Subgroups — C₂×#10624690 #13090176

Order 1458.

404 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624690	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃²×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₂×C₃×C₃²⋊C₉	C₃	1	3	yes	maximal
4	C₂×#6867	C₃	1	9	yes	maximal, complemented
5	C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
6	C₃×C₃²⋊C₉	C₂×C₃	1	3	yes	—
7	#6867	C₂×C₃	1	9	yes	complemented
8	C₂×C₃⁴	C₃²	1	1	yes	characteristic
9	C₂×C₃×3₋¹⁺²	—	3	3	no	—
10	C₂×C₃×3₋¹⁺²	—	3	6	no	—
11	C₂×C₃×3₋¹⁺²	C₉	1	9	yes	complemented
12	C₂×C₃²×C₉	—	3	3	no	—
13	C₂×C₃²×C₉	C₃²	1	3	yes	—
14	C₂×C₃²⋊C₉	—	3	6	no	—
15	C₂×C₃²⋊C₉	C₃²	1	9	yes	—
16	C₃⁴	C₂×C₃²	1	1	yes	characteristic
17	C₃×3₋¹⁺²	—	3	3	no	—
18	C₃×3₋¹⁺²	—	3	6	no	—
19	C₃×3₋¹⁺²	C₂×C₉	1	9	yes	complemented
20	C₃²×C₉	—	3	3	no	—
21	C₃²×C₉	C₂×C₃²	1	3	yes	—
22	C₃²⋊C₉	—	3	6	no	—
23	C₃²⋊C₉	C₂×C₃²	1	9	yes	—
24	C₂×C₃³	—	9	3	no	—
25	C₂×C₃³	C₃×C₉	1	3	yes	—
26	C₂×C₃³	H(3,𝔽₃)	1	3	yes	—
27	C₂×C₃³	3₋¹⁺²	1	6	yes	—
28	C₂×C₃³	C₃³	1	1	yes	characteristic
29	C₂×3₋¹⁺²	—	3	27	no	—
30	C₂×C₃×C₉	—	3	3	no	—
31	C₂×C₃×C₉	—	3	6	no	—
32	C₂×C₃×C₉	—	3	9	no	—
33	C₂×C₃×C₉	—	9	9	no	—
34	C₂×C₃×C₉	C₃×C₉	1	9	yes	complemented
35	C₃³	—	9	3	no	—
36	C₃³	C₂×C₃×C₉	1	3	yes	—
37	C₃³	C₂×H(3,𝔽₃)	1	3	yes	—
38	C₃³	C₂×3₋¹⁺²	1	6	yes	—
39	C₃³	C₂×C₃³	1	1	yes	characteristic
40	3₋¹⁺²	—	3	27	no	—
41	C₃×C₉	—	3	3	no	—
42	C₃×C₉	—	3	6	no	—
43	C₃×C₉	—	3	9	no	—
44	C₃×C₉	—	9	9	no	—
45	C₃×C₉	C₂×C₃×C₉	1	9	yes	complemented
46	C₂×C₃²	—	3	3	no	—
47	C₂×C₃²	—	3	6	no	—
48	C₂×C₃²	—	3	3	no	—
49	C₂×C₃²	—	9	3	no	—
50	C₂×C₃²	—	9	6	no	—
51	C₂×C₃²	C₃²⋊C₉	1	9	yes	—
52	C₂×C₃²	C₃²×C₉	1	1	yes	characteristic
53	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
54	C₂×C₃²	C₃×3₋¹⁺²	1	2	yes	—
55	C₂×C₉	—	3	9	no	—
56	C₂×C₉	—	9	9	no	—
57	C₃²	—	3	3	no	—
58	C₃²	—	3	6	no	—
59	C₃²	—	3	3	no	—
60	C₃²	—	9	3	no	—
61	C₃²	—	9	6	no	—
62	C₃²	C₂×C₃²⋊C₉	1	9	yes	—
63	C₃²	C₂×C₃²×C₉	1	1	yes	characteristic
64	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
65	C₃²	C₂×C₃×3₋¹⁺²	1	2	yes	—
66	C₉	—	3	9	no	—
67	C₉	—	9	9	no	—
68	C₂×C₃	—	3	9	no	—
69	C₂×C₃	—	3	1	no	—
70	C₂×C₃	—	3	2	no	—
71	C₂×C₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
72	C₂×C₃	#6910	1	3	yes	—
73	C₃	—	3	9	no	—
74	C₃	—	3	1	no	—
75	C₃	—	3	2	no	—
76	C₃	C₂×C₃×C₃²⋊C₉	1	1	yes	characteristic
77	C₃	C₂×#6910	1	3	yes	—
78	C₂	#10624690	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃²	C₃×H(3,𝔽₃)
commutator	C₃²	C₂×C₃²×C₉
Frattini, cosocle	C₃³	C₂×C₃³
prime radical	C₂×C₃⁴	C₃²
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃⁴ ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624690	C₂	direct (N × H)
4. C₂×#6867	C₃	semidirect
7. #6867	C₂×C₃	semidirect
11. C₂×C₃×3₋¹⁺²	C₉	semidirect
19. C₃×3₋¹⁺²	C₂×C₉	semidirect
34. C₂×C₃×C₉	C₃×C₉	semidirect
45. C₃×C₉	C₂×C₃×C₉	semidirect
78. C₂	#10624690	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624690	2
C₂×C₃²×3₋¹⁺²	3
C₂×C₃×C₃²⋊C₉	3
C₂×#6867	3

Subgroups — C2×#10624690 #13090176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624690 #13090176