Subgroups — C₃²×C₉²×C₃₇ #41004644

Order 26973.

2132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₃₇	C₃	1	4	yes	maximal
2	C₃×C₉²×C₃₇	C₃	1	36	yes	maximal, direct product factor
3	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
4	C₃²×C₉×C₃₇	C₉	1	108	yes	direct product factor
5	C₃²×C₉×C₃₇	C₃²	1	48	yes	—
6	C₉²×C₃₇	C₃²	1	81	yes	direct product factor
7	C₃³×C₃₇	C₃×C₉	1	36	yes	—
8	C₃³×C₃₇	C₃³	1	4	yes	—
9	C₃×C₉×C₃₇	C₃×C₉	1	432	yes	direct product factor
10	C₃×C₉×C₃₇	C₃³	1	36	yes	—
11	C₃²×C₉²	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃²×C₃₇	C₉²	1	81	yes	direct product factor
13	C₃²×C₃₇	C₃²×C₉	1	48	yes	—
14	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
15	C₉×C₃₇	C₃²×C₉	1	108	yes	direct product factor
16	C₃³×C₉	C₃×C₃₇	1	4	yes	—
17	C₃×C₉²	C₃×C₃₇	1	36	yes	direct product factor
18	C₃×C₃₇	C₃×C₉²	1	36	yes	direct product factor
19	C₃×C₃₇	C₃³×C₉	1	4	yes	—
20	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
21	C₃²×C₉	C₉×C₃₇	1	108	yes	direct product factor
22	C₃²×C₉	C₃²×C₃₇	1	48	yes	—
23	C₉²	C₃²×C₃₇	1	81	yes	direct product factor
24	C₃₇	C₃²×C₉²	1	1	yes	characteristic, direct product factor, Sylow
25	C₃³	C₃×C₉×C₃₇	1	36	yes	—
26	C₃³	C₃³×C₃₇	1	4	yes	—
27	C₃×C₉	C₃×C₉×C₃₇	1	432	yes	direct product factor
28	C₃×C₉	C₃³×C₃₇	1	36	yes	—
29	C₃²	C₉²×C₃₇	1	81	yes	direct product factor
30	C₃²	C₃²×C₉×C₃₇	1	48	yes	—
31	C₃²	C₃⁴×C₃₇	1	1	yes	characteristic
32	C₉	C₃²×C₉×C₃₇	1	108	yes	direct product factor
33	C₃	C₃×C₉²×C₃₇	1	36	yes	direct product factor
34	C₃	C₃³×C₉×C₃₇	1	4	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃²	C₃⁴×C₃₇
socle, prime radical	C₃⁴×C₃₇	C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₉²×C₃₇	C₃	direct (N × H)
4. C₃²×C₉×C₃₇	C₉	direct (N × H)
6. C₉²×C₃₇	C₃²	direct (N × H)
9. C₃×C₉×C₃₇	C₃×C₉	direct (N × H)
11. C₃²×C₉²	C₃₇	direct (N × H)
12. C₃²×C₃₇	C₉²	direct (N × H)
15. C₉×C₃₇	C₃²×C₉	direct (N × H)
17. C₃×C₉²	C₃×C₃₇	direct (N × H)
18. C₃×C₃₇	C₃×C₉²	direct (N × H)
21. C₃²×C₉	C₉×C₃₇	direct (N × H)
23. C₉²	C₃²×C₃₇	direct (N × H)
24. C₃₇	C₃²×C₉²	direct (N × H)
27. C₃×C₉	C₃×C₉×C₃₇	direct (N × H)
29. C₃²	C₉²×C₃₇	direct (N × H)
32. C₉	C₃²×C₉×C₃₇	direct (N × H)
33. C₃	C₃×C₉²×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₉×C₃₇	3
C₃×C₉²×C₃₇	3
C₃²×C₉²	37

Subgroups — C32×C92×C37 #41004644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₉²×C₃₇ #41004644