Subgroups — C₃×AGL(1,𝔽₈)⋊C₉ #13094544

Order 1512.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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