Subgroups — C₃×#16811786⋊C₃ #44501733

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13133724⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#16811786⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×#16811786	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₁⋊(D₃₁⋊C₃)	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	#13133724⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×#13133724	C₂×C₃	1	1	yes	characteristic, complemented
7	#16811786	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₁×C₃₁⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×AGL(1,𝔽₃₁)	—	11	1	no	maximal, Hall
10	C₁₁⋊(D₃₁⋊C₃)	C₃×C₅	1	3	yes	complemented
11	C₃×D₃₄₁	C₃×C₅	1	1	yes	characteristic, complemented
12	#13133724	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃×(C₃₁⋊C₃)⋊C₅	—	11	1	no	Hall
14	C₃×C₁₁×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
15	C₁₁×C₃₁⋊C₃	C₂×C₃×C₅	1	3	yes	complemented
16	C₃²×AGL(1,𝔽₁₁)	—	31	1	no	maximal, Hall
17	C₃×D₃₁⋊C₅	—	11	1	no	—
18	AGL(1,𝔽₃₁)	—	11	3	no	—
19	D₃₄₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₃×D₃₁⋊C₃	—	11	1	no	Hall
21	C₃²×C₁₁⋊C₅	—	31	1	no	Hall
22	C₃×ΓL(1,𝔽₃₂)	—	11	1	no	—
23	(C₃₁⋊C₃)⋊C₅	—	11	3	no	—
24	C₁₁×C₃₁	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
25	C₃×AGL(1,𝔽₁₁)	—	31	1	no	—
26	C₃×AGL(1,𝔽₁₁)	—	31	3	no	—
27	D₃₁⋊C₅	—	11	1	no	Hall
28	C₃×C₃₁⋊C₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
29	C₃²×D₁₁	—	31	1	no	Hall
30	C₃×D₃₁	—	11	1	no	—
31	D₃₁⋊C₃	—	11	3	no	—
32	C₃×C₁₁⋊C₅	—	31	3	no	—
33	C₃×C₁₁⋊C₅	—	31	1	no	—
34	ΓL(1,𝔽₃₂)	—	11	1	no	Hall
35	AGL(1,𝔽₁₁)	—	31	1	no	Hall
36	C₃²×C₁₁	—	31	1	no	Hall
37	C₃×C₃₁	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
38	C₃₁⋊C₃	C₃×AGL(1,𝔽₁₁)	1	3	yes	complemented
39	C₂×C₃²×C₅	—	341	1	no	Hall
40	C₃×D₁₁	—	31	3	no	—
41	C₃×D₁₁	—	31	1	no	—
42	D₃₁	—	11	1	no	Hall
43	C₁₁⋊C₅	—	31	1	no	Hall
44	C₃²×C₅	—	341	1	no	Hall
45	C₃×C₁₁	—	31	3	no	—
46	C₃×C₁₁	AGL(1,𝔽₃₁)	1	1	yes	characteristic, complemented
47	C₃₁	C₃²×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₅	—	341	3	no	—
49	C₂×C₃×C₅	—	341	1	no	—
50	D₁₁	—	31	1	no	Hall
51	C₂×C₃²	—	341	1	no	Hall
52	C₃×C₅	—	341	3	no	—
53	C₃×C₅	—	341	1	no	—
54	C₁₁	C₃×AGL(1,𝔽₃₁)	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₅	—	341	1	no	Hall
56	C₃²	—	31	1	no	Sylow
57	C₂×C₃	—	341	3	no	—
58	C₂×C₃	—	341	1	no	—
59	C₅	—	341	1	no	Sylow
60	C₃	—	31	3	no	—
61	C₃	#16811786⋊C₃	1	1	yes	characteristic, direct product factor
62	C₂	—	341	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#16811786⋊C₃
commutator, cosocle, hypocenter	C₁₁×C₃₁	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#13133724⋊C₃	C₂	semidirect
2. #16811786⋊C₃	C₃	direct (N × H)
3. C₃×#16811786	C₃	semidirect
4. C₃×C₁₁⋊(D₃₁⋊C₃)	C₅	semidirect
5. #13133724⋊C₃	C₂×C₃	semidirect
6. C₃×#13133724	C₂×C₃	semidirect
7. #16811786	C₃²	semidirect
8. C₃×C₁₁×C₃₁⋊C₃	C₂×C₅	semidirect
10. C₁₁⋊(D₃₁⋊C₃)	C₃×C₅	semidirect
11. C₃×D₃₄₁	C₃×C₅	semidirect
12. #13133724	C₂×C₃²	semidirect
14. C₃×C₁₁×C₃₁	C₂×C₃×C₅	semidirect
15. C₁₁×C₃₁⋊C₃	C₂×C₃×C₅	semidirect
19. D₃₄₁	C₃²×C₅	semidirect
24. C₁₁×C₃₁	C₂×C₃²×C₅	semidirect
28. C₃×C₃₁⋊C₃	AGL(1,𝔽₁₁)	semidirect
37. C₃×C₃₁	C₃×AGL(1,𝔽₁₁)	semidirect
38. C₃₁⋊C₃	C₃×AGL(1,𝔽₁₁)	semidirect
46. C₃×C₁₁	AGL(1,𝔽₃₁)	semidirect
47. C₃₁	C₃²×AGL(1,𝔽₁₁)	semidirect
54. C₁₁	C₃×AGL(1,𝔽₃₁)	semidirect
61. C₃	#16811786⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#13133724⋊C₃	2
#16811786⋊C₃	3
C₃×#16811786	3
C₃×C₁₁⋊(D₃₁⋊C₃)	5
C₃×AGL(1,𝔽₃₁)	11
C₃²×AGL(1,𝔽₁₁)	31

Subgroups — C3×#16811786⋊C3 #44501733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#16811786⋊C₃ #44501733