Subgroups — C₃×D₃×#13133722 #44501816

Order 30690.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#13133722	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×#13133722	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₃×#13133722	—	3	1	no	maximal
4	C₃×D₃×C₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×#13133722	—	2	1	no	—
6	C₃×#13133722	D₃	1	1	yes	characteristic, direct product factor
7	C₃×#13133722	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×#13133722	—	3	1	no	Hall
9	C₃²×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×D₃×ΓL(1,𝔽₃₂)	—	11	1	no	maximal, Hall
11	D₃×C₁₁×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented
12	C₂×C₃×C₁₁×C₃₁	—	3	1	no	—
13	#13133722	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃²×ΓL(1,𝔽₃₂)	—	11	1	no	Hall
15	C₃×C₁₁×C₃₁	—	2	1	no	—
16	C₃×C₁₁×C₃₁	C₅×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₁×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	C₃×D₃×C₁₁⋊C₅	—	31	1	no	maximal, Hall
19	C₂×C₃×ΓL(1,𝔽₃₂)	—	33	1	no	—
20	D₃×ΓL(1,𝔽₃₂)	—	11	1	no	—
21	C₂×C₁₁×C₃₁	—	3	1	no	Hall
22	C₃×D₃×C₃₁	C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
23	C₃²×C₁₁⋊C₅	—	31	1	no	Hall
24	C₃×ΓL(1,𝔽₃₂)	—	11	1	no	—
25	C₃×ΓL(1,𝔽₃₂)	—	11	1	no	—
26	C₃×ΓL(1,𝔽₃₂)	—	22	1	no	—
27	C₁₁×C₃₁	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₁⋊C₅	—	93	1	no	—
29	D₃×C₁₁⋊C₅	—	31	1	no	—
30	C₂×ΓL(1,𝔽₃₂)	—	33	1	no	Hall
31	C₃²×C₃₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
32	C₃×D₃×C₁₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₃₁	—	3	1	no	—
34	D₃×C₃₁	C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
35	C₃×C₁₁⋊C₅	—	31	1	no	—
36	C₃×C₁₁⋊C₅	—	31	1	no	—
37	C₃×C₁₁⋊C₅	—	62	1	no	—
38	ΓL(1,𝔽₃₂)	—	11	1	no	Hall
39	C₂×C₁₁⋊C₅	—	93	1	no	Hall
40	C₃²×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
41	C₃×C₃₁	—	2	1	no	—
42	C₃×C₃₁	D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
43	C₃×C₃₁	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
44	C₃×C₅×D₃	—	341	1	no	Hall
45	C₂×C₃×C₁₁	—	3	1	no	—
46	D₃×C₁₁	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
47	C₂×C₃₁	—	3	1	no	Hall
48	C₁₁⋊C₅	—	31	1	no	Hall
49	C₃²×C₅	—	341	1	no	Hall
50	C₃×C₁₁	—	2	1	no	—
51	C₃×C₁₁	D₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
52	C₃×C₁₁	C₂×C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
53	C₃₁	C₃×D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃×C₅	—	1023	1	no	—
55	C₅×D₃	—	341	1	no	—
56	C₂×C₁₁	—	3	1	no	Hall
57	C₃×D₃	#13133722	1	1	yes	characteristic, direct product factor, Hall
58	C₃×C₅	—	341	1	no	—
59	C₃×C₅	—	341	1	no	—
60	C₃×C₅	—	682	1	no	—
61	C₁₁	C₃×D₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₅	—	1023	1	no	Hall
63	C₃²	C₂×#13133722	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	3	1	no	—
65	D₃	C₃×#13133722	1	1	yes	characteristic, direct product factor
66	C₅	—	341	1	no	Sylow
67	C₃	—	2	1	no	—
68	C₃	C₂×C₃×#13133722	1	1	yes	characteristic, complemented
69	C₃	D₃×#13133722	1	1	yes	characteristic, direct product factor
70	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃×#13133722
commutator, cosocle, hypocenter	C₃×C₁₁×C₃₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₃₁	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×#13133722	C₂	semidirect
2. D₃×#13133722	C₃	direct (N × H)
4. C₃×D₃×C₁₁×C₃₁	C₅	semidirect
6. C₃×#13133722	D₃	direct (N × H)
7. C₃×#13133722	C₂×C₃	semidirect
9. C₃²×C₁₁×C₃₁	C₂×C₅	semidirect
11. D₃×C₁₁×C₃₁	C₃×C₅	semidirect
13. #13133722	C₃×D₃	direct (N × H)
16. C₃×C₁₁×C₃₁	C₅×D₃	semidirect
17. C₃×C₁₁×C₃₁	C₂×C₃×C₅	semidirect
22. C₃×D₃×C₃₁	C₁₁⋊C₅	semidirect
27. C₁₁×C₃₁	C₃×C₅×D₃	semidirect
31. C₃²×C₃₁	C₂×C₁₁⋊C₅	semidirect
32. C₃×D₃×C₁₁	ΓL(1,𝔽₃₂)	semidirect
34. D₃×C₃₁	C₃×C₁₁⋊C₅	semidirect
40. C₃²×C₁₁	C₂×ΓL(1,𝔽₃₂)	semidirect
42. C₃×C₃₁	D₃×C₁₁⋊C₅	semidirect
43. C₃×C₃₁	C₂×C₃×C₁₁⋊C₅	semidirect
46. D₃×C₁₁	C₃×ΓL(1,𝔽₃₂)	semidirect
51. C₃×C₁₁	D₃×ΓL(1,𝔽₃₂)	semidirect
52. C₃×C₁₁	C₂×C₃×ΓL(1,𝔽₃₂)	semidirect
53. C₃₁	C₃×D₃×C₁₁⋊C₅	semidirect
57. C₃×D₃	#13133722	direct (N × H)
61. C₁₁	C₃×D₃×ΓL(1,𝔽₃₂)	semidirect
63. C₃²	C₂×#13133722	semidirect
65. D₃	C₃×#13133722	direct (N × H)
68. C₃	C₂×C₃×#13133722	semidirect
69. C₃	D₃×#13133722	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#13133722	2
D₃×#13133722	3
C₂×C₃×#13133722	3
C₃×D₃×C₁₁×C₃₁	5
C₃×D₃×ΓL(1,𝔽₃₂)	11
C₃×D₃×C₁₁⋊C₅	31

Subgroups — C3×D3×#13133722 #44501816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#13133722 #44501816