Subgroups — C₂×#10624776 #13090262

Order 1458.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624776	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃²×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₂×#6891	C₃	1	3	yes	maximal
4	C₂×#6868	C₃	1	9	yes	maximal, complemented
5	C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
6	#6891	C₂×C₃	1	3	yes	—
7	#6868	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	3	no	—
11	C₂×C₃×3₋¹⁺²	—	3	9	no	—
12	C₂×C₃²×C₉	C₃²	1	3	yes	—
13	C₂×C₃²⋊C₉	—	3	6	no	—
14	C₂×C₃²⋊C₉	C₃²	1	9	yes	—
15	C₃⁴	C₂×C₃²	1	1	yes	characteristic
16	C₃×3₋¹⁺²	—	3	3	no	—
17	C₃×3₋¹⁺²	—	3	3	no	—
18	C₃×3₋¹⁺²	—	3	9	no	—
19	C₃²×C₉	C₂×C₃²	1	3	yes	—
20	C₃²⋊C₉	—	3	6	no	—
21	C₃²⋊C₉	C₂×C₃²	1	9	yes	—
22	C₂×C₃³	—	3	3	no	—
23	C₂×C₃³	—	9	2	no	—
24	C₂×C₃³	—	9	1	no	—
25	C₂×C₃³	H(3,𝔽₃)	1	3	yes	—
26	C₂×C₃³	C₃³	1	1	yes	characteristic
27	C₂×3₋¹⁺²	—	3	27	no	—
28	C₂×3₋¹⁺²	—	9	9	no	—
29	C₂×C₃×C₉	—	3	3	no	—
30	C₂×C₃×C₉	—	3	6	no	—
31	C₂×C₃×C₉	—	3	9	no	—
32	C₂×C₃×C₉	3₋¹⁺²	1	9	yes	complemented
33	C₃³	—	3	3	no	—
34	C₃³	—	9	1	no	—
35	C₃³	—	9	2	no	—
36	C₃³	C₂×H(3,𝔽₃)	1	3	yes	—
37	C₃³	C₂×C₃³	1	1	yes	characteristic
38	3₋¹⁺²	—	3	27	no	—
39	3₋¹⁺²	—	9	9	no	—
40	C₃×C₉	—	3	3	no	—
41	C₃×C₉	—	3	6	no	—
42	C₃×C₉	—	3	9	no	—
43	C₃×C₉	C₂×3₋¹⁺²	1	9	yes	complemented
44	C₂×C₃²	—	3	2	no	—
45	C₂×C₃²	—	3	1	no	—
46	C₂×C₃²	—	3	6	no	—
47	C₂×C₃²	—	3	3	no	—
48	C₂×C₃²	—	3	3	no	—
49	C₂×C₃²	—	9	9	no	—
50	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
51	C₂×C₃²	C₃×3₋¹⁺²	1	3	yes	—
52	C₂×C₉	—	3	9	no	—
53	C₂×C₉	—	9	9	no	—
54	C₃²	—	3	1	no	—
55	C₃²	—	3	2	no	—
56	C₃²	—	3	3	no	—
57	C₃²	—	3	3	no	—
58	C₃²	—	3	6	no	—
59	C₃²	—	9	9	no	—
60	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
61	C₃²	C₂×C₃×3₋¹⁺²	1	3	yes	—
62	C₉	—	3	9	no	—
63	C₉	—	9	9	no	—
64	C₂×C₃	—	3	3	no	—
65	C₂×C₃	—	9	3	no	—
66	C₂×C₃	#6891	1	1	yes	characteristic
67	C₂×C₃	#6911	1	1	yes	characteristic
68	C₂×C₃	#6912	1	2	yes	—
69	C₃	—	3	3	no	—
70	C₃	—	9	3	no	—
71	C₃	C₂×#6891	1	1	yes	characteristic
72	C₃	C₂×#6911	1	1	yes	characteristic
73	C₃	C₂×#6912	1	2	yes	—
74	C₂	#10624776	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃²	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₂×C₃³
prime radical	C₂×C₃⁴	C₃²
LCS	G ▷ C₃³ ▷ 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. #10624776	C₂	direct (N × H)
4. C₂×#6868	C₃	semidirect
7. #6868	C₂×C₃	semidirect
32. C₂×C₃×C₉	3₋¹⁺²	semidirect
43. C₃×C₉	C₂×3₋¹⁺²	semidirect
74. C₂	#10624776	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624776	2
C₂×C₃²×3₋¹⁺²	3
C₂×#6891	3
C₂×#6868	3

Subgroups — C2×#10624776 #13090262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624776 #13090262