Subgroups — #41007309

Order 26973.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582491	C₃	1	9	yes	maximal, complemented
2	#22582474	C₃	1	3	yes	maximal
3	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic
4	#15688511	C₃²	1	9	yes	—
5	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
6	C₃₇×C₉⋊C₉	—	3	1	no	—
7	C₃₇×C₉⋊C₉	C₃²	1	3	yes	—
8	C₃₇×C₃²⋊C₉	—	3	1	no	—
9	C₉²×C₃₇	—	3	1	no	—
10	C₃³×C₃₇	3₋¹⁺²	1	1	yes	characteristic
11	C₃×C₉×C₃₇	—	3	3	no	—
12	C₃×C₉×C₃₇	—	3	3	no	—
13	C₃×C₉×C₃₇	3₋¹⁺²	1	1	yes	characteristic
14	C₃×C₉×C₃₇	3₋¹⁺²	1	1	yes	characteristic
15	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
16	#11758601	—	3	9	no	—
17	#10624830	—	37	1	no	maximal, Sylow
18	C₃²×C₃₇	—	3	1	no	—
19	C₃²×C₃₇	—	9	1	no	—
20	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
21	C₉×C₃₇	—	3	1	no	—
22	C₉×C₃₇	—	3	1	no	—
23	C₉×C₃₇	—	9	3	no	—
24	C₉×C₃₇	#737	1	3	yes	—
25	#6887	C₃₇⋊C₃	1	1	yes	characteristic
26	#6875	—	37	9	no	—
27	#6869	—	37	3	no	—
28	C₃×C₃₇	—	3	1	no	—
29	C₃×C₃₇	—	9	1	no	—
30	C₃×C₃₇	#6895	1	1	yes	characteristic
31	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
32	C₂₇⋊C₃	—	37	9	no	—
33	C₉⋊C₉	—	3	1	no	—
34	C₉⋊C₉	C₃×C₃₇⋊C₃	1	3	yes	—
35	C₃²⋊C₉	—	3	1	no	—
36	C₉²	—	3	1	no	—
37	C₃₇	#10624830	1	1	yes	characteristic, complemented, Sylow
38	C₃³	#11758608	1	1	yes	characteristic
39	C₃×C₉	—	3	3	no	—
40	C₃×C₉	—	3	3	no	—
41	C₃×C₉	#11758608	1	1	yes	characteristic
42	C₃×C₉	#11758608	1	1	yes	characteristic
43	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
44	C₂₇	—	111	9	no	—
45	C₃²	—	3	1	no	—
46	C₃²	—	9	1	no	—
47	C₃²	C₃×#11758608	1	1	yes	characteristic
48	C₉	—	3	1	no	—
49	C₉	—	3	1	no	—
50	C₉	—	9	3	no	—
51	C₉	#15688531	1	3	yes	—
52	C₃	—	3	1	no	—
53	C₃	—	9	1	no	—
54	C₃	#22582578	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#22582578
commutator, cosocle	C₃×C₉×C₃₇	C₃³
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃₇×#6887	C₃
socle	C₃×C₃₇	#6895
prime radical	C₃³×C₃₇	3₋¹⁺²
hypercenter	#6887	C₃₇⋊C₃
hypocenter	C₃₇	#10624830
LCS	G ▷ C₃×C₉×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
1. #22582491	C₃	semidirect
37. C₃₇	#10624830	semidirect

Maximal subgroups

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

subgroup	index
#22582491	3
#22582474	3
C₃₇×#6887	3
#10624830	37