Subgroups — AGL(1,𝔽₉)⋊C₄ #64195

Order 288.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,𝔽₉)	C₂	1	1	yes	maximal, characteristic
2	#3777	C₂	1	1	yes	maximal, characteristic
3	#3773	C₂	1	1	yes	maximal, characteristic
4	C₂×#157	—	2	1	no	—
5	C₂×#157	C₂²	1	1	yes	characteristic
6	AGL(1,𝔽₉)	C₄	1	2	yes	complemented
7	#624	—	2	1	no	—
8	C₂×C₃⋊D₃	D₄	1	1	yes	characteristic
9	#157	—	4	1	no	—
10	#157	C₂×C₄	1	1	yes	characteristic
11	#157	Q₈	1	1	yes	characteristic
12	C₃×Dic₃	—	4	1	no	—
13	#106	—	9	1	no	maximal, Sylow
14	C₄×D₃	—	12	1	no	—
15	C₂×C₃²	SD₁₆	1	1	yes	characteristic
16	C₃⋊D₃	C₄⋊C₄	1	1	yes	characteristic
17	C₃⋊D₃	SD₁₆	1	1	yes	characteristic
18	C₂×C₈	—	9	1	no	—
19	C₄⋊C₄	—	9	1	no	—
20	C₄⋊C₄	—	9	1	no	—
21	C₂×D₃	—	12	1	no	—
22	C₃×C₄	—	12	1	no	—
23	Dic₃	—	4	1	no	—
24	C₃²	#106	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₄	—	9	1	no	—
26	C₂×C₄	—	18	1	no	—
27	C₂×C₄	—	18	1	no	—
28	C₈	—	9	2	no	—
29	C₂×C₃	—	4	1	no	—
30	D₃	—	12	1	no	—
31	D₃	—	12	1	no	—
32	C₂²	—	9	1	no	—
33	C₄	—	9	1	no	—
34	C₄	—	9	1	no	—
35	C₄	—	12	1	no	—
36	C₄	—	36	1	no	—
37	C₃	—	4	1	no	—
38	C₂	—	9	1	no	—
39	C₂	—	9	1	no	—
40	C₂	AΓL(1,𝔽₉)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	AΓL(1,𝔽₉)
commutator	#157	C₂×C₄
Fitting, socle	C₂×C₃²	SD₁₆
prime radical	C₂×C₃⋊D₃	D₄
cosocle	C₂×#157	C₂²
hypocenter	C₃²	#106
LCS	G ▷ #157 ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. AGL(1,𝔽₉)	C₄	semidirect
24. C₃²	#106	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.