Subgroups — C₃×D₃₂₈₉ #34089404

Order 19734.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₂₈₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₂₉₉	—	11	1	no	maximal, Hall
5	C₃×D₂₅₃	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₂₃	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₃×D₁₄₃	—	23	1	no	maximal, Hall
8	C₃×C₁₁×C₂₃	D₁₃	1	1	yes	characteristic, complemented, Hall
9	D₂₉₉	—	11	1	no	Hall
10	D₂₅₃	—	13	1	no	Hall
11	C₃×C₁₁×C₁₃	D₂₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₂₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
13	D₁₄₃	—	23	1	no	Hall
14	C₁₁×C₂₃	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₃	C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
16	C₃×D₂₃	—	143	1	no	Hall
17	C₃×D₁₃	—	253	1	no	Hall
18	C₃×C₂₃	D₁₄₃	1	1	yes	characteristic, complemented, Hall
19	C₃×D₁₁	—	299	1	no	Hall
20	D₂₃	—	143	1	no	Hall
21	C₃×C₁₃	D₂₅₃	1	1	yes	characteristic, complemented, Hall
22	C₃×C₁₁	D₂₉₉	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	253	1	no	Hall
24	C₂₃	C₃×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
25	D₁₁	—	299	1	no	Hall
26	C₁₃	C₃×D₂₅₃	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₃×D₂₉₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	3289	1	no	Hall
29	C₃	D₃₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	3289	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃₂₈₉
commutator, cosocle, hypocenter	C₁₁×C₁₃×C₂₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃×C₂₃	C₂
LCS	G ▷ C₁₁×C₁₃×C₂₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×C₂₃	C₂	semidirect
2. D₃₂₈₉	C₃	direct (N × H)
3. C₁₁×C₁₃×C₂₃	C₂×C₃	semidirect
6. C₃×C₁₃×C₂₃	D₁₁	semidirect
8. C₃×C₁₁×C₂₃	D₁₃	semidirect
11. C₃×C₁₁×C₁₃	D₂₃	semidirect
12. C₁₃×C₂₃	C₃×D₁₁	semidirect
14. C₁₁×C₂₃	C₃×D₁₃	semidirect
15. C₁₁×C₁₃	C₃×D₂₃	semidirect
18. C₃×C₂₃	D₁₄₃	semidirect
21. C₃×C₁₃	D₂₅₃	semidirect
22. C₃×C₁₁	D₂₉₉	semidirect
24. C₂₃	C₃×D₁₄₃	semidirect
26. C₁₃	C₃×D₂₅₃	semidirect
27. C₁₁	C₃×D₂₉₉	semidirect
29. C₃	D₃₂₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₁×C₁₃×C₂₃	2
D₃₂₈₉	3
C₃×D₂₉₉	11
C₃×D₂₅₃	13
C₃×D₁₄₃	23

Subgroups — C3×D3289 #34089404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₂₈₉ #34089404