Subgroups — C₃³×C₂₇×C₃₇ #41004704

Order 26973.

1160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₃₇	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₂₇×C₃₇	C₃	1	39	yes	maximal, direct product factor
3	C₃⁴×C₃₇	C₉	1	1	yes	characteristic
4	C₃²×C₉×C₃₇	C₉	1	26	yes	—
5	C₃²×C₉×C₃₇	C₃²	1	13	yes	—
6	C₃×C₂₇×C₃₇	C₃²	1	117	yes	direct product factor
7	C₃³×C₃₇	C₂₇	1	27	yes	direct product factor
8	C₃³×C₃₇	C₃×C₉	1	13	yes	—
9	C₃×C₉×C₃₇	C₃×C₉	1	104	yes	—
10	C₃×C₉×C₃₇	C₃³	1	13	yes	—
11	C₂₇×C₃₇	C₃³	1	27	yes	direct product factor
12	C₃³×C₂₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃²×C₃₇	C₃×C₂₇	1	117	yes	direct product factor
14	C₃²×C₃₇	C₃²×C₉	1	13	yes	—
15	C₉×C₃₇	C₃²×C₉	1	26	yes	—
16	C₉×C₃₇	C₃⁴	1	1	yes	characteristic
17	C₃³×C₉	C₃×C₃₇	1	1	yes	characteristic
18	C₃²×C₂₇	C₃×C₃₇	1	39	yes	direct product factor
19	C₃×C₃₇	C₃²×C₂₇	1	39	yes	direct product factor
20	C₃×C₃₇	C₃³×C₉	1	1	yes	characteristic
21	C₃⁴	C₉×C₃₇	1	1	yes	characteristic
22	C₃²×C₉	C₉×C₃₇	1	26	yes	—
23	C₃²×C₉	C₃²×C₃₇	1	13	yes	—
24	C₃×C₂₇	C₃²×C₃₇	1	117	yes	direct product factor
25	C₃₇	C₃³×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₃³	C₂₇×C₃₇	1	27	yes	direct product factor
27	C₃³	C₃×C₉×C₃₇	1	13	yes	—
28	C₃×C₉	C₃×C₉×C₃₇	1	104	yes	—
29	C₃×C₉	C₃³×C₃₇	1	13	yes	—
30	C₂₇	C₃³×C₃₇	1	27	yes	direct product factor
31	C₃²	C₃×C₂₇×C₃₇	1	117	yes	direct product factor
32	C₃²	C₃²×C₉×C₃₇	1	13	yes	—
33	C₉	C₃²×C₉×C₃₇	1	26	yes	—
34	C₉	C₃⁴×C₃₇	1	1	yes	characteristic
35	C₃	C₃²×C₂₇×C₃₇	1	39	yes	direct product factor
36	C₃	C₃³×C₉×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₃⁴×C₃₇
socle, prime radical	C₃⁴×C₃₇	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₂₇×C₃₇	C₃	direct (N × H)
6. C₃×C₂₇×C₃₇	C₃²	direct (N × H)
7. C₃³×C₃₇	C₂₇	direct (N × H)
11. C₂₇×C₃₇	C₃³	direct (N × H)
12. C₃³×C₂₇	C₃₇	direct (N × H)
13. C₃²×C₃₇	C₃×C₂₇	direct (N × H)
18. C₃²×C₂₇	C₃×C₃₇	direct (N × H)
19. C₃×C₃₇	C₃²×C₂₇	direct (N × H)
24. C₃×C₂₇	C₃²×C₃₇	direct (N × H)
25. C₃₇	C₃³×C₂₇	direct (N × H)
26. C₃³	C₂₇×C₃₇	direct (N × H)
30. C₂₇	C₃³×C₃₇	direct (N × H)
31. C₃²	C₃×C₂₇×C₃₇	direct (N × H)
35. C₃	C₃²×C₂₇×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
C₃²×C₂₇×C₃₇	3
C₃³×C₂₇	37

Subgroups — C33×C27×C37 #41004704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₂₇×C₃₇ #41004704