Subgroups — C₄×ΓL(1,𝔽₈)×C₂₇₁ #36384608

Order 22764.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×ΓL(1,𝔽₈)×C₂₇₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₂₇₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	ΓL(1,𝔽₈)×C₂₇₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₂₇₁	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₂₇₁	—	7	1	no	maximal, Hall
6	C₇×C₂₇₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₂₇₁	—	7	1	no	—
8	C₄×C₂₇₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₂₇₁	—	7	1	no	Hall
10	C₂×C₂₇₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₂₇₁	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×ΓL(1,𝔽₈)	C₂₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×ΓL(1,𝔽₈)	C₂×C₂₇₁	1	1	yes	characteristic
14	C₄×C₇	C₃×C₂₇₁	1	1	yes	characteristic, complemented, Hall
15	ΓL(1,𝔽₈)	C₄×C₂₇₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₇	C₂×C₃×C₂₇₁	1	1	yes	characteristic
17	C₃×C₄	—	7	1	no	Hall
18	C₇	C₃×C₄×C₂₇₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	7	1	no	—
20	C₄	ΓL(1,𝔽₈)×C₂₇₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	7	1	no	Sylow
22	C₂	C₂×ΓL(1,𝔽₈)×C₂₇₁	1	1	yes	characteristic

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.