Subgroups — C₄²×AGL(1,𝔽₉) #11783015

Order 1152.

462 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×AGL(1,𝔽₉)	C₂	1	6	yes	maximal
2	C₄²×#157	C₂	1	1	yes	maximal, characteristic
3	C₂²×AGL(1,𝔽₉)	C₂²	1	4	yes	—
4	C₂×C₄×#157	C₄	1	3	yes	—
5	C₂×C₄×#157	C₂²	1	3	yes	—
6	C₄×AGL(1,𝔽₉)	C₄	1	24	yes	direct product factor
7	C₄²×C₃⋊D₃	C₄	1	1	yes	characteristic
8	C₂²×#157	C₂×C₄	1	3	yes	—
9	C₂²×#157	C₂³	1	1	yes	characteristic
10	C₂×AGL(1,𝔽₉)	C₂×C₄	1	24	yes	—
11	C₂×C₄×C₃⋊D₃	C₂×C₄	1	3	yes	—
12	C₄×#157	C₈	1	12	yes	complemented
13	C₄×#157	C₂×C₄	1	12	yes	—
14	C₃²×C₄²	C₈	1	1	yes	characteristic, complemented
15	C₄×C₃⋊Dic₃	C₈	1	3	yes	complemented
16	C₄²×C₈	—	9	1	no	maximal, Sylow
17	C₄²×D₃	—	12	1	no	—
18	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
19	C₂×#157	C₄²	1	6	yes	—
20	C₂×#157	C₂×C₈	1	12	yes	—
21	C₂×#157	C₂²×C₄	1	6	yes	—
22	AGL(1,𝔽₉)	C₄²	1	16	yes	direct product factor
23	C₂×C₃²×C₄	C₂×C₈	1	3	yes	—
24	C₂×C₃⋊Dic₃	C₂×C₈	1	3	yes	—
25	C₄×C₃⋊D₃	C₄²	1	6	yes	—
26	C₄×C₃⋊D₃	C₂×C₈	1	6	yes	—
27	C₂×C₄×C₈	—	9	6	no	—
28	C₄³	—	9	1	no	—
29	C₂×C₄×D₃	—	12	3	no	—
30	C₃×C₄²	—	4	1	no	—
31	C₄×Dic₃	—	12	3	no	—
32	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₃⋊D₃	C₂×C₄²	1	3	yes	—
34	C₂×C₃⋊D₃	C₂²×C₈	1	3	yes	—
35	#157	C₄×C₈	1	12	yes	complemented
36	#157	C₂×C₄²	1	4	yes	—
37	C₃²×C₄	C₄×C₈	1	6	yes	complemented
38	C₃⋊Dic₃	C₄×C₈	1	6	yes	complemented
39	C₂²×C₈	—	9	4	no	—
40	C₂×C₄²	—	9	3	no	—
41	C₂×C₄²	—	9	3	no	—
42	C₂×C₄²	—	9	1	no	—
43	C₄×C₈	—	9	24	no	—
44	C₂²×D₃	—	12	1	no	—
45	C₂×C₃×C₄	—	4	3	no	—
46	C₂×Dic₃	—	12	3	no	—
47	C₄×D₃	—	12	6	no	—
48	C₄×D₃	—	12	6	no	—
49	C₂×C₃²	C₂×C₄×C₈	1	3	yes	—
50	C₃⋊D₃	C₄³	1	1	yes	characteristic
51	C₃⋊D₃	C₂×C₄×C₈	1	3	yes	—
52	C₂²×C₄	—	9	3	no	—
53	C₂²×C₄	—	9	1	no	—
54	C₂²×C₄	—	9	3	no	—
55	C₂×C₈	—	9	24	no	—
56	C₄²	—	9	12	no	—
57	C₄²	—	9	12	no	—
58	C₄²	—	9	3	no	—
59	C₄²	AGL(1,𝔽₉)	1	1	yes	characteristic, direct product factor
60	C₂²×C₃	—	4	1	no	—
61	C₂×D₃	—	12	3	no	—
62	C₂×D₃	—	12	3	no	—
63	C₃×C₄	—	4	6	no	—
64	Dic₃	—	12	6	no	—
65	C₃²	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
66	C₂³	—	9	1	no	—
67	C₂×C₄	—	9	6	no	—
68	C₂×C₄	—	9	6	no	—
69	C₂×C₄	—	9	12	no	—
70	C₂×C₄	—	9	3	no	—
71	C₂×C₄	—	9	6	no	—
72	C₂×C₄	—	9	6	no	—
73	C₂×C₄	C₂×AGL(1,𝔽₉)	1	3	yes	—
74	C₈	—	9	16	no	—
75	C₂×C₃	—	4	3	no	—
76	D₃	—	12	1	no	—
77	D₃	—	12	3	no	—
78	C₂²	—	9	3	no	—
79	C₂²	—	9	3	no	—
80	C₂²	C₂²×AGL(1,𝔽₉)	1	1	yes	characteristic
81	C₄	—	9	4	no	—
82	C₄	—	9	12	no	—
83	C₄	—	9	6	no	—
84	C₄	C₄×AGL(1,𝔽₉)	1	6	yes	direct product factor
85	C₃	—	4	1	no	—
86	C₂	—	9	1	no	—
87	C₂	—	9	3	no	—
88	C₂	C₂×C₄×AGL(1,𝔽₉)	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₄²	AGL(1,𝔽₉)
commutator, hypocenter	C₃²	C₄²×C₈
Frattini	C₂²	C₂²×AGL(1,𝔽₉)
Fitting	C₃²×C₄²	C₈
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂²×C₃⋊D₃	C₂²×C₄
cosocle	C₂²×#157	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
6. C₄×AGL(1,𝔽₉)	C₄	direct (N × H)
12. C₄×#157	C₈	semidirect
14. C₃²×C₄²	C₈	semidirect
15. C₄×C₃⋊Dic₃	C₈	semidirect
22. AGL(1,𝔽₉)	C₄²	direct (N × H)
35. #157	C₄×C₈	semidirect
37. C₃²×C₄	C₄×C₈	semidirect
38. C₃⋊Dic₃	C₄×C₈	semidirect
59. C₄²	AGL(1,𝔽₉)	direct (N × H)
65. C₃²	C₄²×C₈	semidirect
84. C₄	C₄×AGL(1,𝔽₉)	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×C₄×AGL(1,𝔽₉)	2
C₄²×#157	2
C₄²×C₈	9

Subgroups — C42×AGL(1,𝔽9) #11783015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×AGL(1,𝔽₉) #11783015