Subgroups — C₃²×C₇×D₁₃₃ #30660889

Order 16758.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₁₃₃	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇²×C₁₉	C₂×C₃	1	4	yes	complemented
4	C₃²×D₁₃₃	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₇×D₁₉	—	7	1	no	maximal
6	C₇×D₁₃₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇×C₁₉	—	2	3	no	—
8	C₃²×C₇×C₁₉	D₇	1	1	yes	characteristic, complemented
9	C₃²×C₇×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
10	C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₇×D₇	—	19	1	no	maximal, Hall
12	C₃×D₁₃₃	C₃×C₇	1	4	yes	direct product factor
13	C₃×C₇×D₁₉	—	7	4	no	—
14	C₃²×C₇²	D₁₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇×C₁₉	—	2	12	no	—
16	C₃×C₇×C₁₉	C₃×D₇	1	4	yes	complemented
17	C₃×C₇×C₁₉	C₂×C₃×C₇	1	4	yes	complemented
18	C₃²×D₁₉	—	7	1	no	Hall
19	C₃×C₇×D₇	—	19	4	no	—
20	D₁₃₃	C₃²×C₇	1	1	yes	characteristic, direct product factor
21	C₇×D₁₉	—	7	1	no	—
22	C₃²×C₁₉	C₇×D₇	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇²	C₃×D₁₉	1	4	yes	complemented
24	C₇×C₁₉	—	2	3	no	—
25	C₇×C₁₉	C₃²×D₇	1	1	yes	characteristic, complemented
26	C₇×C₁₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
27	C₂×C₃²×C₇	—	133	1	no	—
28	C₃²×D₇	—	19	1	no	—
29	C₃×D₁₉	—	7	4	no	—
30	C₇×D₇	—	19	1	no	Hall
31	C₃²×C₇	—	2	3	no	—
32	C₃²×C₇	C₇×D₁₉	1	1	yes	characteristic, complemented
33	C₃²×C₇	D₁₃₃	1	1	yes	characteristic, direct product factor
34	C₃×C₁₉	C₃×C₇×D₇	1	4	yes	complemented
35	C₇²	C₃²×D₁₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₇	—	133	4	no	—
37	C₃×D₇	—	19	4	no	—
38	D₁₉	—	7	1	no	Hall
39	C₃×C₇	—	2	12	no	—
40	C₃×C₇	C₃×C₇×D₁₉	1	4	yes	complemented
41	C₃×C₇	C₃×D₁₃₃	1	4	yes	direct product factor
42	C₁₉	C₃²×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃²	—	133	1	no	Hall
44	C₂×C₇	—	133	1	no	—
45	D₇	—	19	1	no	—
46	C₃²	C₇×D₁₃₃	1	1	yes	characteristic, direct product factor, Sylow
47	C₇	—	2	3	no	—
48	C₇	C₃²×C₇×D₁₉	1	1	yes	characteristic, complemented
49	C₇	C₃²×D₁₃₃	1	1	yes	characteristic, direct product factor
50	C₂×C₃	—	133	4	no	—
51	C₃	C₃×C₇×D₁₃₃	1	4	yes	direct product factor
52	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₁₃₃
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₉	C₂
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₁₉	C₂	semidirect
2. C₃×C₇×D₁₃₃	C₃	direct (N × H)
3. C₃×C₇²×C₁₉	C₂×C₃	semidirect
4. C₃²×D₁₃₃	C₇	direct (N × H)
6. C₇×D₁₃₃	C₃²	direct (N × H)
8. C₃²×C₇×C₁₉	D₇	semidirect
9. C₃²×C₇×C₁₉	C₂×C₇	semidirect
10. C₇²×C₁₉	C₂×C₃²	semidirect
12. C₃×D₁₃₃	C₃×C₇	direct (N × H)
14. C₃²×C₇²	D₁₉	semidirect
16. C₃×C₇×C₁₉	C₃×D₇	semidirect
17. C₃×C₇×C₁₉	C₂×C₃×C₇	semidirect
20. D₁₃₃	C₃²×C₇	direct (N × H)
22. C₃²×C₁₉	C₇×D₇	semidirect
23. C₃×C₇²	C₃×D₁₉	semidirect
25. C₇×C₁₉	C₃²×D₇	semidirect
26. C₇×C₁₉	C₂×C₃²×C₇	semidirect
32. C₃²×C₇	C₇×D₁₉	semidirect
33. C₃²×C₇	D₁₃₃	direct (N × H)
34. C₃×C₁₉	C₃×C₇×D₇	semidirect
35. C₇²	C₃²×D₁₉	semidirect
40. C₃×C₇	C₃×C₇×D₁₉	semidirect
41. C₃×C₇	C₃×D₁₃₃	direct (N × H)
42. C₁₉	C₃²×C₇×D₇	semidirect
46. C₃²	C₇×D₁₃₃	direct (N × H)
48. C₇	C₃²×C₇×D₁₉	semidirect
49. C₇	C₃²×D₁₃₃	direct (N × H)
51. C₃	C₃×C₇×D₁₃₃	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×C₇²×C₁₉	2
C₃×C₇×D₁₃₃	3
C₃²×D₁₃₃	7
C₃²×C₇×D₁₉	7
C₃²×C₇×D₇	19

Subgroups — C32×C7×D133 #30660889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×D₁₃₃ #30660889