Subgroups — C₃×D₅₆₇₃ #46801433

Order 34038.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₆₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₈₉₁	—	3	1	no	maximal
4	C₃×C₃₁×C₆₁	—	2	1	no	—
5	C₃×C₃₁×C₆₁	D₃	1	1	yes	characteristic, complemented
6	C₃×C₃₁×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₈₉₁	—	3	1	no	Hall
8	C₃₁×C₆₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₁₈₃	—	31	1	no	maximal, Hall
10	C₃×D₉₃	—	61	1	no	maximal, Hall
11	C₃²×C₆₁	D₃₁	1	1	yes	characteristic, complemented, Hall
12	D₁₈₃	—	31	1	no	—
13	C₃×D₆₁	—	93	1	no	—
14	C₃²×C₃₁	D₆₁	1	1	yes	characteristic, complemented, Hall
15	D₉₃	—	61	1	no	—
16	C₃×D₃₁	—	183	1	no	—
17	C₃×C₆₁	—	2	1	no	—
18	C₃×C₆₁	C₃×D₃₁	1	1	yes	characteristic, complemented
19	C₃×C₆₁	D₉₃	1	1	yes	characteristic, complemented
20	D₆₁	—	93	1	no	Hall
21	C₃×C₃₁	—	2	1	no	—
22	C₃×C₃₁	C₃×D₆₁	1	1	yes	characteristic, complemented
23	C₃×C₃₁	D₁₈₃	1	1	yes	characteristic, complemented
24	D₃₁	—	183	1	no	Hall
25	C₆₁	C₃×D₉₃	1	1	yes	characteristic, complemented, Sylow
26	C₃₁	C₃×D₁₈₃	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1891	1	no	Hall
28	C₃²	D₁₈₉₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	5673	1	no	—
30	D₃	—	1891	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₈₉₁	1	1	yes	characteristic, complemented
33	C₃	D₅₆₇₃	1	1	yes	characteristic, direct product factor
34	C₂	—	5673	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₆₇₃
commutator, cosocle, hypocenter	C₃×C₃₁×C₆₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₃₁×C₆₁	C₂
LCS	G ▷ C₃×C₃₁×C₆₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃₁×C₆₁	C₂	semidirect
2. D₅₆₇₃	C₃	direct (N × H)
5. C₃×C₃₁×C₆₁	D₃	semidirect
6. C₃×C₃₁×C₆₁	C₂×C₃	semidirect
8. C₃₁×C₆₁	C₃×D₃	semidirect
11. C₃²×C₆₁	D₃₁	semidirect
14. C₃²×C₃₁	D₆₁	semidirect
18. C₃×C₆₁	C₃×D₃₁	semidirect
19. C₃×C₆₁	D₉₃	semidirect
22. C₃×C₃₁	C₃×D₆₁	semidirect
23. C₃×C₃₁	D₁₈₃	semidirect
25. C₆₁	C₃×D₉₃	semidirect
26. C₃₁	C₃×D₁₈₃	semidirect
28. C₃²	D₁₈₉₁	semidirect
32. C₃	C₃×D₁₈₉₁	semidirect
33. C₃	D₅₆₇₃	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×C₃₁×C₆₁	2
D₅₆₇₃	3
C₃×D₁₈₉₁	3
C₃×D₁₈₃	31
C₃×D₉₃	61

Subgroups — C3×D5673 #46801433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₆₇₃ #46801433