Subgroups — C₃×C₉×C₁₃₉⋊C₉ #46798531

Order 33777.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃₉⋊C₉	C₃	1	3	yes	maximal
2	C₉×C₁₃₉⋊C₉	C₃	1	9	yes	maximal, direct product factor
3	C₃²×C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic
4	C₃×C₁₃₉⋊C₉	C₉	1	27	yes	direct product factor
5	C₃×C₁₃₉⋊C₉	C₃²	1	9	yes	—
6	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₁₃₉	C₉	1	9	yes	complemented
8	C₃×C₉×C₁₃₉	C₃²	1	3	yes	—
9	C₃²×C₁₃₉	C₃×C₉	1	9	yes	—
10	C₃²×C₁₃₉	C₃×C₉	1	3	yes	—
11	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
12	C₉×C₁₃₉	C₃×C₉	1	9	yes	complemented
13	C₁₃₉⋊C₉	C₃×C₉	1	27	yes	direct product factor
14	C₃×C₁₃₉	C₉²	1	9	yes	complemented
15	C₃×C₁₃₉	C₃²×C₉	1	3	yes	—
16	C₃×C₁₃₉	C₃²×C₉	1	1	yes	characteristic
17	C₃×C₉²	—	139	1	no	maximal, Sylow
18	C₁₃₉	C₃×C₉²	1	1	yes	characteristic, complemented, Sylow
19	C₃²×C₉	—	139	3	no	—
20	C₃²×C₉	C₁₃₉⋊C₃	1	1	yes	characteristic
21	C₉²	—	139	9	no	—
22	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
23	C₃×C₉	—	139	27	no	—
24	C₃×C₉	—	139	9	no	—
25	C₃×C₉	C₁₃₉⋊C₉	1	9	yes	direct product factor
26	C₃×C₉	C₃×C₁₃₉⋊C₃	1	3	yes	—
27	C₃²	C₉×C₁₃₉⋊C₃	1	9	yes	—
28	C₃²	C₃×C₁₃₉⋊C₉	1	3	yes	—
29	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
30	C₉	—	139	27	no	—
31	C₉	C₃×C₁₃₉⋊C₉	1	9	yes	direct product factor
32	C₃	C₉×C₁₃₉⋊C₉	1	9	yes	direct product factor
33	C₃	C₃×C₉×C₁₃₉⋊C₃	1	3	yes	—
34	C₃	C₃²×C₁₃₉⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₉	C₁₃₉⋊C₃
commutator, hypocenter	C₁₃₉	C₃×C₉²
Frattini	C₃²	C₃²×C₁₃₉⋊C₃
Fitting	C₃²×C₉×C₁₃₉	C₃
socle, prime radical	C₃³×C₁₃₉	C₃²
cosocle	C₃²×C₁₃₉	C₃³
LCS	G ▷ C₁₃₉
UCS	C₁ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. C₉×C₁₃₉⋊C₉	C₃	direct (N × H)
4. C₃×C₁₃₉⋊C₉	C₉	direct (N × H)
7. C₃×C₉×C₁₃₉	C₉	semidirect
12. C₉×C₁₃₉	C₃×C₉	semidirect
13. C₁₃₉⋊C₉	C₃×C₉	direct (N × H)
14. C₃×C₁₃₉	C₉²	semidirect
18. C₁₃₉	C₃×C₉²	semidirect
25. C₃×C₉	C₁₃₉⋊C₉	direct (N × H)
31. C₉	C₃×C₁₃₉⋊C₉	direct (N × H)
32. C₃	C₉×C₁₃₉⋊C₉	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×C₁₃₉⋊C₉	3
C₉×C₁₃₉⋊C₉	3
C₃²×C₉×C₁₃₉	3
C₃×C₉²	139

Subgroups — C3×C9×C139⋊C9 #46798531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×C₁₃₉⋊C₉ #46798531