Subgroups — C₄₁⋊GL(2,𝔽₃) #14520179

Order 1968.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	SL(2,𝔽₃)×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#10620284	—	3	1	no	maximal, Hall
3	C₂×D₁₂₃	—	4	1	no	maximal
4	Q₈×C₄₁	D₃	1	1	yes	characteristic, complemented
5	D₁₆₄	—	3	1	no	—
6	#66491	—	3	1	no	—
7	C₂×C₃×C₄₁	—	4	1	no	—
8	D₁₂₃	—	4	2	no	—
9	C₂×D₄₁	—	6	1	no	—
10	C₄×C₄₁	—	3	1	no	—
11	C₃×C₄₁	—	4	1	no	Hall
12	C₂×C₄₁	S₄	1	1	yes	characteristic
13	D₄₁	—	12	1	no	—
14	GL(2,𝔽₃)	—	41	1	no	maximal, Hall
15	C₄₁	GL(2,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
16	SL(2,𝔽₃)	D₄₁	1	1	yes	characteristic, complemented
17	SD₁₆	—	123	1	no	Sylow
18	C₂×D₃	—	164	1	no	—
19	Q₈	D₁₂₃	1	1	yes	characteristic, complemented
20	D₄	—	123	1	no	—
21	C₈	—	123	1	no	—
22	C₂×C₃	—	4	1	no	—
23	D₃	—	164	2	no	—
24	C₂²	—	246	1	no	—
25	C₄	—	3	1	no	—
26	C₃	—	4	1	no	Sylow
27	C₂	—	492	1	no	—
28	C₂	A₄⋊D₄₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄⋊D₄₁
commutator, cosocle, hypocenter	SL(2,𝔽₃)×C₄₁	C₂
Fitting	Q₈×C₄₁	D₃
socle	C₂×C₄₁	S₄
LCS	G ▷ SL(2,𝔽₃)×C₄₁
UCS	C₁ ◁ C₂

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.