Subgroups — C₃×C₉⋊C₉×C₁₀₁ #37589420

Order 24543.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉×C₁₀₁	C₃	1	3	yes	maximal
2	C₃²×C₉×C₁₀₁	C₃	1	1	yes	maximal, characteristic
3	C₉⋊C₉×C₁₀₁	C₃	1	9	yes	maximal, direct product factor
4	C₃³×C₁₀₁	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₁₀₁	—	3	9	no	—
6	C₃×C₉×C₁₀₁	C₉	1	9	yes	complemented
7	C₃×C₉×C₁₀₁	C₃²	1	9	yes	—
8	C₃×C₉×C₁₀₁	C₃²	1	3	yes	—
9	C₃²×C₁₀₁	C₃×C₉	1	3	yes	—
10	C₃²×C₁₀₁	3₋¹⁺²	1	9	yes	—
11	C₃²×C₁₀₁	C₃³	1	1	yes	characteristic
12	C₉×C₁₀₁	—	3	9	no	—
13	C₉×C₁₀₁	C₃×C₉	1	9	yes	complemented
14	C₃×C₁₀₁	C₉⋊C₉	1	9	yes	direct product factor
15	C₃×C₁₀₁	C₃²×C₉	1	1	yes	characteristic
16	C₃×C₁₀₁	C₃×3₋¹⁺²	1	3	yes	—
17	C₃×C₉⋊C₉	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₁₀₁	C₃×C₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²×C₉	C₃×C₁₀₁	1	3	yes	—
20	C₃²×C₉	C₃×C₁₀₁	1	1	yes	characteristic
21	C₉⋊C₉	C₃×C₁₀₁	1	9	yes	direct product factor
22	C₃³	C₃²×C₁₀₁	1	1	yes	characteristic
23	C₃×C₉	—	3	9	no	—
24	C₃×C₉	C₉×C₁₀₁	1	9	yes	complemented
25	C₃×C₉	C₃²×C₁₀₁	1	9	yes	—
26	C₃×C₉	C₃²×C₁₀₁	1	3	yes	—
27	C₃²	C₃×C₉×C₁₀₁	1	3	yes	—
28	C₃²	3₋¹⁺²×C₁₀₁	1	9	yes	—
29	C₃²	C₃³×C₁₀₁	1	1	yes	characteristic
30	C₉	—	3	9	no	—
31	C₉	C₃×C₉×C₁₀₁	1	9	yes	complemented
32	C₃	C₉⋊C₉×C₁₀₁	1	9	yes	direct product factor
33	C₃	C₃²×C₉×C₁₀₁	1	1	yes	characteristic
34	C₃	C₃×3₋¹⁺²×C₁₀₁	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₃³×C₁₀₁	C₃²
commutator	C₃	C₃²×C₉×C₁₀₁
Frattini, cosocle	C₃²	C₃³×C₁₀₁
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉⋊C₉×C₁₀₁	C₃	direct (N × H)
6. C₃×C₉×C₁₀₁	C₉	semidirect
13. C₉×C₁₀₁	C₃×C₉	semidirect
14. C₃×C₁₀₁	C₉⋊C₉	direct (N × H)
17. C₃×C₉⋊C₉	C₁₀₁	direct (N × H)
18. C₁₀₁	C₃×C₉⋊C₉	direct (N × H)
21. C₉⋊C₉	C₃×C₁₀₁	direct (N × H)
24. C₃×C₉	C₉×C₁₀₁	semidirect
31. C₉	C₃×C₉×C₁₀₁	semidirect
32. C₃	C₉⋊C₉×C₁₀₁	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×C₉×C₁₀₁	3
C₉⋊C₉×C₁₀₁	3
C₃×C₉⋊C₉	101

Subgroups — C3×C9⋊C9×C101 #37589420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉⋊C₉×C₁₀₁ #37589420