Subgroups — C₂×#10624886 #13090372

Order 1458.

728 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624886	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃²×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₂×#6895	C₃	1	9	yes	maximal, complemented
4	C₂×#6894	C₃	1	27	yes	maximal, complemented
5	C₂×C₃×C₃²⋊C₉	C₃	1	3	yes	maximal
6	C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
7	#6895	C₂×C₃	1	9	yes	complemented
8	#6894	C₂×C₃	1	27	yes	complemented
9	C₃×C₃²⋊C₉	C₂×C₃	1	3	yes	—
10	C₂×C₃⁴	C₃²	1	1	yes	characteristic
11	C₂×C₃×3₋¹⁺²	—	3	9	no	—
12	C₂×C₃×3₋¹⁺²	C₃²	1	9	yes	—
13	C₂×C₃²×C₉	C₃²	1	3	yes	—
14	C₂×C₃²×C₉	C₃²	1	9	yes	—
15	C₂×C₉⋊C₉	C₃²	1	81	yes	complemented
16	C₂×C₃²⋊C₉	C₃²	1	18	yes	—
17	C₂×C₃²⋊C₉	C₃²	1	9	yes	—
18	C₃⁴	C₂×C₃²	1	1	yes	characteristic
19	C₃×3₋¹⁺²	—	3	9	no	—
20	C₃×3₋¹⁺²	C₂×C₃²	1	9	yes	—
21	C₃²×C₉	C₂×C₃²	1	3	yes	—
22	C₃²×C₉	C₂×C₃²	1	9	yes	—
23	C₉⋊C₉	C₂×C₃²	1	81	yes	complemented
24	C₃²⋊C₉	C₂×C₃²	1	18	yes	—
25	C₃²⋊C₉	C₂×C₃²	1	9	yes	—
26	C₂×C₃³	—	9	3	no	—
27	C₂×C₃³	3₋¹⁺²	1	9	yes	—
28	C₂×C₃³	C₃³	1	1	yes	characteristic
29	C₂×C₃³	C₃³	1	3	yes	—
30	C₂×3₋¹⁺²	—	3	27	no	—
31	C₂×C₃×C₉	—	3	9	no	—
32	C₂×C₃×C₉	—	9	9	no	—
33	C₂×C₃×C₉	C₃³	1	27	yes	—
34	C₂×C₃×C₉	C₃³	1	9	yes	—
35	C₃³	—	9	3	no	—
36	C₃³	C₂×3₋¹⁺²	1	9	yes	—
37	C₃³	C₂×C₃³	1	1	yes	characteristic
38	C₃³	C₂×C₃³	1	3	yes	—
39	3₋¹⁺²	—	3	27	no	—
40	C₃×C₉	—	3	9	no	—
41	C₃×C₉	—	9	9	no	—
42	C₃×C₉	C₂×C₃³	1	27	yes	—
43	C₃×C₉	C₂×C₃³	1	9	yes	—
44	C₂×C₃²	—	3	3	no	—
45	C₂×C₃²	—	3	3	no	—
46	C₂×C₃²	—	3	6	no	—
47	C₂×C₃²	—	9	9	no	—
48	C₂×C₃²	C₃×3₋¹⁺²	1	3	yes	—
49	C₂×C₃²	C₃×3₋¹⁺²	1	9	yes	—
50	C₂×C₃²	C₃⁴	1	1	yes	characteristic
51	C₂×C₉	—	3	9	no	—
52	C₂×C₉	—	3	27	no	—
53	C₃²	—	3	3	no	—
54	C₃²	—	3	3	no	—
55	C₃²	—	3	6	no	—
56	C₃²	—	9	9	no	—
57	C₃²	C₂×C₃×3₋¹⁺²	1	3	yes	—
58	C₃²	C₂×C₃×3₋¹⁺²	1	9	yes	—
59	C₃²	C₂×C₃⁴	1	1	yes	characteristic
60	C₉	—	3	9	no	—
61	C₉	—	3	27	no	—
62	C₂×C₃	—	3	9	no	—
63	C₂×C₃	—	3	3	no	—
64	C₂×C₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
65	C₂×C₃	3₋¹⁺⁴	1	3	yes	—
66	C₃	—	3	9	no	—
67	C₃	—	3	3	no	—
68	C₃	C₂×C₃²×3₋¹⁺²	1	1	yes	characteristic
69	C₃	C₂×3₋¹⁺⁴	1	3	yes	—
70	C₂	#10624886	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×C₃⁴	C₃²
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. #10624886	C₂	direct (N × H)
3. C₂×#6895	C₃	semidirect
4. C₂×#6894	C₃	semidirect
7. #6895	C₂×C₃	semidirect
8. #6894	C₂×C₃	semidirect
15. C₂×C₉⋊C₉	C₃²	semidirect
23. C₉⋊C₉	C₂×C₃²	semidirect
70. C₂	#10624886	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624886	2
C₂×C₃²×3₋¹⁺²	3
C₂×#6895	3
C₂×#6894	3
C₂×C₃×C₃²⋊C₉	3

Subgroups — C2×#10624886 #13090372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624886 #13090372