Subgroups — Q₁₆×ΓL(1,𝔽₈) #66586

Order 336.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×ΓL(1,𝔽₈)	C₂	1	2	yes	maximal
2	C₈×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic
3	C₇×Q₁₆	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
5	C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
6	C₇×Q₈	C₂×C₃	1	2	yes	—
7	C₇×C₈	C₂×C₃	1	1	yes	characteristic
8	C₃×Q₁₆	—	7	1	no	maximal, Hall
9	C₂×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
10	C₄×C₇	—	2	2	no	—
11	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
12	C₃×Q₈	—	7	2	no	—
13	C₃×C₈	—	7	1	no	—
14	ΓL(1,𝔽₈)	Q₁₆	1	1	yes	characteristic, direct product factor, Hall
15	Q₁₆	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₇	C₃×D₄	1	1	yes	characteristic
17	C₃×C₄	—	7	1	no	—
18	C₃×C₄	—	14	2	no	—
19	Q₈	C₂×ΓL(1,𝔽₈)	1	2	yes	—
20	C₈	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
21	C₇	C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃	—	7	1	no	—
23	C₄	—	2	2	no	—
24	C₄	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
25	C₃	—	7	1	no	Sylow
26	C₂	D₄×ΓL(1,𝔽₈)	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.