Subgroups — C₃×C₉×C₂₇×C₄₇ #46804319

Order 34263.

404 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₇×C₄₇	C₃	1	3	yes	maximal
2	C₃×C₉²×C₄₇	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₇×C₄₇	C₃	1	9	yes	maximal, direct product factor
4	C₃²×C₉×C₄₇	C₉	1	3	yes	—
5	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
6	C₃×C₂₇×C₄₇	C₉	1	27	yes	direct product factor
7	C₃×C₂₇×C₄₇	C₃²	1	9	yes	—
8	C₉²×C₄₇	C₉	1	6	yes	—
9	C₉²×C₄₇	C₃²	1	3	yes	—
10	C₃³×C₄₇	C₃×C₉	1	1	yes	characteristic
11	C₃×C₉×C₄₇	C₂₇	1	27	yes	direct product factor
12	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
13	C₃×C₉×C₄₇	C₃×C₉	1	9	yes	—
14	C₃×C₉×C₄₇	C₃×C₉	1	9	yes	—
15	C₃×C₉×C₄₇	C₃³	1	1	yes	characteristic
16	C₂₇×C₄₇	C₃×C₉	1	27	yes	direct product factor
17	C₃×C₉×C₂₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃²×C₄₇	C₉²	1	3	yes	—
19	C₃²×C₄₇	C₃×C₂₇	1	9	yes	—
20	C₃²×C₄₇	C₃²×C₉	1	1	yes	characteristic
21	C₉×C₄₇	C₉²	1	6	yes	—
22	C₉×C₄₇	C₃×C₂₇	1	27	yes	direct product factor
23	C₉×C₄₇	C₃²×C₉	1	3	yes	—
24	C₃²×C₂₇	C₃×C₄₇	1	3	yes	—
25	C₃×C₉²	C₃×C₄₇	1	1	yes	characteristic
26	C₉×C₂₇	C₃×C₄₇	1	9	yes	direct product factor
27	C₃×C₄₇	C₉×C₂₇	1	9	yes	direct product factor
28	C₃×C₄₇	C₃×C₉²	1	1	yes	characteristic
29	C₃×C₄₇	C₃²×C₂₇	1	3	yes	—
30	C₃²×C₉	C₉×C₄₇	1	3	yes	—
31	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
32	C₃×C₂₇	C₉×C₄₇	1	27	yes	direct product factor
33	C₃×C₂₇	C₃²×C₄₇	1	9	yes	—
34	C₉²	C₉×C₄₇	1	6	yes	—
35	C₉²	C₃²×C₄₇	1	3	yes	—
36	C₄₇	C₃×C₉×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
37	C₃³	C₃×C₉×C₄₇	1	1	yes	characteristic
38	C₃×C₉	C₂₇×C₄₇	1	27	yes	direct product factor
39	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
40	C₃×C₉	C₃×C₉×C₄₇	1	9	yes	—
41	C₃×C₉	C₃×C₉×C₄₇	1	9	yes	—
42	C₃×C₉	C₃³×C₄₇	1	1	yes	characteristic
43	C₂₇	C₃×C₉×C₄₇	1	27	yes	direct product factor
44	C₃²	C₉²×C₄₇	1	3	yes	—
45	C₃²	C₃×C₂₇×C₄₇	1	9	yes	—
46	C₃²	C₃²×C₉×C₄₇	1	1	yes	characteristic
47	C₉	C₉²×C₄₇	1	6	yes	—
48	C₉	C₃×C₂₇×C₄₇	1	27	yes	direct product factor
49	C₉	C₃²×C₉×C₄₇	1	3	yes	—
50	C₃	C₉×C₂₇×C₄₇	1	9	yes	direct product factor
51	C₃	C₃×C₉²×C₄₇	1	1	yes	characteristic
52	C₃	C₃²×C₂₇×C₄₇	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₉	C₃³×C₄₇
socle, prime radical	C₃³×C₄₇	C₃×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×C₂₇×C₄₇	C₃	direct (N × H)
6. C₃×C₂₇×C₄₇	C₉	direct (N × H)
11. C₃×C₉×C₄₇	C₂₇	direct (N × H)
16. C₂₇×C₄₇	C₃×C₉	direct (N × H)
17. C₃×C₉×C₂₇	C₄₇	direct (N × H)
22. C₉×C₄₇	C₃×C₂₇	direct (N × H)
26. C₉×C₂₇	C₃×C₄₇	direct (N × H)
27. C₃×C₄₇	C₉×C₂₇	direct (N × H)
32. C₃×C₂₇	C₉×C₄₇	direct (N × H)
36. C₄₇	C₃×C₉×C₂₇	direct (N × H)
38. C₃×C₉	C₂₇×C₄₇	direct (N × H)
43. C₂₇	C₃×C₉×C₄₇	direct (N × H)
48. C₉	C₃×C₂₇×C₄₇	direct (N × H)
50. C₃	C₉×C₂₇×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
C₃²×C₂₇×C₄₇	3
C₃×C₉²×C₄₇	3
C₉×C₂₇×C₄₇	3
C₃×C₉×C₂₇	47

Subgroups — C3×C9×C27×C47 #46804319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×C₂₇×C₄₇ #46804319