Subgroups — D₃×C₁₁²×C₄₃ #44530219

Order 31218.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₁²×C₄₃	—	3	1	no	maximal, Hall
3	C₁₁²×C₄₃	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₁×C₄₃	C₁₁	1	12	yes	maximal, direct product factor
5	C₃×C₁₁×C₄₃	C₂×C₁₁	1	12	yes	complemented
6	C₂×C₁₁×C₄₃	—	3	12	no	—
7	D₃×C₁₁²	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×C₄₃	D₃×C₁₁	1	12	yes	direct product factor
9	C₃×C₁₁²	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
10	D₃×C₄₃	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₁²	—	3	1	no	Hall
12	C₃×C₄₃	C₂×C₁₁²	1	1	yes	characteristic, complemented, Hall
13	C₁₁²	D₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₄₃	—	3	1	no	Hall
15	D₃×C₁₁	C₁₁×C₄₃	1	12	yes	direct product factor
16	C₄₃	D₃×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₁₁	C₂×C₁₁×C₄₃	1	12	yes	complemented
18	C₂×C₁₁	—	3	12	no	—
19	C₁₁	D₃×C₁₁×C₄₃	1	12	yes	direct product factor
20	D₃	C₁₁²×C₄₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₁₁²×C₄₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁²×C₄₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₁²×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₄₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₁²×C₄₃

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.