Subgroups — C₂×AGL(1,𝔽₈)⋊C₉ #11759327

Order 1008.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	AGL(1,𝔽₈)⋊C₉	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₃×AGL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic
3	C₃×AGL(1,𝔽₈)	C₂×C₃	1	1	yes	characteristic
4	C₂²×C₂²⋊C₉	—	7	1	no	maximal, Hall
5	C₂×C₇⋊C₉	—	8	1	no	maximal
6	C₂×AGL(1,𝔽₈)	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₂²⋊C₉	—	7	1	no	—
8	C₂×C₂²⋊C₉	—	7	1	no	—
9	C₂×C₂²⋊C₉	—	7	1	no	—
10	C₇⋊C₉	—	8	1	no	Hall
11	AGL(1,𝔽₈)	C₂×C₉	1	1	yes	characteristic, complemented
12	C₂⁴×C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₂×C₃×C₇	—	8	1	no	—
14	C₂²×C₉	—	28	1	no	—
15	C₂²⋊C₉	—	7	1	no	—
16	C₂³×C₃	—	7	1	no	—
17	C₂³×C₃	—	7	1	no	—
18	C₂³×C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
19	C₃×C₇	—	8	1	no	—
20	C₂×C₉	—	28	1	no	—
21	C₂×C₉	—	28	1	no	—
22	C₂×C₉	—	28	1	no	—
23	C₂⁴	C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₇	—	8	1	no	—
25	C₂²×C₃	—	7	1	no	—
26	C₂²×C₃	—	7	1	no	—
27	C₂²×C₃	—	21	1	no	—
28	C₉	—	28	1	no	Sylow
29	C₂³	—	7	1	no	—
30	C₂³	—	7	1	no	—
31	C₂³	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
32	C₇	—	8	1	no	Sylow
33	C₂×C₃	—	7	1	no	—
34	C₂×C₃	—	7	1	no	—
35	C₂×C₃	AΓL(1,𝔽₈)	1	1	yes	characteristic
36	C₂²	—	7	1	no	—
37	C₂²	—	7	1	no	—
38	C₂²	—	21	1	no	—
39	C₃	C₂×AΓL(1,𝔽₈)	1	1	yes	characteristic
40	C₂	—	7	1	no	—
41	C₂	—	7	1	no	—
42	C₂	AGL(1,𝔽₈)⋊C₉	1	1	yes	characteristic, direct product factor

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.