Subgroups — C₂×C₃×#6861 #13090070

Order 1458.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6861	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×C₃×C₃²⋊C₉	C₃	1	3	yes	maximal
4	C₂×#6861	C₃	1	9	yes	maximal, direct product factor
5	C₃×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
6	C₃×C₃²⋊C₉	C₂×C₃	1	3	yes	—
7	#6861	C₂×C₃	1	9	yes	direct product factor
8	C₂×C₃⁴	C₃²	1	1	yes	characteristic
9	C₂×C₃²×C₉	—	3	1	no	—
10	C₂×C₃²×C₉	—	3	3	no	—
11	C₂×C₃²⋊C₉	—	3	2	no	—
12	C₂×C₃²⋊C₉	—	3	6	no	—
13	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₂×C₃²⋊C₉	C₃²	1	9	yes	—
15	C₃⁴	C₂×C₃²	1	1	yes	characteristic
16	C₃²×C₉	—	3	1	no	—
17	C₃²×C₉	—	3	3	no	—
18	C₃²⋊C₉	—	3	2	no	—
19	C₃²⋊C₉	—	3	6	no	—
20	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
21	C₃²⋊C₉	C₂×C₃²	1	9	yes	—
22	C₂×C₃³	—	3	3	no	—
23	C₂×C₃³	—	3	3	no	—
24	C₂×C₃³	—	3	6	no	—
25	C₂×C₃³	H(3,𝔽₃)	1	2	yes	—
26	C₂×C₃³	H(3,𝔽₃)	1	1	yes	characteristic
27	C₂×C₃³	C₃³	1	1	yes	characteristic
28	C₂×C₃×C₉	—	3	3	no	—
29	C₂×C₃×C₉	—	3	9	no	—
30	C₂×C₃×C₉	—	9	3	no	—
31	C₂×C₃×C₉	—	9	9	no	—
32	C₃³	—	3	3	no	—
33	C₃³	—	3	3	no	—
34	C₃³	—	3	6	no	—
35	C₃³	C₂×H(3,𝔽₃)	1	2	yes	—
36	C₃³	C₂×H(3,𝔽₃)	1	1	yes	characteristic
37	C₃³	C₂×C₃³	1	1	yes	characteristic
38	C₃×C₉	—	3	3	no	—
39	C₃×C₉	—	3	9	no	—
40	C₃×C₉	—	9	3	no	—
41	C₃×C₉	—	9	9	no	—
42	C₂×C₃²	—	3	2	no	—
43	C₂×C₃²	—	3	1	no	—
44	C₂×C₃²	—	3	2	no	—
45	C₂×C₃²	—	3	1	no	—
46	C₂×C₃²	—	3	4	no	—
47	C₂×C₃²	—	3	2	no	—
48	C₂×C₃²	—	9	9	no	—
49	C₂×C₃²	#731	1	3	yes	—
50	C₂×C₃²	#732	1	3	yes	—
51	C₂×C₃²	#733	1	6	yes	—
52	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
53	C₂×C₉	—	9	3	no	—
54	C₂×C₉	—	9	9	no	—
55	C₃²	—	3	2	no	—
56	C₃²	—	3	1	no	—
57	C₃²	—	3	2	no	—
58	C₃²	—	3	1	no	—
59	C₃²	—	3	4	no	—
60	C₃²	—	3	2	no	—
61	C₃²	—	9	9	no	—
62	C₃²	C₂×#731	1	3	yes	—
63	C₃²	C₂×#732	1	3	yes	—
64	C₃²	C₂×#733	1	6	yes	—
65	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
66	C₉	—	9	3	no	—
67	C₉	—	9	9	no	—
68	C₂×C₃	—	9	2	no	—
69	C₂×C₃	—	9	1	no	—
70	C₂×C₃	#6861	1	9	yes	direct product factor
71	C₂×C₃	C₃×#731	1	1	yes	characteristic
72	C₂×C₃	C₃×#732	1	1	yes	characteristic
73	C₂×C₃	C₃×#733	1	2	yes	—
74	C₃	—	9	2	no	—
75	C₃	—	9	1	no	—
76	C₃	C₂×#6861	1	9	yes	direct product factor
77	C₃	C₂×C₃×#731	1	1	yes	characteristic
78	C₃	C₂×C₃×#732	1	1	yes	characteristic
79	C₃	C₂×C₃×#733	1	2	yes	—
80	C₂	C₃×#6861	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃³	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₂×C₃³
prime radical	C₂×C₃⁴	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ C₂×C₃⁴ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#6861	C₂	direct (N × H)
4. C₂×#6861	C₃	direct (N × H)
7. #6861	C₂×C₃	direct (N × H)
70. C₂×C₃	#6861	direct (N × H)
76. C₃	C₂×#6861	direct (N × H)
80. C₂	C₃×#6861	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#6861	2
C₂×C₃×C₃²⋊C₉	3
C₂×#6861	3

Subgroups — C2×C3×#6861 #13090070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#6861 #13090070