Subgroups — C₂×#10624567 #13090053

Order 1458.

524 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624567	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃²×3₋¹⁺²	C₃	1	2	yes	maximal
3	C₂×C₃×C₃²⋊C₉	C₃	1	2	yes	maximal
4	C₂×#6855	C₃	1	9	yes	maximal, complemented
5	C₃²×3₋¹⁺²	C₂×C₃	1	2	yes	—
6	C₃×C₃²⋊C₉	C₂×C₃	1	2	yes	—
7	#6855	C₂×C₃	1	9	yes	complemented
8	C₂×C₃⁴	C₃²	1	1	yes	characteristic
9	C₂×C₃×3₋¹⁺²	—	3	6	no	—
10	C₂×C₃×3₋¹⁺²	—	3	18	no	—
11	C₂×C₃²×C₉	C₃²	1	6	yes	—
12	C₂×C₃²×C₉	C₃²	1	6	yes	—
13	C₂×C₃²⋊C₉	—	3	6	no	—
14	C₃⁴	C₂×C₃²	1	1	yes	characteristic
15	C₃×3₋¹⁺²	—	3	6	no	—
16	C₃×3₋¹⁺²	—	3	18	no	—
17	C₃²×C₉	C₂×C₃²	1	6	yes	—
18	C₃²×C₉	C₂×C₃²	1	6	yes	—
19	C₃²⋊C₉	—	3	6	no	—
20	C₂×C₃³	—	3	6	no	—
21	C₂×C₃³	—	3	6	no	—
22	C₂×C₃³	H(3,𝔽₃)	1	3	yes	—
23	C₂×C₃³	C₃³	1	1	yes	characteristic
24	C₂×3₋¹⁺²	—	3	54	no	—
25	C₂×C₃×C₉	—	3	6	no	—
26	C₂×C₃×C₉	—	3	12	no	—
27	C₂×C₃×C₉	—	3	6	no	—
28	C₂×C₃×C₉	—	3	18	no	—
29	C₂×C₃×C₉	3₋¹⁺²	1	18	yes	complemented
30	C₃³	—	3	6	no	—
31	C₃³	—	3	6	no	—
32	C₃³	C₂×H(3,𝔽₃)	1	3	yes	—
33	C₃³	C₂×C₃³	1	1	yes	characteristic
34	3₋¹⁺²	—	3	54	no	—
35	C₃×C₉	—	3	6	no	—
36	C₃×C₉	—	3	12	no	—
37	C₃×C₉	—	3	6	no	—
38	C₃×C₉	—	3	18	no	—
39	C₃×C₉	C₂×3₋¹⁺²	1	18	yes	complemented
40	C₂×C₃²	—	3	6	no	—
41	C₂×C₃²	—	3	6	no	—
42	C₂×C₃²	—	9	9	no	—
43	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
44	C₂×C₃²	C₃×3₋¹⁺²	1	6	yes	—
45	C₂×C₃²	#737	1	6	yes	—
46	C₂×C₉	—	3	18	no	—
47	C₂×C₉	—	9	6	no	—
48	C₃²	—	3	6	no	—
49	C₃²	—	3	6	no	—
50	C₃²	—	9	9	no	—
51	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
52	C₃²	C₂×C₃×3₋¹⁺²	1	6	yes	—
53	C₃²	C₂×#737	1	6	yes	—
54	C₉	—	3	18	no	—
55	C₉	—	9	6	no	—
56	C₂×C₃	—	9	3	no	—
57	C₂×C₃	#6891	1	2	yes	—
58	C₂×C₃	#6893	1	2	yes	—
59	C₂×C₃	#6896	1	9	yes	—
60	C₃	—	9	3	no	—
61	C₃	C₂×#6891	1	2	yes	—
62	C₃	C₂×#6893	1	2	yes	—
63	C₃	C₂×#6896	1	9	yes	—
64	C₂	#10624567	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃³	C₃³
commutator, Frattini, cosocle	C₃³	C₂×C₃³
prime radical	C₂×C₃⁴	C₃²
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624567	C₂	direct (N × H)
4. C₂×#6855	C₃	semidirect
7. #6855	C₂×C₃	semidirect
29. C₂×C₃×C₉	3₋¹⁺²	semidirect
39. C₃×C₉	C₂×3₋¹⁺²	semidirect
64. C₂	#10624567	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624567	2
C₂×C₃²×3₋¹⁺²	3
C₂×C₃×C₃²⋊C₉	3
C₂×#6855	3

Subgroups — C2×#10624567 #13090053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624567 #13090053