Subgroups — C₂×C₁₁×#11762245 #37558542

Order 23826.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#11762245	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁×C₁₉²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×#11762245	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₁₉⋊C₃	—	19	20	no	maximal
6	#11762245	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₉²	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁×C₁₉⋊C₃	—	19	20	no	—
9	C₂×C₁₁×C₁₉	C₁₉⋊C₃	1	20	yes	complemented
10	C₁₉²	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
11	C₁₁×C₁₉	C₂×C₁₉⋊C₃	1	20	yes	complemented
12	C₂×C₁₉⋊C₃	—	19	20	no	—
13	C₂×C₃×C₁₁	—	361	1	no	Hall
14	C₁₉⋊C₃	—	19	20	no	—
15	C₂×C₁₉	C₁₁×C₁₉⋊C₃	1	20	yes	complemented
16	C₃×C₁₁	—	361	1	no	Hall
17	C₂×C₁₁	#11762245	1	1	yes	characteristic, direct product factor, Hall
18	C₁₉	C₂×C₁₁×C₁₉⋊C₃	1	20	yes	complemented
19	C₁₁	C₂×#11762245	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	361	1	no	Hall
21	C₃	—	361	1	no	Sylow
22	C₂	C₁₁×#11762245	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₁	#11762245
commutator, cosocle, hypocenter	C₁₉²	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₉²	C₃
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₂×C₁₁

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.