Subgroups — #10624799⋊C₂ #13091237

Order 1458.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624799	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₃×#733	—	3	1	no	maximal
3	#6894⋊C₂	C₃	1	2	yes	maximal
4	D₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
5	C₃×D₉⋊C₉	C₃	1	1	yes	maximal, characteristic
6	C₃×#733	D₃	1	1	yes	characteristic
7	#6894	C₂×C₃	1	2	yes	—
8	C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
9	C₃×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic
10	3₋¹⁺²⋊C₉	—	2	2	no	—
11	3₋¹⁺²⋊C₉	—	2	1	no	—
12	#6868	—	2	1	no	—
13	D₃×3₋¹⁺²	—	3	1	no	—
14	D₃×3₋¹⁺²	—	3	2	no	—
15	C₃×D₃×C₉	—	3	1	no	—
16	C₃²×D₉	C₃²	1	1	yes	characteristic
17	C₂×#733	—	9	1	no	—
18	D₉⋊C₉	—	3	1	no	—
19	D₉⋊C₉	—	3	2	no	—
20	C₉×D₉	—	3	1	no	—
21	C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
22	C₃×3₋¹⁺²	C₃×D₃	1	2	yes	—
23	C₃²×C₉	—	2	1	no	—
24	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
25	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
26	#733	—	3	1	no	—
27	#733	—	6	1	no	—
28	C₉⋊C₉	—	3	1	no	—
29	C₉⋊C₉	—	3	2	no	—
30	C₉⋊C₉	—	6	1	no	—
31	C₉⋊C₉	—	6	1	no	—
32	C₉⋊C₉	—	6	2	no	—
33	C₃²⋊C₉	—	2	1	no	—
34	C₃²⋊C₉	—	2	2	no	—
35	C₉²	—	3	1	no	—
36	C₃²×D₃	—	3	1	no	—
37	C₂×3₋¹⁺²	—	9	2	no	—
38	C₂×3₋¹⁺²	—	9	1	no	—
39	C₂×C₃×C₉	—	9	1	no	—
40	D₃×C₉	—	9	1	no	—
41	D₃×C₉	—	9	1	no	—
42	D₃×C₉	—	9	2	no	—
43	C₃×D₉	—	3	1	no	—
44	C₃×D₉	H(3,𝔽₃)	1	1	yes	characteristic
45	C₃³	C₃²×D₃	1	1	yes	characteristic
46	3₋¹⁺²	—	2	1	no	—
47	3₋¹⁺²	—	3	2	no	—
48	3₋¹⁺²	—	6	1	no	—
49	3₋¹⁺²	—	6	2	no	—
50	3₋¹⁺²	AGL(1,ℤ/9)	1	1	yes	characteristic
51	C₃×C₉	—	2	1	no	—
52	C₃×C₉	—	3	1	no	—
53	C₃×C₉	—	3	1	no	—
54	C₃×C₉	—	3	1	no	—
55	C₃×C₉	—	3	2	no	—
56	C₃×C₉	—	3	1	no	—
57	C₃×C₉	—	6	1	no	—
58	C₃×C₉	—	6	1	no	—
59	C₃×C₉	—	6	1	no	—
60	C₃×C₉	—	6	2	no	—
61	C₃×C₉	—	6	1	no	—
62	C₃×C₉	—	18	1	no	—
63	C₃×C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic
64	C₂×C₃²	—	9	1	no	—
65	C₃×D₃	—	3	1	no	—
66	C₃×D₃	—	9	1	no	—
67	C₂×C₉	—	27	1	no	—
68	C₂×C₉	—	27	1	no	—
69	C₂×C₉	—	27	2	no	—
70	D₉	#733	1	1	yes	characteristic, complemented
71	C₃²	—	2	1	no	—
72	C₃²	—	3	1	no	—
73	C₃²	—	6	1	no	—
74	C₃²	D₃×H(3,𝔽₃)	1	1	yes	characteristic
75	C₃²	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
76	C₉	—	2	1	no	—
77	C₉	—	3	1	no	—
78	C₉	—	6	1	no	—
79	C₉	—	6	1	no	—
80	C₉	—	9	1	no	—
81	C₉	—	9	2	no	—
82	C₉	—	18	1	no	—
83	C₉	—	18	2	no	—
84	C₉	—	18	1	no	—
85	C₉	C₂×#733	1	1	yes	characteristic, complemented
86	C₂×C₃	—	9	1	no	—
87	C₂×C₃	—	27	1	no	—
88	D₃	—	3	1	no	—
89	C₃	—	2	1	no	—
90	C₃	—	3	1	no	—
91	C₃	—	6	1	no	—
92	C₃	D₉⋊H(3,𝔽₃)	1	1	yes	characteristic
93	C₃	D₃×#733	1	1	yes	characteristic
94	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃	D₉⋊H(3,𝔽₃)
commutator, cosocle	C₃²×C₉	C₂×C₃²
Frattini	C₃³	C₃²×D₃
Fitting	#10624799	C₂
socle	C₃²	D₃×H(3,𝔽₃)
prime radical	C₃²×D₉	C₃²
hypercenter	3₋¹⁺²	AGL(1,ℤ/9)
hypocenter	C₉	C₂×#733
LCS	G ▷ C₃²×C₉ ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ 3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #10624799	C₂	semidirect
70. D₉	#733	semidirect
85. C₉	C₂×#733	semidirect

Maximal subgroups

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

subgroup	index
#10624799	2
D₃×#733	3
#6894⋊C₂	3
D₉×3₋¹⁺²	3
C₃×D₉⋊C₉	3

Subgroups — #10624799⋊C2 #13091237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624799⋊C₂ #13091237