Subgroups — D₃×#66472 #14519510

Order 1944.

2312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₃⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#66472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66472	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#66472	—	3	1	no	maximal
5	C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	C₄	1	1	yes	characteristic, complemented
6	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
7	C₃⁴×D₃	C₄	1	1	yes	characteristic, complemented
8	C₂×C₃⋊(C₃⋊(C₃⋊D₃))	—	3	1	no	—
9	D₃×C₃⋊(C₃⋊D₃)	—	6	20	no	—
10	#66472	—	3	1	no	—
11	#66472	D₃	1	1	yes	characteristic, direct product factor
12	C₃⁵	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
13	D₃×#157	—	9	10	no	maximal
14	C₂×C₃⁴	—	3	1	no	—
15	C₃⋊(C₃⋊(C₃⋊D₃))	—	3	1	no	—
16	C₃⋊(C₃⋊(C₃⋊D₃))	—	6	20	no	—
17	C₃⋊(C₃⋊(C₃⋊D₃))	—	12	20	no	—
18	C₃⋊(C₃⋊(C₃⋊D₃))	C₂×D₃	1	1	yes	characteristic
19	C₃×C₃⋊(C₃⋊D₃)	—	6	20	no	—
20	C₃³×D₃	—	2	20	no	—
21	C₂×C₃⋊(C₃⋊D₃)	—	18	20	no	—
22	D₃×C₃⋊D₃	—	9	10	no	—
23	D₃×C₃⋊D₃	—	18	60	no	—
24	C₃⋊#157	—	9	10	no	—
25	C₃×#157	—	9	10	no	—
26	C₃⁴	—	2	20	no	—
27	C₃⁴	—	4	20	no	—
28	C₃⁴	C₄×D₃	1	1	yes	characteristic, complemented
29	C₂×#157	—	27	10	no	—
30	C₂×C₃³	—	6	20	no	—
31	C₃⋊(C₃⋊D₃)	—	6	20	no	—
32	C₃⋊(C₃⋊D₃)	—	9	10	no	—
33	C₃⋊(C₃⋊D₃)	—	18	20	no	—
34	C₃⋊(C₃⋊D₃)	—	18	60	no	—
35	C₃⋊(C₃⋊D₃)	—	36	20	no	—
36	C₃⋊(C₃⋊D₃)	—	36	240	no	—
37	C₃×C₃⋊D₃	—	9	10	no	—
38	C₃×C₃⋊D₃	—	18	60	no	—
39	C₃²×D₃	—	2	60	no	—
40	C₃²×D₃	#157	1	10	yes	complemented
41	C₂×C₃⋊D₃	—	27	10	no	—
42	C₂×C₃⋊D₃	—	54	60	no	—
43	D₃²	—	54	20	no	—
44	#157	—	9	10	no	—
45	#157	—	27	10	no	—
46	C₃³	—	2	20	no	—
47	C₃³	—	2	60	no	—
48	C₃³	—	4	240	no	—
49	C₃³	—	4	20	no	—
50	C₃³	C₂×#157	1	10	yes	complemented
51	C₄×D₃	—	81	1	no	—
52	C₂×C₃²	—	3	10	no	—
53	C₂×C₃²	—	6	60	no	—
54	C₃⋊D₃	—	9	10	no	—
55	C₃⋊D₃	—	18	60	no	—
56	C₃⋊D₃	—	27	10	no	—
57	C₃⋊D₃	—	54	20	no	—
58	C₃⋊D₃	—	54	60	no	—
59	C₃⋊D₃	—	108	240	no	—
60	C₃⋊D₃	—	108	20	no	—
61	C₃×D₃	—	2	20	no	—
62	C₃×D₃	—	54	20	no	—
63	C₂×D₃	—	81	1	no	—
64	C₂×D₃	—	162	20	no	—
65	C₃×C₄	—	81	1	no	—
66	Dic₃	—	81	1	no	—
67	C₃²	—	2	60	no	—
68	C₃²	—	2	20	no	—
69	C₃²	—	4	20	no	—
70	C₃²	—	4	240	no	—
71	C₃²	D₃×#157	1	10	yes	complemented
72	C₂×C₄	—	243	1	no	Sylow
73	C₂×C₃	—	6	20	no	—
74	C₂×C₃	—	81	1	no	—
75	D₃	—	54	20	no	—
76	D₃	—	324	20	no	—
77	D₃	—	81	1	no	—
78	D₃	—	162	20	no	—
79	D₃	#66472	1	1	yes	characteristic, direct product factor
80	C₂²	—	243	1	no	—
81	C₄	—	81	1	no	—
82	C₄	—	243	1	no	—
83	C₃	—	2	20	no	—
84	C₃	—	4	20	no	—
85	C₃	C₂×#66472	1	1	yes	characteristic, complemented
86	C₂	—	3	1	no	—
87	C₂	—	81	1	no	—
88	C₂	—	243	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃⁵	C₂×C₄
prime radical	D₃×C₃⋊(C₃⋊(C₃⋊D₃))	C₂
cosocle	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	C₂²
LCS	G ▷ C₃⁵
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃⋊#66472	C₂	semidirect
3. C₃×#66472	C₂	semidirect
5. C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	C₄	semidirect
7. C₃⁴×D₃	C₄	semidirect
11. #66472	D₃	direct (N × H)
12. C₃⁵	C₂×C₄	semidirect
28. C₃⁴	C₄×D₃	semidirect
40. C₃²×D₃	#157	semidirect
50. C₃³	C₂×#157	semidirect
71. C₃²	D₃×#157	semidirect
79. D₃	#66472	direct (N × H)
85. C₃	C₂×#66472	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₃⋊(C₃⋊(C₃⋊D₃))	2
C₃⋊#66472	2
C₃×#66472	2
C₂×#66472	3
D₃×#157	9

Subgroups — D3×#66472 #14519510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#66472 #14519510