Subgroups — C₄⋊AGL(1,𝔽₉) #64216

Order 288.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,𝔽₉)	C₂	1	2	yes	maximal
2	C₄×#157	C₂	1	1	yes	maximal, characteristic
3	C₂×#157	C₄	1	1	yes	characteristic
4	C₂×#157	C₂²	1	1	yes	characteristic
5	AGL(1,𝔽₉)	—	2	2	no	—
6	C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
7	C₂×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
8	#157	—	2	1	no	—
9	#157	D₄	1	1	yes	characteristic
10	#157	Q₈	1	1	yes	characteristic
11	C₃²×C₄	C₈	1	1	yes	characteristic, complemented
12	C₃⋊Dic₃	C₈	1	1	yes	characteristic, complemented
13	C₄⋊C₈	—	9	1	no	maximal, Sylow
14	C₄×D₃	—	12	1	no	—
15	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
16	C₃⋊D₃	C₄⋊C₄	1	1	yes	characteristic
17	C₃⋊D₃	M₁₆	1	1	yes	characteristic
18	C₂×C₈	—	9	2	no	—
19	C₄²	—	9	1	no	—
20	C₂×D₃	—	12	1	no	—
21	C₃×C₄	—	4	1	no	—
22	Dic₃	—	12	1	no	—
23	C₃²	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₄	—	9	1	no	—
25	C₂×C₄	—	9	1	no	—
26	C₂×C₄	—	9	1	no	—
27	C₈	—	18	2	no	—
28	C₂×C₃	—	4	1	no	—
29	D₃	—	12	1	no	—
30	D₃	—	12	1	no	—
31	C₂²	—	9	1	no	—
32	C₄	—	9	1	no	—
33	C₄	—	9	1	no	—
34	C₄	—	9	1	no	—
35	C₄	—	18	1	no	—
36	C₄	AGL(1,𝔽₉)	1	1	yes	characteristic, complemented
37	C₃	—	4	1	no	—
38	C₂	—	9	1	no	—
39	C₂	—	9	1	no	—
40	C₂	C₂×AGL(1,𝔽₉)	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.