Subgroups — #41008294

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	3	no	—
12	C₃×#66524	—	3	2	no	—
13	C₃×#66524	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃×#66524	3₋¹⁺²	1	2	yes	—
15	#11758603	—	9	3	no	—
16	#10624457	—	37	1	no	maximal, Sylow
17	C₃²×C₃₇	—	3	1	no	—
18	C₃²×C₃₇	—	3	1	no	—
19	C₃²×C₃₇	—	3	2	no	—
20	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
21	C₉×C₃₇	—	9	1	no	—
22	#66524	—	3	2	no	—
23	#66524	—	9	2	no	—
24	#66524	#731	1	3	yes	—
25	#6887	—	37	1	no	—
26	C₃²⋊C₂₇	—	37	3	no	—
27	C₃×C₃₇	—	9	1	no	—
28	C₃×C₃₇	#6867	1	1	yes	characteristic
29	C₃×C₃₇	#6872	1	1	yes	characteristic
30	C₃×C₃₇	#6872	1	2	yes	—
31	C₃²×C₉	—	37	1	no	—
32	C₃×C₂₇	—	111	3	no	—
33	C₉⋊C₉	—	111	2	no	—
34	C₃²⋊C₉	—	37	2	no	—
35	C₃²⋊C₉	#66526	1	1	yes	characteristic
36	C₉²	—	111	1	no	—
37	C₃₇	#10624457	1	1	yes	characteristic, complemented, Sylow
38	C₃³	C₃×#66526	1	1	yes	characteristic
39	C₃×C₉	—	3	1	no	—
40	C₃×C₉	—	37	1	no	—
41	C₃×C₉	—	37	2	no	—
42	C₃×C₉	—	111	3	no	—
43	C₃×C₉	—	111	2	no	—
44	C₂₇	—	333	3	no	—
45	C₃²	—	3	1	no	—
46	C₃²	—	3	1	no	—
47	C₃²	—	3	2	no	—
48	C₃²	C₃²⋊#66526	1	1	yes	characteristic
49	C₉	—	9	1	no	—
50	C₉	—	37	3	no	—
51	C₉	—	333	2	no	—
52	C₉	—	111	2	no	—
53	C₃	—	9	1	no	—
54	C₃	#22582692	1	1	yes	characteristic
55	C₃	#22582699	1	1	yes	characteristic
56	C₃	#22582700	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	#10624457
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
37. C₃₇	#10624457	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
#10624457	37