Subgroups — (C₇⋊C₈)⋊C₉ #92575

Order 504.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇⋊C₈	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇⋊C₉	C₄	1	1	yes	characteristic
4	C₃×C₄×C₇	C₂×C₃	1	1	yes	characteristic
5	C₈×C₉	—	7	1	no	maximal, Hall
6	C₇⋊C₉	C₈	1	1	yes	characteristic, complemented, Hall
7	C₇⋊C₈	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₇	C₃×C₄	1	1	yes	characteristic
9	C₄×C₉	—	7	1	no	—
10	C₄×C₇	C₂×C₉	1	1	yes	characteristic
11	C₃×C₈	—	21	1	no	—
12	C₃×C₇	C₃×C₈	1	1	yes	characteristic
13	C₂×C₉	—	7	1	no	—
14	C₂×C₇	C₄×C₉	1	1	yes	characteristic
15	C₃×C₄	AGL(1,𝔽₇)	1	1	yes	characteristic
16	C₉	—	7	1	no	Sylow
17	C₈	—	21	1	no	Sylow
18	C₇	C₈×C₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
20	C₄	D₇⋊C₉	1	1	yes	characteristic
21	C₃	ΓL(1,𝔽₈)⋊C₈	1	1	yes	characteristic
22	C₂	Dic₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃×C₄	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₈×C₉
Fitting, cosocle	C₃×C₄×C₇	C₂×C₃
socle, prime radical	C₂×C₃×C₇	C₃×C₄
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₄

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.