Subgroups — #1131⋊C₃ #66539

Order 336.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic
2	C₈×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#1131	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×AGL(1,𝔽₇)	C₄	1	1	yes	characteristic
6	C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
7	ΓL(1,𝔽₈)⋊C₄	C₄	1	1	yes	characteristic
8	C₄×D₇	C₂×C₃	1	1	yes	characteristic
9	C₇×C₈	C₂×C₃	1	1	yes	characteristic, complemented
10	C₇⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×M₁₆	—	7	1	no	maximal, Hall
12	C₂×ΓL(1,𝔽₈)	C₂×C₄	1	1	yes	characteristic
13	AGL(1,𝔽₇)	—	2	1	no	—
14	C₂×D₇	C₃×C₄	1	1	yes	characteristic
15	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
16	Dic₇	C₃×C₄	1	1	yes	characteristic
17	C₂×C₃×C₄	—	7	1	no	—
18	C₃×C₈	—	7	1	no	—
19	C₃×C₈	—	7	1	no	—
20	ΓL(1,𝔽₈)	M₁₆	1	1	yes	characteristic, complemented, Hall
21	M₁₆	—	7	1	no	Sylow
22	C₂×C₇	C₂×C₃×C₄	1	1	yes	characteristic
23	D₇	—	2	1	no	—
24	C₂²×C₃	—	7	1	no	—
25	C₃×C₄	—	7	1	no	—
26	C₃×C₄	—	7	1	no	—
27	C₂×C₄	—	7	1	no	—
28	C₈	—	7	1	no	—
29	C₈	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
30	C₇	C₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	7	1	no	—
32	C₂×C₃	—	14	1	no	—
33	C₂²	—	7	1	no	—
34	C₄	—	7	1	no	—
35	C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
36	C₃	—	7	1	no	Sylow
37	C₂	—	14	1	no	—
38	C₂	C₄×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.