Subgroups — C₄²×C₁₆×C₃₁ #21469296

Order 7936.

558 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₆×C₃₁	C₂	1	6	yes	maximal
2	C₄²×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₆×C₃₁	C₂²	1	4	yes	—
4	C₂×C₄×C₈×C₃₁	C₄	1	3	yes	—
5	C₂×C₄×C₈×C₃₁	C₂²	1	3	yes	—
6	C₄³×C₃₁	C₄	1	1	yes	characteristic
7	C₄×C₁₆×C₃₁	C₄	1	24	yes	direct product factor
8	C₂²×C₈×C₃₁	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
10	C₂×C₄²×C₃₁	C₈	1	4	yes	—
11	C₂×C₄²×C₃₁	C₂×C₄	1	3	yes	—
12	C₂×C₁₆×C₃₁	C₂×C₄	1	24	yes	—
13	C₄×C₈×C₃₁	C₈	1	12	yes	—
14	C₄×C₈×C₃₁	C₂×C₄	1	12	yes	—
15	C₂²×C₄×C₃₁	C₂×C₈	1	6	yes	—
16	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₈×C₃₁	C₄²	1	6	yes	—
18	C₂×C₈×C₃₁	C₂×C₈	1	12	yes	—
19	C₂×C₈×C₃₁	C₂²×C₄	1	6	yes	—
20	C₄²×C₃₁	C₁₆	1	16	yes	direct product factor
21	C₄²×C₃₁	C₄²	1	6	yes	—
22	C₄²×C₃₁	C₂×C₈	1	6	yes	—
23	C₁₆×C₃₁	C₄²	1	16	yes	direct product factor
24	C₄²×C₁₆	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃₁	C₂²×C₈	1	1	yes	characteristic
26	C₂×C₄×C₃₁	C₄×C₈	1	12	yes	—
27	C₂×C₄×C₃₁	C₂×C₁₆	1	24	yes	—
28	C₂×C₄×C₃₁	C₂×C₄²	1	3	yes	—
29	C₂×C₄×C₃₁	C₂²×C₈	1	3	yes	—
30	C₈×C₃₁	C₄×C₈	1	12	yes	—
31	C₈×C₃₁	C₂×C₄²	1	4	yes	—
32	C₂×C₄×C₁₆	C₂×C₃₁	1	6	yes	—
33	C₄²×C₈	C₂×C₃₁	1	1	yes	characteristic
34	C₂²×C₃₁	C₂×C₄×C₈	1	3	yes	—
35	C₂²×C₃₁	C₂²×C₁₆	1	4	yes	—
36	C₄×C₃₁	C₄×C₁₆	1	24	yes	direct product factor
37	C₄×C₃₁	C₄³	1	1	yes	characteristic
38	C₄×C₃₁	C₂×C₄×C₈	1	3	yes	—
39	C₂²×C₁₆	C₂²×C₃₁	1	4	yes	—
40	C₂×C₄×C₈	C₄×C₃₁	1	3	yes	—
41	C₂×C₄×C₈	C₂²×C₃₁	1	3	yes	—
42	C₄³	C₄×C₃₁	1	1	yes	characteristic
43	C₄×C₁₆	C₄×C₃₁	1	24	yes	direct product factor
44	C₂×C₃₁	C₄²×C₈	1	1	yes	characteristic
45	C₂×C₃₁	C₂×C₄×C₁₆	1	6	yes	—
46	C₂²×C₈	C₂×C₄×C₃₁	1	3	yes	—
47	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
48	C₂×C₄²	C₈×C₃₁	1	4	yes	—
49	C₂×C₄²	C₂×C₄×C₃₁	1	3	yes	—
50	C₂×C₁₆	C₂×C₄×C₃₁	1	24	yes	—
51	C₄×C₈	C₈×C₃₁	1	12	yes	—
52	C₄×C₈	C₂×C₄×C₃₁	1	12	yes	—
53	C₃₁	C₄²×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₄	C₂×C₈×C₃₁	1	6	yes	—
55	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
56	C₂×C₈	C₄²×C₃₁	1	6	yes	—
57	C₂×C₈	C₂×C₈×C₃₁	1	12	yes	—
58	C₂×C₈	C₂²×C₄×C₃₁	1	6	yes	—
59	C₄²	C₁₆×C₃₁	1	16	yes	direct product factor
60	C₄²	C₄²×C₃₁	1	6	yes	—
61	C₄²	C₂×C₈×C₃₁	1	6	yes	—
62	C₁₆	C₄²×C₃₁	1	16	yes	direct product factor
63	C₂³	C₂²×C₈×C₃₁	1	1	yes	characteristic
64	C₂×C₄	C₄×C₈×C₃₁	1	12	yes	—
65	C₂×C₄	C₂×C₁₆×C₃₁	1	24	yes	—
66	C₂×C₄	C₂×C₄²×C₃₁	1	3	yes	—
67	C₂×C₄	C₂²×C₈×C₃₁	1	3	yes	—
68	C₈	C₄×C₈×C₃₁	1	12	yes	—
69	C₈	C₂×C₄²×C₃₁	1	4	yes	—
70	C₂²	C₂×C₄×C₈×C₃₁	1	3	yes	—
71	C₂²	C₂²×C₁₆×C₃₁	1	4	yes	—
72	C₄	C₄×C₁₆×C₃₁	1	24	yes	direct product factor
73	C₄	C₄³×C₃₁	1	1	yes	characteristic
74	C₄	C₂×C₄×C₈×C₃₁	1	3	yes	—
75	C₂	C₄²×C₈×C₃₁	1	1	yes	characteristic
76	C₂	C₂×C₄×C₁₆×C₃₁	1	6	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂²×C₈	C₂³×C₃₁
socle	C₂³×C₃₁	C₂²×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₄×C₁₆×C₃₁	C₄	direct (N × H)
20. C₄²×C₃₁	C₁₆	direct (N × H)
23. C₁₆×C₃₁	C₄²	direct (N × H)
24. C₄²×C₁₆	C₃₁	direct (N × H)
36. C₄×C₃₁	C₄×C₁₆	direct (N × H)
43. C₄×C₁₆	C₄×C₃₁	direct (N × H)
53. C₃₁	C₄²×C₁₆	direct (N × H)
59. C₄²	C₁₆×C₃₁	direct (N × H)
62. C₁₆	C₄²×C₃₁	direct (N × H)
72. C₄	C₄×C₁₆×C₃₁	direct (N × H)

Subgroups — C42×C16×C31 #21469296

Conjugacy classes of subgroups

Complements

Subgroups — C₄²×C₁₆×C₃₁ #21469296