Subgroups — C₃×C₁₃×D₄₇₃ #49146302

Order 36894.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₄₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×D₄₃	—	11	1	no	maximal, Hall
5	C₃×D₄₇₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₄₃	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₁×C₄₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
8	C₁₃×D₄₃	—	11	1	no	Hall
9	D₄₇₃	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₃×D₁₁	—	43	1	no	maximal, Hall
11	C₁₃×C₄₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₄₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₁×C₁₃	D₄₃	1	1	yes	characteristic, complemented, Hall
14	C₁₃×D₁₁	—	43	1	no	Hall
15	C₃×D₄₃	—	11	1	no	Hall
16	C₁₁×C₁₃	C₃×D₄₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄₃	C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
18	D₄₃	—	11	1	no	Hall
19	C₂×C₃×C₁₃	—	473	1	no	Hall
20	C₃×D₁₁	—	43	1	no	Hall
21	C₄₃	C₃×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₃	D₄₇₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₁₁	C₁₃×D₄₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₃	—	473	1	no	Hall
25	D₁₁	—	43	1	no	Hall
26	C₁₃	C₃×D₄₇₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	C₃×C₁₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	473	1	no	Hall
29	C₃	C₁₃×D₄₇₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	473	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₄₇₃
commutator, cosocle, hypocenter	C₁₁×C₄₃	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃×C₄₃	C₂
LCS	G ▷ C₁₁×C₄₃
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×C₄₃	C₂	semidirect
2. C₁₃×D₄₇₃	C₃	direct (N × H)
3. C₁₁×C₁₃×C₄₃	C₂×C₃	semidirect
5. C₃×D₄₇₃	C₁₃	direct (N × H)
6. C₃×C₁₃×C₄₃	D₁₁	semidirect
7. C₃×C₁₁×C₄₃	C₂×C₁₃	semidirect
9. D₄₇₃	C₃×C₁₃	direct (N × H)
11. C₁₃×C₄₃	C₃×D₁₁	semidirect
12. C₁₁×C₄₃	C₂×C₃×C₁₃	semidirect
13. C₃×C₁₁×C₁₃	D₄₃	semidirect
16. C₁₁×C₁₃	C₃×D₄₃	semidirect
17. C₃×C₄₃	C₁₃×D₁₁	semidirect
21. C₄₃	C₃×C₁₃×D₁₁	semidirect
22. C₃×C₁₃	D₄₇₃	direct (N × H)
23. C₃×C₁₁	C₁₃×D₄₃	semidirect
26. C₁₃	C₃×D₄₇₃	direct (N × H)
27. C₁₁	C₃×C₁₃×D₄₃	semidirect
29. C₃	C₁₃×D₄₇₃	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×C₄₃	2
C₁₃×D₄₇₃	3
C₃×C₁₃×D₄₃	11
C₃×D₄₇₃	13
C₃×C₁₃×D₁₁	43

Subgroups — C3×C13×D473 #49146302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×D₄₇₃ #49146302