Subgroups — #36379868

Order 22599.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578886	C₃	1	3	yes	maximal
2	C₃₁⋊#6855	C₃	1	9	yes	maximal
3	C₃×C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₃₁⋊C₉	C₃²	1	9	yes	—
5	#14578886	—	3	9	no	—
6	C₃²×C₉×C₃₁	C₃²	1	3	yes	—
7	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
8	C₉²×C₃₁	C₉	1	9	yes	complemented
9	C₃³×C₃₁	C₃³	1	1	yes	characteristic
10	C₃×C₉×C₃₁	—	3	9	no	—
11	C₃×C₉×C₃₁	C₃×C₉	1	9	yes	—
12	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
13	C₃×C₉×C₃₁	3₋¹⁺²	1	9	yes	—
14	C₃×C₃₁⋊C₉	—	3	9	no	—
15	C₃×C₃₁⋊C₉	—	3	27	no	—
16	#10624553	—	31	1	no	maximal, Sylow
17	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
18	C₃²×C₃₁	C₃×3₋¹⁺²	1	3	yes	—
19	C₃²×C₃₁	#737	1	9	yes	—
20	C₉×C₃₁	—	3	9	no	—
21	C₉×C₃₁	C₉⋊C₉	1	9	yes	—
22	C₃₁⋊C₉	—	9	9	no	—
23	C₃×C₉⋊C₉	—	31	3	no	—
24	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic
25	#6855	—	31	9	no	—
26	C₃×C₃₁	C₃×C₉⋊C₉	1	1	yes	characteristic
27	C₃×C₃₁	#6887	1	3	yes	—
28	C₃×C₃₁	#6899	1	9	yes	—
29	C₃²×C₉	—	31	9	no	—
30	C₃²×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
31	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
32	C₉⋊C₉	—	93	9	no	—
33	C₉²	C₃₁⋊C₉	1	9	yes	complemented
34	C₃₁	#10624553	1	1	yes	characteristic, complemented, Sylow
35	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
36	C₃×C₉	—	3	9	no	—
37	C₃×C₉	—	93	9	no	—
38	C₃×C₉	—	93	27	no	—
39	C₃×C₉	#11719686	1	9	yes	—
40	C₃×C₉	C₃×C₃₁⋊C₉	1	9	yes	—
41	C₃×C₉	C₃×C₃₁⋊C₉	1	3	yes	—
42	C₃²	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
43	C₃²	C₃×#11719686	1	3	yes	—
44	C₃²	#14578912	1	9	yes	—
45	C₉	—	3	9	no	—
46	C₉	—	279	9	no	—
47	C₉	#14578886	1	9	yes	—
48	C₃	C₃×#14578886	1	1	yes	characteristic
49	C₃	#21419296	1	3	yes	—
50	C₃	#21419354	1	9	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₁⋊C₃
commutator	C₃²×C₃₁	C₃²×C₉
Fitting	C₃×C₉²×C₃₁	C₃
socle, prime radical, cosocle	C₃³×C₃₁	C₃³
hypercenter	C₃×C₉²	C₃₁⋊C₃
hypocenter	C₃₁	#10624553
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃³ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
8. C₉²×C₃₁	C₉	semidirect
33. C₉²	C₃₁⋊C₉	semidirect
34. C₃₁	#10624553	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14578886	3
C₃₁⋊#6855	3
C₃×C₉²×C₃₁	3
#10624553	31