Subgroups — C₃²×D₁₄₄₁ #39906348

Order 25938.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₄₄₁	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₁₁×C₁₃₁	C₂×C₃	1	4	yes	complemented
4	D₁₄₄₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₃²×D₁₃₁	—	11	1	no	maximal, Hall
6	C₁₁×C₁₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₁₃₁	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₃×D₁₃₁	—	11	4	no	—
9	C₃×C₁₃₁	C₃×D₁₁	1	4	yes	complemented
10	D₁₃₁	—	11	1	no	Hall
11	C₃²×D₁₁	—	131	1	no	maximal, Hall
12	C₁₃₁	C₃²×D₁₁	1	1	yes	characteristic, complemented, Sylow
13	C₃²×C₁₁	D₁₃₁	1	1	yes	characteristic, complemented, Hall
14	C₃×D₁₁	—	131	4	no	—
15	C₃×C₁₁	C₃×D₁₃₁	1	4	yes	complemented
16	D₁₁	—	131	1	no	Hall
17	C₂×C₃²	—	1441	1	no	Hall
18	C₁₁	C₃²×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
19	C₃²	D₁₄₄₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	1441	4	no	—
21	C₃	C₃×D₁₄₄₁	1	4	yes	direct product factor
22	C₂	—	1441	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₁₄₄₁
commutator, cosocle, hypocenter	C₁₁×C₁₃₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₃₁	C₂
LCS	G ▷ C₁₁×C₁₃₁
UCS	C₁ ◁ C₃²

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.