Subgroups — C₂⁴×D₄₄ #13083409

Order 1408.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₁₁	C₂	1	2	yes	maximal, complemented
2	C₂⁴×C₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×D₄₄	C₂	1	60	yes	maximal, direct product factor
4	C₂⁵×C₁₁	C₂²	1	1	yes	characteristic
5	C₂⁴×D₁₁	—	2	32	no	—
6	C₂⁴×D₁₁	C₂²	1	60	yes	complemented
7	C₂³×C₄×C₁₁	C₂²	1	30	yes	complemented
8	C₂²×D₄₄	C₂²	1	560	yes	direct product factor
9	C₂⁴×C₁₁	D₄	1	16	yes	complemented
10	C₂⁴×C₁₁	C₂³	1	15	yes	—
11	C₂³×D₁₁	—	2	480	no	—
12	C₂³×D₁₁	C₂³	1	280	yes	complemented
13	C₂²×C₄×C₁₁	C₂³	1	140	yes	complemented
14	C₂×D₄₄	C₂³	1	960	yes	direct product factor
15	C₂⁴×D₄	—	11	1	no	maximal, Sylow
16	C₂³×C₁₁	C₂×D₄	1	120	yes	complemented
17	C₂³×C₁₁	C₂⁴	1	35	yes	—
18	C₂²×D₁₁	—	2	1120	no	—
19	C₂²×D₁₁	C₂⁴	1	240	yes	complemented
20	C₂×C₄×C₁₁	C₂⁴	1	120	yes	complemented
21	D₄₄	C₂⁴	1	256	yes	direct product factor
22	C₂⁶	—	11	2	no	—
23	C₂³×D₄	—	11	60	no	—
24	C₂⁴×C₄	D₁₁	1	1	yes	characteristic, complemented
25	C₂²×C₁₁	C₂²×D₄	1	140	yes	complemented
26	C₂²×C₁₁	C₂⁵	1	15	yes	—
27	C₂×D₁₁	—	2	480	no	—
28	C₂×D₁₁	C₂⁵	1	32	yes	complemented
29	C₄×C₁₁	C₂⁵	1	16	yes	complemented
30	C₂⁵	—	11	60	no	—
31	C₂⁵	—	22	32	no	—
32	C₂⁵	C₂×D₁₁	1	1	yes	characteristic
33	C₂²×D₄	—	11	560	no	—
34	C₂³×C₄	C₂×D₁₁	1	30	yes	complemented
35	C₂×C₁₁	C₂³×D₄	1	30	yes	complemented
36	C₂×C₁₁	C₂⁶	1	1	yes	characteristic
37	D₁₁	—	2	32	no	—
38	C₂⁴	—	11	280	no	—
39	C₂⁴	—	22	480	no	—
40	C₂⁴	D₄₄	1	16	yes	direct product factor
41	C₂⁴	C₂²×D₁₁	1	15	yes	—
42	C₂×D₄	—	11	960	no	—
43	C₂²×C₄	C₂²×D₁₁	1	140	yes	complemented
44	C₁₁	C₂⁴×D₄	1	1	yes	characteristic, complemented, Sylow
45	C₂³	—	11	240	no	—
46	C₂³	—	22	1120	no	—
47	C₂³	C₂×D₄₄	1	120	yes	direct product factor
48	C₂³	C₂³×D₁₁	1	35	yes	—
49	D₄	—	11	256	no	—
50	C₂×C₄	C₂³×D₁₁	1	120	yes	complemented
51	C₂²	—	11	32	no	—
52	C₂²	—	22	480	no	—
53	C₂²	C₂²×D₄₄	1	140	yes	direct product factor
54	C₂²	C₂⁴×D₁₁	1	15	yes	—
55	C₄	C₂⁴×D₁₁	1	16	yes	complemented
56	C₂	—	22	32	no	—
57	C₂	C₂³×D₄₄	1	30	yes	direct product factor
58	C₂	C₂⁵×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₁₁
commutator, cosocle	C₂×C₁₁	C₂⁶
Frattini	C₂	C₂⁵×D₁₁
Fitting	C₂⁴×C₄×C₁₁	C₂
socle	C₂⁵×C₁₁	C₂²
hypercenter	C₂⁴×C₄	D₁₁
hypocenter	C₁₁	C₂⁴×D₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁵×D₁₁	C₂	semidirect
2. C₂⁴×C₄×C₁₁	C₂	semidirect
3. C₂³×D₄₄	C₂	direct (N × H)
6. C₂⁴×D₁₁	C₂²	semidirect
7. C₂³×C₄×C₁₁	C₂²	semidirect
8. C₂²×D₄₄	C₂²	direct (N × H)
9. C₂⁴×C₁₁	D₄	semidirect
12. C₂³×D₁₁	C₂³	semidirect
13. C₂²×C₄×C₁₁	C₂³	semidirect
14. C₂×D₄₄	C₂³	direct (N × H)
16. C₂³×C₁₁	C₂×D₄	semidirect
19. C₂²×D₁₁	C₂⁴	semidirect
20. C₂×C₄×C₁₁	C₂⁴	semidirect
21. D₄₄	C₂⁴	direct (N × H)
24. C₂⁴×C₄	D₁₁	semidirect
25. C₂²×C₁₁	C₂²×D₄	semidirect
28. C₂×D₁₁	C₂⁵	semidirect
29. C₄×C₁₁	C₂⁵	semidirect
34. C₂³×C₄	C₂×D₁₁	semidirect
35. C₂×C₁₁	C₂³×D₄	semidirect
40. C₂⁴	D₄₄	direct (N × H)
43. C₂²×C₄	C₂²×D₁₁	semidirect
44. C₁₁	C₂⁴×D₄	semidirect
47. C₂³	C₂×D₄₄	direct (N × H)
50. C₂×C₄	C₂³×D₁₁	semidirect
53. C₂²	C₂²×D₄₄	direct (N × H)
55. C₄	C₂⁴×D₁₁	semidirect
57. C₂	C₂³×D₄₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×D₁₁	2
C₂⁴×C₄×C₁₁	2
C₂³×D₄₄	2
C₂⁴×D₄	11

Subgroups — C24×D44 #13083409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×D₄₄ #13083409