Subgroups — #41008360

Order 26973.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582715	C₃	1	3	yes	maximal, complemented
2	C₃²×#11758601	C₃	1	1	yes	maximal, characteristic
3	#15688534	—	3	3	no	—
4	C₃×#11758601	—	3	1	no	—
5	C₃×#11758601	—	3	2	no	—
6	C₃×#11758601	C₉	1	2	yes	—
7	C₃×#11758601	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
9	C₃³×C₃₇	C₂₇	1	1	yes	characteristic
10	C₃×C₉×C₃₇	—	3	1	no	—
11	C₃×C₉×C₃₇	—	3	2	no	—
12	C₃×C₉×C₃₇	C₂₇	1	2	yes	—
13	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
14	#11758601	—	3	2	no	—
15	#11758601	H(3,𝔽₃)	1	1	yes	characteristic
16	#11758601	3₋¹⁺²	1	2	yes	—
17	#10624502	—	37	1	no	maximal, Sylow
18	C₃²×C₃₇	—	3	3	no	—
19	C₃²×C₃₇	—	3	1	no	—
20	C₃²×C₃₇	C₃×C₂₇	1	1	yes	characteristic
21	C₉×C₃₇	—	3	2	no	—
22	C₉×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
23	C₉×C₃₇	C₂₇⋊C₃	1	2	yes	—
24	C₃²×C₂₇	—	37	1	no	—
25	C₈₁⋊C₃	—	37	3	no	—
26	C₃×C₃₇	—	3	3	no	—
27	C₃×C₃₇	—	3	1	no	—
28	C₃×C₃₇	C₃²⋊C₂₇	1	1	yes	characteristic
29	C₃²×C₉	#66526	1	1	yes	characteristic
30	C₃×C₂₇	—	37	1	no	—
31	C₃×C₂₇	—	37	2	no	—
32	C₃×C₂₇	—	111	1	no	—
33	C₃×C₂₇	—	111	2	no	—
34	C₈₁	—	111	3	no	—
35	C₃₇	#10624502	1	1	yes	characteristic, complemented, Sylow
36	C₃³	#11758603	1	1	yes	characteristic
37	C₃×C₉	—	3	1	no	—
38	C₃×C₉	—	3	2	no	—
39	C₃×C₉	#11758603	1	2	yes	—
40	C₃×C₉	C₃×#66526	1	1	yes	characteristic
41	C₂₇	—	37	1	no	—
42	C₂₇	—	37	2	no	—
43	C₂₇	—	111	2	no	—
44	C₃²	—	3	3	no	—
45	C₃²	—	3	1	no	—
46	C₃²	C₃×#11758603	1	1	yes	characteristic
47	C₉	—	3	2	no	—
48	C₉	C₃²⋊#66526	1	1	yes	characteristic
49	C₉	#15688541	1	2	yes	—
50	C₃	—	3	1	no	—
51	C₃	—	3	3	no	—
52	C₃	C₃²⋊#11758603	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊#66526
commutator	C₃²×C₃₇	C₃×C₂₇
Frattini	C₃×C₉	C₃×#66526
Fitting	C₃²×C₉×C₃₇	C₉
socle	C₃×C₃₇	C₃²⋊C₂₇
prime radical	C₃³×C₃₇	C₂₇
cosocle	C₃×#11758601	C₃²
hypercenter	C₃²×C₉	#66526
hypocenter	C₃₇	#10624502
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #22582715	C₃	semidirect
35. C₃₇	#10624502	semidirect

Maximal subgroups

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

subgroup	index
#22582715	3
C₃²×#11758601	3
#10624502	37