Subgroups — #14519082

Order 1944.

206 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758052	C₂	1	1	yes	maximal, characteristic
2	#92404	C₄	1	1	yes	characteristic
3	H(5,𝔽₃)	C₈	1	1	yes	characteristic, complemented, Sylow
4	C₃⋊AGL(1,𝔽₉)	—	9	4	no	maximal
5	#6249	—	9	6	no	maximal
6	C₃⋊#272	—	12	6	no	—
7	C₃⋊#272	—	12	4	no	—
8	C₃×#157	—	9	4	no	—
9	#1088	—	9	6	no	—
10	C₃×H(3,𝔽₃)	—	4	4	no	—
11	C₃×H(3,𝔽₃)	—	4	6	no	—
12	AGL(1,𝔽₉)	—	27	4	no	—
13	C₃×C₃⋊D₃	—	9	4	no	—
14	C₃×C₃⋊D₃	—	36	3	no	—
15	C₃×C₃⋊D₃	—	36	6	no	—
16	#272	—	9	6	no	—
17	#272	—	36	8	no	—
18	#272	—	36	12	no	—
19	#272	—	36	1	no	—
20	#157	—	9	4	no	—
21	C₃³	—	4	6	no	—
22	C₃³	—	4	3	no	—
23	C₃³	AGL(1,𝔽₉)	1	4	yes	complemented
24	H(3,𝔽₃)	—	4	1	no	—
25	H(3,𝔽₃)	—	4	12	no	—
26	H(3,𝔽₃)	—	4	8	no	—
27	H(3,𝔽₃)	AGL(1,𝔽₉)	1	6	yes	complemented
28	C₃⋊C₈	—	81	1	no	—
29	C₃⋊D₃	—	9	4	no	—
30	C₃⋊D₃	—	36	6	no	—
31	C₃⋊D₃	—	36	3	no	—
32	C₃×D₃	—	108	6	no	—
33	C₃×D₃	—	108	4	no	—
34	C₃×C₄	—	81	1	no	—
35	C₃²	—	4	4	no	—
36	C₃²	—	4	6	no	—
37	C₃²	—	9	4	no	—
38	C₃²	—	36	6	no	—
39	C₃²	—	36	3	no	—
40	C₈	—	243	1	no	Sylow
41	C₂×C₃	—	81	1	no	—
42	D₃	—	108	4	no	—
43	D₃	—	108	6	no	—
44	C₄	—	81	1	no	—
45	C₃	—	12	4	no	—
46	C₃	—	12	6	no	—
47	C₃	#10620192	1	1	yes	characteristic
48	C₂	—	81	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	H(5,𝔽₃)	C₈
Frattini, socle	C₃	#10620192
prime radical	#92404	C₄
cosocle	#11758052	C₂
LCS	G ▷ H(5,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.