Subgroups — D₃×C₇²×C₁₁⋊C₅ #30633521

Order 16170.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₇²×C₁₁⋊C₅	—	3	1	no	maximal, Hall
3	D₃×C₇²×C₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇²×C₁₁⋊C₅	D₃	1	1	yes	characteristic, direct product factor, Hall
5	D₃×C₇×C₁₁⋊C₅	C₇	1	8	yes	maximal, direct product factor
6	C₃×C₇²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₃×C₇²	—	11	1	no	maximal, Hall
8	C₃×C₇×C₁₁⋊C₅	C₂×C₇	1	8	yes	complemented
9	C₂×C₇²×C₁₁	—	3	1	no	Hall
10	C₂×C₇×C₁₁⋊C₅	—	3	8	no	—
11	C₃×C₅×C₇²	—	11	1	no	Hall
12	C₇²×C₁₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₇²	—	33	1	no	Hall
14	D₃×C₇×C₁₁	C₅×C₇	1	8	yes	complemented
15	C₇×C₁₁⋊C₅	D₃×C₇	1	8	yes	direct product factor
16	D₃×C₁₁⋊C₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	D₃×C₇²	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₇²	—	11	1	no	Hall
19	C₃×C₇×C₁₁	C₂×C₅×C₇	1	8	yes	complemented
20	C₅×D₃×C₇	—	11	8	no	—
21	C₃×C₁₁⋊C₅	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₁₁	—	3	8	no	—
23	C₃×C₇²	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₁⋊C₅	—	3	1	no	Hall
25	C₃×C₅×C₇	—	11	8	no	—
26	C₂×C₇²	—	3	1	no	Hall
27	C₇×C₁₁	C₅×D₃×C₇	1	8	yes	complemented
28	C₂×C₅×C₇	—	33	8	no	—
29	D₃×C₁₁	C₅×C₇²	1	1	yes	characteristic, complemented, Hall
30	C₁₁⋊C₅	D₃×C₇²	1	1	yes	characteristic, direct product factor, Hall
31	C₇²	D₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
32	D₃×C₇	C₇×C₁₁⋊C₅	1	8	yes	direct product factor
33	C₅×C₇	—	11	8	no	—
34	C₃×C₁₁	C₂×C₅×C₇²	1	1	yes	characteristic, complemented, Hall
35	C₅×D₃	—	11	1	no	Hall
36	C₂×C₁₁	—	3	1	no	Hall
37	C₃×C₇	C₂×C₇×C₁₁⋊C₅	1	8	yes	complemented
38	C₃×C₅	—	11	1	no	Hall
39	C₂×C₇	—	3	8	no	—
40	C₁₁	C₅×D₃×C₇²	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	33	1	no	Hall
42	C₇	D₃×C₇×C₁₁⋊C₅	1	8	yes	direct product factor
43	D₃	C₇²×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
44	C₅	—	11	1	no	Sylow
45	C₃	C₂×C₇²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²	D₃×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₅×C₇²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₁	C₂×C₅
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₇²

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₁₁⋊C₅	C₂	semidirect
3. D₃×C₇²×C₁₁	C₅	semidirect
4. C₇²×C₁₁⋊C₅	D₃	direct (N × H)
5. D₃×C₇×C₁₁⋊C₅	C₇	direct (N × H)
6. C₃×C₇²×C₁₁	C₂×C₅	semidirect
8. C₃×C₇×C₁₁⋊C₅	C₂×C₇	semidirect
12. C₇²×C₁₁	C₅×D₃	semidirect
14. D₃×C₇×C₁₁	C₅×C₇	semidirect
15. C₇×C₁₁⋊C₅	D₃×C₇	direct (N × H)
16. D₃×C₁₁⋊C₅	C₇²	direct (N × H)
17. D₃×C₇²	C₁₁⋊C₅	direct (N × H)
19. C₃×C₇×C₁₁	C₂×C₅×C₇	semidirect
21. C₃×C₁₁⋊C₅	C₂×C₇²	semidirect
23. C₃×C₇²	C₂×C₁₁⋊C₅	semidirect
27. C₇×C₁₁	C₅×D₃×C₇	semidirect
29. D₃×C₁₁	C₅×C₇²	semidirect
30. C₁₁⋊C₅	D₃×C₇²	direct (N × H)
31. C₇²	D₃×C₁₁⋊C₅	direct (N × H)
32. D₃×C₇	C₇×C₁₁⋊C₅	direct (N × H)
34. C₃×C₁₁	C₂×C₅×C₇²	semidirect
37. C₃×C₇	C₂×C₇×C₁₁⋊C₅	semidirect
40. C₁₁	C₅×D₃×C₇²	semidirect
42. C₇	D₃×C₇×C₁₁⋊C₅	direct (N × H)
43. D₃	C₇²×C₁₁⋊C₅	direct (N × H)
45. C₃	C₂×C₇²×C₁₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇²×C₁₁⋊C₅	2
C₂×C₇²×C₁₁⋊C₅	3
D₃×C₇²×C₁₁	5
D₃×C₇×C₁₁⋊C₅	7
C₅×D₃×C₇²	11

Subgroups — D3×C72×C11⋊C5 #30633521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇²×C₁₁⋊C₅ #30633521