Subgroups — C₃²×C₇×C₉×C₄₉ #72204841

Order 27783.

900 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₇×C₄₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₇×C₉×C₄₉	C₃	1	12	yes	maximal, direct product factor
3	C₃²×C₇²×C₉	C₇	1	1	yes	maximal, characteristic
4	C₃²×C₉×C₄₉	C₇	1	7	yes	maximal, direct product factor
5	C₃²×C₇×C₄₉	C₉	1	9	yes	direct product factor
6	C₃²×C₇×C₄₉	C₃²	1	4	yes	—
7	C₇×C₉×C₄₉	C₃²	1	9	yes	direct product factor
8	C₃³×C₇²	C₃×C₇	1	1	yes	characteristic
9	C₃×C₇²×C₉	C₃×C₇	1	12	yes	—
10	C₃³×C₄₉	C₃×C₇	1	7	yes	—
11	C₃×C₉×C₄₉	C₃×C₇	1	84	yes	direct product factor
12	C₃×C₇×C₄₉	C₃×C₉	1	12	yes	direct product factor
13	C₃×C₇×C₄₉	C₃³	1	1	yes	characteristic
14	C₃²×C₇×C₉	C₄₉	1	7	yes	direct product factor
15	C₃²×C₇×C₉	C₇²	1	1	yes	characteristic
16	C₃²×C₇²	C₇×C₉	1	9	yes	—
17	C₃²×C₇²	C₃²×C₇	1	4	yes	—
18	C₇²×C₉	C₃²×C₇	1	9	yes	—
19	C₃²×C₄₉	C₇×C₉	1	63	yes	direct product factor
20	C₃²×C₄₉	C₃²×C₇	1	28	yes	—
21	C₉×C₄₉	C₃²×C₇	1	63	yes	direct product factor
22	C₇×C₄₉	C₃²×C₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₃³×C₇	C₃×C₄₉	1	7	yes	—
24	C₃³×C₇	C₃×C₇²	1	1	yes	characteristic
25	C₃×C₇×C₉	C₃×C₄₉	1	84	yes	direct product factor
26	C₃×C₇×C₉	C₃×C₇²	1	12	yes	—
27	C₃×C₇²	C₃×C₇×C₉	1	12	yes	—
28	C₃×C₇²	C₃³×C₇	1	1	yes	characteristic
29	C₃×C₄₉	C₃×C₇×C₉	1	84	yes	direct product factor
30	C₃×C₄₉	C₃³×C₇	1	7	yes	—
31	C₃²×C₉	C₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₃²×C₇	C₉×C₄₉	1	63	yes	direct product factor
33	C₃²×C₇	C₃²×C₄₉	1	28	yes	—
34	C₃²×C₇	C₇²×C₉	1	9	yes	—
35	C₃²×C₇	C₃²×C₇²	1	4	yes	—
36	C₇×C₉	C₃²×C₄₉	1	63	yes	direct product factor
37	C₇×C₉	C₃²×C₇²	1	9	yes	—
38	C₇²	C₃²×C₇×C₉	1	1	yes	characteristic
39	C₄₉	C₃²×C₇×C₉	1	7	yes	direct product factor
40	C₃³	C₃×C₇×C₄₉	1	1	yes	characteristic
41	C₃×C₉	C₃×C₇×C₄₉	1	12	yes	direct product factor
42	C₃×C₇	C₃×C₉×C₄₉	1	84	yes	direct product factor
43	C₃×C₇	C₃³×C₄₉	1	7	yes	—
44	C₃×C₇	C₃×C₇²×C₉	1	12	yes	—
45	C₃×C₇	C₃³×C₇²	1	1	yes	characteristic
46	C₃²	C₇×C₉×C₄₉	1	9	yes	direct product factor
47	C₃²	C₃²×C₇×C₄₉	1	4	yes	—
48	C₉	C₃²×C₇×C₄₉	1	9	yes	direct product factor
49	C₇	C₃²×C₉×C₄₉	1	7	yes	direct product factor
50	C₇	C₃²×C₇²×C₉	1	1	yes	characteristic
51	C₃	C₃×C₇×C₉×C₄₉	1	12	yes	direct product factor
52	C₃	C₃³×C₇×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₇	C₃³×C₇²
socle, prime radical	C₃³×C₇²	C₃×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×C₉×C₄₉	C₃	direct (N × H)
4. C₃²×C₉×C₄₉	C₇	direct (N × H)
5. C₃²×C₇×C₄₉	C₉	direct (N × H)
7. C₇×C₉×C₄₉	C₃²	direct (N × H)
11. C₃×C₉×C₄₉	C₃×C₇	direct (N × H)
12. C₃×C₇×C₄₉	C₃×C₉	direct (N × H)
14. C₃²×C₇×C₉	C₄₉	direct (N × H)
19. C₃²×C₄₉	C₇×C₉	direct (N × H)
21. C₉×C₄₉	C₃²×C₇	direct (N × H)
22. C₇×C₄₉	C₃²×C₉	direct (N × H)
25. C₃×C₇×C₉	C₃×C₄₉	direct (N × H)
29. C₃×C₄₉	C₃×C₇×C₉	direct (N × H)
31. C₃²×C₉	C₇×C₄₉	direct (N × H)
32. C₃²×C₇	C₉×C₄₉	direct (N × H)
36. C₇×C₉	C₃²×C₄₉	direct (N × H)
39. C₄₉	C₃²×C₇×C₉	direct (N × H)
41. C₃×C₉	C₃×C₇×C₄₉	direct (N × H)
42. C₃×C₇	C₃×C₉×C₄₉	direct (N × H)
46. C₃²	C₇×C₉×C₄₉	direct (N × H)
48. C₉	C₃²×C₇×C₄₉	direct (N × H)
49. C₇	C₃²×C₉×C₄₉	direct (N × H)
51. C₃	C₃×C₇×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
C₃³×C₇×C₄₉	3
C₃×C₇×C₉×C₄₉	3
C₃²×C₇²×C₉	7
C₃²×C₉×C₄₉	7

Subgroups — C32×C7×C9×C49 #72204841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×C₉×C₄₉ #72204841