Subgroups — #13090670

Order 1458.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624567	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊#4181	C₃	1	1	yes	maximal, characteristic
3	C₃⋊((C₃⋊D₃)⋊C₉)	—	3	1	no	maximal
4	#92158	—	3	3	no	maximal
5	C₃²×3₋¹⁺²	—	2	1	no	—
6	C₃×C₃²⋊C₉	D₃	1	1	yes	characteristic
7	C₃×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
8	#6855	—	2	3	no	—
9	#6855	D₃	1	3	yes	complemented
10	C₃×C₃⋊(C₃⋊D₃)	—	3	1	no	—
11	C₉×C₃⋊D₃	—	9	1	no	—
12	C₃×C₃⋊D₉	—	3	3	no	—
13	#4181	—	9	3	no	—
14	(C₃⋊D₃)⋊C₉	—	9	3	no	—
15	C₃⁴	C₃×D₃	1	1	yes	characteristic
16	C₃×3₋¹⁺²	—	6	9	no	—
17	C₃×3₋¹⁺²	—	6	3	no	—
18	C₃²×C₉	—	2	3	no	—
19	C₃²×C₉	—	2	1	no	—
20	C₃²×C₉	C₃×D₃	1	3	yes	—
21	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
22	C₃²⋊C₉	—	3	3	no	—
23	C₃²⋊C₉	—	3	3	no	—
24	C₃⋊(C₃⋊D₃)	—	3	1	no	—
25	C₃×C₃⋊D₃	—	9	1	no	—
26	C₃×C₃⋊D₃	—	9	3	no	—
27	C₃×C₃⋊D₃	—	27	3	no	—
28	C₃⋊D₉	—	3	3	no	—
29	D₃×C₉	—	27	1	no	—
30	D₃×C₉	—	27	3	no	—
31	C₃×D₉	—	27	3	no	—
32	C₃³	—	3	1	no	—
33	C₃³	—	3	3	no	—
34	C₃³	—	6	1	no	—
35	C₃³	—	6	3	no	—
36	C₃³	(C₃⋊D₃)⋊C₃	1	3	yes	—
37	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
38	3₋¹⁺²	—	6	27	no	—
39	C₃×C₉	—	2	9	no	—
40	C₃×C₉	—	3	3	no	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	3	3	no	—
43	C₃×C₉	—	3	3	no	—
44	C₃×C₉	—	6	6	no	—
45	C₃×C₉	—	6	3	no	—
46	C₃×C₉	—	6	3	no	—
47	C₃×C₉	—	6	1	no	—
48	C₃×C₉	—	6	3	no	—
49	C₃⋊D₃	—	9	1	no	—
50	C₃⋊D₃	—	9	3	no	—
51	C₃⋊D₃	—	27	3	no	—
52	C₃×D₃	—	27	1	no	—
53	C₃×D₃	—	27	3	no	—
54	C₃×D₃	—	81	3	no	—
55	C₂×C₉	—	81	1	no	—
56	D₉	—	27	3	no	—
57	C₃²	—	2	1	no	—
58	C₃²	—	2	3	no	—
59	C₃²	—	3	3	no	—
60	C₃²	—	3	3	no	—
61	C₃²	—	6	3	no	—
62	C₃²	—	9	3	no	—
63	C₃²	—	18	3	no	—
64	C₃²	C₃⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
65	C₃²	#4207	1	3	yes	—
66	C₃²	#4208	1	1	yes	characteristic
67	C₉	—	6	9	no	—
68	C₉	—	9	3	no	—
69	C₉	—	9	1	no	—
70	C₉	—	18	1	no	—
71	C₂×C₃	—	81	1	no	—
72	D₃	—	27	1	no	—
73	D₃	—	27	3	no	—
74	D₃	—	81	3	no	—
75	C₃	—	2	1	no	—
76	C₃	—	2	3	no	—
77	C₃	—	9	3	no	—
78	C₃	#92305	1	1	yes	characteristic
79	C₃	#92306	1	1	yes	characteristic
80	C₃	#92308	1	3	yes	—
81	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#92306
commutator, cosocle, hypocenter	C₃×C₃²⋊C₉	C₂×C₃
Frattini, socle	C₃³	C₃×C₃⋊D₃
Fitting	#10624567	C₂
prime radical	C₃⋊#4181	C₃
LCS	G ▷ C₃×C₃²⋊C₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #10624567	C₂	semidirect
9. #6855	D₃	semidirect

Maximal subgroups

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

subgroup	index
#10624567	2
C₃⋊#4181	3
C₃⋊((C₃⋊D₃)⋊C₉)	3
#92158	3