Subgroups — #41005067

Order 26973.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582510	C₃	1	1	yes	maximal, characteristic, complemented
2	#22582507	C₃	1	1	yes	maximal, characteristic
3	C₉×#11758601	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#6880	C₃	1	1	yes	maximal, characteristic, complemented
5	#15688521	—	3	1	no	—
6	#15688519	—	3	1	no	—
7	C₃×#11758601	—	3	1	no	—
8	C₃₇×#733	—	3	1	no	—
9	C₉²×C₃₇	C₃²	1	1	yes	characteristic
10	3₋¹⁺²×C₃₇	—	9	1	no	—
11	C₃×C₉×C₃₇	—	3	1	no	—
12	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃²⋊(C₃₇⋊C₃)	—	9	1	no	—
14	#11758608	—	9	1	no	—
15	#11758601	—	3	3	no	—
16	#10624537	—	37	1	no	maximal, Sylow
17	C₃²×C₃₇	#732	1	1	yes	characteristic
18	C₃×C₃₇⋊C₃	—	27	1	no	—
19	C₉×C₃₇	—	3	3	no	—
20	C₉×C₃₇	—	3	1	no	—
21	C₉×C₃₇	—	27	1	no	—
22	#66524	—	27	1	no	—
23	#6880	—	37	1	no	—
24	#6880	C₃₇⋊C₃	1	1	yes	characteristic, complemented
25	#6879	—	37	1	no	—
26	C₉×C₂₇	—	37	1	no	—
27	C₃×C₃₇	—	3	1	no	—
28	C₃×C₃₇	#6879	1	1	yes	characteristic
29	C₃₇⋊C₃	—	81	1	no	—
30	#733	—	3	1	no	—
31	#733	—	111	1	no	—
32	#732	—	111	1	no	—
33	C₃×C₂₇	—	111	1	no	—
34	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
35	C₃₇	#10624537	1	1	yes	characteristic, complemented, Sylow
36	3₋¹⁺²	—	9	1	no	—
37	3₋¹⁺²	—	333	1	no	—
38	H(3,𝔽₃)	—	333	1	no	—
39	C₃×C₉	—	3	1	no	—
40	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
41	C₂₇	—	111	3	no	—
42	C₃²	—	999	1	no	—
43	C₃²	#15688518	1	1	yes	characteristic
44	C₉	—	3	3	no	—
45	C₉	—	3	1	no	—
46	C₉	—	27	1	no	—
47	C₉	—	999	1	no	—
48	C₃	—	3	1	no	—
49	C₃	—	2997	1	no	—
50	C₃	#22582506	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#22582506
commutator, cosocle	C₉²×C₃₇	C₃²
Frattini	C₉²	C₃×C₃₇⋊C₃
Fitting	C₃₇×#6880	C₃
socle	C₃×C₃₇	#6879
prime radical	#22582507	C₃
hypercenter	#6880	C₃₇⋊C₃
hypocenter	C₃₇	#10624537
LCS	G ▷ C₉²×C₃₇ ▷ C₃×C₉×C₃₇ ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ C₉² ◁ #6880

Complements

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

N	H ≅ G/N	type
1. #22582510	C₃	semidirect
3. C₉×#11758601	C₃	semidirect
4. C₃₇×#6880	C₃	semidirect
24. #6880	C₃₇⋊C₃	semidirect
35. C₃₇	#10624537	semidirect

Maximal subgroups

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

subgroup	index
#22582510	3
#22582507	3
C₉×#11758601	3
C₃₇×#6880	3
#10624537	37