Subgroups — C₃×#88455 #13047787

Order 1296.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄²	C₃	1	1	yes	maximal, characteristic
2	#88455	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₄²⋊C₉	C₃	1	3	yes	maximal, complemented
4	C₃×#1094	—	4	1	no	maximal
5	C₂×C₃³×C₄	—	3	1	no	—
6	C₃²×C₄²	—	3	3	no	—
7	C₃²×C₄²	C₃²	1	3	yes	—
8	C₃²×C₄²	C₃²	1	1	yes	characteristic
9	C₄²⋊C₉	C₃²	1	9	yes	complemented
10	C₂²×C₃³	A₄	1	1	yes	characteristic
11	C₃³×C₄	—	3	2	no	—
12	#1094	—	4	9	no	—
13	C₃×C₂²⋊C₉	—	4	3	no	—
14	C₃×3₋¹⁺²	—	16	1	no	Sylow
15	C₂×C₃²×C₄	—	3	9	no	—
16	C₂×C₃²×C₄	—	3	3	no	—
17	C₂×C₃²×C₄	—	3	1	no	—
18	C₂×C₃³	—	3	1	no	—
19	C₃×C₄²	—	3	3	no	—
20	C₃×C₄²	3₋¹⁺²	1	3	yes	complemented
21	C₃×C₄²	C₃³	1	1	yes	characteristic
22	C₂²×C₃²	—	3	3	no	—
23	C₂²×C₃²	C₃×A₄	1	3	yes	—
24	C₂²×C₃²	C₃×A₄	1	1	yes	characteristic
25	C₃²×C₄	—	3	18	no	—
26	C₃²×C₄	—	3	6	no	—
27	C₃²×C₄	—	3	2	no	—
28	C₂²⋊C₉	—	4	9	no	—
29	C₃³	C₄²⋊C₃	1	1	yes	characteristic
30	3₋¹⁺²	—	16	9	no	—
31	C₃×C₉	—	16	3	no	—
32	C₂×C₃×C₄	—	3	9	no	—
33	C₂×C₃×C₄	—	3	3	no	—
34	C₂×C₃×C₄	—	3	1	no	—
35	C₂×C₃²	—	3	9	no	—
36	C₂×C₃²	—	3	3	no	—
37	C₂×C₃²	—	3	1	no	—
38	C₄²	C₃×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	3	3	no	—
40	C₂²×C₃	#1094	1	3	yes	—
41	C₂²×C₃	C₃²×A₄	1	1	yes	characteristic
42	C₃×C₄	—	3	18	no	—
43	C₃×C₄	—	3	6	no	—
44	C₃×C₄	—	3	2	no	—
45	C₃²	—	3	3	no	—
46	C₃²	C₃×C₄²⋊C₃	1	3	yes	—
47	C₃²	C₃×C₄²⋊C₃	1	1	yes	characteristic
48	C₉	—	16	9	no	—
49	C₂×C₄	—	3	1	no	—
50	C₂×C₃	—	3	9	no	—
51	C₂×C₃	—	3	3	no	—
52	C₂×C₃	—	3	1	no	—
53	C₂²	C₃×#1094	1	1	yes	characteristic
54	C₄	—	3	2	no	—
55	C₃	—	3	3	no	—
56	C₃	#88455	1	3	yes	direct product factor
57	C₃	C₃²×C₄²⋊C₃	1	1	yes	characteristic
58	C₂	—	3	1	no	—

	subgroup	G/H
center	C₃²	C₃×C₄²⋊C₃
commutator, cosocle	C₃×C₄²	C₃³
Frattini	C₂²×C₃	C₃²×A₄
Fitting	C₃³×C₄²	C₃
socle	C₂²×C₃²	C₃×A₄
prime radical	C₂²×C₃³	A₄
hypercenter	C₃³	C₄²⋊C₃
hypocenter	C₄²	C₃×3₋¹⁺²
LCS	G ▷ C₃×C₄² ▷ C₄²
UCS	C₁ ◁ C₃² ◁ C₃³

Complements

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

N	H ≅ G/N	type
2. #88455	C₃	direct (N × H)
3. C₃×C₄²⋊C₉	C₃	semidirect
9. C₄²⋊C₉	C₃²	semidirect
20. C₃×C₄²	3₋¹⁺²	semidirect
38. C₄²	C₃×3₋¹⁺²	semidirect
56. C₃	#88455	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄²	3
#88455	3
C₃×C₄²⋊C₉	3
C₃×#1094	4

Subgroups — C3×#88455 #13047787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88455 #13047787