Subgroups — #13090678

Order 1458.

155 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624572	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(D₉⋊C₉)	—	3	2	no	maximal
3	#92197	C₃	1	1	yes	maximal, characteristic
4	#92158	—	3	1	no	maximal
5	#92158	—	3	1	no	maximal
6	C₃×C₉⋊C₉	—	2	1	no	—
7	C₃×C₉⋊C₉	D₃	1	2	yes	—
8	#6855	—	2	2	no	—
9	#6855	—	2	1	no	—
10	#6855	D₃	1	1	yes	characteristic
11	#6855	D₃	1	1	yes	characteristic
12	#6855	C₂×C₃	1	1	yes	characteristic
13	C₉×C₃⋊D₃	—	9	1	no	—
14	C₃×C₃⋊D₉	—	3	2	no	—
15	C₃×C₃⋊D₉	—	3	1	no	—
16	C₃×C₃⋊D₉	—	3	1	no	—
17	D₉⋊C₉	—	9	6	no	—
18	C₃²×C₉	—	2	1	no	—
19	C₃²×C₉	—	2	1	no	—
20	C₃²×C₉	—	2	2	no	—
21	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
22	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
23	C₃²×C₉	C₃×D₃	1	2	yes	—
24	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
25	C₉⋊C₉	—	3	6	no	—
26	C₉⋊C₉	—	6	3	no	—
27	C₃×C₃⋊D₃	—	9	1	no	—
28	C₃⋊D₉	—	3	2	no	—
29	C₃⋊D₉	—	3	1	no	—
30	C₃⋊D₉	—	3	1	no	—
31	D₃×C₉	—	27	2	no	—
32	D₃×C₉	—	27	1	no	—
33	D₃×C₉	—	27	1	no	—
34	C₃×D₉	—	9	6	no	—
35	C₃×D₉	—	27	1	no	—
36	C₃×D₉	—	27	1	no	—
37	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
38	C₃×C₉	—	2	3	no	—
39	C₃×C₉	—	3	2	no	—
40	C₃×C₉	—	3	2	no	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	3	1	no	—
43	C₃×C₉	—	3	1	no	—
44	C₃×C₉	—	3	1	no	—
45	C₃×C₉	—	3	1	no	—
46	C₃×C₉	—	3	1	no	—
47	C₃×C₉	—	6	2	no	—
48	C₃×C₉	—	6	2	no	—
49	C₃×C₉	—	6	1	no	—
50	C₃×C₉	—	6	1	no	—
51	C₃×C₉	—	6	1	no	—
52	C₃×C₉	—	6	2	no	—
53	C₃×C₉	—	6	2	no	—
54	C₃×C₉	—	6	2	no	—
55	C₃×C₉	—	6	1	no	—
56	C₃×C₉	—	6	2	no	—
57	C₃×C₉	—	6	2	no	—
58	C₃×C₉	—	6	1	no	—
59	C₃×C₉	AGL(1,ℤ/9)	1	6	yes	—
60	C₃⋊D₃	—	9	1	no	—
61	C₃×D₃	—	27	2	no	—
62	C₃×D₃	—	27	1	no	—
63	C₃×D₃	—	27	1	no	—
64	C₂×C₉	—	81	1	no	—
65	D₉	—	9	6	no	—
66	D₉	—	27	1	no	—
67	D₉	—	27	1	no	—
68	C₃²	—	2	2	no	—
69	C₃²	—	2	1	no	—
70	C₃²	—	2	1	no	—
71	C₃²	C₃⋊AGL(1,ℤ/9)	1	2	yes	—
72	C₃²	#4207	1	1	yes	characteristic
73	C₃²	#4207	1	1	yes	characteristic
74	C₃²	#4208	1	1	yes	characteristic
75	C₉	—	3	6	no	—
76	C₉	—	6	3	no	—
77	C₉	—	9	1	no	—
78	C₉	—	9	1	no	—
79	C₉	—	9	1	no	—
80	C₉	—	18	2	no	—
81	C₉	—	18	1	no	—
82	C₂×C₃	—	81	1	no	—
83	D₃	—	27	2	no	—
84	D₃	—	27	1	no	—
85	D₃	—	27	1	no	—
86	C₃	—	2	1	no	—
87	C₃	—	2	2	no	—
88	C₃	—	2	1	no	—
89	C₃	#6895⋊C₂	1	2	yes	—
90	C₃	#92308	1	1	yes	characteristic
91	C₃	#92309	1	1	yes	characteristic
92	C₃	#92311	1	1	yes	characteristic
93	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#92309
commutator, cosocle, hypocenter	#6855	C₂×C₃
Frattini, socle	C₃³	C₃×C₃⋊D₃
Fitting	#10624572	C₂
prime radical	#92197	C₃
LCS	G ▷ #6855
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #10624572	C₂	semidirect

Maximal subgroups

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

subgroup	index
#10624572	2
C₃⋊(D₉⋊C₉)	3
#92197	3
#92158	3