Subgroups — C₉×AΓL(1,𝔽₈) #13094541

Order 1512.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×AΓL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic
2	C₉×AGL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic, complemented
3	AGL(1,𝔽₈)⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₂×C₉×A₄	—	7	1	no	maximal, Hall
5	C₉×ΓL(1,𝔽₈)	—	8	1	no	maximal, Hall
6	C₃×AGL(1,𝔽₈)	C₃²	1	1	yes	characteristic
7	AΓL(1,𝔽₈)	C₉	1	3	yes	direct product factor
8	C₉×A₄	—	7	1	no	—
9	C₂×C₃×A₄	—	7	1	no	—
10	C₂³×C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	C₂×C₂²⋊C₉	—	7	2	no	—
12	C₃×ΓL(1,𝔽₈)	—	8	1	no	—
13	C₇×C₉	—	8	1	no	—
14	C₇⋊C₉	—	8	2	no	—
15	AGL(1,𝔽₈)	C₃×C₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₉	—	28	1	no	—
17	C₃×A₄	—	7	1	no	—
18	C₂²×C₉	—	7	1	no	—
19	C₂²⋊C₉	—	7	2	no	—
20	C₃×C₉	—	28	1	no	Sylow
21	C₂³×C₃	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₂×A₄	—	7	3	no	—
23	C₃×C₇	—	8	1	no	—
24	ΓL(1,𝔽₈)	—	8	3	no	—
25	C₂×C₃²	—	28	1	no	—
26	C₂×C₉	—	7	1	no	—
27	C₂×C₉	—	28	2	no	—
28	C₂²×C₃	—	7	1	no	—
29	A₄	—	7	3	no	—
30	C₃²	—	28	1	no	—
31	C₉	—	28	2	no	—
32	C₉	AΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
33	C₂³	C₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
34	C₇	—	8	1	no	Sylow
35	C₂×C₃	—	7	1	no	—
36	C₂×C₃	—	28	3	no	—
37	C₂²	—	7	1	no	—
38	C₃	—	28	3	no	—
39	C₃	C₃×AΓL(1,𝔽₈)	1	1	yes	characteristic
40	C₂	—	7	1	no	—

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.