Subgroups — C₈×C₃₂×C₄₁ #23783529

Order 10496.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₂×C₄₁	C₂	1	2	yes	maximal
2	C₈×C₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₄₁	C₄	1	4	yes	—
4	C₄×C₁₆×C₄₁	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
6	C₈²×C₄₁	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₄₁	C₈	1	2	yes	—
8	C₂×C₁₆×C₄₁	C₂×C₄	1	2	yes	—
9	C₄×C₈×C₄₁	C₈	1	2	yes	—
10	C₄×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
11	C₃₂×C₄₁	C₈	1	8	yes	direct product factor
12	C₂×C₈×C₄₁	C₁₆	1	4	yes	—
13	C₂×C₈×C₄₁	C₄²	1	1	yes	characteristic
14	C₂×C₈×C₄₁	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₄₁	C₂×C₈	1	1	yes	characteristic
16	C₁₆×C₄₁	C₁₆	1	4	yes	—
17	C₁₆×C₄₁	C₂×C₈	1	4	yes	—
18	C₂×C₄×C₄₁	C₄×C₈	1	1	yes	characteristic
19	C₂×C₄×C₄₁	C₂×C₁₆	1	2	yes	—
20	C₈×C₄₁	C₃₂	1	8	yes	direct product factor
21	C₈×C₄₁	C₄×C₈	1	2	yes	—
22	C₈×C₄₁	C₂×C₁₆	1	2	yes	—
23	C₈×C₃₂	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂²×C₄₁	C₄×C₁₆	1	1	yes	characteristic
25	C₄×C₄₁	C₈²	1	1	yes	characteristic
26	C₄×C₄₁	C₄×C₁₆	1	1	yes	characteristic
27	C₄×C₄₁	C₂×C₃₂	1	4	yes	—
28	C₄×C₃₂	C₂×C₄₁	1	2	yes	—
29	C₈×C₁₆	C₂×C₄₁	1	1	yes	characteristic
30	C₂×C₄₁	C₈×C₁₆	1	1	yes	characteristic
31	C₂×C₄₁	C₄×C₃₂	1	2	yes	—
32	C₂×C₃₂	C₄×C₄₁	1	4	yes	—
33	C₄×C₁₆	C₄×C₄₁	1	1	yes	characteristic
34	C₄×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
35	C₈²	C₄×C₄₁	1	1	yes	characteristic
36	C₄₁	C₈×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₁₆	C₈×C₄₁	1	2	yes	—
38	C₂×C₁₆	C₂×C₄×C₄₁	1	2	yes	—
39	C₄×C₈	C₈×C₄₁	1	2	yes	—
40	C₄×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
41	C₃₂	C₈×C₄₁	1	8	yes	direct product factor
42	C₂×C₈	C₁₆×C₄₁	1	4	yes	—
43	C₂×C₈	C₄²×C₄₁	1	1	yes	characteristic
44	C₂×C₈	C₂×C₈×C₄₁	1	1	yes	characteristic
45	C₄²	C₂×C₈×C₄₁	1	1	yes	characteristic
46	C₁₆	C₁₆×C₄₁	1	4	yes	—
47	C₁₆	C₂×C₈×C₄₁	1	4	yes	—
48	C₂×C₄	C₄×C₈×C₄₁	1	1	yes	characteristic
49	C₂×C₄	C₂×C₁₆×C₄₁	1	2	yes	—
50	C₈	C₃₂×C₄₁	1	8	yes	direct product factor
51	C₈	C₄×C₈×C₄₁	1	2	yes	—
52	C₈	C₂×C₁₆×C₄₁	1	2	yes	—
53	C₂²	C₄×C₁₆×C₄₁	1	1	yes	characteristic
54	C₄	C₈²×C₄₁	1	1	yes	characteristic
55	C₄	C₄×C₁₆×C₄₁	1	1	yes	characteristic
56	C₄	C₂×C₃₂×C₄₁	1	4	yes	—
57	C₂	C₈×C₁₆×C₄₁	1	1	yes	characteristic
58	C₂	C₄×C₃₂×C₄₁	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₁₆	C₂²×C₄₁
socle, prime radical	C₂²×C₄₁	C₄×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₃₂×C₄₁	C₈	direct (N × H)
20. C₈×C₄₁	C₃₂	direct (N × H)
23. C₈×C₃₂	C₄₁	direct (N × H)
36. C₄₁	C₈×C₃₂	direct (N × H)
41. C₃₂	C₈×C₄₁	direct (N × H)
50. C₈	C₃₂×C₄₁	direct (N × H)

Subgroups — C8×C32×C41 #23783529

Conjugacy classes of subgroups

Complements

Subgroups — C₈×C₃₂×C₄₁ #23783529