Subgroups — C₉×C₃₇×C₇⋊D₇ #45657377

Order 32634.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₃₇×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic
4	C₉×D₇×C₃₇	—	7	8	no	maximal
5	C₃₇×C₇⋊D₇	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₇×C₉×C₃₇	D₇	1	8	yes	complemented
7	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×D₇×C₃₇	—	7	8	no	—
9	C₉×C₇⋊D₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇×C₃₇	C₃×D₇	1	8	yes	—
11	C₂×C₉×C₃₇	—	49	1	no	Hall
12	D₇×C₃₇	—	7	8	no	—
13	C₇²×C₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
14	C₉×C₃₇	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₇⋊D₇	C₃×C₃₇	1	1	yes	characteristic
16	C₇×C₃₇	C₉×D₇	1	8	yes	complemented
17	C₂×C₃×C₃₇	—	49	1	no	—
18	C₃×C₇²	C₂×C₃×C₃₇	1	1	yes	characteristic
19	C₉×D₇	—	7	8	no	—
20	C₃×C₃₇	C₃×C₇⋊D₇	1	1	yes	characteristic
21	C₇⋊D₇	C₉×C₃₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃₇	—	49	1	no	Hall
23	C₇×C₉	D₇×C₃₇	1	8	yes	complemented
24	C₇²	C₂×C₉×C₃₇	1	1	yes	characteristic, complemented, Sylow
25	C₃×D₇	—	7	8	no	—
26	C₃₇	C₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×C₇	C₃×D₇×C₃₇	1	8	yes	—
28	C₂×C₉	—	49	1	no	Hall
29	D₇	—	7	8	no	—
30	C₉	C₃₇×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₇	C₉×D₇×C₃₇	1	8	yes	complemented
32	C₂×C₃	—	49	1	no	—
33	C₃	C₃×C₃₇×C₇⋊D₇	1	1	yes	characteristic
34	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₃₇	C₇⋊D₇
commutator, hypocenter	C₇²	C₂×C₉×C₃₇
Frattini	C₃	C₃×C₃₇×C₇⋊D₇
Fitting	C₇²×C₉×C₃₇	C₂
socle	C₃×C₇²×C₃₇	C₂×C₃
prime radical	C₃×C₃₇×C₇⋊D₇	C₃
cosocle	C₃×C₇²	C₂×C₃×C₃₇
LCS	G ▷ C₇²
UCS	C₁ ◁ C₉×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₇²×C₉×C₃₇	C₂	semidirect
5. C₃₇×C₇⋊D₇	C₉	direct (N × H)
6. C₇×C₉×C₃₇	D₇	semidirect
7. C₇²×C₃₇	C₂×C₉	semidirect
9. C₉×C₇⋊D₇	C₃₇	direct (N × H)
13. C₇²×C₉	C₂×C₃₇	semidirect
14. C₉×C₃₇	C₇⋊D₇	direct (N × H)
16. C₇×C₃₇	C₉×D₇	semidirect
21. C₇⋊D₇	C₉×C₃₇	direct (N × H)
23. C₇×C₉	D₇×C₃₇	semidirect
24. C₇²	C₂×C₉×C₃₇	semidirect
26. C₃₇	C₉×C₇⋊D₇	direct (N × H)
30. C₉	C₃₇×C₇⋊D₇	direct (N × H)
31. C₇	C₉×D₇×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₇²×C₉×C₃₇	2
C₃×C₃₇×C₇⋊D₇	3
C₉×D₇×C₃₇	7
C₉×C₇⋊D₇	37

Subgroups — C9×C37×C7⋊D7 #45657377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₃₇×C₇⋊D₇ #45657377