Subgroups — C₂×C₇₃×D₁₁₁ #44569496

Order 32412.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×D₁₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₃₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇₃×D₃₇	—	3	1	no	maximal, Hall
4	C₃×C₃₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₇×C₇₃	D₃	1	1	yes	characteristic, complemented
6	C₇₃×D₃₇	—	3	2	no	—
7	C₃₇×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃×C₇₃	—	37	1	no	maximal, Hall
9	C₂×D₁₁₁	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₇₃	D₃₇	1	1	yes	characteristic, complemented
11	D₃×C₇₃	—	37	2	no	—
12	C₂²×C₇₃	—	111	1	no	Hall
13	C₂×C₃×C₃₇	C₂×C₇₃	1	1	yes	characteristic, complemented
14	D₁₁₁	C₂×C₇₃	1	2	yes	direct product factor
15	C₃×C₇₃	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃₇	—	3	1	no	Hall
17	C₂×C₇₃	—	111	2	no	—
18	C₂×C₇₃	D₁₁₁	1	1	yes	characteristic, direct product factor
19	C₃×C₃₇	C₂²×C₇₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₇	D₃×C₇₃	1	1	yes	characteristic, complemented
21	D₃₇	—	3	2	no	—
22	C₇₃	C₂×D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
23	C₃₇	C₂×D₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	37	1	no	Hall
25	C₂×C₃	C₇₃×D₃₇	1	1	yes	characteristic, complemented
26	D₃	—	37	2	no	—
27	C₂²	—	111	1	no	Sylow
28	C₃	C₂×C₇₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	111	2	no	—
30	C₂	C₇₃×D₁₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇₃	D₁₁₁
commutator, cosocle, hypocenter	C₃×C₃₇	C₂²×C₇₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₃₇×C₇₃	C₂
LCS	G ▷ C₃×C₃₇
UCS	C₁ ◁ C₂×C₇₃

Complements

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

N	H ≅ G/N	type
1. C₇₃×D₁₁₁	C₂	direct (N × H)
2. C₂×C₃×C₃₇×C₇₃	C₂	semidirect
4. C₃×C₃₇×C₇₃	C₂²	semidirect
5. C₂×C₃₇×C₇₃	D₃	semidirect
7. C₃₇×C₇₃	C₂×D₃	semidirect
9. C₂×D₁₁₁	C₇₃	direct (N × H)
10. C₂×C₃×C₇₃	D₃₇	semidirect
13. C₂×C₃×C₃₇	C₂×C₇₃	semidirect
14. D₁₁₁	C₂×C₇₃	direct (N × H)
15. C₃×C₇₃	C₂×D₃₇	semidirect
18. C₂×C₇₃	D₁₁₁	direct (N × H)
19. C₃×C₃₇	C₂²×C₇₃	semidirect
20. C₂×C₃₇	D₃×C₇₃	semidirect
22. C₇₃	C₂×D₁₁₁	direct (N × H)
23. C₃₇	C₂×D₃×C₇₃	semidirect
25. C₂×C₃	C₇₃×D₃₇	semidirect
28. C₃	C₂×C₇₃×D₃₇	semidirect
30. C₂	C₇₃×D₁₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×D₁₁₁	2
C₂×C₃×C₃₇×C₇₃	2
C₂×C₇₃×D₃₇	3
C₂×D₃×C₇₃	37
C₂×D₁₁₁	73

Subgroups — C2×C73×D111 #44569496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×D₁₁₁ #44569496