Subgroups — C₄×C₆₁×C₆₄ #29510942

Order 15616.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×C₆₄	C₂	1	2	yes	maximal
2	C₄×C₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₆₁	C₄	1	1	yes	characteristic
4	C₂×C₃₂×C₆₁	C₂²	1	1	yes	characteristic
5	C₄×C₁₆×C₆₁	C₄	1	1	yes	characteristic
6	C₆₁×C₆₄	C₄	1	4	yes	direct product factor
7	C₂×C₁₆×C₆₁	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₆₁	C₈	1	1	yes	characteristic
10	C₃₂×C₆₁	C₈	1	2	yes	—
11	C₃₂×C₆₁	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₆₁	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₆₁	C₁₆	1	1	yes	characteristic
15	C₁₆×C₆₁	C₁₆	1	2	yes	—
16	C₁₆×C₆₁	C₄²	1	1	yes	characteristic
17	C₁₆×C₆₁	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₆₁	C₃₂	1	2	yes	—
19	C₂×C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
20	C₈×C₆₁	C₃₂	1	2	yes	—
21	C₈×C₆₁	C₄×C₈	1	1	yes	characteristic
22	C₈×C₆₁	C₂×C₁₆	1	1	yes	characteristic
23	C₄×C₆₄	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂²×C₆₁	C₂×C₃₂	1	1	yes	characteristic
25	C₄×C₆₁	C₆₄	1	4	yes	direct product factor
26	C₄×C₆₁	C₄×C₁₆	1	1	yes	characteristic
27	C₄×C₆₁	C₂×C₃₂	1	1	yes	characteristic
28	C₂×C₆₄	C₂×C₆₁	1	2	yes	—
29	C₄×C₃₂	C₂×C₆₁	1	1	yes	characteristic
30	C₂×C₆₁	C₄×C₃₂	1	1	yes	characteristic
31	C₂×C₆₁	C₂×C₆₄	1	2	yes	—
32	C₂×C₃₂	C₄×C₆₁	1	1	yes	characteristic
33	C₂×C₃₂	C₂²×C₆₁	1	1	yes	characteristic
34	C₄×C₁₆	C₄×C₆₁	1	1	yes	characteristic
35	C₆₄	C₄×C₆₁	1	4	yes	direct product factor
36	C₆₁	C₄×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₁₆	C₈×C₆₁	1	1	yes	characteristic
38	C₂×C₁₆	C₂×C₄×C₆₁	1	1	yes	characteristic
39	C₄×C₈	C₈×C₆₁	1	1	yes	characteristic
40	C₃₂	C₈×C₆₁	1	2	yes	—
41	C₃₂	C₂×C₄×C₆₁	1	2	yes	—
42	C₂×C₈	C₁₆×C₆₁	1	1	yes	characteristic
43	C₂×C₈	C₂×C₈×C₆₁	1	1	yes	characteristic
44	C₄²	C₁₆×C₆₁	1	1	yes	characteristic
45	C₁₆	C₁₆×C₆₁	1	2	yes	—
46	C₁₆	C₄²×C₆₁	1	1	yes	characteristic
47	C₁₆	C₂×C₈×C₆₁	1	1	yes	characteristic
48	C₂×C₄	C₃₂×C₆₁	1	2	yes	—
49	C₂×C₄	C₂×C₁₆×C₆₁	1	1	yes	characteristic
50	C₈	C₃₂×C₆₁	1	2	yes	—
51	C₈	C₄×C₈×C₆₁	1	1	yes	characteristic
52	C₈	C₂×C₁₆×C₆₁	1	1	yes	characteristic
53	C₂²	C₂×C₃₂×C₆₁	1	1	yes	characteristic
54	C₄	C₆₁×C₆₄	1	4	yes	direct product factor
55	C₄	C₄×C₁₆×C₆₁	1	1	yes	characteristic
56	C₄	C₂×C₃₂×C₆₁	1	1	yes	characteristic
57	C₂	C₄×C₃₂×C₆₁	1	1	yes	characteristic
58	C₂	C₂×C₆₁×C₆₄	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃₂	C₂²×C₆₁
socle, prime radical	C₂²×C₆₁	C₂×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₆₁×C₆₄	C₄	direct (N × H)
23. C₄×C₆₄	C₆₁	direct (N × H)
25. C₄×C₆₁	C₆₄	direct (N × H)
35. C₆₄	C₄×C₆₁	direct (N × H)
36. C₆₁	C₄×C₆₄	direct (N × H)
54. C₄	C₆₁×C₆₄	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×C₆₁×C₆₄	2
C₄×C₃₂×C₆₁	2
C₄×C₆₄	61

Subgroups — C4×C61×C64 #29510942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₆₁×C₆₄ #29510942