Subgroups — C₂³×C₁₇×C₃₂ #16891715

Order 4352.

542 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₇×C₃₂	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₈×C₁₇	C₄	1	1	yes	characteristic
4	C₂²×C₁₆×C₁₇	C₄	1	7	yes	—
5	C₂²×C₁₆×C₁₇	C₂²	1	7	yes	—
6	C₂×C₁₇×C₃₂	C₂²	1	28	yes	direct product factor
7	C₂³×C₄×C₁₇	C₈	1	1	yes	characteristic
8	C₂²×C₈×C₁₇	C₈	1	7	yes	—
9	C₂²×C₈×C₁₇	C₂×C₄	1	7	yes	—
10	C₂×C₁₆×C₁₇	C₂×C₄	1	21	yes	—
11	C₂×C₁₆×C₁₇	C₂³	1	7	yes	—
12	C₁₇×C₃₂	C₂³	1	8	yes	direct product factor
13	C₂⁴×C₁₇	C₁₆	1	1	yes	characteristic
14	C₂²×C₄×C₁₇	C₁₆	1	7	yes	—
15	C₂²×C₄×C₁₇	C₂×C₈	1	7	yes	—
16	C₂×C₈×C₁₇	C₂×C₈	1	21	yes	—
17	C₂×C₈×C₁₇	C₂²×C₄	1	7	yes	—
18	C₁₆×C₁₇	C₂²×C₄	1	7	yes	—
19	C₁₆×C₁₇	C₂⁴	1	1	yes	characteristic
20	C₂³×C₃₂	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₁₇	C₃₂	1	8	yes	direct product factor
22	C₂³×C₁₇	C₂×C₁₆	1	7	yes	—
23	C₂×C₄×C₁₇	C₂×C₁₆	1	21	yes	—
24	C₂×C₄×C₁₇	C₂²×C₈	1	7	yes	—
25	C₈×C₁₇	C₂²×C₈	1	7	yes	—
26	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
27	C₂³×C₁₆	C₂×C₁₇	1	1	yes	characteristic
28	C₂²×C₃₂	C₂×C₁₇	1	14	yes	direct product factor
29	C₂²×C₁₇	C₂×C₃₂	1	28	yes	direct product factor
30	C₂²×C₁₇	C₂²×C₁₆	1	7	yes	—
31	C₄×C₁₇	C₂²×C₁₆	1	7	yes	—
32	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
33	C₂³×C₈	C₄×C₁₇	1	1	yes	characteristic
34	C₂²×C₁₆	C₄×C₁₇	1	7	yes	—
35	C₂²×C₁₆	C₂²×C₁₇	1	7	yes	—
36	C₂×C₃₂	C₂²×C₁₇	1	28	yes	direct product factor
37	C₂×C₁₇	C₂²×C₃₂	1	14	yes	direct product factor
38	C₂×C₁₇	C₂³×C₁₆	1	1	yes	characteristic
39	C₂³×C₄	C₈×C₁₇	1	1	yes	characteristic
40	C₂²×C₈	C₈×C₁₇	1	7	yes	—
41	C₂²×C₈	C₂×C₄×C₁₇	1	7	yes	—
42	C₂×C₁₆	C₂×C₄×C₁₇	1	21	yes	—
43	C₂×C₁₆	C₂³×C₁₇	1	7	yes	—
44	C₃₂	C₂³×C₁₇	1	8	yes	direct product factor
45	C₁₇	C₂³×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
46	C₂⁴	C₁₆×C₁₇	1	1	yes	characteristic
47	C₂²×C₄	C₁₆×C₁₇	1	7	yes	—
48	C₂²×C₄	C₂×C₈×C₁₇	1	7	yes	—
49	C₂×C₈	C₂×C₈×C₁₇	1	21	yes	—
50	C₂×C₈	C₂²×C₄×C₁₇	1	7	yes	—
51	C₁₆	C₂²×C₄×C₁₇	1	7	yes	—
52	C₁₆	C₂⁴×C₁₇	1	1	yes	characteristic
53	C₂³	C₁₇×C₃₂	1	8	yes	direct product factor
54	C₂³	C₂×C₁₆×C₁₇	1	7	yes	—
55	C₂×C₄	C₂×C₁₆×C₁₇	1	21	yes	—
56	C₂×C₄	C₂²×C₈×C₁₇	1	7	yes	—
57	C₈	C₂²×C₈×C₁₇	1	7	yes	—
58	C₈	C₂³×C₄×C₁₇	1	1	yes	characteristic
59	C₂²	C₂×C₁₇×C₃₂	1	28	yes	direct product factor
60	C₂²	C₂²×C₁₆×C₁₇	1	7	yes	—
61	C₄	C₂²×C₁₆×C₁₇	1	7	yes	—
62	C₄	C₂³×C₈×C₁₇	1	1	yes	characteristic
63	C₂	C₂²×C₁₇×C₃₂	1	14	yes	direct product factor
64	C₂	C₂³×C₁₆×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂⁴×C₁₇
socle, prime radical	C₂⁴×C₁₇	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₇×C₃₂	C₂	direct (N × H)
6. C₂×C₁₇×C₃₂	C₂²	direct (N × H)
12. C₁₇×C₃₂	C₂³	direct (N × H)
20. C₂³×C₃₂	C₁₇	direct (N × H)
21. C₂³×C₁₇	C₃₂	direct (N × H)
28. C₂²×C₃₂	C₂×C₁₇	direct (N × H)
29. C₂²×C₁₇	C₂×C₃₂	direct (N × H)
36. C₂×C₃₂	C₂²×C₁₇	direct (N × H)
37. C₂×C₁₇	C₂²×C₃₂	direct (N × H)
44. C₃₂	C₂³×C₁₇	direct (N × H)
45. C₁₇	C₂³×C₃₂	direct (N × H)
53. C₂³	C₁₇×C₃₂	direct (N × H)
59. C₂²	C₂×C₁₇×C₃₂	direct (N × H)
63. C₂	C₂²×C₁₇×C₃₂	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₆×C₁₇	2
C₂²×C₁₇×C₃₂	2
C₂³×C₃₂	17

Subgroups — C23×C17×C32 #16891715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₁₇×C₃₂ #16891715