Subgroups — C₃×#10597286 #14268941

Order 1824.

48 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
2	C₃×Dic₇₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#10597286	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×Q₈×C₁₉	—	2	1	no	—
6	C₃×Dic₃₈	—	2	1	no	—
7	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	Q₁₆×C₁₉	C₂×C₃	1	1	yes	characteristic
9	Dic₇₆	C₂×C₃	1	1	yes	characteristic
10	C₁₉⋊C₁₆	C₂×C₃	1	1	yes	characteristic
11	C₃×C₄×C₁₉	—	4	1	no	—
12	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
13	C₃×Dic₁₉	—	4	1	no	—
14	Q₈×C₁₉	—	2	1	no	—
15	Dic₃₈	—	2	1	no	—
16	C₈×C₁₉	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₃×C₁₉	D₈	1	1	yes	characteristic
18	C₃×Q₃₂	—	19	1	no	maximal, Hall
19	C₄×C₁₉	—	4	1	no	—
20	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
21	Dic₁₉	—	4	1	no	—
22	C₃×C₁₉	Q₃₂	1	1	yes	characteristic, complemented, Hall
23	C₃×Q₁₆	—	19	1	no	—
24	C₃×Q₁₆	D₁₉	1	1	yes	characteristic
25	C₃×C₁₆	—	19	1	no	—
26	C₂×C₁₉	C₃×D₈	1	1	yes	characteristic
27	Q₃₂	—	19	1	no	Sylow
28	C₃×Q₈	—	2	1	no	—
29	C₃×Q₈	—	38	1	no	—
30	C₃×C₈	C₂×D₁₉	1	1	yes	characteristic
31	C₁₉	C₃×Q₃₂	1	1	yes	characteristic, complemented, Sylow
32	Q₁₆	—	19	1	no	—
33	Q₁₆	C₃×D₁₉	1	1	yes	characteristic
34	C₁₆	—	19	1	no	—
35	C₃×C₄	—	4	1	no	—
36	C₃×C₄	—	76	1	no	—
37	C₃×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
38	Q₈	—	2	1	no	—
39	Q₈	—	38	1	no	—
40	C₈	C₂×C₃×D₁₉	1	1	yes	characteristic
41	C₂×C₃	#64525	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	—	76	1	no	—
44	C₄	C₃×C₂²⋊D₁₉	1	1	yes	characteristic
45	C₃	#10597286	1	1	yes	characteristic, direct product factor, Sylow
46	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, prime radical	C₂×C₃×C₁₉	D₈
hypercenter	C₃×Q₁₆	D₁₉
hypocenter	C₁₉	C₃×Q₃₂
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
4. #10597286	C₃	direct (N × H)
22. C₃×C₁₉	Q₃₂	semidirect
31. C₁₉	C₃×Q₃₂	semidirect
45. C₃	#10597286	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×Dic₇₆	2
C₃×C₁₉⋊C₁₆	2
#10597286	3
C₃×Q₃₂	19

Subgroups — C3×#10597286 #14268941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10597286 #14268941