Subgroups — #36379683

Order 22599.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419226	C₃	1	1	yes	maximal, characteristic
2	#21419226	C₃	1	2	yes	maximal
3	C₃₁×#6866	C₃	1	1	yes	maximal, characteristic
4	C₃²⋊(C₃₁⋊C₉)	—	3	1	no	—
5	C₃²⋊(C₃₁⋊C₉)	—	3	2	no	—
6	C₃⁴×C₃₁	C₃²	1	1	yes	characteristic
7	C₃₁×C₃²⋊C₉	—	3	1	no	—
8	C₃³×C₃₁	—	3	1	no	—
9	C₃³×C₃₁	—	3	1	no	—
10	C₃³×C₃₁	—	3	2	no	—
11	C₃³×C₃₁	—	9	3	no	—
12	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₉×C₃₁	—	9	1	no	—
14	C₃×C₃₁⋊C₉	—	9	1	no	—
15	C₃×C₃₁⋊C₉	—	9	2	no	—
16	#10624496	—	31	1	no	maximal, Sylow
17	C₃²×C₃₁	—	9	1	no	—
18	C₃²×C₃₁	—	9	3	no	—
19	C₃²×C₃₁	—	9	6	no	—
20	C₃²×C₃₁	—	9	3	no	—
21	C₃²×C₃₁	—	9	1	no	—
22	C₃²×C₃₁	#731	1	1	yes	characteristic
23	C₃²×C₃₁	#731	1	1	yes	characteristic
24	C₃²×C₃₁	#731	1	2	yes	—
25	C₉×C₃₁	—	27	1	no	—
26	C₃₁⋊C₉	—	27	1	no	—
27	C₃₁⋊C₉	—	27	2	no	—
28	#6866	—	31	1	no	—
29	#6866	—	31	2	no	—
30	#6866	C₃₁⋊C₃	1	1	yes	characteristic
31	C₃×C₃₁	—	3	1	no	—
32	C₃×C₃₁	—	3	2	no	—
33	C₃×C₃₁	—	3	1	no	—
34	C₃×C₃₁	—	9	3	no	—
35	C₃×C₃₁	#6862	1	1	yes	characteristic
36	C₃⁴	C₃×C₃₁⋊C₃	1	1	yes	characteristic
37	C₃²⋊C₉	—	3	1	no	—
38	C₃²⋊C₉	—	93	1	no	—
39	C₃²⋊C₉	—	93	2	no	—
40	C₃₁	#10624496	1	1	yes	characteristic, complemented, Sylow
41	C₃³	—	3	1	no	—
42	C₃³	—	3	1	no	—
43	C₃³	—	3	2	no	—
44	C₃³	—	9	3	no	—
45	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
46	C₃×C₉	—	9	1	no	—
47	C₃×C₉	—	279	1	no	—
48	C₃×C₉	—	279	2	no	—
49	C₃²	—	9	1	no	—
50	C₃²	—	9	3	no	—
51	C₃²	—	9	3	no	—
52	C₃²	—	9	6	no	—
53	C₃²	—	9	1	no	—
54	C₃²	#14578896	1	1	yes	characteristic
55	C₃²	#14578897	1	1	yes	characteristic
56	C₃²	#14578898	1	2	yes	—
57	C₉	—	27	1	no	—
58	C₉	—	837	1	no	—
59	C₉	—	837	2	no	—
60	C₃	—	3	1	no	—
61	C₃	—	3	1	no	—
62	C₃	—	3	2	no	—
63	C₃	—	9	3	no	—
64	C₃	C₃₁⋊#6862	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃₁⋊#6862
commutator, prime radical, cosocle	C₃⁴×C₃₁	C₃²
Frattini	C₃⁴	C₃×C₃₁⋊C₃
Fitting	C₃₁×#6866	C₃
socle	C₃×C₃₁	#6862
hypercenter	#6866	C₃₁⋊C₃
hypocenter	C₃₁	#10624496
LCS	G ▷ C₃⁴×C₃₁ ▷ C₃³×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃⁴ ◁ #6866

Complements

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

N	H ≅ G/N	type
40. C₃₁	#10624496	semidirect

Maximal subgroups

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

subgroup	index
#21419226	3
C₃₁×#6866	3
#10624496	31