Subgroups — D₃×D₁₉×C₁₀₇ #37567337

Order 24396.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₉×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₉×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₉×C₁₀₇	—	3	1	no	maximal, Hall
5	C₃×C₁₉×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₉×C₁₀₇	—	3	1	no	—
7	D₁₉×C₁₀₇	—	3	1	no	—
8	D₁₉×C₁₀₇	D₃	1	1	yes	characteristic, direct product factor
9	C₁₉×C₁₀₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃×C₁₀₇	—	19	1	no	maximal, Hall
11	C₂×C₃×C₁₀₇	—	19	1	no	—
12	D₃×C₁₀₇	—	19	1	no	—
13	D₃×C₁₀₇	D₁₉	1	1	yes	characteristic, direct product factor
14	C₂²×C₁₀₇	—	57	1	no	Hall
15	C₃×C₁₀₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	D₃×D₁₉	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₀₇	—	3	1	no	—
18	C₂×C₁₀₇	—	19	1	no	—
19	C₂×C₁₀₇	—	57	1	no	—
20	D₅₇	C₂×C₁₀₇	1	1	yes	characteristic, complemented
21	C₃×D₁₉	C₂×C₁₀₇	1	1	yes	characteristic, complemented
22	D₃×C₁₉	C₂×C₁₀₇	1	1	yes	characteristic, complemented
23	C₁₀₇	D₃×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₁₉	—	3	1	no	Hall
25	C₃×C₁₉	C₂²×C₁₀₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₉	—	3	1	no	—
27	D₁₉	—	3	1	no	—
28	D₁₉	D₃×C₁₀₇	1	1	yes	characteristic, direct product factor
29	C₁₉	C₂×D₃×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	19	1	no	Hall
31	C₂×C₃	—	19	1	no	—
32	D₃	—	19	1	no	—
33	D₃	D₁₉×C₁₀₇	1	1	yes	characteristic, direct product factor
34	C₂²	—	57	1	no	Sylow
35	C₃	C₂×D₁₉×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	19	1	no	—
38	C₂	—	57	1	no	—

	subgroup	G/H
center, hypercenter	C₁₀₇	D₃×D₁₉
commutator, cosocle, hypocenter	C₃×C₁₉	C₂²×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₁₀₇	C₂²
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₁₀₇

Complements

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

N	H ≅ G/N	type
1. C₁₀₇×D₅₇	C₂	semidirect
2. D₃×C₁₉×C₁₀₇	C₂	semidirect
3. C₃×D₁₉×C₁₀₇	C₂	semidirect
5. C₃×C₁₉×C₁₀₇	C₂²	semidirect
8. D₁₉×C₁₀₇	D₃	direct (N × H)
9. C₁₉×C₁₀₇	C₂×D₃	semidirect
13. D₃×C₁₀₇	D₁₉	direct (N × H)
15. C₃×C₁₀₇	C₂×D₁₉	semidirect
16. D₃×D₁₉	C₁₀₇	direct (N × H)
20. D₅₇	C₂×C₁₀₇	semidirect
21. C₃×D₁₉	C₂×C₁₀₇	semidirect
22. D₃×C₁₉	C₂×C₁₀₇	semidirect
23. C₁₀₇	D₃×D₁₉	direct (N × H)
25. C₃×C₁₉	C₂²×C₁₀₇	semidirect
28. D₁₉	D₃×C₁₀₇	direct (N × H)
29. C₁₉	C₂×D₃×C₁₀₇	semidirect
33. D₃	D₁₉×C₁₀₇	direct (N × H)
35. C₃	C₂×D₁₉×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×D₅₇	2
D₃×C₁₉×C₁₀₇	2
C₃×D₁₉×C₁₀₇	2
C₂×D₁₉×C₁₀₇	3
C₂×D₃×C₁₀₇	19
D₃×D₁₉	107

Subgroups — D3×D19×C107 #37567337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₉×C₁₀₇ #37567337