Subgroups — C₃×C₉×#622 #14518583

Order 1944.

308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×#622	C₃	1	1	yes	maximal, characteristic
3	C₉×#622	C₃	1	3	yes	maximal, direct product factor
4	C₂×C₃³×C₉	C₄	1	1	yes	characteristic
5	C₃²×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic
6	C₉×C₃⋊Dic₃	C₂×C₃	1	3	yes	—
7	C₃×C₉×Dic₃	—	6	2	no	—
8	C₃³×C₉	C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃×#622	C₉	1	3	yes	direct product factor
10	C₃×#622	C₃²	1	1	yes	characteristic
11	C₃×C₈×C₉	—	9	1	no	maximal
12	C₂×C₃⁴	C₃×C₄	1	1	yes	characteristic
13	C₂×C₃²×C₉	—	2	2	no	—
14	C₂×C₃²×C₉	—	4	6	no	—
15	C₂×C₃²×C₉	—	4	2	no	—
16	C₂×C₃²×C₉	C₃×C₄	1	3	yes	—
17	C₃×C₃⋊Dic₃	C₂×C₉	1	3	yes	—
18	C₃×C₃⋊Dic₃	C₂×C₃²	1	1	yes	characteristic
19	C₃²×Dic₃	—	6	2	no	—
20	C₃×C₄×C₉	—	9	1	no	—
21	C₉×Dic₃	—	6	6	no	—
22	C₃⁴	C₃×C₈	1	1	yes	characteristic
23	C₃²×C₉	—	2	2	no	—
24	C₃²×C₉	—	4	6	no	—
25	C₃²×C₉	—	4	2	no	—
26	C₃²×C₉	C₃×C₈	1	3	yes	complemented
27	#622	C₃×C₉	1	1	yes	characteristic, direct product factor
28	C₃²×C₈	—	9	1	no	—
29	C₈×C₉	—	9	3	no	—
30	C₂×C₃³	—	2	2	no	—
31	C₂×C₃³	—	4	2	no	—
32	C₂×C₃³	—	4	6	no	—
33	C₂×C₃³	C₄×C₉	1	3	yes	—
34	C₂×C₃³	C₃²×C₄	1	1	yes	characteristic
35	C₂×C₃×C₉	—	2	6	no	—
36	C₂×C₃×C₉	—	4	12	no	—
37	C₂×C₃×C₉	—	4	2	no	—
38	C₂×C₃×C₉	—	4	6	no	—
39	C₂×C₃×C₉	—	4	6	no	—
40	C₂×C₃×C₉	#157	1	1	yes	characteristic
41	C₃²×C₄	—	9	1	no	—
42	C₃⋊Dic₃	C₂×C₃×C₉	1	1	yes	characteristic
43	C₃×Dic₃	—	6	2	no	—
44	C₃×Dic₃	—	6	6	no	—
45	C₄×C₉	—	9	3	no	—
46	C₃³	—	2	2	no	—
47	C₃³	—	4	2	no	—
48	C₃³	—	4	6	no	—
49	C₃³	C₈×C₉	1	3	yes	complemented
50	C₃³	C₃²×C₈	1	1	yes	characteristic
51	C₃×C₉	—	2	6	no	—
52	C₃×C₉	—	4	12	no	—
53	C₃×C₉	—	4	2	no	—
54	C₃×C₉	—	4	6	no	—
55	C₃×C₉	—	4	6	no	—
56	C₃×C₉	#622	1	1	yes	characteristic, direct product factor
57	C₃×C₈	—	9	1	no	—
58	C₃×C₈	—	9	3	no	—
59	C₂×C₃²	—	2	6	no	—
60	C₂×C₃²	—	2	2	no	—
61	C₂×C₃²	—	4	6	no	—
62	C₂×C₃²	—	4	2	no	—
63	C₂×C₃²	—	4	12	no	—
64	C₂×C₃²	—	4	6	no	—
65	C₂×C₃²	—	4	2	no	—
66	C₂×C₃²	C₃×C₄×C₉	1	1	yes	characteristic
67	C₂×C₃²	C₃×#157	1	1	yes	characteristic
68	C₂×C₉	—	4	6	no	—
69	C₂×C₉	C₃×#157	1	3	yes	—
70	C₃×C₄	—	9	3	no	—
71	C₃×C₄	—	9	1	no	—
72	Dic₃	—	6	2	no	—
73	C₃²	—	2	6	no	—
74	C₃²	—	2	2	no	—
75	C₃²	—	4	6	no	—
76	C₃²	—	4	2	no	—
77	C₃²	—	4	12	no	—
78	C₃²	—	4	6	no	—
79	C₃²	—	4	2	no	—
80	C₃²	C₃×C₈×C₉	1	1	yes	characteristic, complemented
81	C₃²	C₃×#622	1	1	yes	characteristic
82	C₉	—	4	6	no	—
83	C₉	C₃×#622	1	3	yes	direct product factor
84	C₈	—	9	1	no	Sylow
85	C₂×C₃	—	2	2	no	—
86	C₂×C₃	—	4	6	no	—
87	C₂×C₃	—	4	2	no	—
88	C₂×C₃	C₉×#157	1	3	yes	—
89	C₂×C₃	C₃²×#157	1	1	yes	characteristic
90	C₄	—	9	1	no	—
91	C₃	—	2	2	no	—
92	C₃	—	4	6	no	—
93	C₃	—	4	2	no	—
94	C₃	C₉×#622	1	3	yes	direct product factor
95	C₃	C₃²×#622	1	1	yes	characteristic
96	C₂	C₃×C₉×#157	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₉	#157
commutator, hypocenter	C₃²	C₃×C₈×C₉
Frattini	C₂×C₃	C₃²×#157
Fitting	C₂×C₃³×C₉	C₄
socle, prime radical	C₂×C₃⁴	C₃×C₄
cosocle	C₃×C₃⋊Dic₃	C₂×C₃²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₉

Complements

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

N	H ≅ G/N	type
3. C₉×#622	C₃	direct (N × H)
8. C₃³×C₉	C₈	semidirect
9. C₃×#622	C₉	direct (N × H)
26. C₃²×C₉	C₃×C₈	semidirect
27. #622	C₃×C₉	direct (N × H)
49. C₃³	C₈×C₉	semidirect
56. C₃×C₉	#622	direct (N × H)
80. C₃²	C₃×C₈×C₉	semidirect
83. C₉	C₃×#622	direct (N × H)
94. C₃	C₉×#622	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×C₉×C₃⋊Dic₃	2
C₃²×#622	3
C₉×#622	3
C₃×C₈×C₉	9

Subgroups — C3×C9×#622 #14518583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#622 #14518583