Subgroups — C₂×#10624884 #13090370

Order 1458.

716 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624884	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃²×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₂×#6900	C₃	1	9	yes	maximal, complemented
4	C₂×#6899	C₃	1	18	yes	maximal, complemented
5	C₂×#6895	C₃	1	6	yes	maximal, complemented
6	C₂×#6891	C₃	1	3	yes	maximal
7	C₂×#6887	C₃	1	3	yes	maximal, complemented
8	C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
9	#6900	C₂×C₃	1	9	yes	complemented
10	#6899	C₂×C₃	1	18	yes	complemented
11	#6895	C₂×C₃	1	6	yes	complemented
12	#6891	C₂×C₃	1	3	yes	—
13	#6887	C₂×C₃	1	3	yes	complemented
14	C₂×C₃⁴	C₃²	1	1	yes	characteristic
15	C₂×C₃×3₋¹⁺²	—	3	9	no	—
16	C₂×C₃×3₋¹⁺²	C₃²	1	6	yes	—
17	C₂×C₃×3₋¹⁺²	C₃²	1	3	yes	—
18	C₂×C₃×3₋¹⁺²	C₃²	1	9	yes	—
19	C₂×C₃²×C₉	C₃²	1	2	yes	—
20	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
21	C₂×C₉⋊C₉	C₃²	1	18	yes	complemented
22	C₂×C₉⋊C₉	C₃²	1	54	yes	complemented
23	C₂×C₃²⋊C₉	C₃²	1	9	yes	—
24	C₂×C₃²⋊C₉	C₃²	1	18	yes	—
25	C₂×C₉²	C₃²	1	9	yes	complemented
26	C₃⁴	C₂×C₃²	1	1	yes	characteristic
27	C₃×3₋¹⁺²	—	3	9	no	—
28	C₃×3₋¹⁺²	C₂×C₃²	1	6	yes	—
29	C₃×3₋¹⁺²	C₂×C₃²	1	3	yes	—
30	C₃×3₋¹⁺²	C₂×C₃²	1	9	yes	—
31	C₃²×C₉	C₂×C₃²	1	2	yes	—
32	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
33	C₉⋊C₉	C₂×C₃²	1	18	yes	complemented
34	C₉⋊C₉	C₂×C₃²	1	54	yes	complemented
35	C₃²⋊C₉	C₂×C₃²	1	9	yes	—
36	C₃²⋊C₉	C₂×C₃²	1	18	yes	—
37	C₉²	C₂×C₃²	1	9	yes	complemented
38	C₂×C₃³	—	3	3	no	—
39	C₂×C₃³	—	9	3	no	—
40	C₂×C₃³	C₃³	1	2	yes	—
41	C₂×C₃³	C₃³	1	1	yes	characteristic
42	C₂×C₃³	C₃³	1	1	yes	characteristic
43	C₂×3₋¹⁺²	—	3	18	no	—
44	C₂×3₋¹⁺²	—	3	9	no	—
45	C₂×3₋¹⁺²	—	9	9	no	—
46	C₂×C₃×C₉	—	3	6	no	—
47	C₂×C₃×C₉	3₋¹⁺²	1	9	yes	complemented
48	C₂×C₃×C₉	C₃³	1	27	yes	—
49	C₂×C₃×C₉	C₃³	1	6	yes	—
50	C₂×C₃×C₉	C₃³	1	3	yes	—
51	C₃³	—	3	3	no	—
52	C₃³	—	9	3	no	—
53	C₃³	C₂×C₃³	1	2	yes	—
54	C₃³	C₂×C₃³	1	1	yes	characteristic
55	C₃³	C₂×C₃³	1	1	yes	characteristic
56	3₋¹⁺²	—	3	18	no	—
57	3₋¹⁺²	—	3	9	no	—
58	3₋¹⁺²	—	9	9	no	—
59	C₃×C₉	—	3	6	no	—
60	C₃×C₉	C₂×3₋¹⁺²	1	9	yes	complemented
61	C₃×C₉	C₂×C₃³	1	27	yes	—
62	C₃×C₉	C₂×C₃³	1	6	yes	—
63	C₃×C₉	C₂×C₃³	1	3	yes	—
64	C₂×C₃²	—	3	3	no	—
65	C₂×C₃²	—	3	2	no	—
66	C₂×C₃²	—	3	1	no	—
67	C₂×C₃²	—	3	3	no	—
68	C₂×C₃²	—	3	6	no	—
69	C₂×C₃²	—	9	9	no	—
70	C₂×C₃²	C₃×3₋¹⁺²	1	3	yes	—
71	C₂×C₃²	C₃⁴	1	1	yes	characteristic
72	C₂×C₉	—	3	6	no	—
73	C₂×C₉	—	3	27	no	—
74	C₂×C₉	C₃×3₋¹⁺²	1	9	yes	—
75	C₃²	—	3	3	no	—
76	C₃²	—	3	2	no	—
77	C₃²	—	3	1	no	—
78	C₃²	—	3	3	no	—
79	C₃²	—	3	6	no	—
80	C₃²	—	9	9	no	—
81	C₃²	C₂×C₃×3₋¹⁺²	1	3	yes	—
82	C₃²	C₂×C₃⁴	1	1	yes	characteristic
83	C₉	—	3	6	no	—
84	C₉	—	3	27	no	—
85	C₉	C₂×C₃×3₋¹⁺²	1	9	yes	—
86	C₂×C₃	—	3	3	no	—
87	C₂×C₃	—	9	1	no	—
88	C₂×C₃	—	9	2	no	—
89	C₂×C₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
90	C₂×C₃	3₋¹⁺⁴	1	3	yes	—
91	C₃	—	3	3	no	—
92	C₃	—	9	1	no	—
93	C₃	—	9	2	no	—
94	C₃	C₂×C₃²×3₋¹⁺²	1	1	yes	characteristic
95	C₃	C₂×3₋¹⁺⁴	1	3	yes	—
96	C₂	#10624884	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. #10624884	C₂	direct (N × H)
3. C₂×#6900	C₃	semidirect
4. C₂×#6899	C₃	semidirect
5. C₂×#6895	C₃	semidirect
7. C₂×#6887	C₃	semidirect
9. #6900	C₂×C₃	semidirect
10. #6899	C₂×C₃	semidirect
11. #6895	C₂×C₃	semidirect
13. #6887	C₂×C₃	semidirect
21. C₂×C₉⋊C₉	C₃²	semidirect
22. C₂×C₉⋊C₉	C₃²	semidirect
25. C₂×C₉²	C₃²	semidirect
33. C₉⋊C₉	C₂×C₃²	semidirect
34. C₉⋊C₉	C₂×C₃²	semidirect
37. C₉²	C₂×C₃²	semidirect
47. C₂×C₃×C₉	3₋¹⁺²	semidirect
60. C₃×C₉	C₂×3₋¹⁺²	semidirect
96. C₂	#10624884	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624884	2
C₂×C₃²×3₋¹⁺²	3
C₂×#6900	3
C₂×#6899	3
C₂×#6895	3
C₂×#6891	3
C₂×#6887	3

Subgroups — C2×#10624884 #13090370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624884 #13090370