Subgroups — C₃×#14578890 #21419367

Order 7533.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#14578890	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₃₁⋊C₂₇	C₃	1	2	yes	maximal, complemented
4	C₃×C₂₇×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₃₁⋊C₃	C₉	1	1	yes	characteristic
6	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
7	C₃×C₃₁⋊C₉	C₉	1	2	yes	—
8	C₉×C₃₁⋊C₃	C₉	1	6	yes	—
9	C₉×C₃₁⋊C₃	C₃²	1	3	yes	—
10	C₂₇×C₃₁	C₃²	1	3	yes	complemented
11	C₃₁⋊C₂₇	C₃²	1	6	yes	complemented
12	C₃²×C₃₁	C₃×C₉	1	1	yes	characteristic
13	C₃×C₃₁⋊C₃	—	3	3	no	—
14	C₃×C₃₁⋊C₃	C₃×C₉	1	3	yes	—
15	C₉×C₃₁	C₃×C₉	1	2	yes	—
16	C₉×C₃₁	C₃³	1	1	yes	characteristic
17	C₃₁⋊C₉	C₃×C₉	1	6	yes	—
18	C₃×C₂₇⋊C₃	—	31	1	no	maximal, Sylow
19	C₃×C₃₁	C₂₇⋊C₃	1	3	yes	complemented
20	C₃×C₃₁	C₃²×C₉	1	1	yes	characteristic
21	C₃₁⋊C₃	—	3	3	no	—
22	C₃²×C₉	—	31	1	no	—
23	C₂₇⋊C₃	—	31	9	no	—
24	C₃×C₂₇	—	31	2	no	—
25	C₃×C₂₇	C₃₁⋊C₃	1	1	yes	characteristic, complemented
26	C₃₁	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃³	—	31	1	no	—
28	C₃×C₉	—	31	2	no	—
29	C₃×C₉	—	31	6	no	—
30	C₃×C₉	—	31	3	no	—
31	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
32	C₂₇	—	31	6	no	—
33	C₂₇	C₃×C₃₁⋊C₃	1	3	yes	complemented
34	C₃²	—	31	3	no	—
35	C₃²	—	93	3	no	—
36	C₃²	C₉×C₃₁⋊C₃	1	1	yes	characteristic
37	C₉	—	31	6	no	—
38	C₉	C₉×C₃₁⋊C₃	1	2	yes	—
39	C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
40	C₃	—	93	3	no	—
41	C₃	#14578890	1	3	yes	direct product factor
42	C₃	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #14578890	C₃	direct (N × H)
3. C₃×C₃₁⋊C₂₇	C₃	semidirect
4. C₃×C₂₇×C₃₁	C₃	semidirect
10. C₂₇×C₃₁	C₃²	semidirect
11. C₃₁⋊C₂₇	C₃²	semidirect
19. C₃×C₃₁	C₂₇⋊C₃	semidirect
25. C₃×C₂₇	C₃₁⋊C₃	semidirect
26. C₃₁	C₃×C₂₇⋊C₃	semidirect
33. C₂₇	C₃×C₃₁⋊C₃	semidirect
41. C₃	#14578890	direct (N × H)

Subgroups — C3×#14578890 #21419367

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#14578890 #21419367