Subgroups — ((C₃⋊D₃)⋊C₉)⋊C₄ #10619532

Order 648.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₃⋊D₃)⋊C₉	C₂	1	1	yes	maximal, characteristic
2	#66328	C₂	1	1	yes	maximal, characteristic, complemented
3	#66316	C₂	1	1	yes	maximal, characteristic, complemented
4	#6294	—	3	1	no	maximal
5	D₃×Dic₉	—	3	1	no	maximal
6	C₂×C₃²⋊C₉	C₂²	1	1	yes	characteristic
7	(C₃⋊D₃)⋊C₉	C₄	1	2	yes	complemented
8	C₂×C₃×C₃⋊D₃	D₃	1	1	yes	characteristic
9	C₃×C₃⋊Dic₃	—	3	1	no	—
10	C₃×C₃⋊Dic₃	—	3	1	no	—
11	C₂×D₃×C₉	—	3	1	no	—
12	C₃⋊Dic₉	D₃	1	1	yes	characteristic, complemented
13	C₃×Dic₉	—	3	1	no	—
14	C₃×Dic₉	—	6	1	no	—
15	C₃²⋊C₉	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	#624	—	9	1	no	—
17	D₃×Dic₃	—	9	1	no	—
18	D₃×Dic₃	—	9	1	no	—
19	C₂×Dic₉	—	9	1	no	—
20	C₂×C₃³	C₂×D₃	1	1	yes	characteristic
21	C₃×C₃⋊D₃	Dic₃	1	2	yes	—
22	C₂×C₃×C₉	—	2	1	no	—
23	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
24	D₃×C₉	—	3	2	no	—
25	C₂×C₃⋊D₃	D₉	1	1	yes	characteristic
26	C₂×C₃×D₃	—	3	1	no	—
27	C₂×C₃×D₃	—	18	1	no	—
28	C₃⋊Dic₃	—	3	1	no	—
29	C₃⋊Dic₃	—	3	1	no	—
30	C₃×Dic₃	—	9	1	no	—
31	C₃×Dic₃	—	9	1	no	—
32	C₃×Dic₃	—	9	1	no	—
33	C₃×Dic₃	—	9	1	no	—
34	C₃×Dic₃	—	18	1	no	—
35	C₃×Dic₃	—	18	1	no	—
36	C₂²×C₉	—	9	1	no	—
37	Dic₉	—	3	1	no	—
38	Dic₉	—	6	1	no	—
39	Dic₉	—	18	1	no	—
40	C₃³	C₂×Dic₃	1	1	yes	characteristic
41	C₃×C₉	—	2	1	no	—
42	C₃×C₉	C₄×D₃	1	1	yes	characteristic, complemented
43	C₂×Dic₃	—	27	1	no	—
44	C₄×D₃	—	27	1	no	—
45	C₄×D₃	—	27	1	no	—
46	C₂×C₃²	—	2	1	no	—
47	C₂×C₃²	—	6	1	no	—
48	C₂×C₃²	—	12	1	no	—
49	C₂×C₃²	C₂×D₉	1	1	yes	characteristic
50	C₂×C₃²	D₃²	1	1	yes	characteristic
51	C₃⋊D₃	Dic₉	1	2	yes	complemented
52	C₃×D₃	—	3	2	no	—
53	C₃×D₃	—	18	2	no	—
54	C₂×C₉	—	6	1	no	—
55	C₂×C₉	—	9	2	no	—
56	C₂×C₉	—	12	1	no	—
57	C₂²×C₃	—	9	1	no	—
58	C₂×D₃	—	3	1	no	—
59	C₂×D₃	—	18	1	no	—
60	C₃×C₄	—	27	1	no	—
61	C₃×C₄	—	27	1	no	—
62	Dic₃	—	9	1	no	—
63	Dic₃	—	9	1	no	—
64	Dic₃	—	9	1	no	—
65	Dic₃	—	9	1	no	—
66	Dic₃	—	18	1	no	—
67	Dic₃	—	18	1	no	—
68	C₃²	—	2	1	no	—
69	C₃²	—	6	1	no	—
70	C₃²	—	12	1	no	—
71	C₃²	C₂×Dic₉	1	1	yes	characteristic, complemented
72	C₃²	D₃×Dic₃	1	1	yes	characteristic
73	C₉	—	6	1	no	—
74	C₉	—	12	1	no	—
75	C₂×C₄	—	81	1	no	Sylow
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	—	6	1	no	—
78	C₂×C₃	—	9	2	no	—
79	C₂×C₃	—	12	1	no	—
80	C₂×C₃	D₃×D₉	1	1	yes	characteristic
81	C₂×C₃	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
82	D₃	—	3	2	no	—
83	D₃	—	18	2	no	—
84	C₂²	—	9	1	no	—
85	C₄	—	27	1	no	—
86	C₄	—	27	1	no	—
87	C₃	—	2	1	no	—
88	C₃	—	6	1	no	—
89	C₃	—	12	1	no	—
90	C₃	D₃×Dic₉	1	1	yes	characteristic
91	C₃	((C₃⋊D₃)⋊C₃)⋊C₄	1	1	yes	characteristic
92	C₂	—	9	2	no	—
93	C₂	((C₃⋊D₃)⋊C₉)⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	((C₃⋊D₃)⋊C₉)⋊C₂
commutator, hypocenter	C₃²⋊C₉	C₂×C₄
Frattini, socle	C₂×C₃²	D₃²
Fitting, cosocle	C₂×C₃²⋊C₉	C₂²
prime radical	C₂×C₃×C₃⋊D₃	D₃
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. #66328	C₂	semidirect
3. #66316	C₂	semidirect
7. (C₃⋊D₃)⋊C₉	C₄	semidirect
12. C₃⋊Dic₉	D₃	semidirect
15. C₃²⋊C₉	C₂×C₄	semidirect
42. C₃×C₉	C₄×D₃	semidirect
51. C₃⋊D₃	Dic₉	semidirect
71. C₃²	C₂×Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×(C₃⋊D₃)⋊C₉	2
#66328	2
#66316	2
#6294	3
D₃×Dic₉	3

Subgroups — ((C3⋊D3)⋊C9)⋊C4 #10619532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ((C₃⋊D₃)⋊C₉)⋊C₄ #10619532