Subgroups — #13091245

Order 1458.

161 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624806	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	#92177	—	3	3	no	maximal
5	#6891	—	2	1	no	—
6	C₃×C₃²⋊C₉	D₃	1	1	yes	characteristic
7	C₃×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
8	#6868	—	2	3	no	—
9	#6868	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	1	no	—
14	#4181	—	9	2	no	—
15	(C₃⋊D₃)⋊C₉	—	9	2	no	—
16	(C₃⋊D₃)⋊C₉	—	9	1	no	—
17	C₃⁴	C₃×D₃	1	1	yes	characteristic
18	C₃×3₋¹⁺²	—	6	1	no	—
19	C₃²×C₉	—	3	1	no	—
20	C₃²×C₉	C₃×D₃	1	3	yes	—
21	C₃²⋊C₉	—	2	1	no	—
22	C₃²⋊C₉	—	2	3	no	—
23	C₃²⋊C₉	—	3	2	no	—
24	C₃²⋊C₉	—	3	1	no	—
25	C₃²⋊C₉	—	3	2	no	—
26	C₃²⋊C₉	—	6	2	no	—
27	C₃²⋊C₉	C₃⋊D₃	1	1	yes	characteristic
28	C₃⋊(C₃⋊D₃)	—	3	1	no	—
29	C₃×C₃⋊D₃	—	9	1	no	—
30	C₃×C₃⋊D₃	—	9	2	no	—
31	C₃×C₃⋊D₃	—	9	1	no	—
32	C₃×C₃⋊D₃	—	27	3	no	—
33	C₃⋊D₉	—	3	3	no	—
34	D₃×C₉	—	27	1	no	—
35	D₃×C₉	—	27	3	no	—
36	C₃×D₉	—	27	3	no	—
37	C₃³	—	3	1	no	—
38	C₃³	—	3	3	no	—
39	C₃³	—	6	1	no	—
40	C₃³	—	18	1	no	—
41	C₃³	(C₃⋊D₃)⋊C₃	1	2	yes	—
42	C₃³	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
43	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
44	3₋¹⁺²	—	18	3	no	—
45	C₃×C₉	—	3	3	no	—
46	C₃×C₉	—	3	1	no	—
47	C₃×C₉	—	3	3	no	—
48	C₃×C₉	—	6	3	no	—
49	C₃×C₉	—	6	1	no	—
50	C₃×C₉	—	6	3	no	—
51	C₃×C₉	—	9	3	no	—
52	C₃⋊D₃	—	9	1	no	—
53	C₃⋊D₃	—	9	2	no	—
54	C₃⋊D₃	—	9	1	no	—
55	C₃⋊D₃	—	27	3	no	—
56	C₃×D₃	—	27	3	no	—
57	C₃×D₃	—	27	1	no	—
58	C₃×D₃	—	81	1	no	—
59	C₃×D₃	—	81	2	no	—
60	C₂×C₉	—	81	1	no	—
61	D₉	—	27	3	no	—
62	C₃²	—	2	1	no	—
63	C₃²	—	3	1	no	—
64	C₃²	—	3	1	no	—
65	C₃²	—	3	2	no	—
66	C₃²	—	3	2	no	—
67	C₃²	—	6	1	no	—
68	C₃²	—	6	1	no	—
69	C₃²	—	6	2	no	—
70	C₃²	—	9	3	no	—
71	C₃²	—	18	3	no	—
72	C₃²	#4179	1	3	yes	—
73	C₃²	C₃⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
74	C₃²	#4208	1	1	yes	characteristic
75	C₉	—	9	3	no	—
76	C₉	—	9	1	no	—
77	C₉	—	18	1	no	—
78	C₉	—	18	3	no	—
79	C₂×C₃	—	81	1	no	—
80	D₃	—	27	3	no	—
81	D₃	—	27	1	no	—
82	D₃	—	81	1	no	—
83	D₃	—	81	2	no	—
84	C₃	—	2	1	no	—
85	C₃	—	3	3	no	—
86	C₃	—	3	1	no	—
87	C₃	—	6	1	no	—
88	C₃	—	9	2	no	—
89	C₃	#92305	1	1	yes	characteristic
90	C₃	C₃⋊#4179	1	1	yes	characteristic
91	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊#4179
commutator, cosocle, hypocenter	C₃×C₃²⋊C₉	C₂×C₃
Frattini	C₃³	C₃×C₃⋊D₃
Fitting	#10624806	C₂
socle	C₃²	C₃⋊((C₃⋊D₃)⋊C₃)
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. #10624806	C₂	semidirect
9. #6868	D₃	semidirect

Maximal subgroups

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

subgroup	index
#10624806	2
C₃⋊#4181	3
C₃⋊((C₃⋊D₃)⋊C₉)	3
#92177	3