Subgroups — C₃×#10619651 #14517485

Order 1944.

396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₉²	C₂	1	1	yes	maximal, characteristic
2	C₃×C₉⋊Dic₉	C₂	1	2	yes	maximal
3	C₃×#6226	—	3	4	no	maximal
4	#10619651	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃×C₉²	C₂²	1	1	yes	characteristic
6	C₃²×C₄×C₉	D₃	1	4	yes	—
7	C₃×C₃⋊Dic₉	—	3	8	no	—
8	C₄×C₉²	—	2	4	no	—
9	C₄×C₉²	C₂×C₃	1	1	yes	characteristic
10	C₉⋊Dic₉	C₂×C₃	1	2	yes	—
11	C₃×C₉²	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×#634	—	9	1	no	—
13	#6226	—	3	4	no	—
14	C₃×Dic₁₈	—	9	12	no	—
15	C₂×C₃²×C₉	C₂×D₃	1	4	yes	—
16	C₂×C₉²	—	2	4	no	—
17	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
18	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
19	C₃×C₃⋊Dic₃	—	9	2	no	—
20	C₃×C₄×C₉	—	2	4	no	—
21	C₃×C₄×C₉	—	2	12	no	—
22	C₃×C₄×C₉	D₉	1	12	yes	—
23	C₃×C₄×C₉	C₃×D₃	1	4	yes	—
24	C₃⋊Dic₉	—	3	8	no	—
25	C₃×Dic₉	—	9	24	no	—
26	C₃²×C₉	Dic₆	1	4	yes	—
27	C₉²	—	2	4	no	—
28	C₉²	C₃×Q₈	1	1	yes	characteristic, complemented
29	#634	—	9	1	no	—
30	C₃×Dic₆	—	27	4	no	—
31	Dic₁₈	—	9	12	no	—
32	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
33	C₂×C₃×C₉	—	2	4	no	—
34	C₂×C₃×C₉	—	2	12	no	—
35	C₂×C₃×C₉	C₂×D₉	1	12	yes	—
36	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
37	C₃²×C₄	—	2	4	no	—
38	C₃²×C₄	C₃⋊D₉	1	4	yes	—
39	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
40	C₃⋊Dic₃	—	9	2	no	—
41	C₃×Dic₃	—	27	8	no	—
42	C₄×C₉	—	2	12	no	—
43	C₄×C₉	C₃×D₉	1	12	yes	—
44	Dic₉	—	9	24	no	—
45	C₃³	#634	1	1	yes	characteristic
46	C₃×C₉	—	2	4	no	—
47	C₃×C₉	—	2	12	no	—
48	C₃×C₉	Dic₁₈	1	12	yes	complemented
49	C₃×C₉	C₃×Dic₆	1	4	yes	—
50	C₃×Q₈	—	81	1	no	—
51	Dic₆	—	27	4	no	—
52	C₂×C₃²	—	2	4	no	—
53	C₂×C₃²	C₂×C₃⋊D₉	1	4	yes	—
54	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
55	C₂×C₉	—	2	12	no	—
56	C₂×C₉	C₂×C₃×D₉	1	12	yes	—
57	C₃×C₄	—	2	4	no	—
58	C₃×C₄	—	81	2	no	—
59	C₃×C₄	C₉⋊D₉	1	1	yes	characteristic
60	C₃×C₄	C₃×C₃⋊D₉	1	4	yes	—
61	Dic₃	—	27	8	no	—
62	C₃²	—	2	4	no	—
63	C₃²	#6226	1	4	yes	—
64	C₃²	C₃×#634	1	1	yes	characteristic
65	C₉	—	2	12	no	—
66	C₉	C₃×Dic₁₈	1	12	yes	complemented
67	Q₈	—	81	1	no	Sylow
68	C₂×C₃	—	2	4	no	—
69	C₂×C₃	C₂×C₉⋊D₉	1	1	yes	characteristic
70	C₂×C₃	C₂×C₃×C₃⋊D₉	1	4	yes	—
71	C₄	—	81	2	no	—
72	C₄	C₃×C₉⋊D₉	1	1	yes	characteristic
73	C₃	—	2	4	no	—
74	C₃	#10619651	1	1	yes	characteristic, direct product factor
75	C₃	C₃×#6226	1	4	yes	—
76	C₂	C₂×C₃×C₉⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×C₉⋊D₉
commutator, cosocle	C₂×C₉²	C₂²×C₃
Frattini	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₃×C₄×C₉²	C₂
socle, prime radical	C₂×C₃³	C₂×C₃⋊D₃
hypercenter	C₃×C₄	C₉⋊D₉
hypocenter	C₉²	C₃×Q₈
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
4. #10619651	C₃	direct (N × H)
11. C₃×C₉²	Q₈	semidirect
28. C₉²	C₃×Q₈	semidirect
48. C₃×C₉	Dic₁₈	semidirect
66. C₉	C₃×Dic₁₈	semidirect
74. C₃	#10619651	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×C₄×C₉²	2
C₃×C₉⋊Dic₉	2
C₃×#6226	3
#10619651	3

Subgroups — C3×#10619651 #14517485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10619651 #14517485