Subgroups — #21419341

Order 7533.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719686	C₃	1	1	yes	maximal, characteristic
2	C₃×#11719687	C₃	1	1	yes	maximal, characteristic
3	#14578886	C₃	1	2	yes	maximal, complemented
4	#14578886	C₃	1	1	yes	maximal, characteristic, complemented
5	(C₃₁⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
6	(C₃₁⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
7	(C₃×C₃₁⋊C₃)⋊C₉	C₃	1	2	yes	maximal
8	C₉×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	C₃₁×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
11	C₃×C₉×C₃₁	C₃²	1	2	yes	—
12	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
14	C₃×C₃₁⋊C₉	C₃²	1	2	yes	—
15	C₃×C₃₁⋊C₉	C₃²	1	2	yes	—
16	C₃×C₃₁⋊C₉	C₃²	1	2	yes	—
17	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
18	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
19	#11719687	—	3	3	no	—
20	#11719686	—	3	3	no	—
21	C₃²×C₃₁	C₃³	1	1	yes	characteristic
22	C₃×C₃₁⋊C₃	—	3	1	no	—
23	C₃×C₃₁⋊C₃	—	3	1	no	—
24	C₃×C₃₁⋊C₃	—	3	2	no	—
25	C₉×C₃₁	—	3	1	no	—
26	C₉×C₃₁	—	3	2	no	—
27	C₉×C₃₁	3₋¹⁺²	1	3	yes	complemented
28	C₃₁⋊C₉	—	3	1	no	—
29	C₃₁⋊C₉	—	3	2	no	—
30	C₃₁⋊C₉	—	3	2	no	—
31	C₃₁⋊C₉	—	3	2	no	—
32	C₃₁⋊C₉	3₋¹⁺²	1	3	yes	complemented
33	#6896	—	31	1	no	maximal, Sylow
34	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
36	C₃×C₃₁	#737	1	2	yes	—
37	C₃₁⋊C₃	—	9	1	no	—
38	C₃×3₋¹⁺²	—	31	1	no	—
39	C₃×3₋¹⁺²	—	31	1	no	—
40	C₉⋊C₉	—	31	2	no	—
41	C₉⋊C₉	—	31	2	no	—
42	C₉⋊C₉	—	31	2	no	—
43	C₉⋊C₉	—	31	1	no	—
44	C₉⋊C₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented
45	C₃²⋊C₉	—	31	2	no	—
46	C₉²	—	31	1	no	—
47	C₃₁	#6896	1	1	yes	characteristic, complemented, Sylow
48	C₃³	—	31	1	no	—
49	3₋¹⁺²	—	93	3	no	—
50	3₋¹⁺²	—	93	3	no	—
51	C₃×C₉	—	31	1	no	—
52	C₃×C₉	—	31	2	no	—
53	C₃×C₉	—	31	2	no	—
54	C₃×C₉	—	31	1	no	—
55	C₃×C₉	—	31	2	no	—
56	C₃×C₉	C₃×C₃₁⋊C₃	1	2	yes	—
57	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
58	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
59	C₃²	—	93	1	no	—
60	C₃²	—	93	1	no	—
61	C₃²	—	93	2	no	—
62	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
63	C₉	—	3	1	no	—
64	C₉	—	3	2	no	—
65	C₉	—	31	3	no	—
66	C₉	—	93	1	no	—
67	C₉	—	93	2	no	—
68	C₉	—	93	2	no	—
69	C₉	—	93	2	no	—
70	C₉	#11719686	1	3	yes	complemented
71	C₃	—	279	1	no	—
72	C₃	3₋¹⁺²×C₃₁⋊C₃	1	1	yes	characteristic
73	C₃	C₃×#11719686	1	1	yes	characteristic
74	C₃	#14578913	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₁⋊C₃
commutator, socle	C₃²×C₃₁	C₃³
Fitting	C₃₁×C₉⋊C₉	C₃
hypercenter	C₉⋊C₉	C₃₁⋊C₃
hypocenter	C₃₁	#6896
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
3. #14578886	C₃	semidirect
4. #14578886	C₃	semidirect
5. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
6. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
8. C₉×C₃₁⋊C₉	C₃	semidirect
9. C₃₁×C₉⋊C₉	C₃	semidirect
27. C₉×C₃₁	3₋¹⁺²	semidirect
32. C₃₁⋊C₉	3₋¹⁺²	semidirect
44. C₉⋊C₉	C₃₁⋊C₃	semidirect
47. C₃₁	#6896	semidirect
70. C₉	#11719686	semidirect