Subgroups — #21419326

Order 7533.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic
2	(C₃₁⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
3	(C₃₁⋊C₉)⋊C₉	C₃	1	3	yes	maximal, complemented
4	C₃²⋊(C₃₁⋊C₉)	C₃	1	2	yes	maximal
5	C₃×3₋¹⁺²×C₃₁	C₃	1	1	yes	maximal, characteristic
6	C₃³×C₃₁	C₃²	1	1	yes	characteristic
7	3₋¹⁺²×C₃₁	—	3	3	no	—
8	C₃×C₉×C₃₁	C₃²	1	3	yes	—
9	C₃×C₃₁⋊C₉	—	3	3	no	—
10	C₃×C₃₁⋊C₉	C₃²	1	6	yes	—
11	C₃×C₃₁⋊C₉	C₃²	1	2	yes	—
12	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
13	C₃²×C₃₁	—	3	1	no	—
14	C₃²×C₃₁	—	3	2	no	—
15	C₃²×C₃₁	3₋¹⁺²	1	3	yes	—
16	C₃²×C₃₁	C₃³	1	1	yes	characteristic
17	C₉×C₃₁	—	3	3	no	—
18	C₃₁⋊C₉	—	3	2	no	—
19	C₃₁⋊C₉	—	3	6	no	—
20	C₃₁⋊C₉	3₋¹⁺²	1	3	yes	complemented
21	#6894	—	31	1	no	maximal, Sylow
22	C₃×C₃₁	—	3	3	no	—
23	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
24	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
25	C₃×C₃₁	#737	1	2	yes	—
26	C₃×3₋¹⁺²	C₃₁⋊C₃	1	1	yes	characteristic
27	C₃²×C₉	—	31	1	no	—
28	C₉⋊C₉	—	31	3	no	—
29	C₉⋊C₉	—	31	6	no	—
30	C₃²⋊C₉	—	31	2	no	—
31	C₃₁	#6894	1	1	yes	characteristic, complemented, Sylow
32	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
33	3₋¹⁺²	—	3	3	no	—
34	C₃×C₉	—	31	1	no	—
35	C₃×C₉	—	31	6	no	—
36	C₃×C₉	—	31	2	no	—
37	C₃×C₉	—	93	3	no	—
38	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
39	C₃²	—	3	1	no	—
40	C₃²	—	3	2	no	—
41	C₃²	#11719689	1	3	yes	—
42	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
43	C₉	—	3	3	no	—
44	C₉	—	31	3	no	—
45	C₉	—	93	2	no	—
46	C₉	—	93	6	no	—
47	C₃	—	3	3	no	—
48	C₃	3₋¹⁺²×C₃₁⋊C₃	1	1	yes	characteristic
49	C₃	C₃×#11719689	1	1	yes	characteristic
50	C₃	#14578913	1	2	yes	—

	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	#6894
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. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
3. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
20. C₃₁⋊C₉	3₋¹⁺²	semidirect
31. C₃₁	#6894	semidirect