Subgroups — #36379660

Order 22599.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419230	C₃	1	1	yes	maximal, characteristic
2	#21419230	C₃	1	2	yes	maximal
3	C₃₁×#6855	C₃	1	1	yes	maximal, characteristic
4	C₃²⋊(C₃₁⋊C₉)	—	3	1	no	—
5	C₃²⋊(C₃₁⋊C₉)	—	3	2	no	—
6	C₃²×C₉×C₃₁	—	3	1	no	—
7	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
8	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₉×C₃₁	—	3	3	no	—
10	C₃×C₉×C₃₁	—	3	1	no	—
11	C₃×C₉×C₃₁	—	3	1	no	—
12	C₃×C₉×C₃₁	—	3	2	no	—
13	C₃×C₉×C₃₁	—	9	2	no	—
14	C₃×C₉×C₃₁	—	9	1	no	—
15	C₃×C₃₁⋊C₉	—	9	1	no	—
16	C₃×C₃₁⋊C₉	—	9	2	no	—
17	#10624492	—	31	1	no	maximal, Sylow
18	C₃²×C₃₁	—	3	1	no	—
19	C₃²×C₃₁	—	3	2	no	—
20	C₃²×C₃₁	#731	1	1	yes	characteristic
21	C₃²×C₃₁	#732	1	1	yes	characteristic
22	C₃²×C₃₁	#733	1	2	yes	—
23	C₉×C₃₁	—	9	3	no	—
24	C₉×C₃₁	—	9	1	no	—
25	C₃₁⋊C₉	—	27	1	no	—
26	C₃₁⋊C₉	—	27	2	no	—
27	#6868	—	31	2	no	—
28	#6868	—	31	1	no	—
29	#6855	C₃₁⋊C₃	1	1	yes	characteristic
30	C₃×C₃₁	—	3	1	no	—
31	C₃×C₃₁	—	3	2	no	—
32	C₃×C₃₁	#6861	1	1	yes	characteristic
33	C₃×C₃₁	#6878	1	1	yes	characteristic
34	C₃×C₃₁	#6883	1	2	yes	—
35	C₃²×C₉	—	3	1	no	—
36	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
37	C₃²⋊C₉	—	93	2	no	—
38	C₃²⋊C₉	—	93	1	no	—
39	C₃₁	#10624492	1	1	yes	characteristic, complemented, Sylow
40	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
41	C₃×C₉	—	3	3	no	—
42	C₃×C₉	—	3	1	no	—
43	C₃×C₉	—	3	1	no	—
44	C₃×C₉	—	3	2	no	—
45	C₃×C₉	—	9	2	no	—
46	C₃×C₉	—	9	1	no	—
47	C₃×C₉	—	279	2	no	—
48	C₃×C₉	—	279	1	no	—
49	C₃²	—	3	2	no	—
50	C₃²	—	3	1	no	—
51	C₃²	#14578896	1	1	yes	characteristic
52	C₃²	#14578900	1	1	yes	characteristic
53	C₃²	#14578901	1	2	yes	—
54	C₉	—	9	3	no	—
55	C₉	—	9	1	no	—
56	C₉	—	837	2	no	—
57	C₉	—	837	1	no	—
58	C₃	—	3	1	no	—
59	C₃	—	3	2	no	—
60	C₃	#21419214	1	1	yes	characteristic
61	C₃	#21419261	1	1	yes	characteristic
62	C₃	#21419281	1	2	yes	—

	subgroup	G/H
center	C₃²	#14578900
commutator, cosocle	C₃²×C₉×C₃₁	C₃²
Frattini	C₃²×C₉	C₃×C₃₁⋊C₃
Fitting	C₃₁×#6855	C₃
socle	C₃²×C₃₁	#732
prime radical	C₃³×C₃₁	H(3,𝔽₃)
hypercenter	#6855	C₃₁⋊C₃
hypocenter	C₃₁	#10624492
LCS	G ▷ C₃²×C₉×C₃₁ ▷ C₃³×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ #6855

Complements

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

N	H ≅ G/N	type
39. C₃₁	#10624492	semidirect

Maximal subgroups

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

subgroup	index
#21419230	3
C₃₁×#6855	3
#10624492	31