Subgroups — #41005087

Order 26973.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#66524	C₃	1	3	yes	maximal
2	#22582441	C₃	1	9	yes	maximal
3	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic
4	C₃²×#66524	C₃²	1	9	yes	—
5	C₉×#66524	C₉	1	27	yes	complemented
6	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
7	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
8	C₉²×C₃₇	C₉	1	9	yes	complemented
9	C₃³×C₃₇	C₃³	1	1	yes	characteristic
10	C₃×C₉×C₃₇	—	3	9	no	—
11	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
12	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
13	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
14	C₃×#66524	—	3	27	no	—
15	C₃×#66524	C₃×C₉	1	27	yes	—
16	#10624544	—	37	1	no	maximal, Sylow
17	C₃²×C₃₇	C₃²×C₉	1	3	yes	—
18	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
19	C₃²×C₃₇	#737	1	9	yes	—
20	C₉×C₃₇	—	3	9	no	—
21	C₉×C₃₇	C₉²	1	9	yes	—
22	#66524	—	3	27	no	—
23	C₃×C₉²	—	37	3	no	—
24	C₃×C₉²	C₃₇⋊C₃	1	1	yes	characteristic
25	#6855	—	37	9	no	—
26	C₃×C₃₇	C₃×C₉²	1	1	yes	characteristic
27	C₃×C₃₇	#6887	1	9	yes	—
28	C₃×C₃₇	#6887	1	3	yes	—
29	C₃²×C₉	—	37	9	no	—
30	C₃²×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
31	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
32	C₉²	—	37	27	no	—
33	C₉²	#66524	1	9	yes	complemented
34	C₃₇	#10624544	1	1	yes	characteristic, complemented, Sylow
35	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
36	C₃×C₉	—	3	9	no	—
37	C₃×C₉	—	37	27	no	—
38	C₃×C₉	—	111	27	no	—
39	C₃×C₉	C₉×C₃₇⋊C₃	1	9	yes	—
40	C₃×C₉	C₃×#66524	1	9	yes	—
41	C₃×C₉	C₃×#66524	1	3	yes	—
42	C₃²	C₃×C₉×C₃₇⋊C₃	1	3	yes	—
43	C₃²	C₃²×#66524	1	1	yes	characteristic
44	C₃²	#15688531	1	9	yes	—
45	C₉	—	3	9	no	—
46	C₉	—	111	27	no	—
47	C₉	C₉×#66524	1	9	yes	—
48	C₃	C₃×C₉×#66524	1	1	yes	characteristic
49	C₃	#22582536	1	9	yes	—
50	C₃	#22582538	1	3	yes	—

	subgroup	G/H
center	C₃²×C₉	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃×C₉²
Frattini	C₃³	C₃²×C₃₇⋊C₃
Fitting	C₃×C₉²×C₃₇	C₃
socle, prime radical, cosocle	C₃³×C₃₇	C₃³
hypercenter	C₃×C₉²	C₃₇⋊C₃
hypocenter	C₃₇	#10624544
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃²×C₉ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
5. C₉×#66524	C₉	semidirect
8. C₉²×C₃₇	C₉	semidirect
33. C₉²	#66524	semidirect
34. C₃₇	#10624544	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#66524	3
#22582441	3
C₃×C₉²×C₃₇	3
#10624544	37