Subgroups — C₂×#10624585 #13090071

Order 1458.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624585	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₉×H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
3	C₂×#6887	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#6861	C₃	1	3	yes	maximal, complemented
5	C₂×#6859	C₃	1	3	yes	maximal, complemented
6	C₂×#6856	C₃	1	3	yes	maximal, complemented
7	C₉×H(3,𝔽₃)	C₂×C₃	1	3	yes	complemented
8	#6887	C₂×C₃	1	1	yes	characteristic, complemented
9	#6861	C₂×C₃	1	3	yes	complemented
10	#6859	C₂×C₃	1	3	yes	complemented
11	#6856	C₂×C₃	1	3	yes	complemented
12	C₂×C₃×H(3,𝔽₃)	C₃²	1	3	yes	—
13	C₂×C₃²×C₉	—	3	3	no	—
14	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
15	C₂×C₉⋊C₉	—	3	2	no	—
16	C₂×C₃²⋊C₉	—	3	6	no	—
17	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
18	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
19	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
20	C₂×C₉²	—	3	1	no	—
21	C₃×H(3,𝔽₃)	C₂×C₃²	1	3	yes	—
22	C₃²×C₉	—	3	3	no	—
23	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
24	C₉⋊C₉	—	3	2	no	—
25	C₃²⋊C₉	—	3	6	no	—
26	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
27	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
28	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
29	C₉²	—	3	1	no	—
30	C₂×C₃³	—	3	3	no	—
31	C₂×C₃³	C₃³	1	1	yes	characteristic
32	C₂×H(3,𝔽₃)	—	3	9	no	—
33	C₂×C₃×C₉	—	3	3	no	—
34	C₂×C₃×C₉	—	3	3	no	—
35	C₂×C₃×C₉	—	3	3	no	—
36	C₂×C₃×C₉	—	3	3	no	—
37	C₂×C₃×C₉	—	9	9	no	—
38	C₂×C₃×C₉	H(3,𝔽₃)	1	2	yes	—
39	C₂×C₃×C₉	H(3,𝔽₃)	1	1	yes	characteristic
40	C₃³	—	3	3	no	—
41	C₃³	C₂×C₃³	1	1	yes	characteristic
42	H(3,𝔽₃)	—	3	9	no	—
43	C₃×C₉	—	3	3	no	—
44	C₃×C₉	—	3	3	no	—
45	C₃×C₉	—	3	3	no	—
46	C₃×C₉	—	3	3	no	—
47	C₃×C₉	—	9	9	no	—
48	C₃×C₉	C₂×H(3,𝔽₃)	1	2	yes	—
49	C₃×C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic
50	C₂×C₃²	—	3	1	no	—
51	C₂×C₃²	—	3	3	no	—
52	C₂×C₃²	—	3	9	no	—
53	C₂×C₃²	—	9	3	no	—
54	C₂×C₃²	—	9	6	no	—
55	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
56	C₂×C₉	—	3	2	no	—
57	C₂×C₉	—	9	3	no	—
58	C₂×C₉	—	9	3	no	—
59	C₂×C₉	—	9	3	no	—
60	C₂×C₉	#732	1	3	yes	—
61	C₃²	—	3	1	no	—
62	C₃²	—	3	3	no	—
63	C₃²	—	3	9	no	—
64	C₃²	—	9	3	no	—
65	C₃²	—	9	6	no	—
66	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
67	C₉	—	3	2	no	—
68	C₉	—	9	3	no	—
69	C₉	—	9	3	no	—
70	C₉	—	9	3	no	—
71	C₉	C₂×#732	1	3	yes	—
72	C₂×C₃	—	9	1	no	—
73	C₂×C₃	—	9	9	no	—
74	C₂×C₃	C₃×#732	1	1	yes	characteristic
75	C₂×C₃	#6908	1	3	yes	—
76	C₃	—	9	1	no	—
77	C₃	—	9	9	no	—
78	C₃	C₂×C₃×#732	1	1	yes	characteristic
79	C₃	C₂×#6908	1	3	yes	—
80	C₂	#10624585	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. #10624585	C₂	direct (N × H)
2. C₂×C₉×H(3,𝔽₃)	C₃	semidirect
3. C₂×#6887	C₃	semidirect
4. C₂×#6861	C₃	semidirect
5. C₂×#6859	C₃	semidirect
6. C₂×#6856	C₃	semidirect
7. C₉×H(3,𝔽₃)	C₂×C₃	semidirect
8. #6887	C₂×C₃	semidirect
9. #6861	C₂×C₃	semidirect
10. #6859	C₂×C₃	semidirect
11. #6856	C₂×C₃	semidirect
80. C₂	#10624585	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624585	2
C₂×C₉×H(3,𝔽₃)	3
C₂×#6887	3
C₂×#6861	3
C₂×#6859	3
C₂×#6856	3

Subgroups — C2×#10624585 #13090071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624585 #13090071