Subgroups — #41005086

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	4	yes	maximal
2	#22582441	C₃	1	8	yes	maximal
3	C₃₇×#6855	C₃	1	1	yes	maximal, characteristic
4	C₃²×#66524	C₃²	1	8	yes	—
5	C₃²×#66524	C₃²	1	1	yes	characteristic
6	C₉×#66524	C₉	1	36	yes	complemented
7	C₃²×C₉×C₃₇	C₃²	1	4	yes	—
8	C₃³×C₃₇	C₃³	1	1	yes	characteristic
9	C₃×C₉×C₃₇	—	3	4	no	—
10	C₃×C₉×C₃₇	—	3	8	no	—
11	C₃×C₉×C₃₇	C₃×C₉	1	12	yes	—
12	C₃×#66524	—	3	24	no	—
13	C₃×#66524	C₃×C₉	1	24	yes	—
14	C₃×#66524	C₃×C₉	1	12	yes	—
15	#10624544	—	37	1	no	maximal, Sylow
16	C₃²×C₃₇	C₃²×C₉	1	4	yes	—
17	C₃²×C₃₇	#737	1	1	yes	characteristic
18	C₃²×C₃₇	#737	1	8	yes	—
19	C₉×C₃₇	—	3	12	no	—
20	#66524	—	3	24	no	—
21	#66524	C₉²	1	9	yes	—
22	C₃×C₉²	—	37	4	no	—
23	#6855	—	37	8	no	—
24	#6855	C₃₇⋊C₃	1	1	yes	characteristic
25	C₃×C₃₇	C₃×C₉²	1	1	yes	characteristic
26	C₃×C₃₇	#6887	1	4	yes	—
27	C₃×C₃₇	#6887	1	8	yes	—
28	C₃²×C₉	—	37	1	no	—
29	C₃²×C₉	—	37	8	no	—
30	C₃²×C₉	C₃×C₃₇⋊C₃	1	4	yes	—
31	C₉²	—	37	36	no	—
32	C₃₇	#10624544	1	1	yes	characteristic, complemented, Sylow
33	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
34	C₃×C₉	—	3	4	no	—
35	C₃×C₉	—	3	8	no	—
36	C₃×C₉	—	37	12	no	—
37	C₃×C₉	—	37	24	no	—
38	C₃×C₉	—	111	24	no	—
39	C₃×C₉	C₉×C₃₇⋊C₃	1	12	yes	—
40	C₃²	C₃×C₉×C₃₇⋊C₃	1	4	yes	—
41	C₃²	#15688530	1	1	yes	characteristic
42	C₃²	#15688532	1	8	yes	—
43	C₉	—	3	12	no	—
44	C₉	—	37	9	no	—
45	C₉	—	111	24	no	—
46	C₃	C₉²×C₃₇⋊C₃	1	1	yes	characteristic
47	C₃	#22582535	1	4	yes	—
48	C₃	#22582537	1	8	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃×C₉²
Fitting	C₃₇×#6855	C₃
socle, prime radical, cosocle	C₃³×C₃₇	C₃³
hypercenter	#6855	C₃₇⋊C₃
hypocenter	C₃₇	#10624544
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ #6855

Complements

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

N	H ≅ G/N	type
6. C₉×#66524	C₉	semidirect
32. 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
C₃₇×#6855	3
#10624544	37