Subgroups — #11757404

Order 972.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊(C₂²⋊C₉)	C₃	1	3	yes	maximal
3	#6861	—	4	1	no	maximal, Sylow
4	C₂×C₃²⋊C₉	—	3	1	no	—
5	C₂²×C₃³	C₃²	1	1	yes	characteristic
6	C₂²×C₃×C₉	—	3	1	no	—
7	C₃×C₂²⋊C₉	—	3	3	no	—
8	C₃²⋊C₉	—	4	3	no	—
9	C₃²⋊C₉	A₄	1	1	yes	characteristic
10	C₂×C₃³	—	3	1	no	—
11	C₂×C₃×C₉	—	3	3	no	—
12	C₂²×C₃²	—	3	1	no	—
13	C₂²×C₃²	—	3	1	no	—
14	C₂²×C₃²	—	3	2	no	—
15	C₂²×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
16	C₂²×C₉	—	9	1	no	—
17	C₂²⋊C₉	—	9	3	no	—
18	C₃³	C₃×A₄	1	1	yes	characteristic
19	C₃×C₉	—	3	1	no	—
20	C₃×C₉	—	12	3	no	—
21	C₂×C₃²	—	3	1	no	—
22	C₂×C₃²	—	3	3	no	—
23	C₂×C₃²	—	9	1	no	—
24	C₂×C₃²	—	9	2	no	—
25	C₂×C₉	—	9	3	no	—
26	C₂²×C₃	—	9	1	no	—
27	C₂²×C₃	#731	1	1	yes	characteristic
28	C₂²×C₃	#732	1	1	yes	characteristic
29	C₂²×C₃	#733	1	2	yes	—
30	C₃²	—	3	1	no	—
31	C₃²	—	3	1	no	—
32	C₃²	—	3	2	no	—
33	C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
34	C₉	—	9	1	no	—
35	C₉	—	36	3	no	—
36	C₂×C₃	—	3	1	no	—
37	C₂×C₃	—	3	1	no	—
38	C₂×C₃	—	3	2	no	—
39	C₂×C₃	—	9	3	no	—
40	C₂²	#6861	1	1	yes	characteristic, complemented, Sylow
41	C₃	—	9	1	no	—
42	C₃	#66358	1	1	yes	characteristic
43	C₃	#66361	1	1	yes	characteristic
44	C₃	#66364	1	2	yes	—
45	C₂	—	3	1	no	—

	subgroup	G/H
center	C₃²	C₂²⋊H(3,𝔽₃)
commutator, prime radical, cosocle	C₂²×C₃³	C₃²
Frattini	C₃³	C₃×A₄
Fitting	C₂²×C₃²⋊C₉	C₃
socle	C₂²×C₃²	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	A₄
hypocenter	C₂²	#6861
LCS	G ▷ C₂²×C₃³ ▷ C₂²×C₃² ▷ C₂²
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

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

N	H ≅ G/N	type
40. C₂²	#6861	semidirect

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