Subgroups — D₂₉×D₃₇⋊C₃ #27166151

Order 12876.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉⋊(D₃₇⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₉×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×D₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₉×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂₉×C₃₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₀₇₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂₉×D₃₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃₇×D₂₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂₉×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃₇⋊C₃	—	29	1	no	maximal, Hall
11	C₂×C₃×D₂₉	—	37	1	no	maximal, Hall
12	C₂×C₃₇⋊C₃	—	29	1	no	—
13	D₃₇⋊C₃	—	29	1	no	—
14	D₃₇⋊C₃	D₂₉	1	1	yes	characteristic, direct product factor
15	C₂×C₃×C₂₉	—	37	1	no	—
16	C₃×D₂₉	—	37	1	no	—
17	C₃×D₂₉	—	37	1	no	—
18	C₂×D₃₇	—	29	1	no	Hall
19	C₂×D₂₉	—	37	1	no	Hall
20	C₃₇⋊C₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₂₉	—	37	1	no	Hall
22	C₂×C₃₇	—	29	1	no	—
23	D₃₇	—	29	1	no	—
24	D₃₇	C₃×D₂₉	1	1	yes	characteristic, complemented
25	C₂×C₂₉	—	37	1	no	—
26	D₂₉	—	37	1	no	—
27	D₂₉	D₃₇⋊C₃	1	1	yes	characteristic, direct product factor
28	C₃₇	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₂₉	C₂×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	1073	1	no	Hall
31	C₂×C₃	—	37	1	no	—
32	C₂×C₃	—	1073	1	no	—
33	C₂×C₃	—	1073	1	no	—
34	C₂²	—	1073	1	no	Sylow
35	C₃	—	37	1	no	Sylow
36	C₂	—	29	1	no	—
37	C₂	—	37	1	no	—
38	C₂	—	1073	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉×C₃₇	C₂²×C₃
LCS	G ▷ C₂₉×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₉⋊(D₃₇⋊C₃)	C₂	semidirect
2. D₂₉×C₃₇⋊C₃	C₂	semidirect
3. C₂₉×D₃₇⋊C₃	C₂	semidirect
4. D₂₉×D₃₇	C₃	semidirect
5. C₂₉×C₃₇⋊C₃	C₂²	semidirect
6. D₁₀₇₃	C₂×C₃	semidirect
7. C₂₉×D₃₇	C₂×C₃	semidirect
8. C₃₇×D₂₉	C₂×C₃	semidirect
9. C₂₉×C₃₇	C₂²×C₃	semidirect
14. D₃₇⋊C₃	D₂₉	direct (N × H)
20. C₃₇⋊C₃	C₂×D₂₉	semidirect
24. D₃₇	C₃×D₂₉	semidirect
27. D₂₉	D₃₇⋊C₃	direct (N × H)
28. C₃₇	C₂×C₃×D₂₉	semidirect
29. C₂₉	C₂×D₃₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₉⋊(D₃₇⋊C₃)	2
D₂₉×C₃₇⋊C₃	2
C₂₉×D₃₇⋊C₃	2
D₂₉×D₃₇	3
C₂×D₃₇⋊C₃	29
C₂×C₃×D₂₉	37

Subgroups — D29×D37⋊C3 #27166151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×D₃₇⋊C₃ #27166151