Subgroups — C₂×#10624790 #13090276

Order 1458.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624790	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×#732	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉⋊H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
4	C₂×C₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×H(3,𝔽₃)⋊C₉	C₃	1	6	yes	maximal, complemented
6	C₂×#6868	C₃	1	2	yes	maximal, complemented
7	C₃×#732	C₂×C₃	1	1	yes	characteristic
8	C₉⋊H(3,𝔽₃)	C₂×C₃	1	3	yes	complemented
9	C₃×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	H(3,𝔽₃)⋊C₉	C₂×C₃	1	6	yes	complemented
11	#6868	C₂×C₃	1	2	yes	complemented
12	C₂×C₃×3₋¹⁺²	—	3	3	no	—
13	C₂×C₃×H(3,𝔽₃)	C₃²	1	3	yes	—
14	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
15	C₂×C₃²×C₉	C₃²	1	2	yes	—
16	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
17	C₂×#732	—	3	3	no	—
18	C₂×C₉⋊C₉	—	3	3	no	—
19	C₂×C₃²⋊C₉	—	3	6	no	—
20	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
21	C₃×3₋¹⁺²	—	3	3	no	—
22	C₃×H(3,𝔽₃)	C₂×C₃²	1	3	yes	—
23	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
24	C₃²×C₉	C₂×C₃²	1	2	yes	—
25	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
26	#732	—	3	3	no	—
27	C₉⋊C₉	—	3	3	no	—
28	C₃²⋊C₉	—	3	6	no	—
29	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
30	C₂×C₃³	—	3	3	no	—
31	C₂×C₃³	C₃³	1	1	yes	characteristic
32	C₂×3₋¹⁺²	—	9	9	no	—
33	C₂×H(3,𝔽₃)	—	3	3	no	—
34	C₂×H(3,𝔽₃)	—	3	6	no	—
35	C₂×C₃×C₉	—	3	1	no	—
36	C₂×C₃×C₉	—	3	2	no	—
37	C₂×C₃×C₉	—	3	6	no	—
38	C₂×C₃×C₉	—	3	2	no	—
39	C₂×C₃×C₉	—	9	1	no	—
40	C₂×C₃×C₉	—	9	2	no	—
41	C₂×C₃×C₉	H(3,𝔽₃)	1	3	yes	—
42	C₂×C₃×C₉	3₋¹⁺²	1	3	yes	complemented
43	C₃³	—	3	3	no	—
44	C₃³	C₂×C₃³	1	1	yes	characteristic
45	3₋¹⁺²	—	9	9	no	—
46	H(3,𝔽₃)	—	3	3	no	—
47	H(3,𝔽₃)	—	3	6	no	—
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	—	3	2	no	—
50	C₃×C₉	—	3	6	no	—
51	C₃×C₉	—	3	2	no	—
52	C₃×C₉	—	9	1	no	—
53	C₃×C₉	—	9	2	no	—
54	C₃×C₉	C₂×H(3,𝔽₃)	1	3	yes	—
55	C₃×C₉	C₂×3₋¹⁺²	1	3	yes	complemented
56	C₂×C₃²	—	3	2	no	—
57	C₂×C₃²	—	3	1	no	—
58	C₂×C₃²	—	9	6	no	—
59	C₂×C₃²	—	9	3	no	—
60	C₂×C₃²	—	9	3	no	—
61	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
62	C₂×C₃²	C₃×3₋¹⁺²	1	1	yes	characteristic
63	C₂×C₃²	#737	1	2	yes	—
64	C₂×C₉	—	3	3	no	—
65	C₂×C₉	—	3	3	no	—
66	C₂×C₉	—	9	2	no	—
67	C₂×C₉	—	9	6	no	—
68	C₃²	—	3	1	no	—
69	C₃²	—	3	2	no	—
70	C₃²	—	9	3	no	—
71	C₃²	—	9	3	no	—
72	C₃²	—	9	6	no	—
73	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
74	C₃²	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
75	C₃²	C₂×#737	1	2	yes	—
76	C₉	—	3	3	no	—
77	C₉	—	3	3	no	—
78	C₉	—	9	6	no	—
79	C₉	—	9	2	no	—
80	C₂×C₃	—	3	1	no	—
81	C₂×C₃	—	3	2	no	—
82	C₂×C₃	—	27	3	no	—
83	C₂×C₃	C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
84	C₂×C₃	#6911	1	1	yes	characteristic
85	C₂×C₃	#6913	1	2	yes	—
86	C₃	—	3	1	no	—
87	C₃	—	3	2	no	—
88	C₃	—	27	3	no	—
89	C₃	C₂×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
90	C₃	C₂×#6911	1	1	yes	characteristic
91	C₃	C₂×#6913	1	2	yes	—
92	C₂	#10624790	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃²	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₂×C₃³
prime radical	C₂×C₃×#732	C₃
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃²×C₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #10624790	C₂	direct (N × H)
3. C₂×C₉⋊H(3,𝔽₃)	C₃	semidirect
4. C₂×C₃×C₉⋊C₉	C₃	semidirect
5. C₂×H(3,𝔽₃)⋊C₉	C₃	semidirect
6. C₂×#6868	C₃	semidirect
8. C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
9. C₃×C₉⋊C₉	C₂×C₃	semidirect
10. H(3,𝔽₃)⋊C₉	C₂×C₃	semidirect
11. #6868	C₂×C₃	semidirect
42. C₂×C₃×C₉	3₋¹⁺²	semidirect
55. C₃×C₉	C₂×3₋¹⁺²	semidirect
92. C₂	#10624790	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624790	2
C₂×C₃×#732	3
C₂×C₉⋊H(3,𝔽₃)	3
C₂×C₃×C₉⋊C₉	3
C₂×H(3,𝔽₃)⋊C₉	3
C₂×#6868	3

Subgroups — C2×#10624790 #13090276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624790 #13090276