Subgroups — #14519081

Order 1944.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758050	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊#272)	C₄	1	1	yes	characteristic
3	C₃²×H(3,𝔽₃)	C₈	1	1	yes	characteristic, complemented, Sylow
4	C₃⋊AGL(1,𝔽₉)	—	9	1	no	maximal
5	#6249	—	9	9	no	maximal
6	C₃×C₃⋊(C₃⋊D₃)	—	12	1	no	—
7	C₃⋊#272	—	12	9	no	—
8	C₃×#157	—	9	1	no	—
9	#1088	—	9	9	no	—
10	C₃⁴	—	4	1	no	—
11	C₃×H(3,𝔽₃)	—	4	9	no	—
12	AGL(1,𝔽₉)	—	27	1	no	—
13	C₃⋊(C₃⋊D₃)	—	12	1	no	—
14	C₃×C₃⋊D₃	—	9	1	no	—
15	C₃×C₃⋊D₃	—	36	12	no	—
16	#272	—	9	9	no	—
17	#272	—	36	18	no	—
18	#157	—	9	1	no	—
19	C₃³	—	4	12	no	—
20	C₃³	—	12	1	no	—
21	C₃³	—	24	4	no	—
22	C₃³	AGL(1,𝔽₉)	1	1	yes	characteristic
23	H(3,𝔽₃)	—	4	18	no	—
24	H(3,𝔽₃)	AGL(1,𝔽₉)	1	9	yes	complemented
25	C₃⋊C₈	—	81	1	no	—
26	C₃⋊D₃	—	9	1	no	—
27	C₃⋊D₃	—	36	12	no	—
28	C₃×D₃	—	108	9	no	—
29	C₃×D₃	—	108	1	no	—
30	C₃×C₄	—	81	1	no	—
31	C₃²	—	4	1	no	—
32	C₃²	—	4	9	no	—
33	C₃²	—	8	1	no	—
34	C₃²	—	12	12	no	—
35	C₃²	—	24	12	no	—
36	C₃²	#6249	1	1	yes	characteristic, complemented
37	C₈	—	243	1	no	Sylow
38	C₂×C₃	—	81	1	no	—
39	D₃	—	108	1	no	—
40	D₃	—	108	9	no	—
41	C₄	—	81	1	no	—
42	C₃	—	4	1	no	—
43	C₃	—	8	1	no	—
44	C₃	—	12	9	no	—
45	C₃	#10620192	1	1	yes	characteristic
46	C₂	—	81	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃²×H(3,𝔽₃)	C₈
Frattini	C₃	#10620192
socle	C₃³	AGL(1,𝔽₉)
prime radical	C₃⋊(C₃⋊#272)	C₄
cosocle	#11758050	C₂
LCS	G ▷ C₃²×H(3,𝔽₃)
UCS	C₁

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

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