Subgroups — C₈₁×#66524 #41004936

Order 26973.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688500	C₃	1	2	yes	maximal
2	C₂₇×#66524	C₃	1	1	yes	maximal, characteristic
3	C₃×C₃₇×C₈₁	C₃	1	1	yes	maximal, characteristic
4	C₃×#11758601	C₉	1	2	yes	—
5	C₉×#66524	C₉	1	1	yes	characteristic
6	#15688500	C₉	1	6	yes	complemented
7	C₃×C₂₇×C₃₇	C₃²	1	1	yes	characteristic
8	C₃₇×C₈₁	C₉	1	3	yes	complemented
9	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
10	C₃×#66524	C₂₇	1	3	yes	—
11	C₂₇×C₃₇	C₃×C₉	1	2	yes	—
12	C₂₇×C₃₇	C₃×C₉	1	1	yes	characteristic
13	#11758601	C₂₇	1	6	yes	—
14	C₉×C₈₁	—	37	1	no	maximal, Sylow
15	C₃²×C₃₇	C₃×C₂₇	1	1	yes	characteristic
16	C₉×C₃₇	C₉²	1	1	yes	characteristic
17	C₉×C₃₇	C₃×C₂₇	1	2	yes	—
18	#66524	C₈₁	1	9	yes	direct product factor
19	C₃×C₈₁	—	37	2	no	—
20	C₃×C₈₁	C₃₇⋊C₃	1	1	yes	characteristic
21	C₉×C₂₇	—	37	1	no	—
22	C₃×C₃₇	C₉×C₂₇	1	1	yes	characteristic
23	C₃×C₃₇	C₃×C₈₁	1	3	yes	—
24	C₃×C₂₇	—	37	2	no	—
25	C₃×C₂₇	C₃×C₃₇⋊C₃	1	1	yes	characteristic
26	C₉²	—	37	1	no	—
27	C₈₁	—	37	6	no	—
28	C₈₁	#66524	1	3	yes	direct product factor
29	C₃₇	C₉×C₈₁	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₉	—	37	3	no	—
31	C₃×C₉	C₉×C₃₇⋊C₃	1	1	yes	characteristic
32	C₂₇	—	37	6	no	—
33	C₂₇	C₉×C₃₇⋊C₃	1	2	yes	—
34	C₂₇	C₃×#66524	1	1	yes	characteristic
35	C₃²	C₂₇×C₃₇⋊C₃	1	1	yes	characteristic
36	C₉	—	37	9	no	—
37	C₉	C₉×#66524	1	1	yes	characteristic
38	C₉	C₂₇×C₃₇⋊C₃	1	2	yes	—
39	C₃	C₂₇×#66524	1	1	yes	characteristic
40	C₃	C₈₁×C₃₇⋊C₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₃×C₈₁	C₃₇⋊C₃
commutator, hypocenter	C₃₇	C₉×C₈₁
Frattini	C₃×C₂₇	C₃×C₃₇⋊C₃
Fitting	C₃×C₃₇×C₈₁	C₃
socle, prime radical	C₃²×C₃₇	C₃×C₂₇
cosocle	C₃×C₂₇×C₃₇	C₃²
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₃×C₈₁

Complements

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

N	H ≅ G/N	type
6. #15688500	C₉	semidirect
8. C₃₇×C₈₁	C₉	semidirect
18. #66524	C₈₁	direct (N × H)
28. C₈₁	#66524	direct (N × H)
29. C₃₇	C₉×C₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688500	3
C₂₇×#66524	3
C₃×C₃₇×C₈₁	3
C₉×C₈₁	37

Subgroups — C81×#66524 #41004936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₁×#66524 #41004936