Subgroups — C₂×#10624883 #13090369

Order 1458.

926 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624883	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃²×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉⋊H(3,𝔽₃)	C₃	1	27	yes	maximal, complemented
4	C₂×#6891	C₃	1	9	yes	maximal, complemented
5	C₂×C₃×C₃²⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃²×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
7	C₉⋊H(3,𝔽₃)	C₂×C₃	1	27	yes	complemented
8	#6891	C₂×C₃	1	9	yes	complemented
9	C₃×C₃²⋊C₉	C₂×C₃	1	3	yes	complemented
10	C₂×C₃⁴	C₃²	1	3	yes	—
11	C₂×C₃⁴	C₃²	1	1	yes	characteristic
12	C₂×C₃×3₋¹⁺²	C₃²	1	27	yes	complemented
13	C₂×C₃×H(3,𝔽₃)	—	3	9	no	—
14	C₂×C₃×H(3,𝔽₃)	C₃²	1	9	yes	—
15	C₂×C₃²×C₉	C₃²	1	9	yes	complemented
16	C₂×C₃²⋊C₉	C₃²	1	9	yes	—
17	C₂×C₃²⋊C₉	C₃²	1	18	yes	complemented
18	C₂×C₃²⋊C₉	C₃²	1	54	yes	complemented
19	C₃⁴	C₂×C₃²	1	3	yes	—
20	C₃⁴	C₂×C₃²	1	1	yes	characteristic
21	C₃×3₋¹⁺²	C₂×C₃²	1	27	yes	complemented
22	C₃×H(3,𝔽₃)	—	3	9	no	—
23	C₃×H(3,𝔽₃)	C₂×C₃²	1	9	yes	—
24	C₃²×C₉	C₂×C₃²	1	9	yes	complemented
25	C₃²⋊C₉	C₂×C₃²	1	9	yes	—
26	C₃²⋊C₉	C₂×C₃²	1	18	yes	complemented
27	C₃²⋊C₉	C₂×C₃²	1	54	yes	complemented
28	C₂×C₃³	—	3	9	no	—
29	C₂×C₃³	—	9	1	no	—
30	C₂×C₃³	—	9	3	no	—
31	C₂×C₃³	—	9	2	no	—
32	C₂×C₃³	—	9	6	no	—
33	C₂×C₃³	3₋¹⁺²	1	9	yes	complemented
34	C₂×C₃³	C₃³	1	9	yes	—
35	C₂×C₃³	C₃³	1	1	yes	characteristic
36	C₂×C₃³	C₃³	1	3	yes	—
37	C₂×3₋¹⁺²	—	9	27	no	—
38	C₂×H(3,𝔽₃)	—	3	27	no	—
39	C₂×C₃×C₉	—	9	9	no	—
40	C₂×C₃×C₉	C₃³	1	27	yes	—
41	C₃³	—	3	9	no	—
42	C₃³	—	9	1	no	—
43	C₃³	—	9	3	no	—
44	C₃³	—	9	2	no	—
45	C₃³	—	9	6	no	—
46	C₃³	C₂×3₋¹⁺²	1	9	yes	complemented
47	C₃³	C₂×C₃³	1	9	yes	—
48	C₃³	C₂×C₃³	1	1	yes	characteristic
49	C₃³	C₂×C₃³	1	3	yes	—
50	3₋¹⁺²	—	9	27	no	—
51	H(3,𝔽₃)	—	3	27	no	—
52	C₃×C₉	—	9	9	no	—
53	C₃×C₉	C₂×C₃³	1	27	yes	—
54	C₂×C₃²	—	3	3	no	—
55	C₂×C₃²	—	3	1	no	—
56	C₂×C₃²	—	3	2	no	—
57	C₂×C₃²	—	3	6	no	—
58	C₂×C₃²	—	3	9	no	—
59	C₂×C₃²	—	3	9	no	—
60	C₂×C₃²	—	3	18	no	—
61	C₂×C₃²	—	9	9	no	—
62	C₂×C₃²	—	9	27	no	—
63	C₂×C₃²	C₃×3₋¹⁺²	1	9	yes	—
64	C₂×C₃²	C₃×3₋¹⁺²	1	3	yes	—
65	C₂×C₃²	C₃⁴	1	1	yes	characteristic
66	C₂×C₉	—	3	27	no	—
67	C₃²	—	3	3	no	—
68	C₃²	—	3	1	no	—
69	C₃²	—	3	2	no	—
70	C₃²	—	3	6	no	—
71	C₃²	—	3	9	no	—
72	C₃²	—	3	9	no	—
73	C₃²	—	3	18	no	—
74	C₃²	—	9	9	no	—
75	C₃²	—	9	27	no	—
76	C₃²	C₂×C₃×3₋¹⁺²	1	9	yes	—
77	C₃²	C₂×C₃×3₋¹⁺²	1	3	yes	—
78	C₃²	C₂×C₃⁴	1	1	yes	characteristic
79	C₉	—	3	27	no	—
80	C₂×C₃	—	3	3	no	—
81	C₂×C₃	—	3	9	no	—
82	C₂×C₃	—	9	9	no	—
83	C₂×C₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
84	C₂×C₃	H(5,𝔽₃)	1	1	yes	characteristic
85	C₂×C₃	3₋¹⁺⁴	1	2	yes	—
86	C₃	—	3	3	no	—
87	C₃	—	3	9	no	—
88	C₃	—	9	9	no	—
89	C₃	C₂×C₃²×3₋¹⁺²	1	1	yes	characteristic
90	C₃	C₂×H(5,𝔽₃)	1	1	yes	characteristic
91	C₃	C₂×3₋¹⁺⁴	1	2	yes	—
92	C₂	#10624883	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. #10624883	C₂	direct (N × H)
3. C₂×C₉⋊H(3,𝔽₃)	C₃	semidirect
4. C₂×#6891	C₃	semidirect
5. C₂×C₃×C₃²⋊C₉	C₃	semidirect
7. C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
8. #6891	C₂×C₃	semidirect
9. C₃×C₃²⋊C₉	C₂×C₃	semidirect
12. C₂×C₃×3₋¹⁺²	C₃²	semidirect
15. C₂×C₃²×C₉	C₃²	semidirect
17. C₂×C₃²⋊C₉	C₃²	semidirect
18. C₂×C₃²⋊C₉	C₃²	semidirect
21. C₃×3₋¹⁺²	C₂×C₃²	semidirect
24. C₃²×C₉	C₂×C₃²	semidirect
26. C₃²⋊C₉	C₂×C₃²	semidirect
27. C₃²⋊C₉	C₂×C₃²	semidirect
33. C₂×C₃³	3₋¹⁺²	semidirect
46. C₃³	C₂×3₋¹⁺²	semidirect
92. C₂	#10624883	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624883	2
C₂×C₃²×H(3,𝔽₃)	3
C₂×C₉⋊H(3,𝔽₃)	3
C₂×#6891	3
C₂×C₃×C₃²⋊C₉	3

Subgroups — C2×#10624883 #13090369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624883 #13090369