Subgroups — #41004922

Order 26973.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582472	C₃	1	3	yes	maximal
2	C₃₇×#6855	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊#66524	—	3	3	no	—
4	C₃²×C₉×C₃₇	—	3	1	no	—
5	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
6	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
7	C₃×C₉×C₃₇	—	3	3	no	—
8	C₃×C₉×C₃₇	—	3	1	no	—
9	C₃×C₉×C₃₇	—	3	1	no	—
10	C₃×C₉×C₃₇	—	3	2	no	—
11	C₃×C₉×C₃₇	—	9	2	no	—
12	C₃×C₉×C₃₇	—	9	1	no	—
13	C₃×#66524	—	9	3	no	—
14	#10624494	—	37	1	no	maximal, Sylow
15	C₃²×C₃₇	—	3	1	no	—
16	C₃²×C₃₇	—	3	2	no	—
17	C₃²×C₃₇	#731	1	1	yes	characteristic
18	C₃²×C₃₇	#732	1	1	yes	characteristic
19	C₃²×C₃₇	#733	1	2	yes	—
20	C₉×C₃₇	—	9	3	no	—
21	C₉×C₃₇	—	9	1	no	—
22	#66524	—	27	3	no	—
23	#6868	—	37	3	no	—
24	#6855	C₃₇⋊C₃	1	1	yes	characteristic
25	C₃×C₃₇	—	3	1	no	—
26	C₃×C₃₇	—	3	2	no	—
27	C₃×C₃₇	#6861	1	1	yes	characteristic
28	C₃×C₃₇	#6879	1	1	yes	characteristic
29	C₃×C₃₇	#6882	1	2	yes	—
30	C₃²×C₉	—	3	1	no	—
31	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
32	C₃²⋊C₉	—	111	3	no	—
33	C₃₇	#10624494	1	1	yes	characteristic, complemented, Sylow
34	C₃³	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
35	C₃×C₉	—	3	3	no	—
36	C₃×C₉	—	3	1	no	—
37	C₃×C₉	—	3	1	no	—
38	C₃×C₉	—	3	2	no	—
39	C₃×C₉	—	9	2	no	—
40	C₃×C₉	—	9	1	no	—
41	C₃×C₉	—	333	3	no	—
42	C₃²	—	3	1	no	—
43	C₃²	—	3	2	no	—
44	C₃²	#15688515	1	1	yes	characteristic
45	C₃²	#15688519	1	1	yes	characteristic
46	C₃²	#15688520	1	2	yes	—
47	C₉	—	9	3	no	—
48	C₉	—	9	1	no	—
49	C₉	—	999	3	no	—
50	C₃	—	3	1	no	—
51	C₃	—	3	2	no	—
52	C₃	#22582456	1	1	yes	characteristic
53	C₃	#22582507	1	1	yes	characteristic
54	C₃	#22582518	1	2	yes	—

	subgroup	G/H
center	C₃²	#15688519
commutator, cosocle	C₃²×C₉×C₃₇	C₃²
Frattini	C₃²×C₉	C₃×C₃₇⋊C₃
Fitting	C₃₇×#6855	C₃
socle	C₃²×C₃₇	#732
prime radical	C₃³×C₃₇	H(3,𝔽₃)
hypercenter	#6855	C₃₇⋊C₃
hypocenter	C₃₇	#10624494
LCS	G ▷ C₃²×C₉×C₃₇ ▷ C₃³×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ #6855

Complements

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

N	H ≅ G/N	type
33. C₃₇	#10624494	semidirect

Maximal subgroups

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

subgroup	index
#22582472	3
C₃₇×#6855	3
#10624494	37