Subgroups — C₃×D₇×D₃₇₃ #44531291

Order 31332.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₆₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₇×C₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×C₃₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₆₁₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₃₇₃	C₂×C₃	1	1	yes	characteristic, complemented
8	D₇×C₃₇₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₃×D₃₇₃	—	7	1	no	maximal, Hall
10	C₇×C₃₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₃₇₃	—	7	1	no	—
12	C₃×D₃₇₃	—	7	1	no	—
13	C₃×D₃₇₃	D₇	1	1	yes	characteristic, direct product factor
14	C₂×D₃₇₃	—	7	1	no	Hall
15	C₃×C₃₇₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃₇₃	—	7	1	no	—
17	D₃₇₃	—	7	1	no	—
18	D₃₇₃	C₃×D₇	1	1	yes	characteristic, direct product factor
19	C₃₇₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×D₇	—	373	1	no	maximal, Hall
21	C₂×C₃×C₇	—	373	1	no	—
22	C₃×D₇	—	373	1	no	—
23	C₃×D₇	D₃₇₃	1	1	yes	characteristic, direct product factor
24	C₂×D₇	—	373	1	no	Hall
25	C₃×C₇	C₂×D₃₇₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇	—	373	1	no	—
27	D₇	—	373	1	no	—
28	D₇	C₃×D₃₇₃	1	1	yes	characteristic, direct product factor
29	C₂²×C₃	—	2611	1	no	Hall
30	C₇	C₂×C₃×D₃₇₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	7	1	no	—
32	C₂×C₃	—	2611	1	no	—
33	C₂×C₃	—	373	1	no	—
34	C₂²	—	2611	1	no	Sylow
35	C₃	D₇×D₃₇₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	7	1	no	—
37	C₂	—	2611	1	no	—
38	C₂	—	373	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₇×D₃₇₃
commutator, cosocle, hypocenter	C₇×C₃₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₃₇₃	C₂²
LCS	G ▷ C₇×C₃₇₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₆₁₁	C₂	semidirect
2. C₃×D₇×C₃₇₃	C₂	semidirect
3. C₃×C₇×D₃₇₃	C₂	semidirect
4. D₇×D₃₇₃	C₃	direct (N × H)
5. C₃×C₇×C₃₇₃	C₂²	semidirect
6. D₂₆₁₁	C₂×C₃	semidirect
7. C₇×D₃₇₃	C₂×C₃	semidirect
8. D₇×C₃₇₃	C₂×C₃	semidirect
10. C₇×C₃₇₃	C₂²×C₃	semidirect
13. C₃×D₃₇₃	D₇	direct (N × H)
15. C₃×C₃₇₃	C₂×D₇	semidirect
18. D₃₇₃	C₃×D₇	direct (N × H)
19. C₃₇₃	C₂×C₃×D₇	semidirect
23. C₃×D₇	D₃₇₃	direct (N × H)
25. C₃×C₇	C₂×D₃₇₃	semidirect
28. D₇	C₃×D₃₇₃	direct (N × H)
30. C₇	C₂×C₃×D₃₇₃	semidirect
35. C₃	D₇×D₃₇₃	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×D₂₆₁₁	2
C₃×D₇×C₃₇₃	2
C₃×C₇×D₃₇₃	2
D₇×D₃₇₃	3
C₂×C₃×D₃₇₃	7
C₂×C₃×D₇	373

Subgroups — C3×D7×D373 #44531291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×D₃₇₃ #44531291