Subgroups — C₂⁶×C₉×C₄₉ #72205246

Order 28224.

25425 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₉×C₄₉	C₂	1	63	yes	maximal, direct product factor
2	C₂⁶×C₃×C₄₉	C₃	1	1	yes	maximal, characteristic
3	C₂⁴×C₉×C₄₉	C₂²	1	651	yes	direct product factor
4	C₂⁵×C₃×C₄₉	C₂×C₃	1	63	yes	—
5	C₂⁶×C₇×C₉	C₇	1	1	yes	maximal, characteristic
6	C₂³×C₉×C₄₉	C₂³	1	1395	yes	direct product factor
7	C₂⁶×C₄₉	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂⁴×C₃×C₄₉	C₂²×C₃	1	651	yes	—
9	C₂⁵×C₇×C₉	C₂×C₇	1	63	yes	—
10	C₂²×C₉×C₄₉	C₂⁴	1	651	yes	direct product factor
11	C₂⁵×C₄₉	C₂×C₉	1	63	yes	direct product factor
12	C₂⁶×C₃×C₇	C₃×C₇	1	1	yes	characteristic
13	C₂³×C₃×C₄₉	C₂³×C₃	1	1395	yes	—
14	C₂⁴×C₇×C₉	C₂²×C₇	1	651	yes	—
15	C₂×C₉×C₄₉	C₂⁵	1	63	yes	direct product factor
16	C₂⁴×C₄₉	C₂²×C₉	1	651	yes	direct product factor
17	C₂⁵×C₃×C₇	C₂×C₃×C₇	1	63	yes	—
18	C₂²×C₃×C₄₉	C₂⁴×C₃	1	651	yes	—
19	C₂⁶×C₉	C₄₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂³×C₇×C₉	C₂³×C₇	1	1395	yes	—
21	C₂⁶×C₇	C₇×C₉	1	1	yes	characteristic
22	C₉×C₄₉	C₂⁶	1	1	yes	characteristic, direct product factor, Hall
23	C₂³×C₄₉	C₂³×C₉	1	1395	yes	direct product factor
24	C₂⁴×C₃×C₇	C₂²×C₃×C₇	1	651	yes	—
25	C₂×C₃×C₄₉	C₂⁵×C₃	1	63	yes	—
26	C₂⁵×C₉	C₂×C₄₉	1	63	yes	direct product factor
27	C₂²×C₇×C₉	C₂⁴×C₇	1	651	yes	—
28	C₂⁵×C₇	C₂×C₇×C₉	1	63	yes	—
29	C₂²×C₄₉	C₂⁴×C₉	1	651	yes	direct product factor
30	C₂⁶×C₃	C₃×C₄₉	1	1	yes	characteristic
31	C₂³×C₃×C₇	C₂³×C₃×C₇	1	1395	yes	—
32	C₃×C₄₉	C₂⁶×C₃	1	1	yes	characteristic
33	C₂⁴×C₉	C₂²×C₄₉	1	651	yes	direct product factor
34	C₂×C₇×C₉	C₂⁵×C₇	1	63	yes	—
35	C₂⁴×C₇	C₂²×C₇×C₉	1	651	yes	—
36	C₂×C₄₉	C₂⁵×C₉	1	63	yes	direct product factor
37	C₂⁵×C₃	C₂×C₃×C₄₉	1	63	yes	—
38	C₂²×C₃×C₇	C₂⁴×C₃×C₇	1	651	yes	—
39	C₂³×C₉	C₂³×C₄₉	1	1395	yes	direct product factor
40	C₂⁶	C₉×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₇×C₉	C₂⁶×C₇	1	1	yes	characteristic
42	C₂³×C₇	C₂³×C₇×C₉	1	1395	yes	—
43	C₄₉	C₂⁶×C₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₂⁴×C₃	C₂²×C₃×C₄₉	1	651	yes	—
45	C₂×C₃×C₇	C₂⁵×C₃×C₇	1	63	yes	—
46	C₂²×C₉	C₂⁴×C₄₉	1	651	yes	direct product factor
47	C₂⁵	C₂×C₉×C₄₉	1	63	yes	direct product factor
48	C₂²×C₇	C₂⁴×C₇×C₉	1	651	yes	—
49	C₂³×C₃	C₂³×C₃×C₄₉	1	1395	yes	—
50	C₃×C₇	C₂⁶×C₃×C₇	1	1	yes	characteristic
51	C₂×C₉	C₂⁵×C₄₉	1	63	yes	direct product factor
52	C₂⁴	C₂²×C₉×C₄₉	1	651	yes	direct product factor
53	C₂×C₇	C₂⁵×C₇×C₉	1	63	yes	—
54	C₂²×C₃	C₂⁴×C₃×C₄₉	1	651	yes	—
55	C₉	C₂⁶×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₂³	C₂³×C₉×C₄₉	1	1395	yes	direct product factor
57	C₇	C₂⁶×C₇×C₉	1	1	yes	characteristic
58	C₂×C₃	C₂⁵×C₃×C₄₉	1	63	yes	—
59	C₂²	C₂⁴×C₉×C₄₉	1	651	yes	direct product factor
60	C₃	C₂⁶×C₃×C₄₉	1	1	yes	characteristic
61	C₂	C₂⁵×C₉×C₄₉	1	63	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₇	C₂⁶×C₃×C₇
socle, prime radical	C₂⁶×C₃×C₇	C₃×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₉×C₄₉	C₂	direct (N × H)
3. C₂⁴×C₉×C₄₉	C₂²	direct (N × H)
6. C₂³×C₉×C₄₉	C₂³	direct (N × H)
7. C₂⁶×C₄₉	C₉	direct (N × H)
10. C₂²×C₉×C₄₉	C₂⁴	direct (N × H)
11. C₂⁵×C₄₉	C₂×C₉	direct (N × H)
15. C₂×C₉×C₄₉	C₂⁵	direct (N × H)
16. C₂⁴×C₄₉	C₂²×C₉	direct (N × H)
19. C₂⁶×C₉	C₄₉	direct (N × H)
22. C₉×C₄₉	C₂⁶	direct (N × H)
23. C₂³×C₄₉	C₂³×C₉	direct (N × H)
26. C₂⁵×C₉	C₂×C₄₉	direct (N × H)
29. C₂²×C₄₉	C₂⁴×C₉	direct (N × H)
33. C₂⁴×C₉	C₂²×C₄₉	direct (N × H)
36. C₂×C₄₉	C₂⁵×C₉	direct (N × H)
39. C₂³×C₉	C₂³×C₄₉	direct (N × H)
40. C₂⁶	C₉×C₄₉	direct (N × H)
43. C₄₉	C₂⁶×C₉	direct (N × H)
46. C₂²×C₉	C₂⁴×C₄₉	direct (N × H)
47. C₂⁵	C₂×C₉×C₄₉	direct (N × H)
51. C₂×C₉	C₂⁵×C₄₉	direct (N × H)
52. C₂⁴	C₂²×C₉×C₄₉	direct (N × H)
55. C₉	C₂⁶×C₄₉	direct (N × H)
56. C₂³	C₂³×C₉×C₄₉	direct (N × H)
59. C₂²	C₂⁴×C₉×C₄₉	direct (N × H)
61. C₂	C₂⁵×C₉×C₄₉	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×C₉×C₄₉	2
C₂⁶×C₃×C₄₉	3
C₂⁶×C₇×C₉	7

Subgroups — C26×C9×C49 #72205246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×C₉×C₄₉ #72205246