Subgroups — C₈×AGL(1,𝔽₈) #90157

Order 448.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×AGL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×AGL(1,𝔽₈)	C₄	1	1	yes	characteristic
3	C₂³×C₈	C₇	1	1	yes	maximal, characteristic, complemented, Sylow
4	AGL(1,𝔽₈)	C₈	1	1	yes	characteristic, direct product factor
5	C₇×C₈	—	8	1	no	maximal
6	C₂³×C₄	C₂×C₇	1	1	yes	characteristic
7	C₂²×C₈	—	7	1	no	—
8	C₂²×C₈	—	7	1	no	—
9	C₄×C₇	—	8	1	no	—
10	C₂⁴	C₄×C₇	1	1	yes	characteristic
11	C₂²×C₄	—	7	1	no	—
12	C₂²×C₄	—	7	1	no	—
13	C₂×C₈	—	7	1	no	—
14	C₂×C₈	—	7	3	no	—
15	C₂×C₇	—	8	1	no	—
16	C₂³	—	7	1	no	—
17	C₂³	—	7	1	no	—
18	C₂³	C₇×C₈	1	1	yes	characteristic, complemented
19	C₂×C₄	—	7	1	no	—
20	C₂×C₄	—	7	3	no	—
21	C₈	—	7	1	no	—
22	C₈	AGL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
23	C₇	—	8	1	no	Sylow
24	C₂²	—	7	1	no	—
25	C₂²	—	7	3	no	—
26	C₂²	—	7	1	no	—
27	C₄	—	7	1	no	—
28	C₄	C₂×AGL(1,𝔽₈)	1	1	yes	characteristic
29	C₂	—	7	1	no	—
30	C₂	—	7	1	no	—
31	C₂	C₄×AGL(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.