Subgroups — C₃⋊(C₉⋊#622) #14518596

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	C₃⋊(C₃⋊#622)	—	3	1	no	maximal
3	C₉⋊#622	—	3	3	no	maximal
4	C₂×C₃³×C₉	C₄	1	1	yes	characteristic
5	C₃²×C₃⋊Dic₃	D₃	1	1	yes	characteristic
6	C₉×C₃⋊Dic₃	D₃	1	3	yes	—
7	C₃×C₉×Dic₃	—	6	2	no	—
8	C₃³×C₉	C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃⋊#622	—	9	3	no	—
10	C₃⋊#622	—	9	1	no	—
11	C₃⋊(C₉⋊C₈)	—	9	1	no	maximal
12	C₂×C₃⁴	Dic₃	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	Dic₃	1	3	yes	—
17	C₃×C₃⋊Dic₃	D₉	1	3	yes	—
18	C₃×C₃⋊Dic₃	C₃⋊D₃	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	—	27	1	no	—
28	C₃⋊(C₃⋊C₈)	—	27	1	no	—
29	C₉⋊C₈	—	27	3	no	—
30	C₂×C₃³	—	2	2	no	—
31	C₂×C₃³	—	4	2	no	—
32	C₂×C₃³	—	4	6	no	—
33	C₂×C₃³	Dic₉	1	3	yes	—
34	C₂×C₃³	C₃⋊Dic₃	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	C₃⋊D₉	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	C₉⋊C₈	1	3	yes	complemented
50	C₃³	C₃⋊(C₃⋊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, complemented
57	C₃⋊C₈	—	81	1	no	—
58	C₃⋊C₈	—	81	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⋊Dic₉	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⋊(C₉⋊C₈)	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	complemented
84	C₈	—	243	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	C₃⋊(C₃⋊#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	complemented
95	C₃	C₃⋊(C₃⋊#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	C₃³×C₉	C₈
Frattini	C₂×C₃	C₃⋊(C₃⋊#157)
Fitting	C₂×C₃³×C₉	C₄
socle, prime radical	C₂×C₃⁴	Dic₃
cosocle	C₃×C₉×C₃⋊Dic₃	C₂
LCS	G ▷ C₃³×C₉
UCS	C₁ ◁ C₂

Complements

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

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

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
C₃⋊(C₃⋊#622)	3
C₉⋊#622	3
C₃⋊(C₉⋊C₈)	9

Subgroups — C3⋊(C9⋊#622) #14518596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₉⋊#622) #14518596