Subgroups — C₂⁴×D₁₇₂ #19149388

Order 5504.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₄₃	C₂	1	2	yes	maximal, complemented
2	C₂³×D₁₇₂	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×D₄₃	—	2	32	no	—
5	C₂⁴×D₄₃	C₂²	1	60	yes	complemented
6	C₂²×D₁₇₂	C₂²	1	560	yes	direct product factor
7	C₂⁵×C₄₃	C₂²	1	1	yes	characteristic
8	C₂³×C₄×C₄₃	C₂²	1	30	yes	complemented
9	C₂⁴×C₄₃	D₄	1	16	yes	complemented
10	C₂⁴×C₄₃	C₂³	1	15	yes	—
11	C₂³×D₄₃	—	2	480	no	—
12	C₂³×D₄₃	C₂³	1	280	yes	complemented
13	C₂²×C₄×C₄₃	C₂³	1	140	yes	complemented
14	C₂×D₁₇₂	C₂³	1	960	yes	direct product factor
15	C₂³×C₄₃	C₂×D₄	1	120	yes	complemented
16	C₂³×C₄₃	C₂⁴	1	35	yes	—
17	C₂²×D₄₃	—	2	1120	no	—
18	C₂²×D₄₃	C₂⁴	1	240	yes	complemented
19	C₂×C₄×C₄₃	C₂⁴	1	120	yes	complemented
20	D₁₇₂	C₂⁴	1	256	yes	direct product factor
21	C₂²×C₄₃	C₂²×D₄	1	140	yes	complemented
22	C₂²×C₄₃	C₂⁵	1	15	yes	—
23	C₂×D₄₃	—	2	480	no	—
24	C₂×D₄₃	C₂⁵	1	32	yes	complemented
25	C₄×C₄₃	C₂⁵	1	16	yes	complemented
26	C₂⁴×D₄	—	43	1	no	maximal, Sylow
27	C₂×C₄₃	C₂³×D₄	1	30	yes	complemented
28	C₂×C₄₃	C₂⁶	1	1	yes	characteristic
29	D₄₃	—	2	32	no	—
30	C₂⁶	—	43	2	no	—
31	C₂³×D₄	—	43	60	no	—
32	C₂⁴×C₄	D₄₃	1	1	yes	characteristic, complemented
33	C₄₃	C₂⁴×D₄	1	1	yes	characteristic, complemented, Sylow
34	C₂⁵	—	43	60	no	—
35	C₂⁵	—	86	32	no	—
36	C₂⁵	C₂×D₄₃	1	1	yes	characteristic
37	C₂²×D₄	—	43	560	no	—
38	C₂³×C₄	C₂×D₄₃	1	30	yes	complemented
39	C₂⁴	—	43	280	no	—
40	C₂⁴	—	86	480	no	—
41	C₂⁴	D₁₇₂	1	16	yes	direct product factor
42	C₂⁴	C₂²×D₄₃	1	15	yes	—
43	C₂×D₄	—	43	960	no	—
44	C₂²×C₄	C₂²×D₄₃	1	140	yes	complemented
45	C₂³	—	43	240	no	—
46	C₂³	—	86	1120	no	—
47	C₂³	C₂×D₁₇₂	1	120	yes	direct product factor
48	C₂³	C₂³×D₄₃	1	35	yes	—
49	D₄	—	43	256	no	—
50	C₂×C₄	C₂³×D₄₃	1	120	yes	complemented
51	C₂²	—	43	32	no	—
52	C₂²	—	86	480	no	—
53	C₂²	C₂²×D₁₇₂	1	140	yes	direct product factor
54	C₂²	C₂⁴×D₄₃	1	15	yes	—
55	C₄	C₂⁴×D₄₃	1	16	yes	complemented
56	C₂	—	86	32	no	—
57	C₂	C₂³×D₁₇₂	1	30	yes	direct product factor
58	C₂	C₂⁵×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₄₃
commutator	C₂×C₄₃	C₂⁶
Frattini	C₂	C₂⁵×D₄₃
Fitting	C₂⁴×C₄×C₄₃	C₂
socle	C₂⁵×C₄₃	C₂²
hypercenter	C₂⁴×C₄	D₄₃
hypocenter	C₄₃	C₂⁴×D₄
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁵×D₄₃	C₂	semidirect
2. C₂³×D₁₇₂	C₂	direct (N × H)
3. C₂⁴×C₄×C₄₃	C₂	semidirect
5. C₂⁴×D₄₃	C₂²	semidirect
6. C₂²×D₁₇₂	C₂²	direct (N × H)
8. C₂³×C₄×C₄₃	C₂²	semidirect
9. C₂⁴×C₄₃	D₄	semidirect
12. C₂³×D₄₃	C₂³	semidirect
13. C₂²×C₄×C₄₃	C₂³	semidirect
14. C₂×D₁₇₂	C₂³	direct (N × H)
15. C₂³×C₄₃	C₂×D₄	semidirect
18. C₂²×D₄₃	C₂⁴	semidirect
19. C₂×C₄×C₄₃	C₂⁴	semidirect
20. D₁₇₂	C₂⁴	direct (N × H)
21. C₂²×C₄₃	C₂²×D₄	semidirect
24. C₂×D₄₃	C₂⁵	semidirect
25. C₄×C₄₃	C₂⁵	semidirect
27. C₂×C₄₃	C₂³×D₄	semidirect
32. C₂⁴×C₄	D₄₃	semidirect
33. C₄₃	C₂⁴×D₄	semidirect
38. C₂³×C₄	C₂×D₄₃	semidirect
41. C₂⁴	D₁₇₂	direct (N × H)
44. C₂²×C₄	C₂²×D₄₃	semidirect
47. C₂³	C₂×D₁₇₂	direct (N × H)
50. C₂×C₄	C₂³×D₄₃	semidirect
53. C₂²	C₂²×D₁₇₂	direct (N × H)
55. C₄	C₂⁴×D₄₃	semidirect
57. C₂	C₂³×D₁₇₂	direct (N × H)

Subgroups — C24×D172 #19149388

Conjugacy classes of subgroups

Complements

Subgroups — C₂⁴×D₁₇₂ #19149388