Subgroups — #21419353

Order 7533.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719687	C₃	1	1	yes	maximal, characteristic
2	#14578887	C₃	1	2	yes	maximal, complemented
3	(C₃₁⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
4	(C₃×C₃₁⋊C₃)⋊C₉	C₃	1	3	yes	maximal
5	C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₃₁	C₃²	1	3	yes	—
8	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
9	C₃×C₃₁⋊C₉	C₃²	1	6	yes	—
10	C₃×C₃₁⋊C₉	C₃²	1	2	yes	—
11	#11719687	—	3	3	no	—
12	C₃²×C₃₁	C₃³	1	1	yes	characteristic
13	C₃×C₃₁⋊C₃	—	3	1	no	—
14	C₃×C₃₁⋊C₃	—	3	3	no	—
15	C₉×C₃₁	—	3	3	no	—
16	C₉×C₃₁	3₋¹⁺²	1	3	yes	—
17	C₃₁⋊C₉	—	3	2	no	—
18	C₃₁⋊C₉	—	3	6	no	—
19	#6899	—	31	1	no	maximal, Sylow
20	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
21	C₃×C₃₁	#737	1	3	yes	—
22	C₃₁⋊C₃	—	9	1	no	—
23	C₃×3₋¹⁺²	—	31	1	no	—
24	C₉⋊C₉	—	31	6	no	—
25	C₉⋊C₉	—	31	2	no	—
26	C₃²⋊C₉	—	31	3	no	—
27	C₉²	C₃₁⋊C₃	1	1	yes	characteristic, complemented
28	C₃₁	#6899	1	1	yes	characteristic, complemented, Sylow
29	C₃³	—	31	1	no	—
30	3₋¹⁺²	—	93	3	no	—
31	C₃×C₉	—	31	6	no	—
32	C₃×C₉	—	31	2	no	—
33	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
34	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
35	C₃²	—	93	1	no	—
36	C₃²	—	93	3	no	—
37	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
38	C₉	—	3	3	no	—
39	C₉	—	93	2	no	—
40	C₉	—	93	6	no	—
41	C₉	#11719687	1	3	yes	—
42	C₃	—	279	1	no	—
43	C₃	C₃×#11719687	1	1	yes	characteristic
44	C₃	#14578912	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₁⋊C₃
commutator, socle	C₃²×C₃₁	C₃³
Fitting	C₉²×C₃₁	C₃
hypercenter	C₉²	C₃₁⋊C₃
hypocenter	C₃₁	#6899
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₉²

Complements

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

N	H ≅ G/N	type
2. #14578887	C₃	semidirect
3. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
5. C₉²×C₃₁	C₃	semidirect
27. C₉²	C₃₁⋊C₃	semidirect
28. C₃₁	#6899	semidirect