Subgroups — C₂×#10624885 #13090371

Order 1458.

716 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624885	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃²×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₂×#6896	C₃	1	27	yes	maximal, complemented
4	C₂×#6895	C₃	1	6	yes	maximal, complemented
5	C₂×#6891	C₃	1	3	yes	maximal
6	C₂×#6887	C₃	1	3	yes	maximal, complemented
7	C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
8	#6896	C₂×C₃	1	27	yes	complemented
9	#6895	C₂×C₃	1	6	yes	complemented
10	#6891	C₂×C₃	1	3	yes	—
11	#6887	C₂×C₃	1	3	yes	complemented
12	C₂×C₃⁴	C₃²	1	1	yes	characteristic
13	C₂×C₃×3₋¹⁺²	—	3	9	no	—
14	C₂×C₃×3₋¹⁺²	C₃²	1	9	yes	—
15	C₂×C₃×3₋¹⁺²	C₃²	1	9	yes	—
16	C₂×C₃²×C₉	C₃²	1	2	yes	—
17	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
18	C₂×C₉⋊C₉	C₃²	1	18	yes	complemented
19	C₂×C₉⋊C₉	C₃²	1	54	yes	complemented
20	C₂×C₃²⋊C₉	C₃²	1	9	yes	—
21	C₂×C₃²⋊C₉	C₃²	1	18	yes	—
22	C₂×C₉²	C₃²	1	9	yes	complemented
23	C₃⁴	C₂×C₃²	1	1	yes	characteristic
24	C₃×3₋¹⁺²	—	3	9	no	—
25	C₃×3₋¹⁺²	C₂×C₃²	1	9	yes	—
26	C₃×3₋¹⁺²	C₂×C₃²	1	9	yes	—
27	C₃²×C₉	C₂×C₃²	1	2	yes	—
28	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
29	C₉⋊C₉	C₂×C₃²	1	18	yes	complemented
30	C₉⋊C₉	C₂×C₃²	1	54	yes	complemented
31	C₃²⋊C₉	C₂×C₃²	1	9	yes	—
32	C₃²⋊C₉	C₂×C₃²	1	18	yes	—
33	C₉²	C₂×C₃²	1	9	yes	complemented
34	C₂×C₃³	—	3	3	no	—
35	C₂×C₃³	—	9	3	no	—
36	C₂×C₃³	C₃³	1	3	yes	—
37	C₂×C₃³	C₃³	1	1	yes	characteristic
38	C₂×3₋¹⁺²	—	3	27	no	—
39	C₂×3₋¹⁺²	—	9	9	no	—
40	C₂×C₃×C₉	—	3	6	no	—
41	C₂×C₃×C₉	3₋¹⁺²	1	9	yes	complemented
42	C₂×C₃×C₉	C₃³	1	27	yes	—
43	C₂×C₃×C₉	C₃³	1	6	yes	—
44	C₂×C₃×C₉	C₃³	1	3	yes	—
45	C₃³	—	3	3	no	—
46	C₃³	—	9	3	no	—
47	C₃³	C₂×C₃³	1	3	yes	—
48	C₃³	C₂×C₃³	1	1	yes	characteristic
49	3₋¹⁺²	—	3	27	no	—
50	3₋¹⁺²	—	9	9	no	—
51	C₃×C₉	—	3	6	no	—
52	C₃×C₉	C₂×3₋¹⁺²	1	9	yes	complemented
53	C₃×C₉	C₂×C₃³	1	27	yes	—
54	C₃×C₉	C₂×C₃³	1	6	yes	—
55	C₃×C₉	C₂×C₃³	1	3	yes	—
56	C₂×C₃²	—	3	3	no	—
57	C₂×C₃²	—	3	3	no	—
58	C₂×C₃²	—	3	3	no	—
59	C₂×C₃²	—	3	6	no	—
60	C₂×C₃²	—	9	9	no	—
61	C₂×C₃²	C₃×3₋¹⁺²	1	3	yes	—
62	C₂×C₃²	C₃⁴	1	1	yes	characteristic
63	C₂×C₉	—	3	6	no	—
64	C₂×C₉	—	3	27	no	—
65	C₂×C₉	C₃×3₋¹⁺²	1	9	yes	—
66	C₃²	—	3	3	no	—
67	C₃²	—	3	3	no	—
68	C₃²	—	3	3	no	—
69	C₃²	—	3	6	no	—
70	C₃²	—	9	9	no	—
71	C₃²	C₂×C₃×3₋¹⁺²	1	3	yes	—
72	C₃²	C₂×C₃⁴	1	1	yes	characteristic
73	C₉	—	3	6	no	—
74	C₉	—	3	27	no	—
75	C₉	C₂×C₃×3₋¹⁺²	1	9	yes	—
76	C₂×C₃	—	3	3	no	—
77	C₂×C₃	—	9	3	no	—
78	C₂×C₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
79	C₂×C₃	3₋¹⁺⁴	1	3	yes	—
80	C₃	—	3	3	no	—
81	C₃	—	9	3	no	—
82	C₃	C₂×C₃²×3₋¹⁺²	1	1	yes	characteristic
83	C₃	C₂×3₋¹⁺⁴	1	3	yes	—
84	C₂	#10624885	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. #10624885	C₂	direct (N × H)
3. C₂×#6896	C₃	semidirect
4. C₂×#6895	C₃	semidirect
6. C₂×#6887	C₃	semidirect
8. #6896	C₂×C₃	semidirect
9. #6895	C₂×C₃	semidirect
11. #6887	C₂×C₃	semidirect
18. C₂×C₉⋊C₉	C₃²	semidirect
19. C₂×C₉⋊C₉	C₃²	semidirect
22. C₂×C₉²	C₃²	semidirect
29. C₉⋊C₉	C₂×C₃²	semidirect
30. C₉⋊C₉	C₂×C₃²	semidirect
33. C₉²	C₂×C₃²	semidirect
41. C₂×C₃×C₉	3₋¹⁺²	semidirect
52. C₃×C₉	C₂×3₋¹⁺²	semidirect
84. C₂	#10624885	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624885	2
C₂×C₃²×3₋¹⁺²	3
C₂×#6896	3
C₂×#6895	3
C₂×#6891	3
C₂×#6887	3

Subgroups — C2×#10624885 #13090371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624885 #13090371