Subgroups — C₂⁴×D₁₈₈ #20258181

Order 6016.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₄₇	C₂	1	2	yes	maximal, complemented
2	C₂³×D₁₈₈	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×D₄₇	—	2	32	no	—
5	C₂⁴×D₄₇	C₂²	1	60	yes	complemented
6	C₂²×D₁₈₈	C₂²	1	560	yes	direct product factor
7	C₂⁵×C₄₇	C₂²	1	1	yes	characteristic
8	C₂³×C₄×C₄₇	C₂²	1	30	yes	complemented
9	C₂⁴×C₄₇	D₄	1	16	yes	complemented
10	C₂⁴×C₄₇	C₂³	1	15	yes	—
11	C₂³×D₄₇	—	2	480	no	—
12	C₂³×D₄₇	C₂³	1	280	yes	complemented
13	C₂²×C₄×C₄₇	C₂³	1	140	yes	complemented
14	C₂×D₁₈₈	C₂³	1	960	yes	direct product factor
15	C₂³×C₄₇	C₂×D₄	1	120	yes	complemented
16	C₂³×C₄₇	C₂⁴	1	35	yes	—
17	C₂²×D₄₇	—	2	1120	no	—
18	C₂²×D₄₇	C₂⁴	1	240	yes	complemented
19	C₂×C₄×C₄₇	C₂⁴	1	120	yes	complemented
20	D₁₈₈	C₂⁴	1	256	yes	direct product factor
21	C₂²×C₄₇	C₂²×D₄	1	140	yes	complemented
22	C₂²×C₄₇	C₂⁵	1	15	yes	—
23	C₂×D₄₇	—	2	480	no	—
24	C₂×D₄₇	C₂⁵	1	32	yes	complemented
25	C₄×C₄₇	C₂⁵	1	16	yes	complemented
26	C₂⁴×D₄	—	47	1	no	maximal, Sylow
27	C₂×C₄₇	C₂³×D₄	1	30	yes	complemented
28	C₂×C₄₇	C₂⁶	1	1	yes	characteristic
29	D₄₇	—	2	32	no	—
30	C₂⁶	—	47	2	no	—
31	C₂³×D₄	—	47	60	no	—
32	C₂⁴×C₄	D₄₇	1	1	yes	characteristic, complemented
33	C₄₇	C₂⁴×D₄	1	1	yes	characteristic, complemented, Sylow
34	C₂⁵	—	47	60	no	—
35	C₂⁵	—	94	32	no	—
36	C₂⁵	C₂×D₄₇	1	1	yes	characteristic
37	C₂²×D₄	—	47	560	no	—
38	C₂³×C₄	C₂×D₄₇	1	30	yes	complemented
39	C₂⁴	—	47	280	no	—
40	C₂⁴	—	94	480	no	—
41	C₂⁴	D₁₈₈	1	16	yes	direct product factor
42	C₂⁴	C₂²×D₄₇	1	15	yes	—
43	C₂×D₄	—	47	960	no	—
44	C₂²×C₄	C₂²×D₄₇	1	140	yes	complemented
45	C₂³	—	47	240	no	—
46	C₂³	—	94	1120	no	—
47	C₂³	C₂×D₁₈₈	1	120	yes	direct product factor
48	C₂³	C₂³×D₄₇	1	35	yes	—
49	D₄	—	47	256	no	—
50	C₂×C₄	C₂³×D₄₇	1	120	yes	complemented
51	C₂²	—	47	32	no	—
52	C₂²	—	94	480	no	—
53	C₂²	C₂²×D₁₈₈	1	140	yes	direct product factor
54	C₂²	C₂⁴×D₄₇	1	15	yes	—
55	C₄	C₂⁴×D₄₇	1	16	yes	complemented
56	C₂	—	94	32	no	—
57	C₂	C₂³×D₁₈₈	1	30	yes	direct product factor
58	C₂	C₂⁵×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₄₇
commutator	C₂×C₄₇	C₂⁶
Frattini	C₂	C₂⁵×D₄₇
Fitting	C₂⁴×C₄×C₄₇	C₂
socle	C₂⁵×C₄₇	C₂²
hypercenter	C₂⁴×C₄	D₄₇
hypocenter	C₄₇	C₂⁴×D₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁵×D₄₇	C₂	semidirect
2. C₂³×D₁₈₈	C₂	direct (N × H)
3. C₂⁴×C₄×C₄₇	C₂	semidirect
5. C₂⁴×D₄₇	C₂²	semidirect
6. C₂²×D₁₈₈	C₂²	direct (N × H)
8. C₂³×C₄×C₄₇	C₂²	semidirect
9. C₂⁴×C₄₇	D₄	semidirect
12. C₂³×D₄₇	C₂³	semidirect
13. C₂²×C₄×C₄₇	C₂³	semidirect
14. C₂×D₁₈₈	C₂³	direct (N × H)
15. C₂³×C₄₇	C₂×D₄	semidirect
18. C₂²×D₄₇	C₂⁴	semidirect
19. C₂×C₄×C₄₇	C₂⁴	semidirect
20. D₁₈₈	C₂⁴	direct (N × H)
21. C₂²×C₄₇	C₂²×D₄	semidirect
24. C₂×D₄₇	C₂⁵	semidirect
25. C₄×C₄₇	C₂⁵	semidirect
27. C₂×C₄₇	C₂³×D₄	semidirect
32. C₂⁴×C₄	D₄₇	semidirect
33. C₄₇	C₂⁴×D₄	semidirect
38. C₂³×C₄	C₂×D₄₇	semidirect
41. C₂⁴	D₁₈₈	direct (N × H)
44. C₂²×C₄	C₂²×D₄₇	semidirect
47. C₂³	C₂×D₁₈₈	direct (N × H)
50. C₂×C₄	C₂³×D₄₇	semidirect
53. C₂²	C₂²×D₁₈₈	direct (N × H)
55. C₄	C₂⁴×D₄₇	semidirect
57. C₂	C₂³×D₁₈₈	direct (N × H)

Subgroups — C24×D188 #20258181

Conjugacy classes of subgroups

Complements

Subgroups — C₂⁴×D₁₈₈ #20258181