Subgroups — C₃×#22582586 #41007590

Order 26973.

692 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582586	C₃	1	27	yes	maximal, direct product factor
2	C₃×#15688504	C₃	1	8	yes	maximal, complemented
3	C₃×#15688502	C₃	1	4	yes	maximal
4	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
6	C₃²×#66524	C₃²	1	8	yes	—
7	#15688504	C₃²	1	72	yes	complemented
8	#15688502	C₃²	1	36	yes	—
9	C₃²×C₉×C₃₇	C₃²	1	4	yes	—
10	C₉²×C₃₇	C₃²	1	9	yes	complemented
11	C₃³×C₃₇	C₃³	1	1	yes	characteristic
12	C₃²×C₃₇⋊C₃	—	3	12	no	—
13	C₃²×C₃₇⋊C₃	C₃³	1	3	yes	—
14	C₃×C₉×C₃₇	—	3	12	no	—
15	C₃×C₉×C₃₇	C₃³	1	12	yes	—
16	C₃×#66524	—	3	24	no	—
17	C₃×#66524	C₃³	1	24	yes	—
18	C₃×#6897	—	37	1	no	maximal, Sylow
19	C₃²×C₃₇	#737	1	12	yes	—
20	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
21	C₃×C₃₇⋊C₃	—	3	12	no	—
22	C₃×C₃₇⋊C₃	—	9	9	no	—
23	C₉×C₃₇	—	3	12	no	—
24	#66524	—	3	24	no	—
25	#6897	—	37	27	no	—
26	C₃×C₉⋊C₉	—	37	8	no	—
27	C₃×C₃²⋊C₉	—	37	4	no	—
28	C₃×C₉²	C₃₇⋊C₃	1	1	yes	characteristic, complemented
29	C₃×C₃₇	#6897	1	9	yes	complemented
30	C₃×C₃₇	C₃×#737	1	4	yes	—
31	C₃₇⋊C₃	—	9	3	no	—
32	C₃⁴	—	37	1	no	—
33	C₃²×C₉	—	37	8	no	—
34	C₃²×C₉	C₃×C₃₇⋊C₃	1	4	yes	—
35	C₉⋊C₉	—	37	72	no	—
36	C₃²⋊C₉	—	37	36	no	—
37	C₉²	C₃×C₃₇⋊C₃	1	9	yes	complemented
38	C₃₇	C₃×#6897	1	1	yes	characteristic, complemented, Sylow
39	C₃³	—	37	3	no	—
40	C₃³	—	111	12	no	—
41	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
42	C₃×C₉	—	3	12	no	—
43	C₃×C₉	—	37	24	no	—
44	C₃×C₉	—	111	24	no	—
45	C₃×C₉	C₃²×C₃₇⋊C₃	1	12	yes	—
46	C₃²	—	333	9	no	—
47	C₃²	—	111	12	no	—
48	C₃²	#15688531	1	12	yes	—
49	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
50	C₉	—	3	12	no	—
51	C₉	—	111	24	no	—
52	C₃	—	333	3	no	—
53	C₃	#22582586	1	9	yes	direct product factor
54	C₃	C₃×#15688531	1	4	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₃₇⋊C₃
commutator, cosocle	C₃²×C₃₇	C₃⁴
Frattini	C₃²	C₃³×C₃₇⋊C₃
Fitting	C₃×C₉²×C₃₇	C₃
socle	C₃³×C₃₇	C₃³
prime radical	C₃³×C₃₇⋊C₃	C₃²
hypercenter	C₃×C₉²	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#6897
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
1. #22582586	C₃	direct (N × H)
2. C₃×#15688504	C₃	semidirect
4. C₃×C₉²×C₃₇	C₃	semidirect
7. #15688504	C₃²	semidirect
10. C₉²×C₃₇	C₃²	semidirect
28. C₃×C₉²	C₃₇⋊C₃	semidirect
29. C₃×C₃₇	#6897	semidirect
37. C₉²	C₃×C₃₇⋊C₃	semidirect
38. C₃₇	C₃×#6897	semidirect
53. C₃	#22582586	direct (N × H)

Maximal subgroups

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

subgroup	index
#22582586	3
C₃×#15688504	3
C₃×#15688502	3
C₃×C₉²×C₃₇	3
C₃×#6897	37

Subgroups — C3×#22582586 #41007590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582586 #41007590