Subgroups — D₃×AGL(1,𝔽₈) #66742

Order 336.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×AGL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×AGL(1,𝔽₈)	—	3	1	no	maximal, Hall
3	AGL(1,𝔽₈)	D₃	1	1	yes	characteristic, direct product factor
4	C₂³×D₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	D₃×C₇	—	8	1	no	maximal
6	C₂³×C₃	C₂×C₇	1	1	yes	characteristic, complemented
7	C₂²×D₃	—	7	1	no	—
8	C₂²×D₃	—	7	1	no	—
9	C₃×C₇	—	8	1	no	Hall
10	C₂⁴	—	3	1	no	Sylow
11	C₂×C₇	—	24	1	no	—
12	C₂²×C₃	—	7	1	no	—
13	C₂×D₃	—	7	1	no	—
14	C₂×D₃	—	7	3	no	—
15	C₂³	—	21	1	no	—
16	C₂³	—	21	1	no	—
17	C₂³	D₃×C₇	1	1	yes	characteristic, complemented
18	C₇	—	8	1	no	Sylow
19	C₂×C₃	—	7	1	no	—
20	D₃	—	7	1	no	—
21	D₃	AGL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
22	C₂²	—	7	1	no	—
23	C₂²	—	21	1	no	—
24	C₂²	—	21	3	no	—
25	C₃	C₂×AGL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
26	C₂	—	3	1	no	—
27	C₂	—	7	1	no	—
28	C₂	—	21	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂³×C₃	C₂×C₇
LCS	G ▷ C₂³×C₃
UCS	C₁

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.