Subgroups — #21419359

Order 7533.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719689	C₃	1	3	yes	maximal
2	#14578887	C₃	1	1	yes	maximal, characteristic, complemented
3	#14578886	C₃	1	1	yes	maximal, characteristic, complemented
4	(C₃₁⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₉×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×3₋¹⁺²×C₃₁	C₃	1	1	yes	maximal, characteristic
7	C₃³×C₃₁	C₃²	1	1	yes	characteristic
8	3₋¹⁺²×C₃₁	—	3	3	no	—
9	C₃×C₉×C₃₁	C₃²	1	2	yes	—
10	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
11	#11719689	—	3	9	no	—
12	C₃×C₃₁⋊C₉	C₃²	1	3	yes	—
13	C₃×C₃₁⋊C₉	C₃²	1	3	yes	—
14	C₃×C₃₁⋊C₉	C₃²	1	3	yes	—
15	C₃²×C₃₁	—	3	3	no	—
16	C₃²×C₃₁	—	3	1	no	—
17	C₃²×C₃₁	C₃³	1	1	yes	characteristic
18	C₉×C₃₁	—	3	2	no	—
19	C₉×C₃₁	3₋¹⁺²	1	3	yes	complemented
20	C₃₁⋊C₉	—	3	3	no	—
21	C₃₁⋊C₉	—	3	3	no	—
22	C₃₁⋊C₉	3₋¹⁺²	1	9	yes	complemented
23	#6900	—	31	1	no	maximal, Sylow
24	C₃×C₃₁	—	9	1	no	—
25	C₃×C₃₁	C₃×3₋¹⁺²	1	3	yes	—
26	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
27	C₃×3₋¹⁺²	—	31	3	no	—
28	C₃×3₋¹⁺²	C₃₁⋊C₃	1	1	yes	characteristic
29	C₉⋊C₉	—	31	6	no	—
30	C₉⋊C₉	—	31	1	no	—
31	C₉⋊C₉	—	31	1	no	—
32	C₉²	—	31	1	no	—
33	C₃₁	#6900	1	1	yes	characteristic, complemented, Sylow
34	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
35	3₋¹⁺²	—	3	3	no	—
36	3₋¹⁺²	—	93	9	no	—
37	C₃×C₉	—	31	3	no	—
38	C₃×C₉	—	31	3	no	—
39	C₃×C₉	—	31	3	no	—
40	C₃×C₉	C₃×C₃₁⋊C₃	1	2	yes	—
41	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
42	C₃²	—	3	3	no	—
43	C₃²	—	3	1	no	—
44	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
45	C₉	—	3	2	no	—
46	C₉	—	31	9	no	—
47	C₉	—	93	3	no	—
48	C₉	—	93	3	no	—
49	C₉	#11719689	1	3	yes	complemented
50	C₃	—	9	1	no	—
51	C₃	3₋¹⁺²×C₃₁⋊C₃	1	3	yes	—
52	C₃	C₃×#11719689	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₁⋊C₃
commutator, socle	C₃²×C₃₁	C₃³
Fitting	C₃×3₋¹⁺²×C₃₁	C₃
hypercenter	C₃×3₋¹⁺²	C₃₁⋊C₃
hypocenter	C₃₁	#6900
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #14578887	C₃	semidirect
3. #14578886	C₃	semidirect
4. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
5. C₉×C₃₁⋊C₉	C₃	semidirect
19. C₉×C₃₁	3₋¹⁺²	semidirect
22. C₃₁⋊C₉	3₋¹⁺²	semidirect
33. C₃₁	#6900	semidirect
49. C₉	#11719689	semidirect