Subgroups — C₂×#10624902 #13090388

Order 1458.

644 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624902	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#6898	C₃	1	9	yes	maximal, complemented
3	C₂×#6896	C₃	1	9	yes	maximal, complemented
4	C₂×#6895	C₃	1	12	yes	maximal, complemented
5	C₂×#6891	C₃	1	2	yes	maximal
6	C₂×#6887	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	#6896	C₂×C₃	1	9	yes	complemented
10	#6895	C₂×C₃	1	12	yes	complemented
11	#6891	C₂×C₃	1	2	yes	—
12	#6887	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	12	yes	—
24	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
25	C₂×C₉²	C₃²	1	9	yes	complemented
26	C₃⁴	C₂×C₃²	1	1	yes	characteristic
27	C₃×3₋¹⁺²	C₂×C₃²	1	6	yes	—
28	C₃²×C₉	C₂×C₃²	1	6	yes	—
29	C₉⋊C₉	C₂×C₃²	1	36	yes	complemented
30	C₉⋊C₉	C₂×C₃²	1	36	yes	complemented
31	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
32	C₃²⋊C₉	C₂×C₃²	1	4	yes	—
33	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
34	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
35	C₃²⋊C₉	C₂×C₃²	1	12	yes	—
36	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
37	C₉²	C₂×C₃²	1	9	yes	complemented
38	C₂×C₃³	—	3	6	no	—
39	C₂×C₃³	—	9	2	no	—
40	C₂×C₃³	C₃³	1	1	yes	characteristic
41	C₂×C₃³	C₃³	1	1	yes	characteristic
42	C₂×C₃³	C₃³	1	2	yes	—
43	C₂×3₋¹⁺²	—	9	6	no	—
44	C₂×C₃×C₉	—	3	18	no	—
45	C₂×C₃×C₉	C₃³	1	6	yes	—
46	C₂×C₃×C₉	C₃³	1	18	yes	—
47	C₂×C₃×C₉	C₃³	1	12	yes	—
48	C₃³	—	3	6	no	—
49	C₃³	—	9	2	no	—
50	C₃³	C₂×C₃³	1	1	yes	characteristic
51	C₃³	C₂×C₃³	1	1	yes	characteristic
52	C₃³	C₂×C₃³	1	2	yes	—
53	3₋¹⁺²	—	9	6	no	—
54	C₃×C₉	—	3	18	no	—
55	C₃×C₉	C₂×C₃³	1	6	yes	—
56	C₃×C₉	C₂×C₃³	1	18	yes	—
57	C₃×C₉	C₂×C₃³	1	12	yes	—
58	C₂×C₃²	—	3	2	no	—
59	C₂×C₃²	—	3	4	no	—
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	—	9	9	no	—
65	C₂×C₃²	#737	1	6	yes	—
66	C₂×C₃²	C₃⁴	1	1	yes	characteristic
67	C₂×C₉	—	3	6	no	—
68	C₂×C₉	—	3	12	no	—
69	C₂×C₉	—	3	18	no	—
70	C₃²	—	3	2	no	—
71	C₃²	—	3	4	no	—
72	C₃²	—	3	2	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	3	2	no	—
75	C₃²	—	3	2	no	—
76	C₃²	—	9	9	no	—
77	C₃²	C₂×#737	1	6	yes	—
78	C₃²	C₂×C₃⁴	1	1	yes	characteristic
79	C₉	—	3	6	no	—
80	C₉	—	3	12	no	—
81	C₉	—	3	18	no	—
82	C₂×C₃	—	3	6	no	—
83	C₂×C₃	—	9	1	no	—
84	C₂×C₃	—	9	1	no	—
85	C₂×C₃	C₃×#737	1	2	yes	—
86	C₂×C₃	3₋¹⁺⁴	1	2	yes	—
87	C₃	—	3	6	no	—
88	C₃	—	9	1	no	—
89	C₃	—	9	1	no	—
90	C₃	C₂×C₃×#737	1	2	yes	—
91	C₃	C₂×3₋¹⁺⁴	1	2	yes	—
92	C₂	#10624902	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. #10624902	C₂	direct (N × H)
2. C₂×#6898	C₃	semidirect
3. C₂×#6896	C₃	semidirect
4. C₂×#6895	C₃	semidirect
6. C₂×#6887	C₃	semidirect
8. #6898	C₂×C₃	semidirect
9. #6896	C₂×C₃	semidirect
10. #6895	C₂×C₃	semidirect
12. #6887	C₂×C₃	semidirect
17. C₂×C₉⋊C₉	C₃²	semidirect
18. C₂×C₉⋊C₉	C₃²	semidirect
25. C₂×C₉²	C₃²	semidirect
29. C₉⋊C₉	C₂×C₃²	semidirect
30. C₉⋊C₉	C₂×C₃²	semidirect
37. C₉²	C₂×C₃²	semidirect
92. C₂	#10624902	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624902	2
C₂×#6898	3
C₂×#6896	3
C₂×#6895	3
C₂×#6891	3
C₂×#6887	3
C₂×C₃×C₃²⋊C₉	3

Subgroups — C2×#10624902 #13090388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624902 #13090388