Subgroups — C₂×C₄³×C₁₇ #14525271

Order 2176.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₁₇	C₂	1	7	yes	maximal
2	C₄³×C₁₇	C₂	1	8	yes	maximal, direct product factor
3	C₂³×C₄×C₁₇	C₂²	1	7	yes	—
4	C₂×C₄²×C₁₇	C₄	1	56	yes	direct product factor
5	C₂×C₄²×C₁₇	C₂²	1	28	yes	—
6	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
7	C₂²×C₄×C₁₇	C₂×C₄	1	84	yes	—
8	C₂²×C₄×C₁₇	C₂³	1	14	yes	—
9	C₄²×C₁₇	C₂×C₄	1	112	yes	direct product factor
10	C₂³×C₁₇	C₂²×C₄	1	14	yes	—
11	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
12	C₂×C₄×C₁₇	C₄²	1	112	yes	direct product factor
13	C₂×C₄×C₁₇	C₂²×C₄	1	84	yes	—
14	C₂×C₄³	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₁₇	C₂×C₄²	1	28	yes	—
16	C₂²×C₁₇	C₂³×C₄	1	7	yes	—
17	C₄×C₁₇	C₂×C₄²	1	56	yes	direct product factor
18	C₂²×C₄²	C₂×C₁₇	1	7	yes	—
19	C₄³	C₂×C₁₇	1	8	yes	direct product factor
20	C₂×C₁₇	C₄³	1	8	yes	direct product factor
21	C₂×C₁₇	C₂²×C₄²	1	7	yes	—
22	C₂³×C₄	C₂²×C₁₇	1	7	yes	—
23	C₂×C₄²	C₄×C₁₇	1	56	yes	direct product factor
24	C₂×C₄²	C₂²×C₁₇	1	28	yes	—
25	C₁₇	C₂×C₄³	1	1	yes	characteristic, direct product factor, Sylow
26	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
27	C₂²×C₄	C₂×C₄×C₁₇	1	84	yes	—
28	C₂²×C₄	C₂³×C₁₇	1	14	yes	—
29	C₄²	C₂×C₄×C₁₇	1	112	yes	direct product factor
30	C₂³	C₂²×C₄×C₁₇	1	14	yes	—
31	C₂³	C₂⁴×C₁₇	1	1	yes	characteristic
32	C₂×C₄	C₄²×C₁₇	1	112	yes	direct product factor
33	C₂×C₄	C₂²×C₄×C₁₇	1	84	yes	—
34	C₂²	C₂×C₄²×C₁₇	1	28	yes	—
35	C₂²	C₂³×C₄×C₁₇	1	7	yes	—
36	C₄	C₂×C₄²×C₁₇	1	56	yes	direct product factor
37	C₂	C₄³×C₁₇	1	8	yes	direct product factor
38	C₂	C₂²×C₄²×C₁₇	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂⁴×C₁₇
socle, prime radical	C₂⁴×C₁₇	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄³×C₁₇	C₂	direct (N × H)
4. C₂×C₄²×C₁₇	C₄	direct (N × H)
9. C₄²×C₁₇	C₂×C₄	direct (N × H)
12. C₂×C₄×C₁₇	C₄²	direct (N × H)
14. C₂×C₄³	C₁₇	direct (N × H)
17. C₄×C₁₇	C₂×C₄²	direct (N × H)
19. C₄³	C₂×C₁₇	direct (N × H)
20. C₂×C₁₇	C₄³	direct (N × H)
23. C₂×C₄²	C₄×C₁₇	direct (N × H)
25. C₁₇	C₂×C₄³	direct (N × H)
29. C₄²	C₂×C₄×C₁₇	direct (N × H)
32. C₂×C₄	C₄²×C₁₇	direct (N × H)
36. C₄	C₂×C₄²×C₁₇	direct (N × H)
37. C₂	C₄³×C₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄²×C₁₇	2
C₄³×C₁₇	2
C₂×C₄³	17

Subgroups — C2×C43×C17 #14525271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄³×C₁₇ #14525271