Subgroups — C₂×C₄₉×C₁₂₈ #72190882

Order 12544.

69 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₉×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₄₉×C₁₂₈	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃₂×C₄₉	C₄	1	1	yes	characteristic
4	C₄₉×C₆₄	C₄	1	1	yes	characteristic
5	C₄₉×C₆₄	C₂²	1	1	yes	characteristic
6	C₂×C₇×C₁₂₈	C₇	1	1	yes	maximal, characteristic
7	C₂×C₁₆×C₄₉	C₈	1	1	yes	characteristic
8	C₃₂×C₄₉	C₈	1	1	yes	characteristic
9	C₃₂×C₄₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₇×C₆₄	C₂×C₇	1	1	yes	characteristic
11	C₇×C₁₂₈	C₂×C₇	1	2	yes	—
12	C₂×C₈×C₄₉	C₁₆	1	1	yes	characteristic
13	C₁₆×C₄₉	C₁₆	1	1	yes	characteristic
14	C₁₆×C₄₉	C₂×C₈	1	1	yes	characteristic
15	C₂×C₇×C₃₂	C₄×C₇	1	1	yes	characteristic
16	C₇×C₆₄	C₄×C₇	1	1	yes	characteristic
17	C₇×C₆₄	C₂²×C₇	1	1	yes	characteristic
18	C₂×C₄×C₄₉	C₃₂	1	1	yes	characteristic
19	C₈×C₄₉	C₃₂	1	1	yes	characteristic
20	C₈×C₄₉	C₂×C₁₆	1	1	yes	characteristic
21	C₂×C₁₂₈	C₄₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₇×C₁₆	C₇×C₈	1	1	yes	characteristic
23	C₇×C₃₂	C₇×C₈	1	1	yes	characteristic
24	C₇×C₃₂	C₂×C₄×C₇	1	1	yes	characteristic
25	C₂²×C₄₉	C₆₄	1	1	yes	characteristic
26	C₄×C₄₉	C₆₄	1	1	yes	characteristic
27	C₄×C₄₉	C₂×C₃₂	1	1	yes	characteristic
28	C₂×C₆₄	C₂×C₄₉	1	1	yes	characteristic
29	C₁₂₈	C₂×C₄₉	1	2	yes	direct product factor
30	C₂×C₇×C₈	C₇×C₁₆	1	1	yes	characteristic
31	C₇×C₁₆	C₇×C₁₆	1	1	yes	characteristic
32	C₇×C₁₆	C₂×C₇×C₈	1	1	yes	characteristic
33	C₂×C₄₉	C₁₂₈	1	2	yes	direct product factor
34	C₂×C₄₉	C₂×C₆₄	1	1	yes	characteristic
35	C₂×C₃₂	C₄×C₄₉	1	1	yes	characteristic
36	C₆₄	C₄×C₄₉	1	1	yes	characteristic
37	C₆₄	C₂²×C₄₉	1	1	yes	characteristic
38	C₂×C₄×C₇	C₇×C₃₂	1	1	yes	characteristic
39	C₇×C₈	C₇×C₃₂	1	1	yes	characteristic
40	C₇×C₈	C₂×C₇×C₁₆	1	1	yes	characteristic
41	C₄₉	C₂×C₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₁₆	C₈×C₄₉	1	1	yes	characteristic
43	C₃₂	C₈×C₄₉	1	1	yes	characteristic
44	C₃₂	C₂×C₄×C₄₉	1	1	yes	characteristic
45	C₂²×C₇	C₇×C₆₄	1	1	yes	characteristic
46	C₄×C₇	C₇×C₆₄	1	1	yes	characteristic
47	C₄×C₇	C₂×C₇×C₃₂	1	1	yes	characteristic
48	C₂×C₈	C₁₆×C₄₉	1	1	yes	characteristic
49	C₁₆	C₁₆×C₄₉	1	1	yes	characteristic
50	C₁₆	C₂×C₈×C₄₉	1	1	yes	characteristic
51	C₂×C₇	C₇×C₁₂₈	1	2	yes	—
52	C₂×C₇	C₂×C₇×C₆₄	1	1	yes	characteristic
53	C₂×C₄	C₃₂×C₄₉	1	1	yes	characteristic
54	C₈	C₃₂×C₄₉	1	1	yes	characteristic
55	C₈	C₂×C₁₆×C₄₉	1	1	yes	characteristic
56	C₇	C₂×C₇×C₁₂₈	1	1	yes	characteristic
57	C₂²	C₄₉×C₆₄	1	1	yes	characteristic
58	C₄	C₄₉×C₆₄	1	1	yes	characteristic
59	C₄	C₂×C₃₂×C₄₉	1	1	yes	characteristic
60	C₂	C₄₉×C₁₂₈	1	2	yes	direct product factor
61	C₂	C₂×C₄₉×C₆₄	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇×C₆₄	C₂²×C₇
socle, prime radical	C₂²×C₇	C₇×C₆₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₉×C₁₂₈	C₂	direct (N × H)
21. C₂×C₁₂₈	C₄₉	direct (N × H)
29. C₁₂₈	C₂×C₄₉	direct (N × H)
33. C₂×C₄₉	C₁₂₈	direct (N × H)
41. C₄₉	C₂×C₁₂₈	direct (N × H)
60. C₂	C₄₉×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×C₄₉×C₆₄	2
C₄₉×C₁₂₈	2
C₂×C₇×C₁₂₈	7

Subgroups — C2×C49×C128 #72190882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₉×C₁₂₈ #72190882