Subgroups — #13091468

Order 1458.

728 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624880	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃²×(C₃⋊D₃)⋊C₃	—	3	4	no	maximal
3	#92300	C₃	1	4	yes	maximal, complemented
4	C₃²×H(3,𝔽₃)	D₃	1	4	yes	complemented
5	C₃²⋊H(3,𝔽₃)	—	2	4	no	—
6	C₃²⋊H(3,𝔽₃)	—	2	12	no	—
7	C₃²⋊H(3,𝔽₃)	C₂×C₃	1	4	yes	complemented
8	C₃²×C₃⋊D₃	—	3	4	no	—
9	C₃³×D₃	—	9	1	no	—
10	C₃⋊#272	C₃²	1	1	yes	characteristic, complemented
11	C₃×(C₃⋊D₃)⋊C₃	—	3	36	no	—
12	C₃×(C₃⋊D₃)⋊C₃	—	3	12	no	—
13	C₃⁴	—	2	4	no	—
14	C₃⁴	C₃×D₃	1	4	yes	complemented
15	C₃⁴	C₃⋊D₃	1	1	yes	characteristic
16	C₃×H(3,𝔽₃)	—	2	12	no	—
17	C₃×H(3,𝔽₃)	—	2	1	no	—
18	C₃×H(3,𝔽₃)	—	2	6	no	—
19	C₃×H(3,𝔽₃)	—	2	8	no	—
20	C₃×H(3,𝔽₃)	—	2	6	no	—
21	C₃×H(3,𝔽₃)	—	2	3	no	—
22	C₃×H(3,𝔽₃)	—	2	4	no	—
23	C₃×H(3,𝔽₃)	—	2	12	no	—
24	C₃×H(3,𝔽₃)	—	3	36	no	—
25	C₃×H(3,𝔽₃)	C₃×D₃	1	12	yes	complemented
26	C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic, complemented
27	C₂×C₃³	—	27	1	no	—
28	C₃×C₃⋊D₃	—	3	12	no	—
29	C₃×C₃⋊D₃	—	3	4	no	—
30	C₃²×D₃	—	9	9	no	—
31	C₃²×D₃	—	9	4	no	—
32	C₃²×D₃	—	27	4	no	—
33	#272	—	27	1	no	—
34	(C₃⋊D₃)⋊C₃	—	3	36	no	—
35	C₃³	—	2	4	no	—
36	C₃³	—	2	12	no	—
37	C₃³	—	3	12	no	—
38	C₃³	—	6	12	no	—
39	C₃³	—	9	1	no	—
40	C₃³	—	9	4	no	—
41	C₃³	—	18	4	no	—
42	C₃³	—	18	1	no	—
43	C₃³	—	18	4	no	—
44	C₃³	—	18	8	no	—
45	C₃³	#272	1	9	yes	complemented
46	C₃³	C₃²×D₃	1	4	yes	—
47	C₃³	C₃×C₃⋊D₃	1	4	yes	—
48	H(3,𝔽₃)	—	3	36	no	—
49	H(3,𝔽₃)	—	6	36	no	—
50	H(3,𝔽₃)	—	9	1	no	—
51	H(3,𝔽₃)	—	18	4	no	—
52	H(3,𝔽₃)	—	18	12	no	—
53	H(3,𝔽₃)	—	18	1	no	—
54	H(3,𝔽₃)	—	18	8	no	—
55	H(3,𝔽₃)	—	18	6	no	—
56	H(3,𝔽₃)	—	18	6	no	—
57	H(3,𝔽₃)	—	18	3	no	—
58	C₂×C₃²	—	27	4	no	—
59	C₂×C₃²	—	27	9	no	—
60	C₃⋊D₃	—	3	4	no	—
61	C₃×D₃	—	9	12	no	—
62	C₃×D₃	—	9	1	no	—
63	C₃×D₃	—	27	4	no	—
64	C₃×D₃	—	27	12	no	—
65	C₃²	—	3	4	no	—
66	C₃²	—	3	4	no	—
67	C₃²	—	3	4	no	—
68	C₃²	—	6	4	no	—
69	C₃²	—	6	4	no	—
70	C₃²	—	6	4	no	—
71	C₃²	—	6	4	no	—
72	C₃²	—	6	24	no	—
73	C₃²	—	6	12	no	—
74	C₃²	—	6	4	no	—
75	C₃²	—	6	4	no	—
76	C₃²	—	6	12	no	—
77	C₃²	—	9	9	no	—
78	C₃²	—	9	12	no	—
79	C₃²	—	18	12	no	—
80	C₃²	—	18	36	no	—
81	C₃²	C₃×#272	1	12	yes	—
82	C₃²	C₃²×C₃⋊D₃	1	1	yes	characteristic
83	C₂×C₃	—	27	12	no	—
84	C₂×C₃	—	27	1	no	—
85	D₃	—	9	1	no	—
86	D₃	—	27	4	no	—
87	C₃	—	2	1	no	—
88	C₃	—	3	12	no	—
89	C₃	—	9	4	no	—
90	C₃	—	18	4	no	—
91	C₃	—	18	12	no	—
92	C₃	C₃²×#272	1	1	yes	characteristic
93	C₃	#92391	1	1	yes	characteristic
94	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#92391
commutator, cosocle, hypocenter	C₃×H(3,𝔽₃)	C₂×C₃²
Frattini, socle	C₃²	C₃²×C₃⋊D₃
Fitting	#10624880	C₂
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #10624880	C₂	semidirect
3. #92300	C₃	semidirect
4. C₃²×H(3,𝔽₃)	D₃	semidirect
7. C₃²⋊H(3,𝔽₃)	C₂×C₃	semidirect
10. C₃⋊#272	C₃²	semidirect
14. C₃⁴	C₃×D₃	semidirect
25. C₃×H(3,𝔽₃)	C₃×D₃	semidirect
26. C₃×H(3,𝔽₃)	C₂×C₃²	semidirect
45. C₃³	#272	semidirect

Maximal subgroups

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

subgroup	index
#10624880	2
C₃²×(C₃⋊D₃)⋊C₃	3
#92300	3