Subgroups — C₇×C₉×D₂₂₁ #42123791

Order 27846.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₂₂₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
4	C₉×D₂₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₂₂₁	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₇×C₉×D₁₇	—	13	1	no	maximal, Hall
7	C₉×C₁₃×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₉×D₁₃	—	17	1	no	maximal, Hall
9	C₇×C₁₃×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×D₂₂₁	C₃×C₇	1	1	yes	characteristic
11	C₇×C₉×C₁₇	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇×C₉×C₁₃	D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₇×D₁₇	—	13	1	no	—
14	C₃×C₁₃×C₁₇	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₇×D₁₃	—	17	1	no	—
16	D₂₂₁	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇×C₁₇	C₃×D₁₃	1	1	yes	characteristic
18	C₉×D₁₇	—	13	1	no	Hall
19	C₃×C₇×C₁₃	C₃×D₁₇	1	1	yes	characteristic
20	C₇×D₁₇	—	13	1	no	Hall
21	C₉×D₁₃	—	17	1	no	Hall
22	C₁₃×C₁₇	C₂×C₇×C₉	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₃	—	17	1	no	Hall
24	C₉×C₁₇	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₉	—	221	1	no	Hall
26	C₇×C₁₇	C₉×D₁₃	1	1	yes	characteristic, complemented, Hall
27	C₉×C₁₃	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
28	C₃×D₁₇	—	13	1	no	—
29	C₇×C₁₃	C₉×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₃	—	17	1	no	—
31	C₇×C₉	D₂₂₁	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₇	C₃×C₇×D₁₃	1	1	yes	characteristic
33	C₂×C₃×C₇	—	221	1	no	—
34	C₃×C₁₃	C₃×C₇×D₁₇	1	1	yes	characteristic
35	D₁₇	—	13	1	no	Hall
36	D₁₃	—	17	1	no	Hall
37	C₃×C₇	C₃×D₂₂₁	1	1	yes	characteristic
38	C₂×C₉	—	221	1	no	Hall
39	C₁₇	C₇×C₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	221	1	no	Hall
41	C₁₃	C₇×C₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
42	C₉	C₇×D₂₂₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₇	C₉×D₂₂₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃	—	221	1	no	—
45	C₃	C₃×C₇×D₂₂₁	1	1	yes	characteristic
46	C₂	—	221	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₉	D₂₂₁
commutator, hypocenter	C₁₃×C₁₇	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×D₂₂₁
Fitting	C₇×C₉×C₁₃×C₁₇	C₂
socle	C₃×C₇×C₁₃×C₁₇	C₂×C₃
prime radical	C₃×C₇×D₂₂₁	C₃
cosocle	C₃×C₁₃×C₁₇	C₂×C₃×C₇
LCS	G ▷ C₁₃×C₁₇
UCS	C₁ ◁ C₇×C₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₁₃×C₁₇	C₂	semidirect
4. C₉×D₂₂₁	C₇	direct (N × H)
5. C₇×D₂₂₁	C₉	direct (N × H)
7. C₉×C₁₃×C₁₇	C₂×C₇	semidirect
9. C₇×C₁₃×C₁₇	C₂×C₉	semidirect
11. C₇×C₉×C₁₇	D₁₃	semidirect
12. C₇×C₉×C₁₃	D₁₇	semidirect
16. D₂₂₁	C₇×C₉	direct (N × H)
22. C₁₃×C₁₇	C₂×C₇×C₉	semidirect
24. C₉×C₁₇	C₇×D₁₃	semidirect
26. C₇×C₁₇	C₉×D₁₃	semidirect
27. C₉×C₁₃	C₇×D₁₇	semidirect
29. C₇×C₁₃	C₉×D₁₇	semidirect
31. C₇×C₉	D₂₂₁	direct (N × H)
39. C₁₇	C₇×C₉×D₁₃	semidirect
41. C₁₃	C₇×C₉×D₁₇	semidirect
42. C₉	C₇×D₂₂₁	direct (N × H)
43. C₇	C₉×D₂₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₉×C₁₃×C₁₇	2
C₃×C₇×D₂₂₁	3
C₉×D₂₂₁	7
C₇×C₉×D₁₇	13
C₇×C₉×D₁₃	17

Subgroups — C7×C9×D221 #42123791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×D₂₂₁ #42123791