Subgroups — C₃×SD₁₆×C₁₉ #11744901

Order 912.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₁₉	—	2	1	no	—
6	C₃×C₄×C₁₉	—	2	1	no	—
7	C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	Q₈×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₄×C₁₉	C₂×C₃	1	1	yes	characteristic
10	C₈×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₁₉	—	4	1	no	—
12	C₂×C₃×C₁₉	D₄	1	1	yes	characteristic
13	C₂²×C₁₉	—	2	1	no	—
14	C₄×C₁₉	—	2	1	no	—
15	C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
16	C₃×C₁₉	SD₁₆	1	1	yes	characteristic, direct product factor, Hall
17	C₃×SD₁₆	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₁₉	—	4	1	no	—
19	C₂×C₁₉	C₃×D₄	1	1	yes	characteristic
20	C₃×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
21	C₃×D₄	C₂×C₁₉	1	1	yes	characteristic
22	C₃×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
23	C₁₉	C₃×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
24	SD₁₆	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃	—	2	1	no	—
26	C₃×C₄	—	2	1	no	—
27	C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
28	Q₈	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
29	D₄	C₂×C₃×C₁₉	1	1	yes	characteristic
30	C₈	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
31	C₂×C₃	—	4	1	no	—
32	C₂×C₃	D₄×C₁₉	1	1	yes	characteristic
33	C₂²	—	2	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
36	C₃	SD₁₆×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	4	1	no	—
38	C₂	C₃×D₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₁₉	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃×C₁₉
prime radical	C₃×D₄×C₁₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₁₉ ◁ C₃×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₁₉	C₂	semidirect
3. C₃×C₈×C₁₉	C₂	semidirect
4. SD₁₆×C₁₉	C₃	direct (N × H)
8. Q₈×C₁₉	C₂×C₃	semidirect
10. C₈×C₁₉	C₂×C₃	semidirect
16. C₃×C₁₉	SD₁₆	direct (N × H)
17. C₃×SD₁₆	C₁₉	direct (N × H)
20. C₃×Q₈	C₂×C₁₉	semidirect
22. C₃×C₈	C₂×C₁₉	semidirect
23. C₁₉	C₃×SD₁₆	direct (N × H)
24. SD₁₆	C₃×C₁₉	direct (N × H)
28. Q₈	C₂×C₃×C₁₉	semidirect
30. C₈	C₂×C₃×C₁₉	semidirect
36. C₃	SD₁₆×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×Q₈×C₁₉	2
C₃×D₄×C₁₉	2
C₃×C₈×C₁₉	2
SD₁₆×C₁₉	3
C₃×SD₁₆	19

Subgroups — C3×SD16×C19 #11744901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×SD₁₆×C₁₉ #11744901