Subgroups — C₂²×AGL(1,𝔽₉) #64382

Order 288.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#157	C₂	1	1	yes	maximal, characteristic
2	C₂×AGL(1,𝔽₉)	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃⋊D₃	C₄	1	1	yes	characteristic
4	C₂×#157	C₄	1	3	yes	—
5	C₂×#157	C₂²	1	3	yes	—
6	AGL(1,𝔽₉)	C₂²	1	4	yes	direct product factor
7	C₂²×C₃²	C₈	1	1	yes	characteristic, complemented
8	C₂×C₃⋊D₃	C₈	1	3	yes	complemented
9	C₂×C₃⋊D₃	C₂×C₄	1	3	yes	—
10	#157	C₂×C₄	1	3	yes	—
11	#157	C₂³	1	1	yes	characteristic
12	C₂²×C₈	—	9	1	no	maximal, Sylow
13	C₂²×D₃	—	12	1	no	—
14	C₂×C₃²	C₂×C₈	1	3	yes	complemented
15	C₃⋊D₃	C₂×C₈	1	3	yes	complemented
16	C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
17	C₂²×C₄	—	9	1	no	—
18	C₂×C₈	—	9	6	no	—
19	C₂²×C₃	—	4	1	no	—
20	C₂×D₃	—	12	3	no	—
21	C₂×D₃	—	12	3	no	—
22	C₃²	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
23	C₂³	—	9	1	no	—
24	C₂×C₄	—	9	3	no	—
25	C₂×C₄	—	9	3	no	—
26	C₈	—	9	4	no	—
27	C₂×C₃	—	4	3	no	—
28	D₃	—	12	3	no	—
29	D₃	—	12	1	no	—
30	C₂²	—	9	3	no	—
31	C₂²	—	9	3	no	—
32	C₂²	AGL(1,𝔽₉)	1	1	yes	characteristic, direct product factor
33	C₄	—	9	1	no	—
34	C₄	—	9	3	no	—
35	C₃	—	4	1	no	—
36	C₂	—	9	1	no	—
37	C₂	—	9	3	no	—
38	C₂	C₂×AGL(1,𝔽₉)	1	3	yes	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.