Subgroups — C₂⁴×C₂²⋊D₄₇ #20258180

Order 6016.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊D₄₇	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁶×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₄₇	—	2	16	no	—
6	C₂⁴×D₄₇	C₂²	1	30	yes	complemented
7	C₂²×C₂²⋊D₄₇	C₂²	1	560	yes	direct product factor
8	C₂³×Dic₄₇	C₂²	1	30	yes	complemented
9	C₂⁵×C₄₇	—	2	16	no	—
10	C₂⁵×C₄₇	C₂²	1	1	yes	characteristic
11	C₂⁵×C₄₇	C₂²	1	30	yes	complemented
12	C₂⁴×C₄₇	—	2	240	no	—
13	C₂⁴×C₄₇	D₄	1	16	yes	complemented
14	C₂⁴×C₄₇	C₂³	1	15	yes	—
15	C₂⁴×C₄₇	C₂³	1	140	yes	complemented
16	C₂³×D₄₇	—	2	240	no	—
17	C₂³×D₄₇	C₂³	1	140	yes	complemented
18	C₂×C₂²⋊D₄₇	C₂³	1	960	yes	direct product factor
19	C₂²×Dic₄₇	C₂³	1	140	yes	complemented
20	C₂³×C₄₇	—	2	560	no	—
21	C₂³×C₄₇	C₂×D₄	1	120	yes	complemented
22	C₂³×C₄₇	C₂⁴	1	35	yes	—
23	C₂³×C₄₇	C₂⁴	1	120	yes	complemented
24	C₂²×D₄₇	—	2	560	no	—
25	C₂²×D₄₇	C₂⁴	1	120	yes	complemented
26	C₂²⋊D₄₇	C₂⁴	1	256	yes	direct product factor
27	C₂×Dic₄₇	C₂⁴	1	120	yes	complemented
28	C₂²×C₄₇	—	2	240	no	—
29	C₂²×C₄₇	C₂²×D₄	1	140	yes	complemented
30	C₂²×C₄₇	C₂⁵	1	15	yes	—
31	C₂²×C₄₇	C₂⁵	1	16	yes	complemented
32	C₂×D₄₇	—	2	240	no	—
33	C₂×D₄₇	C₂⁵	1	16	yes	complemented
34	Dic₄₇	C₂⁵	1	16	yes	complemented
35	C₂⁴×D₄	—	47	1	no	maximal, Sylow
36	C₂×C₄₇	—	2	16	no	—
37	C₂×C₄₇	C₂³×D₄	1	30	yes	complemented
38	C₂×C₄₇	C₂⁶	1	1	yes	characteristic
39	D₄₇	—	2	16	no	—
40	C₂⁶	—	47	1	no	—
41	C₂⁶	D₄₇	1	1	yes	characteristic, complemented
42	C₂³×D₄	—	47	60	no	—
43	C₂⁴×C₄	—	47	1	no	—
44	C₄₇	C₂⁴×D₄	1	1	yes	characteristic, complemented, Sylow
45	C₂⁵	—	2	16	no	—
46	C₂⁵	—	47	30	no	—
47	C₂⁵	—	94	16	no	—
48	C₂⁵	C₂×D₄₇	1	1	yes	characteristic
49	C₂⁵	C₂×D₄₇	1	30	yes	complemented
50	C₂²×D₄	—	47	560	no	—
51	C₂³×C₄	—	47	30	no	—
52	C₂⁴	—	2	240	no	—
53	C₂⁴	—	47	140	no	—
54	C₂⁴	—	94	240	no	—
55	C₂⁴	C₂²⋊D₄₇	1	16	yes	direct product factor
56	C₂⁴	C₂²×D₄₇	1	15	yes	—
57	C₂⁴	C₂²×D₄₇	1	140	yes	complemented
58	C₂×D₄	—	47	960	no	—
59	C₂²×C₄	—	47	140	no	—
60	C₂³	—	2	560	no	—
61	C₂³	—	47	120	no	—
62	C₂³	—	94	560	no	—
63	C₂³	C₂×C₂²⋊D₄₇	1	120	yes	direct product factor
64	C₂³	C₂³×D₄₇	1	35	yes	—
65	C₂³	C₂³×D₄₇	1	120	yes	complemented
66	D₄	—	47	256	no	—
67	C₂×C₄	—	47	120	no	—
68	C₂²	—	2	240	no	—
69	C₂²	—	47	16	no	—
70	C₂²	—	94	240	no	—
71	C₂²	C₂²×C₂²⋊D₄₇	1	140	yes	direct product factor
72	C₂²	C₂⁴×D₄₇	1	15	yes	—
73	C₂²	C₂⁴×D₄₇	1	16	yes	complemented
74	C₄	—	47	16	no	—
75	C₂	—	2	16	no	—
76	C₂	—	94	16	no	—
77	C₂	C₂³×C₂²⋊D₄₇	1	30	yes	direct product factor
78	C₂	C₂⁵×D₄₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂⁵×D₄₇	C₂	semidirect
2. C₂³×C₂²⋊D₄₇	C₂	direct (N × H)
3. C₂⁴×Dic₄₇	C₂	semidirect
4. C₂⁶×C₄₇	C₂	semidirect
6. C₂⁴×D₄₇	C₂²	semidirect
7. C₂²×C₂²⋊D₄₇	C₂²	direct (N × H)
8. C₂³×Dic₄₇	C₂²	semidirect
11. C₂⁵×C₄₇	C₂²	semidirect
13. C₂⁴×C₄₇	D₄	semidirect
15. C₂⁴×C₄₇	C₂³	semidirect
17. C₂³×D₄₇	C₂³	semidirect
18. C₂×C₂²⋊D₄₇	C₂³	direct (N × H)
19. C₂²×Dic₄₇	C₂³	semidirect
21. C₂³×C₄₇	C₂×D₄	semidirect
23. C₂³×C₄₇	C₂⁴	semidirect
25. C₂²×D₄₇	C₂⁴	semidirect
26. C₂²⋊D₄₇	C₂⁴	direct (N × H)
27. C₂×Dic₄₇	C₂⁴	semidirect
29. C₂²×C₄₇	C₂²×D₄	semidirect
31. C₂²×C₄₇	C₂⁵	semidirect
33. C₂×D₄₇	C₂⁵	semidirect
34. Dic₄₇	C₂⁵	semidirect
37. C₂×C₄₇	C₂³×D₄	semidirect
41. C₂⁶	D₄₇	semidirect
44. C₄₇	C₂⁴×D₄	semidirect
49. C₂⁵	C₂×D₄₇	semidirect
55. C₂⁴	C₂²⋊D₄₇	direct (N × H)
57. C₂⁴	C₂²×D₄₇	semidirect
63. C₂³	C₂×C₂²⋊D₄₇	direct (N × H)
65. C₂³	C₂³×D₄₇	semidirect
71. C₂²	C₂²×C₂²⋊D₄₇	direct (N × H)
73. C₂²	C₂⁴×D₄₇	semidirect
77. C₂	C₂³×C₂²⋊D₄₇	direct (N × H)

Subgroups — C24×C22⋊D47 #20258180

Conjugacy classes of subgroups

Complements

Subgroups — C₂⁴×C₂²⋊D₄₇ #20258180