Subgroups — C₂²×C₄³×C₃₁ #21490744

Order 7936.

8094 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₃₁	C₂	1	7	yes	maximal
2	C₂×C₄³×C₃₁	C₂	1	24	yes	maximal, direct product factor
3	C₂⁴×C₄×C₃₁	C₂²	1	7	yes	—
4	C₂²×C₄²×C₃₁	C₄	1	112	yes	direct product factor
5	C₂²×C₄²×C₃₁	C₂²	1	84	yes	—
6	C₄³×C₃₁	C₂²	1	64	yes	direct product factor
7	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
8	C₂³×C₄×C₃₁	C₂×C₄	1	168	yes	—
9	C₂³×C₄×C₃₁	C₂³	1	42	yes	—
10	C₂×C₄²×C₃₁	C₂×C₄	1	672	yes	direct product factor
11	C₂×C₄²×C₃₁	C₂³	1	112	yes	—
12	C₂⁴×C₃₁	C₂²×C₄	1	28	yes	—
13	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
14	C₂²×C₄×C₃₁	C₄²	1	448	yes	direct product factor
15	C₂²×C₄×C₃₁	C₂²×C₄	1	504	yes	—
16	C₂²×C₄×C₃₁	C₂⁴	1	28	yes	—
17	C₄²×C₃₁	C₂²×C₄	1	448	yes	direct product factor
18	C₂²×C₄³	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₃₁	C₂×C₄²	1	112	yes	—
20	C₂³×C₃₁	C₂³×C₄	1	42	yes	—
21	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
22	C₂×C₄×C₃₁	C₂×C₄²	1	672	yes	direct product factor
23	C₂×C₄×C₃₁	C₂³×C₄	1	168	yes	—
24	C₂³×C₄²	C₂×C₃₁	1	7	yes	—
25	C₂×C₄³	C₂×C₃₁	1	24	yes	direct product factor
26	C₂²×C₃₁	C₄³	1	64	yes	direct product factor
27	C₂²×C₃₁	C₂²×C₄²	1	84	yes	—
28	C₂²×C₃₁	C₂⁴×C₄	1	7	yes	—
29	C₄×C₃₁	C₂²×C₄²	1	112	yes	direct product factor
30	C₂⁴×C₄	C₂²×C₃₁	1	7	yes	—
31	C₂²×C₄²	C₄×C₃₁	1	112	yes	direct product factor
32	C₂²×C₄²	C₂²×C₃₁	1	84	yes	—
33	C₄³	C₂²×C₃₁	1	64	yes	direct product factor
34	C₂×C₃₁	C₂×C₄³	1	24	yes	direct product factor
35	C₂×C₃₁	C₂³×C₄²	1	7	yes	—
36	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
37	C₂³×C₄	C₂×C₄×C₃₁	1	168	yes	—
38	C₂³×C₄	C₂³×C₃₁	1	42	yes	—
39	C₂×C₄²	C₂×C₄×C₃₁	1	672	yes	direct product factor
40	C₂×C₄²	C₂³×C₃₁	1	112	yes	—
41	C₃₁	C₂²×C₄³	1	1	yes	characteristic, direct product factor, Sylow
42	C₂⁴	C₂²×C₄×C₃₁	1	28	yes	—
43	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
44	C₂²×C₄	C₄²×C₃₁	1	448	yes	direct product factor
45	C₂²×C₄	C₂²×C₄×C₃₁	1	504	yes	—
46	C₂²×C₄	C₂⁴×C₃₁	1	28	yes	—
47	C₄²	C₂²×C₄×C₃₁	1	448	yes	direct product factor
48	C₂³	C₂×C₄²×C₃₁	1	112	yes	—
49	C₂³	C₂³×C₄×C₃₁	1	42	yes	—
50	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
51	C₂×C₄	C₂×C₄²×C₃₁	1	672	yes	direct product factor
52	C₂×C₄	C₂³×C₄×C₃₁	1	168	yes	—
53	C₂²	C₄³×C₃₁	1	64	yes	direct product factor
54	C₂²	C₂²×C₄²×C₃₁	1	84	yes	—
55	C₂²	C₂⁴×C₄×C₃₁	1	7	yes	—
56	C₄	C₂²×C₄²×C₃₁	1	112	yes	direct product factor
57	C₂	C₂×C₄³×C₃₁	1	24	yes	direct product factor
58	C₂	C₂³×C₄²×C₃₁	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂³	C₂⁵×C₃₁
socle	C₂⁵×C₃₁	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄³×C₃₁	C₂	direct (N × H)
4. C₂²×C₄²×C₃₁	C₄	direct (N × H)
6. C₄³×C₃₁	C₂²	direct (N × H)
10. C₂×C₄²×C₃₁	C₂×C₄	direct (N × H)
14. C₂²×C₄×C₃₁	C₄²	direct (N × H)
17. C₄²×C₃₁	C₂²×C₄	direct (N × H)
18. C₂²×C₄³	C₃₁	direct (N × H)
22. C₂×C₄×C₃₁	C₂×C₄²	direct (N × H)
25. C₂×C₄³	C₂×C₃₁	direct (N × H)
26. C₂²×C₃₁	C₄³	direct (N × H)
29. C₄×C₃₁	C₂²×C₄²	direct (N × H)
31. C₂²×C₄²	C₄×C₃₁	direct (N × H)
33. C₄³	C₂²×C₃₁	direct (N × H)
34. C₂×C₃₁	C₂×C₄³	direct (N × H)
39. C₂×C₄²	C₂×C₄×C₃₁	direct (N × H)
41. C₃₁	C₂²×C₄³	direct (N × H)
44. C₂²×C₄	C₄²×C₃₁	direct (N × H)
47. C₄²	C₂²×C₄×C₃₁	direct (N × H)
51. C₂×C₄	C₂×C₄²×C₃₁	direct (N × H)
53. C₂²	C₄³×C₃₁	direct (N × H)
56. C₄	C₂²×C₄²×C₃₁	direct (N × H)
57. C₂	C₂×C₄³×C₃₁	direct (N × H)

Subgroups — C22×C43×C31 #21490744

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₄³×C₃₁ #21490744