Subgroups — C₃×C₇²×D₃₇⋊C₃ #45657496

Order 32634.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇²×D₃₇⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₇²×C₃₇⋊C₃	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×C₇×D₃₇⋊C₃	C₇	1	8	yes	maximal, direct product factor
7	C₇²×D₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×C₃₇⋊C₃	C₂×C₇	1	8	yes	complemented
9	C₇²×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×D₃₇	C₃×C₇	1	8	yes	complemented
11	C₇×D₃₇⋊C₃	C₃×C₇	1	24	yes	direct product factor
12	C₂×C₃²×C₇²	—	37	1	no	maximal, Hall
13	C₃×C₇×C₃₇	C₂×C₃×C₇	1	8	yes	complemented
14	C₇×C₃₇⋊C₃	C₂×C₃×C₇	1	24	yes	complemented
15	C₃×D₃₇⋊C₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
16	C₇×D₃₇	C₃²×C₇	1	8	yes	complemented
17	C₃²×C₇²	—	37	1	no	Hall
18	C₃×C₃₇⋊C₃	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₇²	—	37	3	no	—
20	C₂×C₃×C₇²	—	37	1	no	—
21	C₇×C₃₇	C₂×C₃²×C₇	1	8	yes	complemented
22	C₃×D₃₇	C₃×C₇²	1	1	yes	characteristic, complemented
23	D₃₇⋊C₃	C₃×C₇²	1	3	yes	direct product factor
24	C₃×C₇²	—	37	3	no	—
25	C₃×C₇²	D₃₇⋊C₃	1	1	yes	characteristic, direct product factor
26	C₂×C₃²×C₇	—	37	8	no	—
27	C₃×C₃₇	C₂×C₃×C₇²	1	1	yes	characteristic, complemented
28	C₃₇⋊C₃	C₂×C₃×C₇²	1	3	yes	complemented
29	C₂×C₇²	—	37	1	no	Hall
30	D₃₇	C₃²×C₇²	1	1	yes	characteristic, complemented, Hall
31	C₃²×C₇	—	37	8	no	—
32	C₇²	C₃×D₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃×C₇	—	37	24	no	—
34	C₂×C₃×C₇	—	37	8	no	—
35	C₃₇	C₂×C₃²×C₇²	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₇	—	37	24	no	—
37	C₃×C₇	C₇×D₃₇⋊C₃	1	8	yes	direct product factor
38	C₂×C₃²	—	37	1	no	Hall
39	C₂×C₇	—	37	8	no	—
40	C₃²	—	37	1	no	Sylow
41	C₇	C₃×C₇×D₃₇⋊C₃	1	8	yes	direct product factor
42	C₂×C₃	—	37	3	no	—
43	C₂×C₃	—	37	1	no	—
44	C₃	—	37	3	no	—
45	C₃	C₇²×D₃₇⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇²	D₃₇⋊C₃
commutator, cosocle, hypocenter	C₃₇	C₂×C₃²×C₇²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₃₇	C₂×C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₃×C₇²

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₃₇⋊C₃	C₂	semidirect
2. C₃×C₇²×D₃₇	C₃	semidirect
3. C₇²×D₃₇⋊C₃	C₃	direct (N × H)
4. C₇²×C₃₇⋊C₃	C₂×C₃	semidirect
5. C₃×C₇²×C₃₇	C₂×C₃	semidirect
6. C₃×C₇×D₃₇⋊C₃	C₇	direct (N × H)
7. C₇²×D₃₇	C₃²	semidirect
8. C₃×C₇×C₃₇⋊C₃	C₂×C₇	semidirect
9. C₇²×C₃₇	C₂×C₃²	semidirect
10. C₃×C₇×D₃₇	C₃×C₇	semidirect
11. C₇×D₃₇⋊C₃	C₃×C₇	direct (N × H)
13. C₃×C₇×C₃₇	C₂×C₃×C₇	semidirect
14. C₇×C₃₇⋊C₃	C₂×C₃×C₇	semidirect
15. C₃×D₃₇⋊C₃	C₇²	direct (N × H)
16. C₇×D₃₇	C₃²×C₇	semidirect
18. C₃×C₃₇⋊C₃	C₂×C₇²	semidirect
21. C₇×C₃₇	C₂×C₃²×C₇	semidirect
22. C₃×D₃₇	C₃×C₇²	semidirect
23. D₃₇⋊C₃	C₃×C₇²	direct (N × H)
25. C₃×C₇²	D₃₇⋊C₃	direct (N × H)
27. C₃×C₃₇	C₂×C₃×C₇²	semidirect
28. C₃₇⋊C₃	C₂×C₃×C₇²	semidirect
30. D₃₇	C₃²×C₇²	semidirect
32. C₇²	C₃×D₃₇⋊C₃	direct (N × H)
35. C₃₇	C₂×C₃²×C₇²	semidirect
37. C₃×C₇	C₇×D₃₇⋊C₃	direct (N × H)
41. C₇	C₃×C₇×D₃₇⋊C₃	direct (N × H)
45. C₃	C₇²×D₃₇⋊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×C₇²×C₃₇⋊C₃	2
C₃×C₇²×D₃₇	3
C₇²×D₃₇⋊C₃	3
C₃×C₇×D₃₇⋊C₃	7
C₂×C₃²×C₇²	37

Subgroups — C3×C72×D37⋊C3 #45657496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇²×D₃₇⋊C₃ #45657496