Subgroups — C₂⁶×C₈×C₄₇ #72201370

Order 24064.

163972 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×C₈×C₄₇	C₂	1	126	yes	maximal, direct product factor
3	C₂⁷×C₄₇	C₄	1	1	yes	characteristic
4	C₂⁵×C₄×C₄₇	C₄	1	63	yes	—
5	C₂⁵×C₄×C₄₇	C₂²	1	63	yes	—
6	C₂⁴×C₈×C₄₇	C₂²	1	2604	yes	direct product factor
7	C₂⁶×C₄₇	C₈	1	64	yes	direct product factor
8	C₂⁶×C₄₇	C₂×C₄	1	63	yes	—
9	C₂⁴×C₄×C₄₇	C₂×C₄	1	1953	yes	—
10	C₂⁴×C₄×C₄₇	C₂³	1	651	yes	—
11	C₂³×C₈×C₄₇	C₂³	1	11160	yes	direct product factor
12	C₂⁵×C₄₇	C₂×C₈	1	2016	yes	direct product factor
13	C₂⁵×C₄₇	C₂²×C₄	1	651	yes	—
14	C₂³×C₄×C₄₇	C₂²×C₄	1	9765	yes	—
15	C₂³×C₄×C₄₇	C₂⁴	1	1395	yes	—
16	C₂²×C₈×C₄₇	C₂⁴	1	10416	yes	direct product factor
17	C₂⁴×C₄₇	C₂²×C₈	1	10416	yes	direct product factor
18	C₂⁴×C₄₇	C₂³×C₄	1	1395	yes	—
19	C₂²×C₄×C₄₇	C₂³×C₄	1	9765	yes	—
20	C₂²×C₄×C₄₇	C₂⁵	1	651	yes	—
21	C₂×C₈×C₄₇	C₂⁵	1	2016	yes	direct product factor
22	C₂⁶×C₈	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂³×C₄₇	C₂³×C₈	1	11160	yes	direct product factor
24	C₂³×C₄₇	C₂⁴×C₄	1	651	yes	—
25	C₂×C₄×C₄₇	C₂⁴×C₄	1	1953	yes	—
26	C₂×C₄×C₄₇	C₂⁶	1	63	yes	—
27	C₈×C₄₇	C₂⁶	1	64	yes	direct product factor
28	C₂⁶×C₄	C₂×C₄₇	1	1	yes	characteristic
29	C₂⁵×C₈	C₂×C₄₇	1	126	yes	direct product factor
30	C₂²×C₄₇	C₂⁴×C₈	1	2604	yes	direct product factor
31	C₂²×C₄₇	C₂⁵×C₄	1	63	yes	—
32	C₄×C₄₇	C₂⁵×C₄	1	63	yes	—
33	C₄×C₄₇	C₂⁷	1	1	yes	characteristic
34	C₂⁷	C₄×C₄₇	1	1	yes	characteristic
35	C₂⁵×C₄	C₄×C₄₇	1	63	yes	—
36	C₂⁵×C₄	C₂²×C₄₇	1	63	yes	—
37	C₂⁴×C₈	C₂²×C₄₇	1	2604	yes	direct product factor
38	C₂×C₄₇	C₂⁵×C₈	1	126	yes	direct product factor
39	C₂×C₄₇	C₂⁶×C₄	1	1	yes	characteristic
40	C₂⁶	C₈×C₄₇	1	64	yes	direct product factor
41	C₂⁶	C₂×C₄×C₄₇	1	63	yes	—
42	C₂⁴×C₄	C₂×C₄×C₄₇	1	1953	yes	—
43	C₂⁴×C₄	C₂³×C₄₇	1	651	yes	—
44	C₂³×C₈	C₂³×C₄₇	1	11160	yes	direct product factor
45	C₄₇	C₂⁶×C₈	1	1	yes	characteristic, direct product factor, Sylow
46	C₂⁵	C₂×C₈×C₄₇	1	2016	yes	direct product factor
47	C₂⁵	C₂²×C₄×C₄₇	1	651	yes	—
48	C₂³×C₄	C₂²×C₄×C₄₇	1	9765	yes	—
49	C₂³×C₄	C₂⁴×C₄₇	1	1395	yes	—
50	C₂²×C₈	C₂⁴×C₄₇	1	10416	yes	direct product factor
51	C₂⁴	C₂²×C₈×C₄₇	1	10416	yes	direct product factor
52	C₂⁴	C₂³×C₄×C₄₇	1	1395	yes	—
53	C₂²×C₄	C₂³×C₄×C₄₇	1	9765	yes	—
54	C₂²×C₄	C₂⁵×C₄₇	1	651	yes	—
55	C₂×C₈	C₂⁵×C₄₇	1	2016	yes	direct product factor
56	C₂³	C₂³×C₈×C₄₇	1	11160	yes	direct product factor
57	C₂³	C₂⁴×C₄×C₄₇	1	651	yes	—
58	C₂×C₄	C₂⁴×C₄×C₄₇	1	1953	yes	—
59	C₂×C₄	C₂⁶×C₄₇	1	63	yes	—
60	C₈	C₂⁶×C₄₇	1	64	yes	direct product factor
61	C₂²	C₂⁴×C₈×C₄₇	1	2604	yes	direct product factor
62	C₂²	C₂⁵×C₄×C₄₇	1	63	yes	—
63	C₄	C₂⁵×C₄×C₄₇	1	63	yes	—
64	C₄	C₂⁷×C₄₇	1	1	yes	characteristic
65	C₂	C₂⁵×C₈×C₄₇	1	126	yes	direct product factor
66	C₂	C₂⁶×C₄×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁷×C₄₇
socle, prime radical	C₂⁷×C₄₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁵×C₈×C₄₇	C₂	direct (N × H)
6. C₂⁴×C₈×C₄₇	C₂²	direct (N × H)
7. C₂⁶×C₄₇	C₈	direct (N × H)
11. C₂³×C₈×C₄₇	C₂³	direct (N × H)
12. C₂⁵×C₄₇	C₂×C₈	direct (N × H)
16. C₂²×C₈×C₄₇	C₂⁴	direct (N × H)
17. C₂⁴×C₄₇	C₂²×C₈	direct (N × H)
21. C₂×C₈×C₄₇	C₂⁵	direct (N × H)
22. C₂⁶×C₈	C₄₇	direct (N × H)
23. C₂³×C₄₇	C₂³×C₈	direct (N × H)
27. C₈×C₄₇	C₂⁶	direct (N × H)
29. C₂⁵×C₈	C₂×C₄₇	direct (N × H)
30. C₂²×C₄₇	C₂⁴×C₈	direct (N × H)
37. C₂⁴×C₈	C₂²×C₄₇	direct (N × H)
38. C₂×C₄₇	C₂⁵×C₈	direct (N × H)
40. C₂⁶	C₈×C₄₇	direct (N × H)
44. C₂³×C₈	C₂³×C₄₇	direct (N × H)
45. C₄₇	C₂⁶×C₈	direct (N × H)
46. C₂⁵	C₂×C₈×C₄₇	direct (N × H)
50. C₂²×C₈	C₂⁴×C₄₇	direct (N × H)
51. C₂⁴	C₂²×C₈×C₄₇	direct (N × H)
55. C₂×C₈	C₂⁵×C₄₇	direct (N × H)
56. C₂³	C₂³×C₈×C₄₇	direct (N × H)
60. C₈	C₂⁶×C₄₇	direct (N × H)
61. C₂²	C₂⁴×C₈×C₄₇	direct (N × H)
65. C₂	C₂⁵×C₈×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
C₂⁶×C₄×C₄₇	2
C₂⁵×C₈×C₄₇	2
C₂⁶×C₈	47

Subgroups — C26×C8×C47 #72201370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×C₈×C₄₇ #72201370