Subgroups — C₃²×C₉×C₃₁⋊C₃ #21419422

Order 7533.

792 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₃₁⋊C₉	C₃	1	2	yes	maximal, complemented
3	C₃×C₉×C₃₁⋊C₃	C₃	1	36	yes	maximal, direct product factor
4	C₃²×C₉×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₁	C₃²	1	1	yes	characteristic
6	C₃²×C₃₁⋊C₃	C₉	1	27	yes	direct product factor
7	C₃²×C₃₁⋊C₃	C₃²	1	12	yes	—
8	C₃×C₉×C₃₁	C₃²	1	12	yes	complemented
9	C₃×C₃₁⋊C₉	C₃²	1	24	yes	complemented
10	C₉×C₃₁⋊C₃	C₃²	1	81	yes	direct product factor
11	C₃²×C₃₁	C₃×C₉	1	9	yes	complemented
12	C₃²×C₃₁	C₃³	1	4	yes	—
13	C₃×C₃₁⋊C₃	C₃×C₉	1	108	yes	direct product factor
14	C₃×C₃₁⋊C₃	C₃³	1	9	yes	—
15	C₉×C₃₁	C₃³	1	9	yes	complemented
16	C₃₁⋊C₉	C₃³	1	18	yes	complemented
17	C₃³×C₉	—	31	1	no	maximal, Sylow
18	C₃×C₃₁	C₃²×C₉	1	12	yes	complemented
19	C₃×C₃₁	C₃⁴	1	1	yes	characteristic
20	C₃₁⋊C₃	C₃²×C₉	1	27	yes	direct product factor
21	C₃⁴	—	31	1	no	—
22	C₃²×C₉	—	31	2	no	—
23	C₃²×C₉	—	31	36	no	—
24	C₃²×C₉	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
25	C₃₁	C₃³×C₉	1	1	yes	characteristic, complemented, Sylow
26	C₃³	—	31	27	no	—
27	C₃³	—	31	12	no	—
28	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
29	C₃×C₉	—	31	24	no	—
30	C₃×C₉	—	31	81	no	—
31	C₃×C₉	C₃×C₃₁⋊C₃	1	12	yes	direct product factor
32	C₃²	—	31	108	no	—
33	C₃²	—	31	9	no	—
34	C₃²	C₉×C₃₁⋊C₃	1	9	yes	direct product factor
35	C₃²	C₃²×C₃₁⋊C₃	1	4	yes	—
36	C₉	—	31	18	no	—
37	C₉	C₃²×C₃₁⋊C₃	1	9	yes	direct product factor
38	C₃	—	31	27	no	—
39	C₃	C₃×C₉×C₃₁⋊C₃	1	12	yes	direct product factor
40	C₃	C₃³×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₉	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₃³×C₉
Frattini	C₃	C₃³×C₃₁⋊C₃
Fitting	C₃²×C₉×C₃₁	C₃
socle	C₃³×C₃₁	C₃²
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. C₃²×C₃₁⋊C₉	C₃	semidirect
3. C₃×C₉×C₃₁⋊C₃	C₃	direct (N × H)
4. C₃²×C₉×C₃₁	C₃	semidirect
6. C₃²×C₃₁⋊C₃	C₉	direct (N × H)
8. C₃×C₉×C₃₁	C₃²	semidirect
9. C₃×C₃₁⋊C₉	C₃²	semidirect
10. C₉×C₃₁⋊C₃	C₃²	direct (N × H)
11. C₃²×C₃₁	C₃×C₉	semidirect
13. C₃×C₃₁⋊C₃	C₃×C₉	direct (N × H)
15. C₉×C₃₁	C₃³	semidirect
16. C₃₁⋊C₉	C₃³	semidirect
18. C₃×C₃₁	C₃²×C₉	semidirect
20. C₃₁⋊C₃	C₃²×C₉	direct (N × H)
24. C₃²×C₉	C₃₁⋊C₃	direct (N × H)
25. C₃₁	C₃³×C₉	semidirect
31. C₃×C₉	C₃×C₃₁⋊C₃	direct (N × H)
34. C₃²	C₉×C₃₁⋊C₃	direct (N × H)
37. C₉	C₃²×C₃₁⋊C₃	direct (N × H)
39. C₃	C₃×C₉×C₃₁⋊C₃	direct (N × H)

Subgroups — C32×C9×C31⋊C3 #21419422

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₉×C₃₁⋊C₃ #21419422