Subgroups — C₂³×D₁₇₂ #14583721

Order 2752.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄₃	C₂	1	2	yes	maximal, complemented
2	C₂²×D₁₇₂	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×C₄₃	C₂²	1	1	yes	characteristic
5	C₂³×D₄₃	—	2	16	no	—
6	C₂³×D₄₃	C₂²	1	28	yes	complemented
7	C₂²×C₄×C₄₃	C₂²	1	14	yes	complemented
8	C₂×D₁₇₂	C₂²	1	112	yes	direct product factor
9	C₂³×C₄₃	D₄	1	8	yes	complemented
10	C₂³×C₄₃	C₂³	1	7	yes	—
11	C₂²×D₄₃	—	2	112	no	—
12	C₂²×D₄₃	C₂³	1	56	yes	complemented
13	C₂×C₄×C₄₃	C₂³	1	28	yes	complemented
14	D₁₇₂	C₂³	1	64	yes	direct product factor
15	C₂²×C₄₃	C₂×D₄	1	28	yes	complemented
16	C₂²×C₄₃	C₂⁴	1	7	yes	—
17	C₂×D₄₃	—	2	112	no	—
18	C₂×D₄₃	C₂⁴	1	16	yes	complemented
19	C₄×C₄₃	C₂⁴	1	8	yes	complemented
20	C₂×C₄₃	C₂²×D₄	1	14	yes	complemented
21	C₂×C₄₃	C₂⁵	1	1	yes	characteristic
22	D₄₃	—	2	16	no	—
23	C₂³×D₄	—	43	1	no	maximal, Sylow
24	C₄₃	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
25	C₂⁵	—	43	2	no	—
26	C₂²×D₄	—	43	28	no	—
27	C₂³×C₄	D₄₃	1	1	yes	characteristic, complemented
28	C₂⁴	—	43	28	no	—
29	C₂⁴	—	86	16	no	—
30	C₂⁴	C₂×D₄₃	1	1	yes	characteristic
31	C₂×D₄	—	43	112	no	—
32	C₂²×C₄	C₂×D₄₃	1	14	yes	complemented
33	C₂³	—	43	56	no	—
34	C₂³	—	86	112	no	—
35	C₂³	D₁₇₂	1	8	yes	direct product factor
36	C₂³	C₂²×D₄₃	1	7	yes	—
37	D₄	—	43	64	no	—
38	C₂×C₄	C₂²×D₄₃	1	28	yes	complemented
39	C₂²	—	43	16	no	—
40	C₂²	—	86	112	no	—
41	C₂²	C₂×D₁₇₂	1	28	yes	direct product factor
42	C₂²	C₂³×D₄₃	1	7	yes	—
43	C₄	C₂³×D₄₃	1	8	yes	complemented
44	C₂	—	86	16	no	—
45	C₂	C₂²×D₁₇₂	1	14	yes	direct product factor
46	C₂	C₂⁴×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₄₃
commutator, cosocle	C₂×C₄₃	C₂⁵
Frattini	C₂	C₂⁴×D₄₃
Fitting	C₂³×C₄×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂²
hypercenter	C₂³×C₄	D₄₃
hypocenter	C₄₃	C₂³×D₄
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₄₃	C₂	semidirect
2. C₂²×D₁₇₂	C₂	direct (N × H)
3. C₂³×C₄×C₄₃	C₂	semidirect
6. C₂³×D₄₃	C₂²	semidirect
7. C₂²×C₄×C₄₃	C₂²	semidirect
8. C₂×D₁₇₂	C₂²	direct (N × H)
9. C₂³×C₄₃	D₄	semidirect
12. C₂²×D₄₃	C₂³	semidirect
13. C₂×C₄×C₄₃	C₂³	semidirect
14. D₁₇₂	C₂³	direct (N × H)
15. C₂²×C₄₃	C₂×D₄	semidirect
18. C₂×D₄₃	C₂⁴	semidirect
19. C₄×C₄₃	C₂⁴	semidirect
20. C₂×C₄₃	C₂²×D₄	semidirect
24. C₄₃	C₂³×D₄	semidirect
27. C₂³×C₄	D₄₃	semidirect
32. C₂²×C₄	C₂×D₄₃	semidirect
35. C₂³	D₁₇₂	direct (N × H)
38. C₂×C₄	C₂²×D₄₃	semidirect
41. C₂²	C₂×D₁₇₂	direct (N × H)
43. C₄	C₂³×D₄₃	semidirect
45. C₂	C₂²×D₁₇₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄₃	2
C₂²×D₁₇₂	2
C₂³×C₄×C₄₃	2
C₂³×D₄	43

Subgroups — C23×D172 #14583721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₁₇₂ #14583721