Subgroups — C₄×AGL(1,𝔽₉) #64215

Order 288.

52 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)	C₄	1	4	yes	direct product factor
6	C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
7	C₂×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
8	#157	C₈	1	2	yes	complemented
9	#157	C₂×C₄	1	2	yes	—
10	C₃²×C₄	C₈	1	1	yes	characteristic, complemented
11	C₃⋊Dic₃	C₈	1	1	yes	characteristic, complemented
12	C₄×C₈	—	9	1	no	maximal, Sylow
13	C₄×D₃	—	12	1	no	—
14	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
15	C₃⋊D₃	C₄²	1	1	yes	characteristic
16	C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₈	—	9	2	no	—
18	C₄²	—	9	1	no	—
19	C₂×D₃	—	12	1	no	—
20	C₃×C₄	—	4	1	no	—
21	Dic₃	—	12	1	no	—
22	C₃²	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₄	—	9	1	no	—
24	C₂×C₄	—	9	1	no	—
25	C₂×C₄	—	9	1	no	—
26	C₈	—	9	4	no	—
27	C₂×C₃	—	4	1	no	—
28	D₃	—	12	1	no	—
29	D₃	—	12	1	no	—
30	C₂²	—	9	1	no	—
31	C₄	—	9	2	no	—
32	C₄	—	9	2	no	—
33	C₄	—	9	1	no	—
34	C₄	AGL(1,𝔽₉)	1	1	yes	characteristic, direct product factor
35	C₃	—	4	1	no	—
36	C₂	—	9	1	no	—
37	C₂	—	9	1	no	—
38	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.