Subgroups — C₂×C₁₁×C₃₆₁⋊C₃ #37558513

Order 23826.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁×C₃₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₃₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₆₁⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₁₉⋊C₃	—	19	1	no	maximal
6	C₃₆₁⋊C₃	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃₆₁	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁×C₁₉⋊C₃	—	19	1	no	—
9	C₂×C₁₁×C₁₉	C₁₉⋊C₃	1	1	yes	characteristic
10	C₃₆₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
11	C₁₁×C₁₉	C₂×C₁₉⋊C₃	1	1	yes	characteristic
12	C₂×C₁₉⋊C₃	—	19	1	no	—
13	C₂×C₃×C₁₁	—	361	1	no	Hall
14	C₁₉⋊C₃	—	19	1	no	—
15	C₂×C₁₉	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic
16	C₃×C₁₁	—	361	1	no	Hall
17	C₂×C₁₁	C₃₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₉	C₂×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic
19	C₁₁	C₂×C₃₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	361	1	no	Hall
21	C₃	—	361	1	no	Sylow
22	C₂	C₁₁×C₃₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₁	C₃₆₁⋊C₃
commutator, cosocle, hypocenter	C₃₆₁	C₂×C₃×C₁₁
Frattini	C₁₉	C₂×C₁₁×C₁₉⋊C₃
Fitting	C₂×C₁₁×C₃₆₁	C₃
socle	C₂×C₁₁×C₁₉	C₁₉⋊C₃
LCS	G ▷ C₃₆₁
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.