Subgroups — C₃×C₁₁²×D₄₁ #44446708

Order 29766.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁²×D₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁²×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×D₄₁	C₁₁	1	12	yes	maximal, direct product factor
5	C₃×C₁₁×C₄₁	C₂×C₁₁	1	12	yes	complemented
6	C₁₁×D₄₁	C₃×C₁₁	1	12	yes	direct product factor
7	C₂×C₃×C₁₁²	—	41	1	no	maximal, Hall
8	C₁₁×C₄₁	C₂×C₃×C₁₁	1	12	yes	complemented
9	C₃×C₁₁²	D₄₁	1	1	yes	characteristic, direct product factor, Hall
10	C₃×D₄₁	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₁²	—	41	1	no	Hall
12	C₃×C₄₁	C₂×C₁₁²	1	1	yes	characteristic, complemented, Hall
13	C₁₁²	C₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
14	D₄₁	C₃×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₁₁	—	41	12	no	—
16	C₄₁	C₂×C₃×C₁₁²	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₁₁	C₁₁×D₄₁	1	12	yes	direct product factor
18	C₂×C₁₁	—	41	12	no	—
19	C₁₁	C₃×C₁₁×D₄₁	1	12	yes	direct product factor
20	C₂×C₃	—	41	1	no	Hall
21	C₃	C₁₁²×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	41	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁²	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂×C₃×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₄₁	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₃×C₁₁²

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.