Finite Group Databasebeta

← C₉³×C₃₇ #41004331

Subgroups — C₉³×C₃₇ #41004331

Order 26973.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉²×C₃₇	C₃	1	13	yes	maximal
2	C₃²×C₉×C₃₇	C₃²	1	13	yes	—
3	C₉²×C₃₇	C₉	1	117	yes	direct product factor
4	C₃³×C₃₇	C₃³	1	1	yes	characteristic
5	C₃×C₉×C₃₇	C₃×C₉	1	156	yes	—
6	C₉³	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃²×C₃₇	C₃²×C₉	1	13	yes	—
8	C₉×C₃₇	C₉²	1	117	yes	direct product factor
9	C₃×C₉²	C₃×C₃₇	1	13	yes	—
10	C₃×C₃₇	C₃×C₉²	1	13	yes	—
11	C₃²×C₉	C₃²×C₃₇	1	13	yes	—
12	C₉²	C₉×C₃₇	1	117	yes	direct product factor
13	C₃₇	C₉³	1	1	yes	characteristic, direct product factor, Sylow
14	C₃³	C₃³×C₃₇	1	1	yes	characteristic
15	C₃×C₉	C₃×C₉×C₃₇	1	156	yes	—
16	C₃²	C₃²×C₉×C₃₇	1	13	yes	—
17	C₉	C₉²×C₃₇	1	117	yes	direct product factor
18	C₃	C₃×C₉²×C₃₇	1	13	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃³	C₃³×C₃₇
socle, prime radical	C₃³×C₃₇	C₃³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉²×C₃₇	C₉	direct (N × H)
6. C₉³	C₃₇	direct (N × H)
8. C₉×C₃₇	C₉²	direct (N × H)
12. C₉²	C₉×C₃₇	direct (N × H)
13. C₃₇	C₉³	direct (N × H)
17. C₉	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
C₃×C₉²×C₃₇	3
C₉³	37