C₄×C₄₇	1	1	yes	characteristic
61	C₂²×C₄	C₂×C₄²×C₄₇	1	84	yes	—
62	C₂²×C₄	C₂²×C₈×C₄₇	1	112	yes	—
63	C₂²×C₄	C₂³×C₄×C₄₇	1	14	yes	—
64	C₂×C₈	C₂×C₄²×C₄₇	1	224	yes	—
65	C₄²	C₄×C₈×C₄₇	1	448	yes	direct product factor
66	C₄²	C₂×C₄²×C₄₇	1	112	yes	—
67	C₂³	C₂²×C₄²×C₄₇	1	7	yes	—
68	C₂³	C₂³×C₈×C₄₇	1	8	yes	—
69	C₂×C₄	C₄³×C₄₇	1	56	yes	—
70	C₂×C₄	C₂×C₄×C₈×C₄₇	1	336	yes	—
71	C₂×C₄	C₂²×C₄²×C₄₇	1	28	yes	—
72	C₈	C₄³×C₄₇	1	64	yes	direct product factor
73	C₂²	C₂×C₄³×C₄₇	1	7	yes	—
74	C₂²	C₂²×C₄×C₈×C₄₇	1	28	yes	—
75	C₄	C₄²×C₈×C₄₇	1	112	yes	direct product factor
76	C₄	C₂×C₄³×C₄₇	1	8	yes	—
77	C₂	C₄⁴×C₄₇	1	1	yes	characteristic
78	C₂	C₂×C₄²×C₈×C₄₇	1	14	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³×C₄	C₂⁴×C₄₇
socle, prime radical	C₂⁴×C₄₇	C₂³×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄²×C₈×C₄₇	C₄	direct (N × H)
11. C₄³×C₄₇	C₈	direct (N × H)
19. C₄×C₈×C₄₇	C₄²	direct (N × H)
25. C₄²×C₄₇	C₄×C₈	direct (N × H)
27. C₄³×C₈	C₄₇	direct (N × H)
33. C₈×C₄₇	C₄³	direct (N × H)
38. C₄×C₄₇	C₄²×C₈	direct (N × H)
43. C₄²×C₈	C₄×C₄₇	direct (N × H)
50. C₄³	C₈×C₄₇	direct (N × H)
52. C₄₇	C₄³×C₈	direct (N × H)
59. C₄×C₈	C₄²×C₄₇	direct (N × H)
65. C₄²	C₄×C₈×C₄₇	direct (N × H)
72. C₈	C₄³×C₄₇	direct (N × H)
75. C₄	C₄²×C₈×C₄₇	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×C₈×C₄₇	2
C₄⁴×C₄₇	2
C₄³×C₈	47

Subgroups — C43×C8×C47 #72201365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×C₈×C₄₇ #72201365