Subgroups — C₄×C₄₇×C₁₂₈ #72201347

Order 24064.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₁₂₈	C₂	1	2	yes	maximal
2	C₄×C₄₇×C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×C₆₄	C₄	1	1	yes	characteristic
4	C₂×C₄₇×C₆₄	C₂²	1	1	yes	characteristic
5	C₄×C₃₂×C₄₇	C₄	1	1	yes	characteristic
6	C₄₇×C₁₂₈	C₄	1	4	yes	direct product factor
7	C₂×C₃₂×C₄₇	C₈	1	1	yes	characteristic
8	C₂×C₃₂×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₄×C₁₆×C₄₇	C₈	1	1	yes	characteristic
10	C₄₇×C₆₄	C₈	1	2	yes	—
11	C₄₇×C₆₄	C₂×C₄	1	2	yes	—
12	C₂×C₁₆×C₄₇	C₁₆	1	1	yes	characteristic
13	C₂×C₁₆×C₄₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₈×C₄₇	C₁₆	1	1	yes	characteristic
15	C₃₂×C₄₇	C₁₆	1	2	yes	—
16	C₃₂×C₄₇	C₄²	1	1	yes	characteristic
17	C₃₂×C₄₇	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₃₂	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂×C₁₆	1	1	yes	characteristic
20	C₄²×C₄₇	C₃₂	1	1	yes	characteristic
21	C₁₆×C₄₇	C₃₂	1	2	yes	—
22	C₁₆×C₄₇	C₄×C₈	1	1	yes	characteristic
23	C₁₆×C₄₇	C₂×C₁₆	1	1	yes	characteristic
24	C₄×C₁₂₈	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₄×C₄₇	C₆₄	1	2	yes	—
26	C₂×C₄×C₄₇	C₂×C₃₂	1	1	yes	characteristic
27	C₈×C₄₇	C₆₄	1	2	yes	—
28	C₈×C₄₇	C₄×C₁₆	1	1	yes	characteristic
29	C₈×C₄₇	C₂×C₃₂	1	1	yes	characteristic
30	C₂×C₁₂₈	C₂×C₄₇	1	2	yes	—
31	C₄×C₆₄	C₂×C₄₇	1	1	yes	characteristic
32	C₂²×C₄₇	C₂×C₆₄	1	1	yes	characteristic
33	C₄×C₄₇	C₁₂₈	1	4	yes	direct product factor
34	C₄×C₄₇	C₄×C₃₂	1	1	yes	characteristic
35	C₄×C₄₇	C₂×C₆₄	1	1	yes	characteristic
36	C₂×C₆₄	C₄×C₄₇	1	1	yes	characteristic
37	C₂×C₆₄	C₂²×C₄₇	1	1	yes	characteristic
38	C₄×C₃₂	C₄×C₄₇	1	1	yes	characteristic
39	C₁₂₈	C₄×C₄₇	1	4	yes	direct product factor
40	C₂×C₄₇	C₄×C₆₄	1	1	yes	characteristic
41	C₂×C₄₇	C₂×C₁₂₈	1	2	yes	—
42	C₂×C₃₂	C₈×C₄₇	1	1	yes	characteristic
43	C₂×C₃₂	C₂×C₄×C₄₇	1	1	yes	characteristic
44	C₄×C₁₆	C₈×C₄₇	1	1	yes	characteristic
45	C₆₄	C₈×C₄₇	1	2	yes	—
46	C₆₄	C₂×C₄×C₄₇	1	2	yes	—
47	C₄₇	C₄×C₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₁₆	C₁₆×C₄₇	1	1	yes	characteristic
49	C₂×C₁₆	C₂×C₈×C₄₇	1	1	yes	characteristic
50	C₄×C₈	C₁₆×C₄₇	1	1	yes	characteristic
51	C₃₂	C₁₆×C₄₇	1	2	yes	—
52	C₃₂	C₄²×C₄₇	1	1	yes	characteristic
53	C₃₂	C₂×C₈×C₄₇	1	1	yes	characteristic
54	C₂×C₈	C₃₂×C₄₇	1	1	yes	characteristic
55	C₂×C₈	C₂×C₁₆×C₄₇	1	1	yes	characteristic
56	C₄²	C₃₂×C₄₇	1	1	yes	characteristic
57	C₁₆	C₃₂×C₄₇	1	2	yes	—
58	C₁₆	C₄×C₈×C₄₇	1	1	yes	characteristic
59	C₁₆	C₂×C₁₆×C₄₇	1	1	yes	characteristic
60	C₂×C₄	C₄₇×C₆₄	1	2	yes	—
61	C₂×C₄	C₂×C₃₂×C₄₇	1	1	yes	characteristic
62	C₈	C₄₇×C₆₄	1	2	yes	—
63	C₈	C₄×C₁₆×C₄₇	1	1	yes	characteristic
64	C₈	C₂×C₃₂×C₄₇	1	1	yes	characteristic
65	C₂²	C₂×C₄₇×C₆₄	1	1	yes	characteristic
66	C₄	C₄₇×C₁₂₈	1	4	yes	direct product factor
67	C₄	C₄×C₃₂×C₄₇	1	1	yes	characteristic
68	C₄	C₂×C₄₇×C₆₄	1	1	yes	characteristic
69	C₂	C₄×C₄₇×C₆₄	1	1	yes	characteristic
70	C₂	C₂×C₄₇×C₁₂₈	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₆₄	C₂²×C₄₇
socle, prime radical	C₂²×C₄₇	C₂×C₆₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄₇×C₁₂₈	C₄	direct (N × H)
24. C₄×C₁₂₈	C₄₇	direct (N × H)
33. C₄×C₄₇	C₁₂₈	direct (N × H)
39. C₁₂₈	C₄×C₄₇	direct (N × H)
47. C₄₇	C₄×C₁₂₈	direct (N × H)
66. C₄	C₄₇×C₁₂₈	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×C₄₇×C₁₂₈	2
C₄×C₄₇×C₆₄	2
C₄×C₁₂₈	47

Subgroups — C4×C47×C128 #72201347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₇×C₁₂₈ #72201347