Subgroups — C₃×D₃×C₂²⋊C₉ #10620065

Order 648.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×D₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₃×C₂²⋊C₉	—	3	1	no	maximal
4	D₃×C₂²⋊C₉	C₃	1	3	yes	maximal, direct product factor
5	C₃×D₃×C₉	—	4	1	no	maximal
6	C₂²×C₃³	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃²×D₃	—	3	1	no	—
8	C₂×C₃²×D₃	—	3	1	no	—
9	C₃×C₂²⋊C₉	—	2	1	no	—
10	C₃×C₂²⋊C₉	—	2	3	no	—
11	C₃×C₂²⋊C₉	D₃	1	1	yes	characteristic, direct product factor
12	C₃×C₂²⋊C₉	C₂×C₃	1	3	yes	complemented
13	C₃²×C₉	—	4	1	no	Sylow
14	C₂³×C₃²	—	3	1	no	—
15	C₂²×C₃×D₃	C₉	1	3	yes	complemented
16	C₂²×C₃×D₃	C₃²	1	1	yes	characteristic
17	C₂×C₂²⋊C₉	—	3	3	no	—
18	C₂×C₃³	—	3	1	no	—
19	C₃²×D₃	—	3	1	no	—
20	C₃²×D₃	A₄	1	1	yes	characteristic
21	C₂×C₃×C₉	—	12	1	no	—
22	D₃×C₉	—	4	3	no	—
23	C₂²×C₃²	—	2	3	no	—
24	C₂²×C₃²	—	2	1	no	—
25	C₂²×C₃²	—	9	1	no	—
26	C₂²×C₃²	—	9	1	no	—
27	C₂²×C₃²	C₂×C₉	1	3	yes	complemented
28	C₂²×C₃²	C₃×D₃	1	1	yes	characteristic
29	C₂²×C₃²	C₂×C₃²	1	1	yes	characteristic
30	C₂×C₃×D₃	—	3	3	no	—
31	C₂×C₃×D₃	—	3	1	no	—
32	C₂×C₃×D₃	—	3	3	no	—
33	C₂×C₃×D₃	—	3	1	no	—
34	C₂²⋊C₉	—	2	3	no	—
35	C₂²⋊C₉	C₃×D₃	1	3	yes	direct product factor
36	C₃³	C₂×A₄	1	1	yes	characteristic
37	C₃×C₉	—	4	1	no	—
38	C₃×C₉	—	4	3	no	—
39	C₃×C₉	—	8	3	no	—
40	C₃×C₉	—	8	1	no	—
41	C₂³×C₃	—	3	3	no	—
42	C₂³×C₃	—	3	1	no	—
43	C₂²×D₃	C₃×C₉	1	1	yes	characteristic, complemented
44	C₂×C₃²	—	3	1	no	—
45	C₂×C₃²	—	3	1	no	—
46	C₂×C₃²	—	3	3	no	—
47	C₂×C₃²	—	3	1	no	—
48	C₂×C₃²	—	6	3	no	—
49	C₂×C₃²	—	6	1	no	—
50	C₂×C₃²	—	9	1	no	—
51	C₃×D₃	—	3	3	no	—
52	C₃×D₃	—	3	1	no	—
53	C₃×D₃	C₂²⋊C₉	1	3	yes	direct product factor
54	C₃×D₃	C₃×A₄	1	1	yes	characteristic
55	C₂×C₉	—	12	3	no	—
56	C₂²×C₃	—	2	3	no	—
57	C₂²×C₃	—	2	1	no	—
58	C₂²×C₃	—	9	3	no	—
59	C₂²×C₃	—	9	1	no	—
60	C₂²×C₃	—	9	3	no	—
61	C₂²×C₃	—	9	1	no	—
62	C₂²×C₃	D₃×C₉	1	3	yes	complemented
63	C₂²×C₃	C₂×C₃×C₉	1	1	yes	characteristic, complemented
64	C₂²×C₃	C₃²×D₃	1	1	yes	characteristic
65	C₂×D₃	—	3	1	no	—
66	C₂×D₃	—	3	1	no	—
67	C₃²	—	2	3	no	—
68	C₃²	—	2	1	no	—
69	C₃²	C₂×C₂²⋊C₉	1	3	yes	complemented
70	C₃²	D₃×A₄	1	1	yes	characteristic
71	C₃²	C₂×C₃×A₄	1	1	yes	characteristic
72	C₉	—	4	3	no	—
73	C₉	—	8	3	no	—
74	C₂³	—	3	1	no	Sylow
75	C₂×C₃	—	3	3	no	—
76	C₂×C₃	—	3	3	no	—
77	C₂×C₃	—	3	1	no	—
78	C₂×C₃	—	3	1	no	—
79	C₂×C₃	—	3	1	no	—
80	C₂×C₃	—	6	3	no	—
81	C₂×C₃	—	6	1	no	—
82	C₂×C₃	—	9	3	no	—
83	C₂×C₃	—	9	1	no	—
84	D₃	—	3	1	no	—
85	D₃	C₃×C₂²⋊C₉	1	1	yes	characteristic, direct product factor
86	C₂²	—	9	1	no	—
87	C₂²	—	9	1	no	—
88	C₂²	C₃×D₃×C₉	1	1	yes	characteristic, complemented
89	C₃	—	2	3	no	—
90	C₃	—	2	1	no	—
91	C₃	D₃×C₂²⋊C₉	1	3	yes	direct product factor
92	C₃	C₂×C₃×C₂²⋊C₉	1	1	yes	characteristic, complemented
93	C₃	C₃×D₃×A₄	1	1	yes	characteristic
94	C₂	—	3	1	no	—
95	C₂	—	3	1	no	—
96	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	D₃×A₄
commutator, hypocenter	C₂²×C₃	C₂×C₃×C₉
Frattini	C₃	C₃×D₃×A₄
Fitting, socle	C₂²×C₃³	C₂×C₃
prime radical	C₂²×C₃²×D₃	C₃
cosocle	C₂²×C₃²	C₂×C₃²
LCS	G ▷ C₂²×C₃
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂²⋊C₉	C₂	semidirect
4. D₃×C₂²⋊C₉	C₃	direct (N × H)
11. C₃×C₂²⋊C₉	D₃	direct (N × H)
12. C₃×C₂²⋊C₉	C₂×C₃	semidirect
15. C₂²×C₃×D₃	C₉	semidirect
27. C₂²×C₃²	C₂×C₉	semidirect
35. C₂²⋊C₉	C₃×D₃	direct (N × H)
43. C₂²×D₃	C₃×C₉	semidirect
53. C₃×D₃	C₂²⋊C₉	direct (N × H)
62. C₂²×C₃	D₃×C₉	semidirect
63. C₂²×C₃	C₂×C₃×C₉	semidirect
69. C₃²	C₂×C₂²⋊C₉	semidirect
85. D₃	C₃×C₂²⋊C₉	direct (N × H)
88. C₂²	C₃×D₃×C₉	semidirect
91. C₃	D₃×C₂²⋊C₉	direct (N × H)
92. C₃	C₂×C₃×C₂²⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₂²⋊C₉	2
C₂²×C₃²×D₃	3
C₂×C₃×C₂²⋊C₉	3
D₃×C₂²⋊C₉	3
C₃×D₃×C₉	4

Subgroups — C3×D3×C22⋊C9 #10620065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₂²⋊C₉ #10620065