Subgroups — D₉×C₃₇×C₄₉ #45657241

Order 32634.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₇×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₃₇×C₄₉	—	3	1	no	maximal
3	C₃×C₃₇×C₄₉	D₃	1	1	yes	characteristic
4	C₇×D₉×C₃₇	C₇	1	1	yes	maximal, characteristic
5	C₂×C₃₇×C₄₉	—	9	1	no	Hall
6	C₇×C₉×C₃₇	C₂×C₇	1	1	yes	characteristic
7	C₃₇×C₄₉	D₉	1	1	yes	characteristic, direct product factor, Hall
8	D₃×C₇×C₃₇	—	3	1	no	—
9	D₉×C₄₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇×C₃₇	D₃×C₇	1	1	yes	characteristic
11	D₉×C₃₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇×C₃₇	—	9	1	no	—
13	C₉×C₄₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
14	C₉×C₃₇	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
15	D₃×C₄₉	—	3	1	no	—
16	C₇×C₃₇	C₇×D₉	1	1	yes	characteristic
17	D₃×C₃₇	—	3	1	no	—
18	C₃×C₄₉	D₃×C₃₇	1	1	yes	characteristic
19	C₇×D₉	C₇×C₃₇	1	1	yes	characteristic
20	C₃×C₃₇	D₃×C₄₉	1	1	yes	characteristic
21	C₂×C₄₉	—	9	1	no	Hall
22	C₂×C₃₇	—	9	1	no	Hall
23	C₇×C₉	C₂×C₇×C₃₇	1	1	yes	characteristic
24	C₄₉	D₉×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
25	D₃×C₇	—	3	1	no	—
26	C₃₇	D₉×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×C₇	D₃×C₇×C₃₇	1	1	yes	characteristic
28	D₉	C₃₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇	—	9	1	no	—
30	C₉	C₂×C₃₇×C₄₉	1	1	yes	characteristic, complemented, Sylow
31	C₇	C₇×D₉×C₃₇	1	1	yes	characteristic
32	D₃	—	3	1	no	—
33	C₃	D₃×C₃₇×C₄₉	1	1	yes	characteristic
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇×C₄₉	D₉
commutator, hypocenter	C₉	C₂×C₃₇×C₄₉
Frattini	C₃×C₇	D₃×C₇×C₃₇
Fitting	C₉×C₃₇×C₄₉	C₂
socle	C₃×C₇×C₃₇	D₃×C₇
prime radical	C₇×D₉×C₃₇	C₇
cosocle	C₇×C₉	C₂×C₇×C₃₇
LCS	G ▷ C₉
UCS	C₁ ◁ C₃₇×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₃₇×C₄₉	C₂	semidirect
7. C₃₇×C₄₉	D₉	direct (N × H)
9. D₉×C₄₉	C₃₇	direct (N × H)
11. D₉×C₃₇	C₄₉	direct (N × H)
13. C₉×C₄₉	C₂×C₃₇	semidirect
14. C₉×C₃₇	C₂×C₄₉	semidirect
24. C₄₉	D₉×C₃₇	direct (N × H)
26. C₃₇	D₉×C₄₉	direct (N × H)
28. D₉	C₃₇×C₄₉	direct (N × H)
30. C₉	C₂×C₃₇×C₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₃₇×C₄₉	2
D₃×C₃₇×C₄₉	3
C₇×D₉×C₃₇	7
D₉×C₄₉	37

Subgroups — D9×C37×C49 #45657241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×C₃₇×C₄₉ #45657241