Subgroups — C₃²×C₇×D₂₄₇ #44528025

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₂₄₇	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	4	yes	complemented
4	C₃²×D₂₄₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₂₄₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₇×D₁₉	—	13	1	no	maximal, Hall
7	C₃²×C₁₃×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₇×D₁₃	—	19	1	no	maximal, Hall
10	C₃×D₂₄₇	C₃×C₇	1	4	yes	direct product factor
11	C₃²×C₇×C₁₉	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₇×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₃×C₇×D₁₉	—	13	4	no	—
14	C₃×C₁₃×C₁₉	C₂×C₃×C₇	1	4	yes	complemented
15	C₃×C₇×D₁₃	—	19	4	no	—
16	D₂₄₇	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇×C₁₉	C₃×D₁₃	1	4	yes	complemented
18	C₃²×D₁₉	—	13	1	no	Hall
19	C₃×C₇×C₁₃	C₃×D₁₉	1	4	yes	complemented
20	C₇×D₁₉	—	13	1	no	Hall
21	C₁₃×C₁₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₃²×D₁₃	—	19	1	no	Hall
23	C₇×D₁₃	—	19	1	no	Hall
24	C₃²×C₁₉	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₇×C₁₉	C₃²×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃²×C₇	—	247	1	no	Hall
27	C₃²×C₁₃	C₇×D₁₉	1	1	yes	characteristic, complemented, Hall
28	C₃×D₁₉	—	13	4	no	—
29	C₇×C₁₃	C₃²×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₃	—	19	4	no	—
31	C₃²×C₇	D₂₄₇	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₉	C₃×C₇×D₁₃	1	4	yes	complemented
33	C₂×C₃×C₇	—	247	4	no	—
34	C₃×C₁₃	C₃×C₇×D₁₉	1	4	yes	complemented
35	D₁₉	—	13	1	no	Hall
36	D₁₃	—	19	1	no	Hall
37	C₃×C₇	C₃×D₂₄₇	1	4	yes	direct product factor
38	C₁₉	C₃²×C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₃²	—	247	1	no	Hall
40	C₂×C₇	—	247	1	no	Hall
41	C₁₃	C₃²×C₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
42	C₃²	C₇×D₂₄₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₇	C₃²×D₂₄₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃	—	247	4	no	—
45	C₃	C₃×C₇×D₂₄₇	1	4	yes	direct product factor
46	C₂	—	247	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₂₄₇
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₃×C₁₉	C₂	semidirect
2. C₃×C₇×D₂₄₇	C₃	direct (N × H)
3. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
4. C₃²×D₂₄₇	C₇	direct (N × H)
5. C₇×D₂₄₇	C₃²	direct (N × H)
7. C₃²×C₁₃×C₁₉	C₂×C₇	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
10. C₃×D₂₄₇	C₃×C₇	direct (N × H)
11. C₃²×C₇×C₁₉	D₁₃	semidirect
12. C₃²×C₇×C₁₃	D₁₉	semidirect
14. C₃×C₁₃×C₁₉	C₂×C₃×C₇	semidirect
16. D₂₄₇	C₃²×C₇	direct (N × H)
17. C₃×C₇×C₁₉	C₃×D₁₃	semidirect
19. C₃×C₇×C₁₃	C₃×D₁₉	semidirect
21. C₁₃×C₁₉	C₂×C₃²×C₇	semidirect
24. C₃²×C₁₉	C₇×D₁₃	semidirect
25. C₇×C₁₉	C₃²×D₁₃	semidirect
27. C₃²×C₁₃	C₇×D₁₉	semidirect
29. C₇×C₁₃	C₃²×D₁₉	semidirect
31. C₃²×C₇	D₂₄₇	direct (N × H)
32. C₃×C₁₉	C₃×C₇×D₁₃	semidirect
34. C₃×C₁₃	C₃×C₇×D₁₉	semidirect
37. C₃×C₇	C₃×D₂₄₇	direct (N × H)
38. C₁₉	C₃²×C₇×D₁₃	semidirect
41. C₁₃	C₃²×C₇×D₁₉	semidirect
42. C₃²	C₇×D₂₄₇	direct (N × H)
43. C₇	C₃²×D₂₄₇	direct (N × H)
45. C₃	C₃×C₇×D₂₄₇	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×C₇×C₁₃×C₁₉	2
C₃×C₇×D₂₄₇	3
C₃²×D₂₄₇	7
C₃²×C₇×D₁₉	13
C₃²×C₇×D₁₃	19

Subgroups — C32×C7×D247 #44528025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×D₂₄₇ #44528025