Subgroups — #13090677

Order 1458.

134 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	#92197	C₃	1	1	yes	maximal, characteristic
3	#92158	—	3	2	no	maximal
4	#92158	—	3	2	no	maximal
5	C₃×C₉⋊C₉	—	2	2	no	—
6	#6855	—	2	2	no	—
7	#6855	D₃	1	2	yes	—
8	#6855	D₃	1	2	yes	—
9	#6855	C₂×C₃	1	1	yes	characteristic
10	C₉×C₃⋊D₃	—	9	1	no	—
11	C₃×C₃⋊D₉	—	3	2	no	—
12	C₃×C₃⋊D₉	—	3	2	no	—
13	C₃²×C₉	—	2	2	no	—
14	C₃²×C₉	—	2	2	no	—
15	C₃²×C₉	C₃×D₃	1	2	yes	—
16	C₃²×C₉	C₃×D₃	1	2	yes	—
17	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
18	C₉⋊C₉	—	6	6	no	—
19	C₃×C₃⋊D₃	—	9	1	no	—
20	C₃⋊D₉	—	3	2	no	—
21	C₃⋊D₉	—	3	2	no	—
22	D₃×C₉	—	27	2	no	—
23	D₃×C₉	—	27	2	no	—
24	C₃×D₉	—	27	2	no	—
25	C₃×D₉	—	27	2	no	—
26	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
27	C₃×C₉	—	2	6	no	—
28	C₃×C₉	—	3	2	no	—
29	C₃×C₉	—	3	2	no	—
30	C₃×C₉	—	3	2	no	—
31	C₃×C₉	—	3	2	no	—
32	C₃×C₉	—	3	2	no	—
33	C₃×C₉	—	3	2	no	—
34	C₃×C₉	—	6	4	no	—
35	C₃×C₉	—	6	2	no	—
36	C₃×C₉	—	6	2	no	—
37	C₃×C₉	—	6	2	no	—
38	C₃×C₉	—	6	4	no	—
39	C₃×C₉	—	6	2	no	—
40	C₃×C₉	—	6	2	no	—
41	C₃⋊D₃	—	9	1	no	—
42	C₃×D₃	—	27	2	no	—
43	C₃×D₃	—	27	2	no	—
44	C₂×C₉	—	81	1	no	—
45	D₉	—	27	2	no	—
46	D₉	—	27	2	no	—
47	C₃²	—	2	2	no	—
48	C₃²	—	2	2	no	—
49	C₃²	#4207	1	2	yes	—
50	C₃²	#4207	1	2	yes	—
51	C₃²	#4208	1	1	yes	characteristic
52	C₉	—	6	6	no	—
53	C₉	—	9	2	no	—
54	C₉	—	9	2	no	—
55	C₉	—	9	1	no	—
56	C₉	—	18	2	no	—
57	C₂×C₃	—	81	1	no	—
58	D₃	—	27	2	no	—
59	D₃	—	27	2	no	—
60	C₃	—	2	2	no	—
61	C₃	—	2	2	no	—
62	C₃	#92308	1	2	yes	—
63	C₃	#92311	1	2	yes	—
64	C₃	#92312	1	1	yes	characteristic
65	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#92312
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
#92197	3
#92158	3