Subgroups — C₂²×C₃₁×C₆₄ #21470494

Order 7936.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×C₆₄	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₁₆×C₃₁	C₄	1	1	yes	characteristic
4	C₂×C₃₁×C₃₂	C₄	1	3	yes	—
5	C₂×C₃₁×C₃₂	C₂²	1	3	yes	—
6	C₃₁×C₆₄	C₂²	1	4	yes	direct product factor
7	C₂²×C₈×C₃₁	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₃₁	C₈	1	3	yes	—
9	C₂×C₁₆×C₃₁	C₂×C₄	1	3	yes	—
10	C₃₁×C₃₂	C₂×C₄	1	3	yes	—
11	C₃₁×C₃₂	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₃₁	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₃₁	C₁₆	1	3	yes	—
14	C₂×C₈×C₃₁	C₂×C₈	1	3	yes	—
15	C₁₆×C₃₁	C₂×C₈	1	3	yes	—
16	C₁₆×C₃₁	C₂²×C₄	1	1	yes	characteristic
17	C₂²×C₆₄	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂³×C₃₁	C₃₂	1	1	yes	characteristic
19	C₂×C₄×C₃₁	C₃₂	1	3	yes	—
20	C₂×C₄×C₃₁	C₂×C₁₆	1	3	yes	—
21	C₈×C₃₁	C₂×C₁₆	1	3	yes	—
22	C₈×C₃₁	C₂²×C₈	1	1	yes	characteristic
23	C₂²×C₃₂	C₂×C₃₁	1	1	yes	characteristic
24	C₂×C₆₄	C₂×C₃₁	1	6	yes	direct product factor
25	C₂²×C₃₁	C₆₄	1	4	yes	direct product factor
26	C₂²×C₃₁	C₂×C₃₂	1	3	yes	—
27	C₄×C₃₁	C₂×C₃₂	1	3	yes	—
28	C₄×C₃₁	C₂²×C₁₆	1	1	yes	characteristic
29	C₂²×C₁₆	C₄×C₃₁	1	1	yes	characteristic
30	C₂×C₃₂	C₄×C₃₁	1	3	yes	—
31	C₂×C₃₂	C₂²×C₃₁	1	3	yes	—
32	C₆₄	C₂²×C₃₁	1	4	yes	direct product factor
33	C₂×C₃₁	C₂×C₆₄	1	6	yes	direct product factor
34	C₂×C₃₁	C₂²×C₃₂	1	1	yes	characteristic
35	C₂²×C₈	C₈×C₃₁	1	1	yes	characteristic
36	C₂×C₁₆	C₈×C₃₁	1	3	yes	—
37	C₂×C₁₆	C₂×C₄×C₃₁	1	3	yes	—
38	C₃₂	C₂×C₄×C₃₁	1	3	yes	—
39	C₃₂	C₂³×C₃₁	1	1	yes	characteristic
40	C₃₁	C₂²×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₄	C₁₆×C₃₁	1	1	yes	characteristic
42	C₂×C₈	C₁₆×C₃₁	1	3	yes	—
43	C₂×C₈	C₂×C₈×C₃₁	1	3	yes	—
44	C₁₆	C₂×C₈×C₃₁	1	3	yes	—
45	C₁₆	C₂²×C₄×C₃₁	1	1	yes	characteristic
46	C₂³	C₃₁×C₃₂	1	1	yes	characteristic
47	C₂×C₄	C₃₁×C₃₂	1	3	yes	—
48	C₂×C₄	C₂×C₁₆×C₃₁	1	3	yes	—
49	C₈	C₂×C₁₆×C₃₁	1	3	yes	—
50	C₈	C₂²×C₈×C₃₁	1	1	yes	characteristic
51	C₂²	C₃₁×C₆₄	1	4	yes	direct product factor
52	C₂²	C₂×C₃₁×C₃₂	1	3	yes	—
53	C₄	C₂×C₃₁×C₃₂	1	3	yes	—
54	C₄	C₂²×C₁₆×C₃₁	1	1	yes	characteristic
55	C₂	C₂×C₃₁×C₆₄	1	6	yes	direct product factor
56	C₂	C₂²×C₃₁×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃₂	C₂³×C₃₁
socle	C₂³×C₃₁	C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×C₆₄	C₂	direct (N × H)
6. C₃₁×C₆₄	C₂²	direct (N × H)
17. C₂²×C₆₄	C₃₁	direct (N × H)
24. C₂×C₆₄	C₂×C₃₁	direct (N × H)
25. C₂²×C₃₁	C₆₄	direct (N × H)
32. C₆₄	C₂²×C₃₁	direct (N × H)
33. C₂×C₃₁	C₂×C₆₄	direct (N × H)
40. C₃₁	C₂²×C₆₄	direct (N × H)
51. C₂²	C₃₁×C₆₄	direct (N × H)
55. C₂	C₂×C₃₁×C₆₄	direct (N × H)

Subgroups — C22×C31×C64 #21470494

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₃₁×C₆₄ #21470494