Subgroups — D₃×C₁₉×D₁₄₉ #46800813

Order 33972.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₄₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₉×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×D₁₄₉	—	3	1	no	maximal, Hall
5	C₃×C₁₉×C₁₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₉×C₁₄₉	—	3	1	no	—
7	C₁₉×D₁₄₉	—	3	1	no	—
8	C₁₉×D₁₄₉	D₃	1	1	yes	characteristic, direct product factor
9	C₁₉×C₁₄₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₁₄₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₄₄₇	C₂×C₁₉	1	1	yes	characteristic, complemented
12	C₃×D₁₄₉	C₂×C₁₉	1	1	yes	characteristic, complemented
13	D₃×C₁₄₉	C₂×C₁₉	1	1	yes	characteristic, complemented
14	C₂×D₁₄₉	—	3	1	no	Hall
15	C₃×C₁₄₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₄₉	—	3	1	no	—
17	D₁₄₉	—	3	1	no	—
18	D₁₄₉	D₃×C₁₉	1	1	yes	characteristic, direct product factor
19	C₂×D₃×C₁₉	—	149	1	no	maximal, Hall
20	C₁₄₉	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₉	—	149	1	no	—
22	D₃×C₁₉	—	149	1	no	—
23	D₃×C₁₉	D₁₄₉	1	1	yes	characteristic, direct product factor
24	C₂²×C₁₉	—	447	1	no	Hall
25	C₃×C₁₉	C₂×D₁₄₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₉	—	3	1	no	—
27	C₂×C₁₉	—	149	1	no	—
28	C₂×C₁₉	—	447	1	no	—
29	C₁₉	D₃×D₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×D₃	—	149	1	no	Hall
31	C₂×C₃	—	149	1	no	—
32	D₃	—	149	1	no	—
33	D₃	C₁₉×D₁₄₉	1	1	yes	characteristic, direct product factor
34	C₂²	—	447	1	no	Sylow
35	C₃	C₂×C₁₉×D₁₄₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	149	1	no	—
38	C₂	—	447	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₃×D₁₄₉
commutator, cosocle, hypocenter	C₃×C₁₄₉	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₁₄₉	C₂²
LCS	G ▷ C₃×C₁₄₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₄₄₇	C₂	semidirect
2. D₃×C₁₉×C₁₄₉	C₂	semidirect
3. C₃×C₁₉×D₁₄₉	C₂	semidirect
5. C₃×C₁₉×C₁₄₉	C₂²	semidirect
8. C₁₉×D₁₄₉	D₃	direct (N × H)
9. C₁₉×C₁₄₉	C₂×D₃	semidirect
10. D₃×D₁₄₉	C₁₉	direct (N × H)
11. D₄₄₇	C₂×C₁₉	semidirect
12. C₃×D₁₄₉	C₂×C₁₉	semidirect
13. D₃×C₁₄₉	C₂×C₁₉	semidirect
15. C₃×C₁₄₉	C₂²×C₁₉	semidirect
18. D₁₄₉	D₃×C₁₉	direct (N × H)
20. C₁₄₉	C₂×D₃×C₁₉	semidirect
23. D₃×C₁₉	D₁₄₉	direct (N × H)
25. C₃×C₁₉	C₂×D₁₄₉	semidirect
29. C₁₉	D₃×D₁₄₉	direct (N × H)
33. D₃	C₁₉×D₁₄₉	direct (N × H)
35. C₃	C₂×C₁₉×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×D₄₄₇	2
D₃×C₁₉×C₁₄₉	2
C₃×C₁₉×D₁₄₉	2
C₂×C₁₉×D₁₄₉	3
D₃×D₁₄₉	19
C₂×D₃×C₁₉	149

Subgroups — D3×C19×D149 #46800813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₉×D₁₄₉ #46800813