Subgroups — C₂×#10624906 #13090392

Order 1458.

644 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624906	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#6898	C₃	1	9	yes	maximal, complemented
3	C₂×#6897	C₃	1	9	yes	maximal, complemented
4	C₂×#6894	C₃	1	12	yes	maximal, complemented
5	C₂×#6891	C₃	1	2	yes	maximal
6	C₂×C₉×3₋¹⁺²	C₃	1	6	yes	maximal, complemented
7	C₂×C₃×C₃²⋊C₉	C₃	1	2	yes	maximal
8	#6898	C₂×C₃	1	9	yes	complemented
9	#6897	C₂×C₃	1	9	yes	complemented
10	#6894	C₂×C₃	1	12	yes	complemented
11	#6891	C₂×C₃	1	2	yes	—
12	C₉×3₋¹⁺²	C₂×C₃	1	6	yes	complemented
13	C₃×C₃²⋊C₉	C₂×C₃	1	2	yes	—
14	C₂×C₃⁴	C₃²	1	1	yes	characteristic
15	C₂×C₃×3₋¹⁺²	C₃²	1	6	yes	—
16	C₂×C₃²×C₉	C₃²	1	6	yes	—
17	C₂×C₉⋊C₉	C₃²	1	36	yes	complemented
18	C₂×C₉⋊C₉	C₃²	1	36	yes	complemented
19	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
20	C₂×C₃²⋊C₉	C₃²	1	4	yes	—
21	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
22	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
23	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
24	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
25	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
26	C₂×C₉²	C₃²	1	9	yes	complemented
27	C₃⁴	C₂×C₃²	1	1	yes	characteristic
28	C₃×3₋¹⁺²	C₂×C₃²	1	6	yes	—
29	C₃²×C₉	C₂×C₃²	1	6	yes	—
30	C₉⋊C₉	C₂×C₃²	1	36	yes	complemented
31	C₉⋊C₉	C₂×C₃²	1	36	yes	complemented
32	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
33	C₃²⋊C₉	C₂×C₃²	1	4	yes	—
34	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
35	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
36	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
37	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
38	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
39	C₉²	C₂×C₃²	1	9	yes	complemented
40	C₂×C₃³	—	3	6	no	—
41	C₂×C₃³	—	9	2	no	—
42	C₂×C₃³	C₃³	1	1	yes	characteristic
43	C₂×C₃³	C₃³	1	1	yes	characteristic
44	C₂×C₃³	C₃³	1	2	yes	—
45	C₂×3₋¹⁺²	—	3	18	no	—
46	C₂×C₃×C₉	—	9	6	no	—
47	C₂×C₃×C₉	C₃³	1	6	yes	—
48	C₂×C₃×C₉	C₃³	1	18	yes	—
49	C₂×C₃×C₉	C₃³	1	12	yes	—
50	C₃³	—	3	6	no	—
51	C₃³	—	9	2	no	—
52	C₃³	C₂×C₃³	1	1	yes	characteristic
53	C₃³	C₂×C₃³	1	1	yes	characteristic
54	C₃³	C₂×C₃³	1	2	yes	—
55	3₋¹⁺²	—	3	18	no	—
56	C₃×C₉	—	9	6	no	—
57	C₃×C₉	C₂×C₃³	1	6	yes	—
58	C₃×C₉	C₂×C₃³	1	18	yes	—
59	C₃×C₉	C₂×C₃³	1	12	yes	—
60	C₂×C₃²	—	3	2	no	—
61	C₂×C₃²	—	3	2	no	—
62	C₂×C₃²	—	3	2	no	—
63	C₂×C₃²	—	3	2	no	—
64	C₂×C₃²	—	3	2	no	—
65	C₂×C₃²	—	3	2	no	—
66	C₂×C₃²	—	3	2	no	—
67	C₂×C₃²	—	9	9	no	—
68	C₂×C₃²	#737	1	6	yes	—
69	C₂×C₃²	C₃⁴	1	1	yes	characteristic
70	C₂×C₉	—	3	18	no	—
71	C₂×C₉	—	3	6	no	—
72	C₂×C₉	—	3	12	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	3	2	no	—
75	C₃²	—	3	2	no	—
76	C₃²	—	3	2	no	—
77	C₃²	—	3	2	no	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	9	9	no	—
81	C₃²	C₂×#737	1	6	yes	—
82	C₃²	C₂×C₃⁴	1	1	yes	characteristic
83	C₉	—	3	18	no	—
84	C₉	—	3	6	no	—
85	C₉	—	3	12	no	—
86	C₂×C₃	—	3	6	no	—
87	C₂×C₃	—	9	1	no	—
88	C₂×C₃	—	9	1	no	—
89	C₂×C₃	C₃×#737	1	2	yes	—
90	C₂×C₃	3₋¹⁺⁴	1	2	yes	—
91	C₃	—	3	6	no	—
92	C₃	—	9	1	no	—
93	C₃	—	9	1	no	—
94	C₃	C₂×C₃×#737	1	2	yes	—
95	C₃	C₂×3₋¹⁺⁴	1	2	yes	—
96	C₂	#10624906	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. #10624906	C₂	direct (N × H)
2. C₂×#6898	C₃	semidirect
3. C₂×#6897	C₃	semidirect
4. C₂×#6894	C₃	semidirect
6. C₂×C₉×3₋¹⁺²	C₃	semidirect
8. #6898	C₂×C₃	semidirect
9. #6897	C₂×C₃	semidirect
10. #6894	C₂×C₃	semidirect
12. C₉×3₋¹⁺²	C₂×C₃	semidirect
17. C₂×C₉⋊C₉	C₃²	semidirect
18. C₂×C₉⋊C₉	C₃²	semidirect
26. C₂×C₉²	C₃²	semidirect
30. C₉⋊C₉	C₂×C₃²	semidirect
31. C₉⋊C₉	C₂×C₃²	semidirect
39. C₉²	C₂×C₃²	semidirect
96. C₂	#10624906	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624906	2
C₂×#6898	3
C₂×#6897	3
C₂×#6894	3
C₂×#6891	3
C₂×C₉×3₋¹⁺²	3
C₂×C₃×C₃²⋊C₉	3

Subgroups — C2×#10624906 #13090392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624906 #13090392