Subgroups — C₃⋊#19096726 #28413708

Order 14706.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578575	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#19096726	—	3	1	no	maximal
3	C₁₉×D₁₂₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#14578575	—	2	1	no	—
6	#14578575	D₃	1	1	yes	characteristic, complemented
7	C₁₉×D₄₃	—	3	1	no	Hall
8	C₁₉×C₄₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊(D₄₃⋊C₃)	—	19	1	no	maximal, Hall
10	C₃×C₄₃⋊C₃	—	19	1	no	Hall
11	D₃×C₁₉⋊C₃	—	43	1	no	maximal, Hall
12	D₁₂₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented
13	D₄₃⋊C₃	—	57	1	no	—
14	C₃×C₁₉⋊C₃	—	86	1	no	Hall
15	C₃×C₄₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
16	C₄₃⋊C₃	—	19	1	no	—
17	C₄₃⋊C₃	—	38	1	no	—
18	D₃×C₁₉	—	43	1	no	—
19	C₂×C₁₉⋊C₃	—	129	1	no	—
20	D₄₃	—	3	1	no	Hall
21	C₃×C₁₉	D₄₃⋊C₃	1	1	yes	characteristic, complemented
22	C₁₉⋊C₃	—	86	1	no	—
23	C₁₉⋊C₃	—	86	1	no	—
24	C₄₃	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₉	—	129	1	no	Hall
26	C₁₉	C₃⋊(D₄₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	817	1	no	Hall
28	C₃²	—	1634	1	no	Sylow
29	C₂×C₃	—	2451	1	no	—
30	D₃	—	43	1	no	—
31	C₃	—	1634	1	no	—
32	C₃	—	1634	1	no	—
33	C₃	#19096726	1	1	yes	characteristic, complemented
34	C₂	—	129	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₄₃	C₂×C₃
LCS	G ▷ C₃×C₁₉×C₄₃
UCS	C₁

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

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