Subgroups — #41008299

Order 26973.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#11758603	C₃	1	3	yes	maximal
2	#22582535	C₃	1	1	yes	maximal, characteristic
3	C₃×#11758603	—	3	3	no	—
4	C₃²×#66524	C₃²	1	1	yes	characteristic
5	#15688504	—	3	2	no	—
6	C₃²⋊#66524	C₉	1	2	yes	—
7	C₉×#66524	—	3	1	no	—
8	C₃₇×C₃²⋊C₉	C₉	1	1	yes	characteristic
9	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
10	C₃×C₉×C₃₇	—	3	1	no	—
11	C₃×#66524	—	3	1	no	—
12	C₃×#66524	—	3	2	no	—
13	C₃×#66524	—	3	2	no	—
14	C₃×#66524	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃×#66524	3₋¹⁺²	1	2	yes	—
16	#11758603	—	9	3	no	—
17	#10624461	—	37	1	no	maximal, Sylow
18	C₃²×C₃₇	—	3	1	no	—
19	C₃²×C₃₇	—	3	1	no	—
20	C₃²×C₃₇	—	3	2	no	—
21	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
22	C₉×C₃₇	—	9	1	no	—
23	#66524	—	3	2	no	—
24	#66524	—	9	2	no	—
25	#66524	#732	1	1	yes	characteristic
26	#66524	#733	1	2	yes	—
27	#6887	—	37	1	no	—
28	C₃²⋊C₂₇	—	37	3	no	—
29	C₃×C₃₇	—	9	1	no	—
30	C₃×C₃₇	#6868	1	1	yes	characteristic
31	C₃×C₃₇	#6873	1	1	yes	characteristic
32	C₃×C₃₇	#6873	1	2	yes	—
33	C₃²×C₉	—	37	1	no	—
34	C₃×C₂₇	—	111	3	no	—
35	C₉⋊C₉	—	111	2	no	—
36	C₃²⋊C₉	—	37	2	no	—
37	C₃²⋊C₉	#66526	1	1	yes	characteristic
38	C₉²	—	111	1	no	—
39	C₃₇	#10624461	1	1	yes	characteristic, complemented, Sylow
40	C₃³	C₃×#66526	1	1	yes	characteristic
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	37	1	no	—
43	C₃×C₉	—	37	2	no	—
44	C₃×C₉	—	111	1	no	—
45	C₃×C₉	—	111	2	no	—
46	C₃×C₉	—	111	2	no	—
47	C₂₇	—	333	3	no	—
48	C₃²	—	3	1	no	—
49	C₃²	—	3	1	no	—
50	C₃²	—	3	2	no	—
51	C₃²	C₃²⋊#66526	1	1	yes	characteristic
52	C₉	—	9	1	no	—
53	C₉	—	37	1	no	—
54	C₉	—	37	2	no	—
55	C₉	—	333	2	no	—
56	C₉	—	111	2	no	—
57	C₃	—	9	1	no	—
58	C₃	#22582693	1	1	yes	characteristic
59	C₃	#22582701	1	1	yes	characteristic
60	C₃	#22582702	1	2	yes	—

	subgroup	G/H
center	C₃²	C₃²⋊#66526
commutator, prime radical	C₃³×C₃₇	C₃×C₉
Frattini	C₃³	C₃×#66526
Fitting	C₃₇×C₃²⋊C₉	C₉
socle	C₃²×C₃₇	C₃²⋊C₉
cosocle	C₃²×#66524	C₃²
hypercenter	C₃²⋊C₉	#66526
hypocenter	C₃₇	#10624461
LCS	G ▷ C₃³×C₃₇ ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
39. C₃₇	#10624461	semidirect

Maximal subgroups

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

subgroup	index
C₃²⋊#11758603	3
#22582535	3
#10624461	37