Subgroups — #21419306

Order 7533.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719689	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic
3	(C₃₁⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
4	C₃²⋊(C₃₁⋊C₉)	C₃	1	1	yes	maximal, characteristic
5	C₉×C₃₁⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃₁×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
7	C₃³×C₃₁	C₃²	1	1	yes	characteristic
8	C₃×C₉×C₃₁	C₃²	1	3	yes	—
9	#11719689	C₉	1	9	yes	complemented
10	C₃×C₃₁⋊C₉	—	3	3	no	—
11	C₃×C₃₁⋊C₉	C₃²	1	3	yes	—
12	C₃×C₃₁⋊C₉	C₃²	1	2	yes	—
13	C₃×C₃₁⋊C₉	C₃²	1	3	yes	—
14	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
15	C₃²×C₃₁	—	3	1	no	—
16	C₃²×C₃₁	—	3	1	no	—
17	C₃²×C₃₁	—	3	1	no	—
18	C₃²×C₃₁	C₃×C₉	1	3	yes	—
19	C₃²×C₃₁	C₃³	1	1	yes	characteristic
20	C₉×C₃₁	—	3	3	no	—
21	C₃₁⋊C₉	—	3	2	no	—
22	C₃₁⋊C₉	—	3	3	no	—
23	C₃₁⋊C₉	C₃×C₉	1	9	yes	complemented
24	C₃₁⋊C₉	3₋¹⁺²	1	3	yes	complemented
25	C₉×3₋¹⁺²	—	31	1	no	maximal, Sylow
26	C₃×C₃₁	—	3	3	no	—
27	C₃×C₃₁	C₃²×C₉	1	1	yes	characteristic
28	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₃₁	#737	1	1	yes	characteristic
30	C₃×C₃₁	#737	1	1	yes	characteristic
31	C₃×3₋¹⁺²	—	31	1	no	—
32	C₃²×C₉	—	31	1	no	—
33	C₉⋊C₉	—	31	6	no	—
34	C₃²⋊C₉	—	31	1	no	—
35	C₃²⋊C₉	C₃₁⋊C₃	1	1	yes	characteristic
36	C₉²	—	31	3	no	—
37	C₃₁	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
38	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
39	3₋¹⁺²	—	31	9	no	—
40	C₃×C₉	—	31	1	no	—
41	C₃×C₉	—	31	3	no	—
42	C₃×C₉	—	31	3	no	—
43	C₃×C₉	—	31	2	no	—
44	C₃×C₉	—	93	3	no	—
45	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
46	C₃²	—	3	1	no	—
47	C₃²	—	3	1	no	—
48	C₃²	—	3	1	no	—
49	C₃²	C₉×C₃₁⋊C₃	1	3	yes	—
50	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
51	C₉	—	3	3	no	—
52	C₉	—	31	9	no	—
53	C₉	—	31	3	no	—
54	C₉	—	93	2	no	—
55	C₉	—	93	3	no	—
56	C₃	—	3	3	no	—
57	C₃	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic
58	C₃	3₋¹⁺²×C₃₁⋊C₃	1	1	yes	characteristic
59	C₃	#14578911	1	1	yes	characteristic
60	C₃	#14578913	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃²×C₉
Fitting	C₃₁×C₃²⋊C₉	C₃
socle	C₃²×C₃₁	C₃³
hypercenter	C₃²⋊C₉	C₃₁⋊C₃
hypocenter	C₃₁	C₉×3₋¹⁺²
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
5. C₉×C₃₁⋊C₉	C₃	semidirect
9. #11719689	C₉	semidirect
23. C₃₁⋊C₉	C₃×C₉	semidirect
24. C₃₁⋊C₉	3₋¹⁺²	semidirect
37. C₃₁	C₉×3₋¹⁺²	semidirect