Subgroups — C₂×#10624607 #13090093

Order 1458.

452 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624607	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃²×3₋¹⁺²	C₃	1	2	yes	maximal
3	C₂×#6891	C₃	1	2	yes	maximal
4	C₂×#6860	C₃	1	9	yes	maximal, complemented
5	C₃²×3₋¹⁺²	C₂×C₃	1	2	yes	—
6	#6891	C₂×C₃	1	2	yes	—
7	#6860	C₂×C₃	1	9	yes	complemented
8	C₂×C₃⁴	C₃²	1	1	yes	characteristic
9	C₂×C₃×3₋¹⁺²	—	3	2	no	—
10	C₂×C₃×3₋¹⁺²	—	3	2	no	—
11	C₂×C₃×3₋¹⁺²	—	3	18	no	—
12	C₂×C₃×3₋¹⁺²	—	3	2	no	—
13	C₂×C₃×3₋¹⁺²	C₃²	1	6	yes	—
14	C₂×C₃²×C₉	—	3	2	no	—
15	C₂×C₃²⋊C₉	—	3	2	no	—
16	C₂×C₃²⋊C₉	—	3	2	no	—
17	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
18	C₃⁴	C₂×C₃²	1	1	yes	characteristic
19	C₃×3₋¹⁺²	—	3	2	no	—
20	C₃×3₋¹⁺²	—	3	2	no	—
21	C₃×3₋¹⁺²	—	3	18	no	—
22	C₃×3₋¹⁺²	—	3	2	no	—
23	C₃×3₋¹⁺²	C₂×C₃²	1	6	yes	—
24	C₃²×C₉	—	3	2	no	—
25	C₃²⋊C₉	—	3	2	no	—
26	C₃²⋊C₉	—	3	2	no	—
27	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
28	C₂×C₃³	—	3	6	no	—
29	C₂×C₃³	—	9	2	no	—
30	C₂×C₃³	H(3,𝔽₃)	1	1	yes	characteristic
31	C₂×C₃³	H(3,𝔽₃)	1	2	yes	—
32	C₂×C₃³	C₃³	1	1	yes	characteristic
33	C₂×3₋¹⁺²	—	3	18	no	—
34	C₂×3₋¹⁺²	—	3	18	no	—
35	C₂×3₋¹⁺²	—	3	18	no	—
36	C₂×3₋¹⁺²	—	9	6	no	—
37	C₂×C₃×C₉	—	3	18	no	—
38	C₂×C₃×C₉	—	3	6	no	—
39	C₂×C₃×C₉	—	3	6	no	—
40	C₃³	—	3	6	no	—
41	C₃³	—	9	2	no	—
42	C₃³	C₂×H(3,𝔽₃)	1	1	yes	characteristic
43	C₃³	C₂×H(3,𝔽₃)	1	2	yes	—
44	C₃³	C₂×C₃³	1	1	yes	characteristic
45	3₋¹⁺²	—	3	18	no	—
46	3₋¹⁺²	—	3	18	no	—
47	3₋¹⁺²	—	3	18	no	—
48	3₋¹⁺²	—	9	6	no	—
49	C₃×C₉	—	3	18	no	—
50	C₃×C₉	—	3	6	no	—
51	C₃×C₉	—	3	6	no	—
52	C₂×C₃²	—	3	4	no	—
53	C₂×C₃²	—	3	2	no	—
54	C₂×C₃²	—	3	2	no	—
55	C₂×C₃²	—	3	2	no	—
56	C₂×C₃²	—	3	2	no	—
57	C₂×C₃²	—	3	2	no	—
58	C₂×C₃²	—	9	9	no	—
59	C₂×C₃²	AΣL(1,𝔽₂₇)	1	6	yes	—
60	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
61	C₂×C₉	—	3	18	no	—
62	C₂×C₉	—	9	6	no	—
63	C₃²	—	3	2	no	—
64	C₃²	—	3	4	no	—
65	C₃²	—	3	2	no	—
66	C₃²	—	3	2	no	—
67	C₃²	—	3	2	no	—
68	C₃²	—	3	2	no	—
69	C₃²	—	9	9	no	—
70	C₃²	C₂×AΣL(1,𝔽₂₇)	1	6	yes	—
71	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
72	C₉	—	3	18	no	—
73	C₉	—	9	6	no	—
74	C₂×C₃	—	3	6	no	—
75	C₂×C₃	—	9	1	no	—
76	C₂×C₃	—	9	1	no	—
77	C₂×C₃	C₃×AΣL(1,𝔽₂₇)	1	2	yes	—
78	C₂×C₃	#6912	1	2	yes	—
79	C₃	—	3	6	no	—
80	C₃	—	9	1	no	—
81	C₃	—	9	1	no	—
82	C₃	C₂×C₃×AΣL(1,𝔽₂₇)	1	2	yes	—
83	C₃	C₂×#6912	1	2	yes	—
84	C₂	#10624607	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 ▷ C₃² ▷ 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. #10624607	C₂	direct (N × H)
4. C₂×#6860	C₃	semidirect
7. #6860	C₂×C₃	semidirect
84. C₂	#10624607	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624607	2
C₂×C₃²×3₋¹⁺²	3
C₂×#6891	3
C₂×#6860	3

Subgroups — C2×#10624607 #13090093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624607 #13090093