Subgroups — C₃×#10597285 #14268940

Order 1824.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₅₂	C₂	1	1	yes	maximal, characteristic
3	C₃×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597285	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×Q₈×C₁₉	—	2	1	no	—
6	C₃×D₇₆	—	2	1	no	—
7	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	Q₁₆×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₁₅₂	C₂×C₃	1	1	yes	characteristic
10	C₁₉⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×D₁₉	—	4	1	no	—
12	C₃×C₄×C₁₉	—	4	1	no	—
13	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
14	Q₈×C₁₉	—	2	1	no	—
15	D₇₆	—	2	1	no	—
16	C₈×C₁₉	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₃×C₁₉	D₈	1	1	yes	characteristic
18	C₃×D₁₉	—	8	1	no	—
19	C₃×SD₃₂	—	19	1	no	maximal, Hall
20	C₂×D₁₉	—	4	1	no	—
21	C₄×C₁₉	—	4	1	no	—
22	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
23	C₃×C₁₉	SD₃₂	1	1	yes	characteristic, complemented, Hall
24	C₃×Q₁₆	D₁₉	1	1	yes	characteristic, complemented
25	C₃×D₈	—	19	1	no	—
26	C₃×C₁₆	—	19	1	no	—
27	C₂×C₁₉	C₃×D₈	1	1	yes	characteristic
28	D₁₉	—	8	1	no	—
29	SD₃₂	—	19	1	no	Sylow
30	C₃×Q₈	—	2	1	no	—
31	C₃×D₄	—	38	1	no	—
32	C₃×C₈	C₂×D₁₉	1	1	yes	characteristic
33	C₁₉	C₃×SD₃₂	1	1	yes	characteristic, complemented, Sylow
34	Q₁₆	C₃×D₁₉	1	1	yes	characteristic, complemented
35	D₈	—	19	1	no	—
36	C₁₆	—	19	1	no	—
37	C₂²×C₃	—	76	1	no	—
38	C₃×C₄	—	4	1	no	—
39	C₃×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
40	Q₈	—	2	1	no	—
41	D₄	—	38	1	no	—
42	C₈	C₂×C₃×D₁₉	1	1	yes	characteristic
43	C₂×C₃	—	152	1	no	—
44	C₂×C₃	#64525	1	1	yes	characteristic
45	C₂²	—	76	1	no	—
46	C₄	—	4	1	no	—
47	C₄	C₃×C₂²⋊D₁₉	1	1	yes	characteristic
48	C₃	#10597285	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	152	1	no	—
50	C₂	C₃×#64525	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#64525
commutator, cosocle	C₈×C₁₉	C₂²×C₃
Frattini	C₈	C₂×C₃×D₁₉
Fitting	C₃×Q₁₆×C₁₉	C₂
socle	C₂×C₃×C₁₉	D₈
prime radical	C₃×D₁₅₂	C₂
hypercenter	C₃×Q₁₆	D₁₉
hypocenter	C₁₉	C₃×SD₃₂
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×Q₁₆×C₁₉	C₂	semidirect
3. C₃×C₁₉⋊C₁₆	C₂	semidirect
4. #10597285	C₃	direct (N × H)
8. Q₁₆×C₁₉	C₂×C₃	semidirect
10. C₁₉⋊C₁₆	C₂×C₃	semidirect
23. C₃×C₁₉	SD₃₂	semidirect
24. C₃×Q₁₆	D₁₉	semidirect
33. C₁₉	C₃×SD₃₂	semidirect
34. Q₁₆	C₃×D₁₉	semidirect
48. C₃	#10597285	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×Q₁₆×C₁₉	2
C₃×D₁₅₂	2
C₃×C₁₉⋊C₁₆	2
#10597285	3
C₃×SD₃₂	19

Subgroups — C3×#10597285 #14268940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10597285 #14268940