Subgroups — D₇₃×D₁₁₁ #44569477

Order 32412.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×D₁₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃₇×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₇×D₇₃	—	3	1	no	maximal, Hall
5	C₃×C₃₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₇₀₁	—	3	1	no	—
7	C₃₇×D₇₃	D₃	1	1	yes	characteristic, complemented
8	C₇₃×D₃₇	—	3	1	no	—
9	C₃₇×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₇₃	—	37	1	no	maximal, Hall
11	C₂×D₁₁₁	—	73	1	no	maximal, Hall
12	D₂₁₉	—	37	1	no	—
13	C₃×D₇₃	D₃₇	1	1	yes	characteristic, complemented
14	D₃×C₇₃	—	37	1	no	—
15	C₂×D₇₃	—	111	1	no	Hall
16	C₂×C₃×C₃₇	—	73	1	no	—
17	D₁₁₁	—	73	1	no	—
18	D₁₁₁	D₇₃	1	1	yes	characteristic, direct product factor
19	C₃×C₇₃	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₇	—	219	1	no	Hall
21	C₂×C₇₃	—	111	1	no	—
22	D₇₃	—	111	1	no	—
23	D₇₃	D₁₁₁	1	1	yes	characteristic, direct product factor
24	C₃×C₃₇	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃₇	—	73	1	no	—
26	D₃₇	—	3	1	no	—
27	D₃₇	—	219	1	no	—
28	C₇₃	C₂×D₁₁₁	1	1	yes	characteristic, complemented, Sylow
29	C₃₇	D₃×D₇₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2701	1	no	Hall
31	C₂×C₃	—	73	1	no	—
32	D₃	—	37	1	no	—
33	D₃	—	2701	1	no	—
34	C₂²	—	8103	1	no	Sylow
35	C₃	D₃₇×D₇₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	73	1	no	—
37	C₂	—	111	1	no	—
38	C₂	—	8103	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₈₁₀₃	C₂	semidirect
2. C₇₃×D₁₁₁	C₂	semidirect
3. C₃×C₃₇×D₇₃	C₂	semidirect
5. C₃×C₃₇×C₇₃	C₂²	semidirect
7. C₃₇×D₇₃	D₃	semidirect
9. C₃₇×C₇₃	C₂×D₃	semidirect
13. C₃×D₇₃	D₃₇	semidirect
18. D₁₁₁	D₇₃	direct (N × H)
19. C₃×C₇₃	C₂×D₃₇	semidirect
23. D₇₃	D₁₁₁	direct (N × H)
24. C₃×C₃₇	C₂×D₇₃	semidirect
28. C₇₃	C₂×D₁₁₁	semidirect
29. C₃₇	D₃×D₇₃	semidirect
35. C₃	D₃₇×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
D₈₁₀₃	2
C₇₃×D₁₁₁	2
C₃×C₃₇×D₇₃	2
D₃₇×D₇₃	3
D₃×D₇₃	37
C₂×D₁₁₁	73

Subgroups — D73×D111 #44569477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₃×D₁₁₁ #44569477