Subgroups — #41004979

Order 26973.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582470	C₃	1	3	yes	maximal
2	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊#66524	—	3	3	no	—
4	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
5	C₃₇×C₉⋊C₉	—	3	2	no	—
6	C₃₇×C₃²⋊C₉	—	3	1	no	—
7	C₉²×C₃₇	C₉	1	3	yes	complemented
8	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₉×C₃₇	—	3	3	no	—
10	C₃×C₉×C₃₇	—	3	3	no	—
11	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
12	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
13	C₃×#66524	—	9	3	no	—
14	#10624513	—	37	1	no	maximal, Sylow
15	C₃²×C₃₇	—	9	1	no	—
16	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
17	C₃²×C₃₇	#731	1	3	yes	—
18	C₉×C₃₇	—	3	1	no	—
19	C₉×C₃₇	—	3	2	no	—
20	C₉×C₃₇	—	9	3	no	—
21	#66524	—	27	3	no	—
22	#6887	C₃₇⋊C₃	1	1	yes	characteristic
23	#6867	—	37	3	no	—
24	C₃×C₃₇	—	3	3	no	—
25	C₃×C₃₇	—	3	1	no	—
26	C₃×C₃₇	#6867	1	1	yes	characteristic
27	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
28	C₉⋊C₉	—	3	2	no	—
29	C₃²⋊C₉	—	3	1	no	—
30	C₃²⋊C₉	—	111	3	no	—
31	C₉²	#66524	1	3	yes	complemented
32	C₃₇	#10624513	1	1	yes	characteristic, complemented, Sylow
33	C₃³	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	—	3	3	no	—
36	C₃×C₉	—	333	3	no	—
37	C₃×C₉	C₃×#66524	1	1	yes	characteristic
38	C₃×C₉	#11758608	1	2	yes	—
39	C₃²	—	9	1	no	—
40	C₃²	C₃²⋊#66524	1	1	yes	characteristic
41	C₃²	#15688516	1	3	yes	—
42	C₉	—	3	1	no	—
43	C₉	—	3	2	no	—
44	C₉	—	9	3	no	—
45	C₉	—	999	3	no	—
46	C₃	—	3	1	no	—
47	C₃	—	3	3	no	—
48	C₃	#22582470	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#22582470
commutator	C₃×C₉×C₃₇	C₃×C₉
Frattini	C₃²×C₉	C₃×C₃₇⋊C₃
Fitting	C₃₇×#6887	C₃
socle	C₃×C₃₇	#6867
prime radical	C₃³×C₃₇	H(3,𝔽₃)
cosocle	C₃²×C₉×C₃₇	C₃²
hypercenter	#6887	C₃₇⋊C₃
hypocenter	C₃₇	#10624513
LCS	G ▷ C₃×C₉×C₃₇ ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
7. C₉²×C₃₇	C₉	semidirect
31. C₉²	#66524	semidirect
32. C₃₇	#10624513	semidirect

Maximal subgroups

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

subgroup	index
#22582470	3
C₃₇×#6887	3
#10624513	37