Subgroups — #41006323

Order 26973.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688511	C₃	1	2	yes	maximal
2	C₃²×#11758601	C₃	1	1	yes	maximal, characteristic
3	#22582489	C₃	1	9	yes	maximal, complemented
4	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic
5	#15688511	—	3	6	no	—
6	C₃×#11758601	—	3	3	no	—
7	C₃×#11758601	C₃²	1	3	yes	—
8	C₃×#11758601	C₃²	1	6	yes	—
9	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
10	C₃₇×C₉⋊C₉	C₉	1	6	yes	—
11	C₃₇×C₃²⋊C₉	C₉	1	3	yes	—
12	C₉²×C₃₇	C₃²	1	3	yes	—
13	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
15	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
16	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
17	C₃×C₉×C₃₇	3₋¹⁺²	1	6	yes	—
18	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
19	#11758601	—	3	3	no	—
20	#11758601	—	3	6	no	—
21	#10624707	—	37	1	no	maximal, Sylow
22	C₃²×C₃₇	—	3	3	no	—
23	C₃²×C₃₇	C₉⋊C₉	1	3	yes	—
24	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
25	C₉×C₃₇	—	3	9	no	—
26	C₉×C₃₇	C₉⋊C₉	1	6	yes	—
27	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₉×C₃₇	C₃×3₋¹⁺²	1	2	yes	—
29	C₃×C₂₇⋊C₃	—	37	2	no	—
30	C₃²×C₂₇	—	37	1	no	—
31	#6887	C₃₇⋊C₃	1	1	yes	characteristic
32	C₉⋊C₂₇	—	37	9	no	—
33	C₃×C₃₇	—	3	3	no	—
34	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
35	C₃×C₃₇	#6903	1	3	yes	—
36	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
37	C₂₇⋊C₃	—	111	6	no	—
38	C₃×C₂₇	—	37	3	no	—
39	C₃×C₂₇	—	37	6	no	—
40	C₃×C₂₇	—	111	3	no	—
41	C₉⋊C₉	#66524	1	6	yes	—
42	C₃²⋊C₉	#66524	1	3	yes	—
43	C₉²	C₃×C₃₇⋊C₃	1	3	yes	—
44	C₃₇	#10624707	1	1	yes	characteristic, complemented, Sylow
45	C₃³	C₃×#66524	1	1	yes	characteristic
46	C₃×C₉	#11758605	1	3	yes	—
47	C₃×C₉	#11758605	1	6	yes	—
48	C₃×C₉	C₃×#66524	1	9	yes	—
49	C₃×C₉	C₃×#66524	1	2	yes	—
50	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
51	C₂₇	—	111	3	no	—
52	C₂₇	—	111	6	no	—
53	C₃²	—	3	3	no	—
54	C₃²	#15688505	1	3	yes	—
55	C₃²	C₃²×#66524	1	1	yes	characteristic
56	C₉	—	3	9	no	—
57	C₉	#15688505	1	6	yes	—
58	C₉	C₃×#11758605	1	1	yes	characteristic
59	C₉	C₃×#11758605	1	2	yes	—
60	C₃	—	3	3	no	—
61	C₃	C₃×#15688505	1	1	yes	characteristic
62	C₃	#22582613	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
commutator, socle	C₃²×C₃₇	C₃²×C₉
Fitting	C₃₇×#6887	C₃
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	#6887	C₃₇⋊C₃
hypocenter	C₃₇	#10624707
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
3. #22582489	C₃	semidirect
44. C₃₇	#10624707	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688511	3
C₃²×#11758601	3
#22582489	3
C₃₇×#6887	3
#10624707	37