Subgroups — C₃×#14578892 #21419369

Order 7533.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578892	C₃	1	9	yes	maximal, direct product factor
2	C₃×C₃₁⋊C₂₇	C₃	1	3	yes	maximal, complemented
3	C₃²×C₉×C₃₁	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₃₁	C₉	1	1	yes	characteristic
5	C₃×C₉×C₃₁	C₉	1	6	yes	—
6	C₃×C₉×C₃₁	C₉	1	2	yes	—
7	C₃×C₉×C₃₁	C₃²	1	3	yes	—
8	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
9	C₃₁⋊C₂₇	C₃²	1	9	yes	complemented
10	C₃²×C₃₁	—	3	3	no	—
11	C₃²×C₃₁	C₃×C₉	1	3	yes	—
12	C₃²×C₃₁	C₃×C₉	1	1	yes	characteristic
13	C₉×C₃₁	C₃×C₉	1	6	yes	—
14	C₉×C₃₁	C₃×C₉	1	2	yes	—
15	C₉×C₃₁	C₃³	1	1	yes	characteristic
16	C₃×C₂₇⋊C₃	—	31	1	no	maximal, Sylow
17	C₃×C₃₁	—	3	3	no	—
18	C₃×C₃₁	C₂₇⋊C₃	1	3	yes	complemented
19	C₃×C₃₁	C₃²×C₉	1	1	yes	characteristic
20	C₃²×C₉	C₃₁⋊C₃	1	1	yes	characteristic
21	C₂₇⋊C₃	—	31	9	no	—
22	C₃×C₂₇	—	31	3	no	—
23	C₃₁	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃³	C₃₁⋊C₉	1	1	yes	characteristic
25	C₃×C₉	C₃₁⋊C₉	1	2	yes	—
26	C₃×C₉	C₃₁⋊C₉	1	6	yes	—
27	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
28	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
29	C₂₇	—	31	9	no	—
30	C₃²	—	3	3	no	—
31	C₃²	C₃×C₃₁⋊C₉	1	3	yes	—
32	C₃²	C₃×C₃₁⋊C₉	1	1	yes	characteristic
33	C₉	C₃×C₃₁⋊C₉	1	6	yes	—
34	C₉	C₃×C₃₁⋊C₉	1	2	yes	—
35	C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
36	C₃	—	3	3	no	—
37	C₃	#14578892	1	3	yes	direct product factor
38	C₃	C₃²×C₃₁⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃²×C₉
Frattini	C₉	C₃²×C₃₁⋊C₃
Fitting	C₃²×C₉×C₃₁	C₃
socle	C₃²×C₃₁	C₃×C₉
hypercenter	C₃²×C₉	C₃₁⋊C₃
hypocenter	C₃₁	C₃×C₂₇⋊C₃
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #14578892	C₃	direct (N × H)
2. C₃×C₃₁⋊C₂₇	C₃	semidirect
9. C₃₁⋊C₂₇	C₃²	semidirect
18. C₃×C₃₁	C₂₇⋊C₃	semidirect
23. C₃₁	C₃×C₂₇⋊C₃	semidirect
37. C₃	#14578892	direct (N × H)

Subgroups — C3×#14578892 #21419369

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#14578892 #21419369