Subgroups — D₂₉×D₂₈₇ #45685643

Order 33292.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₃₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×D₂₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₄₁×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₂₉×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₉×D₄₁	—	7	1	no	maximal, Hall
6	D₁₁₈₉	—	7	1	no	—
7	C₂₉×D₄₁	—	7	1	no	—
8	C₄₁×D₂₉	D₇	1	1	yes	characteristic, complemented
9	C₂₉×C₄₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
10	C₂×D₂₈₇	—	29	1	no	maximal, Hall
11	D₇×D₂₉	—	41	1	no	maximal, Hall
12	C₂×C₇×C₄₁	—	29	1	no	—
13	D₂₈₇	—	29	1	no	—
14	D₂₈₇	D₂₉	1	1	yes	characteristic, direct product factor
15	D₂₀₃	—	41	1	no	—
16	C₇×D₂₉	D₄₁	1	1	yes	characteristic, complemented
17	D₇×C₂₉	—	41	1	no	—
18	C₇×C₄₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
19	C₇×C₂₉	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₄₁	—	203	1	no	Hall
21	C₂×D₂₉	—	287	1	no	Hall
22	C₂×C₄₁	—	29	1	no	—
23	D₄₁	—	7	1	no	—
24	D₄₁	—	203	1	no	—
25	C₂×C₂₉	—	287	1	no	—
26	D₂₉	—	287	1	no	—
27	D₂₉	D₂₈₇	1	1	yes	characteristic, direct product factor
28	C₄₁	D₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₂₉	C₂×D₂₈₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₇	—	1189	1	no	Hall
31	C₂×C₇	—	29	1	no	—
32	D₇	—	41	1	no	—
33	D₇	—	1189	1	no	—
34	C₇	D₂₉×D₄₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8323	1	no	Sylow
36	C₂	—	29	1	no	—
37	C₂	—	287	1	no	—
38	C₂	—	8323	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₂₉×C₄₁	C₂²
LCS	G ▷ C₇×C₂₉×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₃₂₃	C₂	semidirect
2. C₂₉×D₂₈₇	C₂	semidirect
3. C₇×C₄₁×D₂₉	C₂	semidirect
4. C₇×C₂₉×C₄₁	C₂²	semidirect
8. C₄₁×D₂₉	D₇	semidirect
9. C₂₉×C₄₁	C₂×D₇	semidirect
14. D₂₈₇	D₂₉	direct (N × H)
16. C₇×D₂₉	D₄₁	semidirect
18. C₇×C₄₁	C₂×D₂₉	semidirect
19. C₇×C₂₉	C₂×D₄₁	semidirect
27. D₂₉	D₂₈₇	direct (N × H)
28. C₄₁	D₇×D₂₉	semidirect
29. C₂₉	C₂×D₂₈₇	semidirect
34. C₇	D₂₉×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
D₈₃₂₃	2
C₂₉×D₂₈₇	2
C₇×C₄₁×D₂₉	2
D₂₉×D₄₁	7
C₂×D₂₈₇	29
D₇×D₂₉	41

Subgroups — D29×D287 #45685643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×D₂₈₇ #45685643