Subgroups — C₃×C₁₇×D₂₁₉ #36375256

Order 22338.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₂₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₇×D₇₃	—	3	1	no	maximal
4	C₃×C₁₇×C₇₃	—	2	1	no	—
5	C₃×C₁₇×C₇₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₇×D₇₃	—	3	1	no	Hall
8	C₃×D₂₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₇×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₇₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
11	D₂₁₉	C₃×C₁₇	1	1	yes	characteristic, direct product factor
12	C₃×D₇₃	—	3	1	no	—
13	C₃×D₃×C₁₇	—	73	1	no	maximal, Hall
14	C₃×C₇₃	—	2	1	no	—
15	C₃×C₇₃	D₃×C₁₇	1	1	yes	characteristic, complemented
16	C₃×C₇₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
17	C₃²×C₁₇	D₇₃	1	1	yes	characteristic, complemented, Hall
18	D₇₃	—	3	1	no	Hall
19	C₂×C₃×C₁₇	—	219	1	no	—
20	D₃×C₁₇	—	73	1	no	—
21	C₇₃	C₃×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₇	—	2	1	no	—
23	C₃×C₁₇	C₃×D₇₃	1	1	yes	characteristic, complemented
24	C₃×C₁₇	D₂₁₉	1	1	yes	characteristic, direct product factor
25	C₂×C₁₇	—	219	1	no	Hall
26	C₃×D₃	—	73	1	no	Hall
27	C₁₇	C₃×D₂₁₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₃²	C₁₇×D₇₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	219	1	no	—
30	D₃	—	73	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×C₁₇×D₇₃	1	1	yes	characteristic, complemented
33	C₃	C₁₇×D₂₁₉	1	1	yes	characteristic, direct product factor
34	C₂	—	219	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₂₁₉
commutator, cosocle, hypocenter	C₃×C₇₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₇₃	C₂
LCS	G ▷ C₃×C₇₃
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇×C₇₃	C₂	semidirect
2. C₁₇×D₂₁₉	C₃	direct (N × H)
5. C₃×C₁₇×C₇₃	D₃	semidirect
6. C₃×C₁₇×C₇₃	C₂×C₃	semidirect
8. C₃×D₂₁₉	C₁₇	direct (N × H)
9. C₁₇×C₇₃	C₃×D₃	semidirect
10. C₃²×C₇₃	C₂×C₁₇	semidirect
11. D₂₁₉	C₃×C₁₇	direct (N × H)
15. C₃×C₇₃	D₃×C₁₇	semidirect
16. C₃×C₇₃	C₂×C₃×C₁₇	semidirect
17. C₃²×C₁₇	D₇₃	semidirect
21. C₇₃	C₃×D₃×C₁₇	semidirect
23. C₃×C₁₇	C₃×D₇₃	semidirect
24. C₃×C₁₇	D₂₁₉	direct (N × H)
27. C₁₇	C₃×D₂₁₉	direct (N × H)
28. C₃²	C₁₇×D₇₃	semidirect
32. C₃	C₃×C₁₇×D₇₃	semidirect
33. C₃	C₁₇×D₂₁₉	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×C₁₇×C₇₃	2
C₁₇×D₂₁₉	3
C₃×C₁₇×D₇₃	3
C₃×D₂₁₉	17
C₃×D₃×C₁₇	73

Subgroups — C3×C17×D219 #36375256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×D₂₁₉ #36375256