Subgroups — #41004779

Order 26973.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#11758601	C₃	1	3	yes	maximal
2	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic
3	C₃×#11758601	—	3	3	no	—
4	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
5	C₃₇×C₉⋊C₉	—	3	2	no	—
6	C₃₇×C₃²⋊C₉	C₉	1	3	yes	—
7	C₉²×C₃₇	—	3	1	no	—
8	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
9	C₃×C₉×C₃₇	—	3	1	no	—
10	C₃×C₉×C₃₇	—	3	2	no	—
11	C₃×C₉×C₃₇	—	3	3	no	—
12	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
14	#11758601	—	9	3	no	—
15	#10624458	—	37	1	no	maximal, Sylow
16	C₃²×C₃₇	—	3	1	no	—
17	C₃²×C₃₇	—	3	3	no	—
18	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
19	C₉×C₃₇	—	3	2	no	—
20	C₉×C₃₇	—	9	3	no	—
21	C₉×C₃₇	#732	1	1	yes	characteristic
22	C₉×C₃₇	#733	1	2	yes	—
23	#6887	C₃₇⋊C₃	1	1	yes	characteristic
24	C₃²⋊C₂₇	—	37	3	no	—
25	C₃×C₃₇	—	9	1	no	—
26	C₃×C₃₇	#6868	1	1	yes	characteristic
27	C₃×C₃₇	#6872	1	3	yes	—
28	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
29	C₃×C₂₇	—	111	3	no	—
30	C₉⋊C₉	—	3	2	no	—
31	C₃²⋊C₉	#66524	1	3	yes	—
32	C₉²	—	3	1	no	—
33	C₃₇	#10624458	1	1	yes	characteristic, complemented, Sylow
34	C₃³	C₃×#66524	1	1	yes	characteristic
35	C₃×C₉	—	3	1	no	—
36	C₃×C₉	—	3	2	no	—
37	C₃×C₉	—	3	3	no	—
38	C₃×C₉	#11758608	1	2	yes	—
39	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
40	C₂₇	—	333	3	no	—
41	C₃²	—	3	1	no	—
42	C₃²	—	3	3	no	—
43	C₃²	C₃²⋊#66524	1	1	yes	characteristic
44	C₉	—	3	2	no	—
45	C₉	—	9	3	no	—
46	C₉	#15688519	1	1	yes	characteristic
47	C₉	#15688521	1	2	yes	—
48	C₃	—	9	1	no	—
49	C₃	#22582472	1	1	yes	characteristic
50	C₃	#22582483	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₃₇⋊C₃)
commutator, prime radical	C₃³×C₃₇	C₃×C₉
Frattini	C₃²×C₉	C₃×C₃₇⋊C₃
Fitting	C₃₇×#6887	C₃
socle	C₃²×C₃₇	C₃²⋊C₉
cosocle	C₃²×C₉×C₃₇	C₃²
hypercenter	#6887	C₃₇⋊C₃
hypocenter	C₃₇	#10624458
LCS	G ▷ C₃³×C₃₇ ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
33. C₃₇	#10624458	semidirect

Maximal subgroups

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

subgroup	index
C₃²⋊#11758601	3
C₃₇×#6887	3
#10624458	37