Subgroups — #21419243

Order 7533.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578912	C₃	1	1	yes	maximal, characteristic
2	#14578892	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃₁⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃₁×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
6	C₃²⋊(C₃₁⋊C₃)	C₉	1	1	yes	characteristic
7	#11719689	C₉	1	2	yes	—
8	#11719687	—	3	1	no	—
9	#11719686	—	3	1	no	—
10	C₉×C₃₁⋊C₃	—	3	1	no	—
11	C₂₇×C₃₁	—	3	1	no	—
12	C₃₁⋊C₂₇	—	3	1	no	—
13	C₃₁⋊C₂₇	—	3	1	no	—
14	C₃²×C₃₁	C₃×C₉	1	1	yes	characteristic
15	C₃×C₃₁⋊C₃	—	3	1	no	—
16	C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
17	C₉×C₃₁	3₋¹⁺²	1	1	yes	characteristic
18	C₉×C₃₁	3₋¹⁺²	1	1	yes	characteristic
19	C₃₁⋊C₉	—	3	2	no	—
20	#6873	—	31	1	no	maximal, Sylow
21	C₃×C₃₁	—	3	1	no	—
22	C₃×C₃₁	C₃²⋊C₉	1	1	yes	characteristic
23	C₃₁⋊C₃	—	9	1	no	—
24	#737	—	31	1	no	—
25	C₂₇⋊C₃	—	31	1	no	—
26	C₂₇⋊C₃	C₃₁⋊C₃	1	1	yes	characteristic, complemented
27	C₃×C₂₇	—	31	1	no	—
28	C₃₁	#6873	1	1	yes	characteristic, complemented, Sylow
29	3₋¹⁺²	—	31	2	no	—
30	3₋¹⁺²	—	93	1	no	—
31	3₋¹⁺²	—	93	1	no	—
32	H(3,𝔽₃)	—	31	1	no	—
33	C₃×C₉	—	93	1	no	—
34	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
35	C₂₇	—	3	1	no	—
36	C₂₇	—	93	1	no	—
37	C₂₇	—	93	1	no	—
38	C₃²	—	93	1	no	—
39	C₃²	C₉×C₃₁⋊C₃	1	1	yes	characteristic
40	C₉	—	93	2	no	—
41	C₉	#11719686	1	1	yes	characteristic
42	C₉	#11719687	1	1	yes	characteristic
43	C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
44	C₃	—	3	1	no	—
45	C₃	—	279	1	no	—
46	C₃	(C₃×C₃₁⋊C₃)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊(C₃₁⋊C₃)
commutator	C₃²×C₃₁	C₃×C₉
Frattini	C₃×C₉	C₃×C₃₁⋊C₃
Fitting	C₃₁×C₂₇⋊C₃	C₃
socle	C₃×C₃₁	C₃²⋊C₉
hypercenter	C₂₇⋊C₃	C₃₁⋊C₃
hypocenter	C₃₁	#6873
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #14578892	C₃	semidirect
3. C₃×C₃₁⋊C₂₇	C₃	semidirect
4. C₃₁×C₂₇⋊C₃	C₃	semidirect
26. C₂₇⋊C₃	C₃₁⋊C₃	semidirect
28. C₃₁	#6873	semidirect