Subgroups — C₃₇×#10624564 #41004353

Order 26973.

662 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×H(3,𝔽₃)×C₃₇	C₃	1	1	yes	maximal, characteristic
2	C₃×C₃₇×C₃²⋊C₉	C₃	1	12	yes	maximal, complemented
3	C₃⁴×C₃₇	C₃²	1	4	yes	—
4	C₃×H(3,𝔽₃)×C₃₇	—	3	12	no	—
5	C₃²×C₉×C₃₇	C₃²	1	9	yes	—
6	C₃₇×C₃²⋊C₉	—	3	36	no	—
7	C₃³×C₃₇	—	3	12	no	—
8	C₃³×C₃₇	—	3	36	no	—
9	C₃³×C₃₇	H(3,𝔽₃)	1	12	yes	—
10	C₃³×C₃₇	C₃³	1	1	yes	characteristic
11	H(3,𝔽₃)×C₃₇	—	3	27	no	—
12	C₃×C₉×C₃₇	—	3	36	no	—
13	#10624564	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃²×C₃₇	—	3	12	no	—
15	C₃²×C₃₇	—	3	36	no	—
16	C₃²×C₃₇	—	9	36	no	—
17	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	4	yes	—
18	C₃²×C₃₇	#737	1	9	yes	—
19	C₉×C₃₇	—	9	9	no	—
20	C₃²×H(3,𝔽₃)	C₃×C₃₇	1	1	yes	characteristic
21	C₃×C₃²⋊C₉	C₃×C₃₇	1	12	yes	complemented
22	C₃×C₃₇	—	9	12	no	—
23	C₃×C₃₇	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
24	C₃×C₃₇	#6893	1	12	yes	—
25	C₃⁴	C₃²×C₃₇	1	4	yes	—
26	C₃×H(3,𝔽₃)	—	3	12	no	—
27	C₃²×C₉	C₃²×C₃₇	1	9	yes	—
28	C₃²⋊C₉	—	3	36	no	—
29	C₃₇	#10624564	1	1	yes	characteristic, direct product factor, Sylow
30	C₃³	—	3	12	no	—
31	C₃³	—	3	36	no	—
32	C₃³	H(3,𝔽₃)×C₃₇	1	12	yes	—
33	C₃³	C₃³×C₃₇	1	1	yes	characteristic
34	H(3,𝔽₃)	—	3	27	no	—
35	C₃×C₉	—	3	36	no	—
36	C₃²	—	3	12	no	—
37	C₃²	—	3	36	no	—
38	C₃²	—	9	36	no	—
39	C₃²	C₃×H(3,𝔽₃)×C₃₇	1	4	yes	—
40	C₃²	C₃₇×#737	1	9	yes	—
41	C₉	—	9	9	no	—
42	C₃	—	9	12	no	—
43	C₃	C₃₇×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
44	C₃	C₃₇×#6893	1	12	yes	—

	subgroup	G/H
center, socle	C₃³×C₃₇	C₃³
commutator, Frattini, cosocle	C₃³	C₃³×C₃₇
prime radical	C₃²×H(3,𝔽₃)×C₃₇	C₃
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₃₇×C₃²⋊C₉	C₃	semidirect
13. #10624564	C₃₇	direct (N × H)
21. C₃×C₃²⋊C₉	C₃×C₃₇	semidirect
29. C₃₇	#10624564	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×H(3,𝔽₃)×C₃₇	3
C₃×C₃₇×C₃²⋊C₉	3
#10624564	37

Subgroups — C37×#10624564 #41004353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624564 #41004353