Subgroups — C₂×ΓL(1,𝔽₈)⋊Q₈ #66652

Order 336.

76 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	C₂×ΓL(1,𝔽₈)⋊C₄	C₂	1	2	yes	maximal
3	ΓL(1,𝔽₈)⋊Q₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₁₄	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂²×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
6	C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
7	ΓL(1,𝔽₈)⋊C₄	C₂²	1	4	yes	—
8	C₂×C₄×C₇	C₂×C₃	1	1	yes	characteristic
9	C₂×Dic₇	C₂×C₃	1	2	yes	—
10	Dic₁₄	C₂×C₃	1	4	yes	complemented
11	C₂×C₃×Q₈	—	7	1	no	maximal, Hall
12	C₂×ΓL(1,𝔽₈)	Q₈	1	2	yes	complemented
13	C₂×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
14	C₂²×C₇	C₂²×C₃	1	1	yes	characteristic
15	C₄×C₇	C₂²×C₃	1	2	yes	—
16	Dic₇	C₂²×C₃	1	4	yes	—
17	C₃×Q₈	—	7	4	no	—
18	C₂×C₃×C₄	—	7	2	no	—
19	C₂×C₃×C₄	—	7	1	no	—
20	ΓL(1,𝔽₈)	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
21	C₂×Q₈	—	7	1	no	Sylow
22	C₂×C₇	C₃×Q₈	1	2	yes	complemented
23	C₂×C₇	C₂³×C₃	1	1	yes	characteristic
24	C₂²×C₃	—	7	1	no	—
25	C₃×C₄	—	7	4	no	—
26	C₃×C₄	—	7	2	no	—
27	Q₈	—	7	4	no	—
28	C₂×C₄	—	7	2	no	—
29	C₂×C₄	AGL(1,𝔽₇)	1	1	yes	characteristic
30	C₇	C₂×C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	7	2	no	—
32	C₂×C₃	—	7	1	no	—
33	C₂²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
34	C₄	—	7	4	no	—
35	C₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
36	C₃	—	7	1	no	Sylow
37	C₂	ΓL(1,𝔽₈)⋊Q₈	1	2	yes	direct product factor
38	C₂	C₂²×AGL(1,𝔽₇)	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.