Subgroups — #22582637

Order 8991.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11758608	C₃	1	2	yes	maximal, complemented
2	C₃×C₃²⋊(C₃₇⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	#15688512	C₃	1	9	yes	maximal, complemented
4	C₃×H(3,𝔽₃)×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₇	—	3	1	no	—
6	C₃³×C₃₇	C₃²	1	1	yes	characteristic
7	C₃²×C₃₇⋊C₃	C₃²	1	3	yes	complemented
8	H(3,𝔽₃)×C₃₇	—	3	2	no	—
9	H(3,𝔽₃)×C₃₇	C₃²	1	3	yes	—
10	C₃²⋊(C₃₇⋊C₃)	—	3	2	no	—
11	C₃²⋊(C₃₇⋊C₃)	—	3	1	no	—
12	#11758608	—	3	2	no	—
13	#11758608	—	3	2	no	—
14	#11758608	C₃²	1	6	yes	complemented
15	C₃×#66524	—	3	2	no	—
16	C₃²×C₃₇	—	3	3	no	—
17	C₃²×C₃₇	—	9	1	no	—
18	C₃²×C₃₇	—	9	3	no	—
19	C₃²×C₃₇	H(3,𝔽₃)	1	2	yes	—
20	C₃²×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃²×C₃₇	C₃³	1	1	yes	characteristic
22	C₃×C₃₇⋊C₃	—	3	3	no	—
23	C₃×C₃₇⋊C₃	—	9	3	no	—
24	#66524	—	3	6	no	—
25	#6909	—	37	1	no	maximal, Sylow
26	C₃×C₃₇	—	3	1	no	—
27	C₃×C₃₇	—	3	1	no	—
28	C₃×C₃₇	—	3	2	no	—
29	C₃×C₃₇	—	9	3	no	—
30	C₃×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₃₇⋊C₃	—	9	3	no	—
32	C₃×3₋¹⁺²	—	37	2	no	—
33	C₃×H(3,𝔽₃)	—	37	1	no	—
34	C₃×H(3,𝔽₃)	C₃₇⋊C₃	1	1	yes	characteristic, complemented
35	AΣL(1,𝔽₂₇)	—	37	9	no	—
36	C₃₇	#6909	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	3	1	no	—
38	C₃³	—	37	3	no	—
39	C₃³	C₃×C₃₇⋊C₃	1	1	yes	characteristic
40	3₋¹⁺²	—	37	6	no	—
41	3₋¹⁺²	—	111	2	no	—
42	3₋¹⁺²	—	111	2	no	—
43	H(3,𝔽₃)	—	3	2	no	—
44	H(3,𝔽₃)	—	111	2	no	—
45	H(3,𝔽₃)	—	111	1	no	—
46	H(3,𝔽₃)	C₃×C₃₇⋊C₃	1	3	yes	—
47	C₃×C₉	—	111	2	no	—
48	C₃²	—	3	3	no	—
49	C₃²	—	9	1	no	—
50	C₃²	—	9	3	no	—
51	C₃²	—	333	3	no	—
52	C₃²	—	111	3	no	—
53	C₃²	C₃²⋊(C₃₇⋊C₃)	1	2	yes	—
54	C₃²	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
55	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
56	C₉	—	111	6	no	—
57	C₃	—	3	1	no	—
58	C₃	—	3	1	no	—
59	C₃	—	3	2	no	—
60	C₃	—	9	3	no	—
61	C₃	—	333	3	no	—
62	C₃	C₃×C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊(C₃₇⋊C₃)
commutator	C₃²×C₃₇	C₃³
Frattini	C₃²	C₃²×C₃₇⋊C₃
Fitting	C₃×H(3,𝔽₃)×C₃₇	C₃
socle	C₃×C₃₇	C₃×H(3,𝔽₃)
hypercenter	C₃×H(3,𝔽₃)	C₃₇⋊C₃
hypocenter	C₃₇	#6909
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#11758608	C₃	semidirect
2. C₃×C₃²⋊(C₃₇⋊C₃)	C₃	semidirect
3. #15688512	C₃	semidirect
4. C₃×H(3,𝔽₃)×C₃₇	C₃	semidirect
7. C₃²×C₃₇⋊C₃	C₃²	semidirect
14. #11758608	C₃²	semidirect
34. C₃×H(3,𝔽₃)	C₃₇⋊C₃	semidirect
36. C₃₇	#6909	semidirect