Subgroups — D₂₉×D₁₄₃ #30658705

Order 16588.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₁₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×D₁₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₃×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₃×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×D₂₉	—	11	1	no	maximal, Hall
6	D₁₁×D₂₉	—	13	1	no	maximal, Hall
7	D₃₇₇	—	11	1	no	—
8	C₁₃×D₂₉	D₁₁	1	1	yes	characteristic, complemented
9	D₁₃×C₂₉	—	11	1	no	—
10	D₃₁₉	—	13	1	no	—
11	C₁₁×D₂₉	D₁₃	1	1	yes	characteristic, complemented
12	D₁₁×C₂₉	—	13	1	no	—
13	C₂×D₁₄₃	—	29	1	no	maximal, Hall
14	C₁₃×C₂₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₂₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁×C₁₃	—	29	1	no	—
17	D₁₄₃	—	29	1	no	—
18	D₁₄₃	D₂₉	1	1	yes	characteristic, direct product factor
19	C₁₁×C₁₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
20	C₂×D₂₉	—	143	1	no	Hall
21	C₂×C₂₉	—	143	1	no	—
22	D₂₉	—	143	1	no	—
23	D₂₉	D₁₄₃	1	1	yes	characteristic, direct product factor
24	C₂×D₁₃	—	319	1	no	Hall
25	C₂×D₁₁	—	377	1	no	Hall
26	C₂₉	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₃	—	29	1	no	—
28	D₁₃	—	11	1	no	—
29	D₁₃	—	319	1	no	—
30	C₂×C₁₁	—	29	1	no	—
31	D₁₁	—	13	1	no	—
32	D₁₁	—	377	1	no	—
33	C₁₃	D₁₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
34	C₁₁	D₁₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	4147	1	no	Sylow
36	C₂	—	29	1	no	—
37	C₂	—	4147	1	no	—
38	C₂	—	143	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₃×C₂₉	C₂²
LCS	G ▷ C₁₁×C₁₃×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₄₁₄₇	C₂	semidirect
2. C₂₉×D₁₄₃	C₂	semidirect
3. C₁₁×C₁₃×D₂₉	C₂	semidirect
4. C₁₁×C₁₃×C₂₉	C₂²	semidirect
8. C₁₃×D₂₉	D₁₁	semidirect
11. C₁₁×D₂₉	D₁₃	semidirect
14. C₁₃×C₂₉	C₂×D₁₁	semidirect
15. C₁₁×C₂₉	C₂×D₁₃	semidirect
18. D₁₄₃	D₂₉	direct (N × H)
19. C₁₁×C₁₃	C₂×D₂₉	semidirect
23. D₂₉	D₁₄₃	direct (N × H)
26. C₂₉	C₂×D₁₄₃	semidirect
33. C₁₃	D₁₁×D₂₉	semidirect
34. C₁₁	D₁₃×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
D₄₁₄₇	2
C₂₉×D₁₄₃	2
C₁₁×C₁₃×D₂₉	2
D₁₃×D₂₉	11
D₁₁×D₂₉	13
C₂×D₁₄₃	29

Subgroups — D29×D143 #30658705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×D₁₄₃ #30658705