Subgroups — C₃₇×#10624532 #41004321

Order 26973.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₈₁⋊C₃	C₃	1	3	yes	maximal
2	C₃₇×#6864	C₃	1	1	yes	maximal, characteristic
3	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
4	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
5	C₃×C₂₇×C₃₇	C₃²	1	1	yes	characteristic
6	C₉²×C₃₇	C₉	1	1	yes	characteristic
7	C₃₇×C₈₁	—	3	3	no	—
8	C₃×C₉×C₃₇	—	3	1	no	—
9	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
10	C₂₇×C₃₇	—	3	1	no	—
11	C₂₇×C₃₇	C₂₇	1	3	yes	—
12	C₂₇×C₃₇	3₋¹⁺²	1	3	yes	—
13	#10624532	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃²×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
15	C₉×C₃₇	—	9	1	no	—
16	C₉×C₃₇	C₉⋊C₉	1	1	yes	characteristic
17	C₉×C₃₇	C₃×C₂₇	1	1	yes	characteristic
18	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
19	C₈₁⋊C₃	C₃×C₃₇	1	3	yes	—
20	#6864	C₃×C₃₇	1	1	yes	characteristic
21	C₃×C₃₇	—	3	1	no	—
22	C₃×C₃₇	C₉⋊C₂₇	1	1	yes	characteristic
23	C₃×C₂₇	C₉×C₃₇	1	1	yes	characteristic
24	C₃×C₂₇	C₉×C₃₇	1	1	yes	characteristic
25	C₃×C₂₇	C₃²×C₃₇	1	1	yes	characteristic
26	C₉²	C₉×C₃₇	1	1	yes	characteristic
27	C₈₁	—	3	3	no	—
28	C₃₇	#10624532	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₉	—	3	1	no	—
30	C₃×C₉	C₃×C₉×C₃₇	1	1	yes	characteristic
31	C₂₇	—	3	1	no	—
32	C₂₇	C₂₇×C₃₇	1	3	yes	—
33	C₂₇	3₋¹⁺²×C₃₇	1	3	yes	—
34	C₃²	C₃₇×C₂₇⋊C₃	1	1	yes	characteristic
35	C₉	—	9	1	no	—
36	C₉	C₃₇×C₉⋊C₉	1	1	yes	characteristic
37	C₉	C₃×C₂₇×C₃₇	1	1	yes	characteristic
38	C₉	C₃₇×C₂₇⋊C₃	1	1	yes	characteristic
39	C₃	—	3	1	no	—
40	C₃	C₃₇×C₉⋊C₂₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
13. #10624532	C₃₇	direct (N × H)
28. C₃₇	#10624532	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×C₈₁⋊C₃	3
C₃₇×#6864	3
#10624532	37

Subgroups — C37×#10624532 #41004321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624532 #41004321