Subgroups — C₂⁴×C₄²×C₄₇ #26102336

Order 12032.

24030 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₄₇	C₂	1	3	yes	maximal
2	C₂³×C₄²×C₄₇	C₂	1	60	yes	maximal, direct product factor
3	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
4	C₂⁴×C₄×C₄₇	C₄	1	96	yes	direct product factor
5	C₂⁴×C₄×C₄₇	C₂²	1	90	yes	—
6	C₂²×C₄²×C₄₇	C₂²	1	560	yes	direct product factor
7	C₂⁵×C₄₇	C₂×C₄	1	48	yes	—
8	C₂⁵×C₄₇	C₂³	1	15	yes	—
9	C₂³×C₄×C₄₇	C₂×C₄	1	1440	yes	direct product factor
10	C₂³×C₄×C₄₇	C₂³	1	420	yes	—
11	C₂×C₄²×C₄₇	C₂³	1	960	yes	direct product factor
12	C₂⁴×C₄₇	C₄²	1	256	yes	direct product factor
13	C₂⁴×C₄₇	C₂²×C₄	1	360	yes	—
14	C₂⁴×C₄₇	C₂⁴	1	35	yes	—
15	C₂²×C₄×C₄₇	C₂²×C₄	1	3360	yes	direct product factor
16	C₂²×C₄×C₄₇	C₂⁴	1	360	yes	—
17	C₄²×C₄₇	C₂⁴	1	256	yes	direct product factor
18	C₂³×C₄₇	C₂×C₄²	1	960	yes	direct product factor
19	C₂³×C₄₇	C₂³×C₄	1	420	yes	—
20	C₂³×C₄₇	C₂⁵	1	15	yes	—
21	C₂×C₄×C₄₇	C₂³×C₄	1	1440	yes	direct product factor
22	C₂×C₄×C₄₇	C₂⁵	1	48	yes	—
23	C₂⁴×C₄²	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂²×C₄₇	C₂²×C₄²	1	560	yes	direct product factor
25	C₂²×C₄₇	C₂⁴×C₄	1	90	yes	—
26	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
27	C₄×C₄₇	C₂⁴×C₄	1	96	yes	direct product factor
28	C₂⁵×C₄	C₂×C₄₇	1	3	yes	—
29	C₂³×C₄²	C₂×C₄₇	1	60	yes	direct product factor
30	C₂×C₄₇	C₂³×C₄²	1	60	yes	direct product factor
31	C₂×C₄₇	C₂⁵×C₄	1	3	yes	—
32	C₂⁶	C₂²×C₄₇	1	1	yes	characteristic
33	C₂⁴×C₄	C₄×C₄₇	1	96	yes	direct product factor
34	C₂⁴×C₄	C₂²×C₄₇	1	90	yes	—
35	C₂²×C₄²	C₂²×C₄₇	1	560	yes	direct product factor
36	C₄₇	C₂⁴×C₄²	1	1	yes	characteristic, direct product factor, Sylow
37	C₂⁵	C₂×C₄×C₄₇	1	48	yes	—
38	C₂⁵	C₂³×C₄₇	1	15	yes	—
39	C₂³×C₄	C₂×C₄×C₄₇	1	1440	yes	direct product factor
40	C₂³×C₄	C₂³×C₄₇	1	420	yes	—
41	C₂×C₄²	C₂³×C₄₇	1	960	yes	direct product factor
42	C₂⁴	C₄²×C₄₇	1	256	yes	direct product factor
43	C₂⁴	C₂²×C₄×C₄₇	1	360	yes	—
44	C₂⁴	C₂⁴×C₄₇	1	35	yes	—
45	C₂²×C₄	C₂²×C₄×C₄₇	1	3360	yes	direct product factor
46	C₂²×C₄	C₂⁴×C₄₇	1	360	yes	—
47	C₄²	C₂⁴×C₄₇	1	256	yes	direct product factor
48	C₂³	C₂×C₄²×C₄₇	1	960	yes	direct product factor
49	C₂³	C₂³×C₄×C₄₇	1	420	yes	—
50	C₂³	C₂⁵×C₄₇	1	15	yes	—
51	C₂×C₄	C₂³×C₄×C₄₇	1	1440	yes	direct product factor
52	C₂×C₄	C₂⁵×C₄₇	1	48	yes	—
53	C₂²	C₂²×C₄²×C₄₇	1	560	yes	direct product factor
54	C₂²	C₂⁴×C₄×C₄₇	1	90	yes	—
55	C₂²	C₂⁶×C₄₇	1	1	yes	characteristic
56	C₄	C₂⁴×C₄×C₄₇	1	96	yes	direct product factor
57	C₂	C₂³×C₄²×C₄₇	1	60	yes	direct product factor
58	C₂	C₂⁵×C₄×C₄₇	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁶×C₄₇
socle, prime radical	C₂⁶×C₄₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄²×C₄₇	C₂	direct (N × H)
4. C₂⁴×C₄×C₄₇	C₄	direct (N × H)
6. C₂²×C₄²×C₄₇	C₂²	direct (N × H)
9. C₂³×C₄×C₄₇	C₂×C₄	direct (N × H)
11. C₂×C₄²×C₄₇	C₂³	direct (N × H)
12. C₂⁴×C₄₇	C₄²	direct (N × H)
15. C₂²×C₄×C₄₇	C₂²×C₄	direct (N × H)
17. C₄²×C₄₇	C₂⁴	direct (N × H)
18. C₂³×C₄₇	C₂×C₄²	direct (N × H)
21. C₂×C₄×C₄₇	C₂³×C₄	direct (N × H)
23. C₂⁴×C₄²	C₄₇	direct (N × H)
24. C₂²×C₄₇	C₂²×C₄²	direct (N × H)
27. C₄×C₄₇	C₂⁴×C₄	direct (N × H)
29. C₂³×C₄²	C₂×C₄₇	direct (N × H)
30. C₂×C₄₇	C₂³×C₄²	direct (N × H)
33. C₂⁴×C₄	C₄×C₄₇	direct (N × H)
35. C₂²×C₄²	C₂²×C₄₇	direct (N × H)
36. C₄₇	C₂⁴×C₄²	direct (N × H)
39. C₂³×C₄	C₂×C₄×C₄₇	direct (N × H)
41. C₂×C₄²	C₂³×C₄₇	direct (N × H)
42. C₂⁴	C₄²×C₄₇	direct (N × H)
45. C₂²×C₄	C₂²×C₄×C₄₇	direct (N × H)
47. C₄²	C₂⁴×C₄₇	direct (N × H)
48. C₂³	C₂×C₄²×C₄₇	direct (N × H)
51. C₂×C₄	C₂³×C₄×C₄₇	direct (N × H)
53. C₂²	C₂²×C₄²×C₄₇	direct (N × H)
56. C₄	C₂⁴×C₄×C₄₇	direct (N × H)
57. C₂	C₂³×C₄²×C₄₇	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×C₄×C₄₇	2
C₂³×C₄²×C₄₇	2
C₂⁴×C₄²	47

Subgroups — C24×C42×C47 #26102336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄²×C₄₇ #26102336