Subgroups — #41008361

Order 26973.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582715	C₃	1	3	yes	maximal, complemented
2	C₃×C₂₇×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#15688534	—	3	3	no	—
4	C₃×C₉×C₃₇⋊C₃	C₉	1	1	yes	characteristic
5	C₃×#11758601	C₉	1	1	yes	characteristic
6	C₃×#11758601	C₃²	1	1	yes	characteristic
7	C₂₇×C₃₇⋊C₃	—	3	1	no	—
8	C₂₇×C₃₇⋊C₃	—	3	2	no	—
9	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
10	C₃²×C₃₇⋊C₃	C₂₇	1	1	yes	characteristic
11	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
12	C₃×#66524	C₂₇	1	2	yes	—
13	C₉×C₃₇⋊C₃	—	3	1	no	—
14	C₉×C₃₇⋊C₃	—	3	1	no	—
15	C₉×C₃₇⋊C₃	—	3	1	no	—
16	C₂₇×C₃₇	—	3	1	no	—
17	#11758601	—	3	1	no	—
18	#11758601	H(3,𝔽₃)	1	1	yes	characteristic
19	#11758601	3₋¹⁺²	1	2	yes	—
20	#10624502	—	37	1	no	maximal, Sylow
21	C₃²×C₃₇	C₃×C₂₇	1	1	yes	characteristic
22	C₃×C₃₇⋊C₃	—	3	1	no	—
23	C₃×C₃₇⋊C₃	—	3	3	no	—
24	C₉×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
25	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
26	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
27	#66524	—	3	2	no	—
28	C₃²×C₂₇	—	37	1	no	—
29	C₈₁⋊C₃	—	37	3	no	—
30	C₃×C₃₇	—	3	1	no	—
31	C₃×C₃₇	C₃²⋊C₂₇	1	1	yes	characteristic
32	C₃₇⋊C₃	—	3	3	no	—
33	C₃²×C₉	—	37	1	no	—
34	C₃×C₂₇	—	37	1	no	—
35	C₃×C₂₇	—	37	1	no	—
36	C₃×C₂₇	—	111	1	no	—
37	C₃×C₂₇	—	111	2	no	—
38	C₃×C₂₇	#66526	1	1	yes	characteristic
39	C₈₁	—	111	3	no	—
40	C₃₇	#10624502	1	1	yes	characteristic, complemented, Sylow
41	C₃³	—	37	1	no	—
42	C₃×C₉	—	37	2	no	—
43	C₃×C₉	—	111	1	no	—
44	C₃×C₉	—	111	1	no	—
45	C₃×C₉	—	111	1	no	—
46	C₃×C₉	C₃×#66526	1	1	yes	characteristic
47	C₂₇	—	3	1	no	—
48	C₂₇	—	37	1	no	—
49	C₂₇	—	37	2	no	—
50	C₂₇	—	111	1	no	—
51	C₃²	—	111	3	no	—
52	C₃²	—	111	1	no	—
53	C₃²	(C₃₇⋊C₃)⋊C₂₇	1	1	yes	characteristic
54	C₉	—	111	2	no	—
55	C₉	C₃²⋊#66526	1	1	yes	characteristic
56	C₉	#15688542	1	1	yes	characteristic
57	C₉	#15688543	1	1	yes	characteristic
58	C₃	—	3	1	no	—
59	C₃	—	111	3	no	—
60	C₃	#22582690	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊#66526
commutator	C₃²×C₃₇	C₃×C₂₇
Frattini	C₃×C₉	C₃×#66526
Fitting	C₃×C₂₇×C₃₇	C₉
socle	C₃×C₃₇	C₃²⋊C₂₇
prime radical	C₃²×C₃₇⋊C₃	C₂₇
cosocle	C₃×#11758601	C₃²
hypercenter	C₃×C₂₇	#66526
hypocenter	C₃₇	#10624502
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
1. #22582715	C₃	semidirect
40. C₃₇	#10624502	semidirect

Maximal subgroups

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

subgroup	index
#22582715	3
C₃×C₂₇×C₃₇⋊C₃	3
#10624502	37