Subgroups — #13090905

Order 1458.

323 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624688	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊(C₃⋊D₉)	—	3	1	no	maximal
3	#92296	—	3	3	no	maximal
4	#92209	—	3	3	no	maximal
5	#92208	—	3	3	no	maximal
6	#92207	—	3	3	no	maximal
7	C₃³×C₉	D₃	1	1	yes	characteristic
8	#6887	D₃	1	3	yes	complemented
9	#6868	D₃	1	3	yes	complemented
10	#6867	D₃	1	3	yes	complemented
11	#6866	D₃	1	3	yes	—
12	C₃×C₃⋊(C₃⋊D₃)	—	9	1	no	—
13	C₃⋊(C₃⋊D₉)	—	3	1	no	—
14	C₃×C₃⋊D₉	—	9	9	no	—
15	C₃×C₃⋊D₉	—	9	1	no	—
16	C₃×C₃⋊D₉	—	9	1	no	—
17	C₃×C₃⋊D₉	—	9	1	no	—
18	C₉⋊D₉	—	3	3	no	—
19	#4169	—	9	9	no	—
20	C₃⁴	C₃⋊D₃	1	1	yes	characteristic
21	C₃²×C₉	—	3	1	no	—
22	C₃²×C₉	—	6	3	no	—
23	C₃²×C₉	—	6	1	no	—
24	C₃²×C₉	D₉	1	9	yes	complemented
25	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
26	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
27	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
28	C₉⋊C₉	—	6	3	no	—
29	C₃²⋊C₉	C₃⋊D₃	1	9	yes	—
30	C₉²	—	3	3	no	—
31	C₃⋊(C₃⋊D₃)	—	9	1	no	—
32	C₃×C₃⋊D₃	—	27	9	no	—
33	C₃×C₃⋊D₃	—	27	3	no	—
34	C₃×C₃⋊D₃	—	27	1	no	—
35	C₃⋊D₉	—	9	1	no	—
36	C₃⋊D₉	—	9	1	no	—
37	C₃⋊D₉	—	9	9	no	—
38	C₃⋊D₉	—	9	1	no	—
39	C₃⋊D₉	—	9	9	no	—
40	C₃×D₉	—	27	3	no	—
41	C₃×D₉	—	27	3	no	—
42	C₃×D₉	—	27	3	no	—
43	C₃³	—	3	1	no	—
44	C₃³	—	3	9	no	—
45	C₃³	—	6	1	no	—
46	C₃³	C₃⋊D₉	1	3	yes	—
47	C₃³	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
48	C₃×C₉	—	2	1	no	—
49	C₃×C₉	—	2	3	no	—
50	C₃×C₉	—	3	1	no	—
51	C₃×C₉	—	3	1	no	—
52	C₃×C₉	—	3	9	no	—
53	C₃×C₉	—	3	9	no	—
54	C₃×C₉	—	6	9	no	—
55	C₃×C₉	—	6	1	no	—
56	C₃×C₉	—	6	1	no	—
57	C₃×C₉	C₃⋊D₉	1	3	yes	—
58	C₃×C₉	C₃⋊D₉	1	3	yes	—
59	C₃×C₉	C₃⋊D₉	1	3	yes	—
60	C₃×C₉	#272	1	1	yes	characteristic
61	C₃⋊D₃	—	27	3	no	—
62	C₃⋊D₃	—	27	9	no	—
63	C₃⋊D₃	—	27	1	no	—
64	C₃×D₃	—	81	9	no	—
65	C₃×D₃	—	81	3	no	—
66	C₃×D₃	—	81	1	no	—
67	D₉	—	27	3	no	—
68	D₉	—	27	3	no	—
69	D₉	—	27	3	no	—
70	D₉	—	81	9	no	—
71	C₃²	—	2	1	no	—
72	C₃²	—	3	9	no	—
73	C₃²	—	3	3	no	—
74	C₃²	—	3	9	no	—
75	C₃²	—	3	3	no	—
76	C₃²	—	6	9	no	—
77	C₃²	C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
78	C₃²	C₃⋊#272	1	1	yes	characteristic
79	C₉	—	2	3	no	—
80	C₉	—	3	3	no	—
81	C₉	—	3	3	no	—
82	C₉	—	9	9	no	—
83	C₉	#4181	1	3	yes	—
84	C₂×C₃	—	243	1	no	—
85	D₃	—	81	9	no	—
86	D₃	—	81	1	no	—
87	D₃	—	81	3	no	—
88	C₃	—	3	9	no	—
89	C₃	—	3	1	no	—
90	C₃	—	6	1	no	—
91	C₃	C₃⋊#4181	1	1	yes	characteristic
92	C₃	#92344	1	3	yes	—
93	C₂	—	243	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#10624688	C₂
Frattini	C₃³	C₃⋊(C₃⋊D₃)
socle	C₃²	C₃⋊#272
LCS	G ▷ #10624688
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #10624688	C₂	semidirect
8. #6887	D₃	semidirect
9. #6868	D₃	semidirect
10. #6867	D₃	semidirect
24. C₃²×C₉	D₉	semidirect

Maximal subgroups

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

subgroup	index
#10624688	2
C₃×C₃⋊(C₃⋊D₉)	3
#92296	3
#92209	3
#92208	3
#92207	3