Subgroups — C₃×AGL(1,𝔽₉)⋊C₄ #11724097

Order 864.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×AGL(1,𝔽₉)	C₂	1	1	yes	maximal, characteristic
2	C₃×#3777	C₂	1	1	yes	maximal, characteristic
3	C₃×#3773	C₂	1	1	yes	maximal, characteristic
4	AGL(1,𝔽₉)⋊C₄	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃×#157	—	2	1	no	—
6	C₂×C₃×#157	C₂²	1	1	yes	characteristic
7	C₃×AGL(1,𝔽₉)	C₄	1	2	yes	complemented
8	C₃×#624	—	2	1	no	—
9	C₂×AGL(1,𝔽₉)	C₂×C₃	1	1	yes	characteristic
10	#3777	C₂×C₃	1	1	yes	characteristic
11	#3773	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
13	C₃×#157	—	4	1	no	—
14	C₃×#157	C₂×C₄	1	1	yes	characteristic
15	C₃×#157	Q₈	1	1	yes	characteristic
16	C₃²×Dic₃	—	4	1	no	—
17	C₃×#106	—	9	1	no	maximal
18	C₂×#157	—	2	1	no	—
19	C₂×#157	C₂²×C₃	1	1	yes	characteristic
20	AGL(1,𝔽₉)	C₃×C₄	1	2	yes	complemented
21	C₃×C₄×D₃	—	12	1	no	—
22	#624	—	2	1	no	—
23	C₂×C₃³	SD₁₆	1	1	yes	characteristic
24	C₃×C₃⋊D₃	C₄⋊C₄	1	1	yes	characteristic
25	C₃×C₃⋊D₃	SD₁₆	1	1	yes	characteristic
26	C₂×C₃×C₈	—	9	1	no	—
27	C₃×C₄⋊C₄	—	9	1	no	—
28	C₃×C₄⋊C₄	—	9	1	no	—
29	C₂×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
30	C₂×C₃×D₃	—	12	1	no	—
31	#157	—	4	1	no	—
32	#157	C₂×C₃×C₄	1	1	yes	characteristic
33	#157	C₃×Q₈	1	1	yes	characteristic
34	C₃²×C₄	—	12	1	no	—
35	C₃×Dic₃	—	4	1	no	—
36	C₃×Dic₃	—	4	1	no	—
37	C₃×Dic₃	—	8	1	no	—
38	#106	—	9	1	no	Sylow
39	C₃³	#106	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₄	—	9	1	no	—
41	C₂×C₃×C₄	—	18	1	no	—
42	C₂×C₃×C₄	—	18	1	no	—
43	C₄×D₃	—	12	1	no	—
44	C₃×C₈	—	9	2	no	—
45	C₂×C₃²	—	4	1	no	—
46	C₂×C₃²	—	8	1	no	—
47	C₂×C₃²	C₃×SD₁₆	1	1	yes	characteristic
48	C₃⋊D₃	C₃×C₄⋊C₄	1	1	yes	characteristic
49	C₃⋊D₃	C₃×SD₁₆	1	1	yes	characteristic
50	C₃×D₃	—	12	1	no	—
51	C₃×D₃	—	12	1	no	—
52	C₂×C₈	—	9	1	no	—
53	C₄⋊C₄	—	9	1	no	—
54	C₄⋊C₄	—	9	1	no	—
55	C₂²×C₃	—	9	1	no	—
56	C₂×D₃	—	12	1	no	—
57	C₃×C₄	—	9	1	no	—
58	C₃×C₄	—	9	1	no	—
59	C₃×C₄	—	12	1	no	—
60	C₃×C₄	—	12	1	no	—
61	C₃×C₄	—	24	1	no	—
62	C₃×C₄	—	36	1	no	—
63	Dic₃	—	4	1	no	—
64	C₃²	—	4	1	no	—
65	C₃²	—	8	1	no	—
66	C₃²	C₃×#106	1	1	yes	characteristic, complemented
67	C₂×C₄	—	9	1	no	—
68	C₂×C₄	—	18	1	no	—
69	C₂×C₄	—	18	1	no	—
70	C₈	—	9	2	no	—
71	C₂×C₃	—	4	1	no	—
72	C₂×C₃	—	8	1	no	—
73	C₂×C₃	—	9	1	no	—
74	C₂×C₃	—	9	1	no	—
75	C₂×C₃	AΓL(1,𝔽₉)	1	1	yes	characteristic
76	D₃	—	12	1	no	—
77	D₃	—	12	1	no	—
78	C₂²	—	9	1	no	—
79	C₄	—	9	1	no	—
80	C₄	—	9	1	no	—
81	C₄	—	12	1	no	—
82	C₄	—	36	1	no	—
83	C₃	—	4	1	no	—
84	C₃	—	8	1	no	—
85	C₃	AGL(1,𝔽₉)⋊C₄	1	1	yes	characteristic, direct product factor
86	C₂	—	9	1	no	—
87	C₂	—	9	1	no	—
88	C₂	C₃×AΓL(1,𝔽₉)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	AΓL(1,𝔽₉)
commutator	#157	C₂×C₃×C₄
Frattini	C₂	C₃×AΓL(1,𝔽₉)
Fitting, socle	C₂×C₃³	SD₁₆
prime radical	C₂×C₃×C₃⋊D₃	D₄
cosocle	C₂×#157	C₂²×C₃
hypocenter	C₃²	C₃×#106
LCS	G ▷ #157 ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
4. AGL(1,𝔽₉)⋊C₄	C₃	direct (N × H)
7. C₃×AGL(1,𝔽₉)	C₄	semidirect
20. AGL(1,𝔽₉)	C₃×C₄	semidirect
39. C₃³	#106	semidirect
66. C₃²	C₃×#106	semidirect
85. C₃	AGL(1,𝔽₉)⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×AGL(1,𝔽₉)	2
C₃×#3777	2
C₃×#3773	2
AGL(1,𝔽₉)⋊C₄	3
C₃×#106	9

Subgroups — C3×AGL(1,𝔽9)⋊C4 #11724097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×AGL(1,𝔽₉)⋊C₄ #11724097