Subgroups — D₃×C₁₁×C₁₉² #37558549

Order 23826.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₁×C₁₉²	—	3	1	no	maximal, Hall
3	C₁₁×C₁₉²	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₉²	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₃×C₁₁×C₁₉	C₁₉	1	20	yes	maximal, direct product factor
6	C₃×C₁₉²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₉²	—	3	1	no	Hall
8	C₃×C₁₁×C₁₉	C₂×C₁₉	1	20	yes	complemented
9	C₂×C₁₁×C₁₉	—	3	20	no	—
10	C₁₉²	D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₁₁×C₁₉	D₃×C₁₉	1	20	yes	direct product factor
12	D₃×C₁₉	C₁₁×C₁₉	1	20	yes	direct product factor
13	D₃×C₁₁	C₁₉²	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₉	C₂×C₁₁×C₁₉	1	20	yes	complemented
15	C₂×C₁₉	—	3	20	no	—
16	C₃×C₁₁	C₂×C₁₉²	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁	—	3	1	no	Hall
18	C₁₉	D₃×C₁₁×C₁₉	1	20	yes	direct product factor
19	C₁₁	D₃×C₁₉²	1	1	yes	characteristic, direct product factor, Sylow
20	D₃	C₁₁×C₁₉²	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₁₁×C₁₉²	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₉²	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₁×C₁₉²
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₉²	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₁×C₁₉²

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.