Subgroups — D₄₇×D₅₇ #24924277

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₆₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₄₇	—	3	1	no	maximal, Hall
5	C₃×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₈₉₃	—	3	1	no	—
7	C₁₉×D₄₇	D₃	1	1	yes	characteristic, complemented
8	D₁₉×C₄₇	—	3	1	no	—
9	C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₄₇	—	19	1	no	maximal, Hall
11	D₁₄₁	—	19	1	no	—
12	C₃×D₄₇	D₁₉	1	1	yes	characteristic, complemented
13	D₃×C₄₇	—	19	1	no	—
14	C₂×D₅₇	—	47	1	no	maximal, Hall
15	C₂×D₄₇	—	57	1	no	Hall
16	C₃×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₉	—	47	1	no	—
18	D₅₇	—	47	1	no	—
19	D₅₇	D₄₇	1	1	yes	characteristic, direct product factor
20	C₂×C₄₇	—	57	1	no	—
21	D₄₇	—	57	1	no	—
22	D₄₇	D₅₇	1	1	yes	characteristic, direct product factor
23	C₂×D₁₉	—	141	1	no	Hall
24	C₃×C₁₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
25	C₄₇	C₂×D₅₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₉	—	47	1	no	—
27	D₁₉	—	3	1	no	—
28	D₁₉	—	141	1	no	—
29	C₁₉	D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	893	1	no	Hall
31	C₂×C₃	—	47	1	no	—
32	D₃	—	19	1	no	—
33	D₃	—	893	1	no	—
34	C₂²	—	2679	1	no	Sylow
35	C₃	D₁₉×D₄₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	47	1	no	—
37	C₂	—	57	1	no	—
38	C₂	—	2679	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₄₇	C₂²
LCS	G ▷ C₃×C₁₉×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₂₆₇₉	C₂	semidirect
2. C₄₇×D₅₇	C₂	semidirect
3. C₃×C₁₉×D₄₇	C₂	semidirect
5. C₃×C₁₉×C₄₇	C₂²	semidirect
7. C₁₉×D₄₇	D₃	semidirect
9. C₁₉×C₄₇	C₂×D₃	semidirect
12. C₃×D₄₇	D₁₉	semidirect
16. C₃×C₄₇	C₂×D₁₉	semidirect
19. D₅₇	D₄₇	direct (N × H)
22. D₄₇	D₅₇	direct (N × H)
24. C₃×C₁₉	C₂×D₄₇	semidirect
25. C₄₇	C₂×D₅₇	semidirect
29. C₁₉	D₃×D₄₇	semidirect
35. C₃	D₁₉×D₄₇	semidirect

Subgroups — D47×D57 #24924277

Conjugacy classes of subgroups

Complements

Subgroups — D₄₇×D₅₇ #24924277