Subgroups — C₂×ΓL(1,𝔽₈)⋊C₈ #66543

Order 336.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic
2	ΓL(1,𝔽₈)⋊C₈	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇⋊C₈	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂²×ΓL(1,𝔽₈)	C₄	1	1	yes	characteristic
5	C₄×ΓL(1,𝔽₈)	C₄	1	1	yes	characteristic
6	C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₇	C₂×C₃	1	1	yes	characteristic
8	C₇⋊C₈	C₂×C₃	1	2	yes	complemented
9	C₂×C₃×C₈	—	7	1	no	maximal, Hall
10	C₂×ΓL(1,𝔽₈)	C₈	1	2	yes	complemented
11	C₂×ΓL(1,𝔽₈)	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₇	C₃×C₄	1	1	yes	characteristic
13	C₄×C₇	C₃×C₄	1	1	yes	characteristic
14	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×C₄	—	7	1	no	—
16	C₃×C₈	—	7	2	no	—
17	ΓL(1,𝔽₈)	C₂×C₈	1	1	yes	characteristic, complemented, Hall
18	C₂×C₈	—	7	1	no	Sylow
19	C₂×C₇	C₃×C₈	1	2	yes	complemented
20	C₂×C₇	C₂×C₃×C₄	1	1	yes	characteristic
21	C₂²×C₃	—	7	1	no	—
22	C₃×C₄	—	7	1	no	—
23	C₃×C₄	—	7	1	no	—
24	C₂×C₄	AGL(1,𝔽₇)	1	1	yes	characteristic
25	C₈	—	7	2	no	—
26	C₇	C₂×C₃×C₈	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	7	2	no	—
28	C₂×C₃	—	7	1	no	—
29	C₂²	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
30	C₄	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
31	C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
32	C₃	—	7	1	no	Sylow
33	C₂	ΓL(1,𝔽₈)⋊C₈	1	2	yes	direct product factor
34	C₂	C₂×ΓL(1,𝔽₈)⋊C₄	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.