Subgroups — #36379936

Order 22599.

662 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₃₁⋊C₉)	C₃	1	12	yes	maximal, complemented
2	C₃²×H(3,𝔽₃)×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₃₁⋊C₉	C₃²	1	9	yes	—
4	C₃²⋊(C₃₁⋊C₉)	—	3	36	no	—
5	C₃⁴×C₃₁	C₃²	1	4	yes	—
6	C₃×H(3,𝔽₃)×C₃₁	—	3	12	no	—
7	C₃³×C₃₁	—	3	12	no	—
8	C₃³×C₃₁	—	3	36	no	—
9	C₃³×C₃₁	H(3,𝔽₃)	1	12	yes	—
10	C₃³×C₃₁	C₃³	1	1	yes	characteristic
11	H(3,𝔽₃)×C₃₁	—	3	27	no	—
12	C₃×C₃₁⋊C₉	—	3	36	no	—
13	#10624564	—	31	1	no	maximal, Sylow
14	C₃²×C₃₁	—	3	12	no	—
15	C₃²×C₃₁	—	3	36	no	—
16	C₃²×C₃₁	—	9	36	no	—
17	C₃²×C₃₁	C₃×H(3,𝔽₃)	1	4	yes	—
18	C₃²×C₃₁	#737	1	9	yes	—
19	C₃₁⋊C₉	—	9	9	no	—
20	C₃²×H(3,𝔽₃)	C₃₁⋊C₃	1	1	yes	characteristic
21	C₃×C₃²⋊C₉	—	31	12	no	—
22	C₃×C₃₁	—	9	12	no	—
23	C₃×C₃₁	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
24	C₃×C₃₁	#6893	1	12	yes	—
25	C₃⁴	C₃×C₃₁⋊C₃	1	4	yes	—
26	C₃×H(3,𝔽₃)	—	3	12	no	—
27	C₃²×C₉	—	31	9	no	—
28	C₃²⋊C₉	—	93	36	no	—
29	C₃₁	#10624564	1	1	yes	characteristic, complemented, Sylow
30	C₃³	—	3	12	no	—
31	C₃³	—	3	36	no	—
32	C₃³	C₃²⋊(C₃₁⋊C₃)	1	12	yes	—
33	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
34	H(3,𝔽₃)	—	3	27	no	—
35	C₃×C₉	—	93	36	no	—
36	C₃²	—	3	12	no	—
37	C₃²	—	3	36	no	—
38	C₃²	—	9	36	no	—
39	C₃²	C₃×C₃²⋊(C₃₁⋊C₃)	1	4	yes	—
40	C₃²	#14578911	1	9	yes	—
41	C₉	—	279	9	no	—
42	C₃	—	9	12	no	—
43	C₃	#21419308	1	1	yes	characteristic
44	C₃	#21419320	1	12	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₁⋊C₃
commutator, socle, cosocle	C₃³×C₃₁	C₃³
Fitting, prime radical	C₃²×H(3,𝔽₃)×C₃₁	C₃
hypercenter	C₃²×H(3,𝔽₃)	C₃₁⋊C₃
hypocenter	C₃₁	#10624564
LCS	G ▷ C₃³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×C₃²⋊(C₃₁⋊C₉)	C₃	semidirect
29. C₃₁	#10624564	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃²⋊(C₃₁⋊C₉)	3
C₃²×H(3,𝔽₃)×C₃₁	3
#10624564	31