Subgroups — C₃⋊(C₃⋊AGL(1,𝔽₄₇)) #34085613

Order 19458.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₇⋊C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊AGL(1,𝔽₄₇)	—	3	4	no	maximal
3	C₃×C₄₇⋊C₂₃	D₃	1	4	yes	complemented
4	AGL(1,𝔽₄₇)	—	9	1	no	Hall
5	C₄₇⋊C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₁₄₁	C₂₃	1	1	yes	maximal, characteristic, complemented, Hall
7	C₃²×C₄₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
8	C₃⋊D₃×C₂₃	—	47	1	no	maximal, Hall
9	D₁₄₁	—	3	4	no	—
10	C₃²×C₂₃	—	47	1	no	Hall
11	C₃×C₄₇	D₃×C₂₃	1	4	yes	complemented
12	D₃×C₂₃	—	141	4	no	—
13	D₄₇	—	9	1	no	Hall
14	C₃×C₂₃	—	47	4	no	—
15	C₄₇	C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₃	—	423	1	no	Hall
17	C₂₃	—	47	1	no	Sylow
18	C₃⋊D₃	—	1081	1	no	Hall
19	C₃²	AGL(1,𝔽₄₇)	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3243	4	no	—
21	C₃	C₃⋊AGL(1,𝔽₄₇)	1	4	yes	complemented
22	C₂	—	9729	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₄₇	C₂×C₂₃
LCS	G ▷ C₃²×C₄₇
UCS	C₁

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.