Subgroups — C₃₇×#10624675 #41004464

Order 26973.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6891	C₃	1	4	yes	maximal
2	C₃₇×#6862	C₃	1	9	yes	maximal, complemented
3	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
4	C₃×3₋¹⁺²×C₃₇	—	3	4	no	—
5	C₃₇×C₃²⋊C₉	—	3	8	no	—
6	C₃₇×C₃²⋊C₉	C₃²	1	12	yes	—
7	C₃³×C₃₇	—	9	4	no	—
8	C₃³×C₃₇	H(3,𝔽₃)	1	2	yes	—
9	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃³×C₃₇	C₃³	1	1	yes	characteristic
11	3₋¹⁺²×C₃₇	—	9	12	no	—
12	C₃×C₉×C₃₇	—	3	12	no	—
13	#10624675	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃²×C₃₇	—	3	4	no	—
15	C₃²×C₃₇	—	3	8	no	—
16	C₃²×C₃₇	—	3	4	no	—
17	C₃²×C₃₇	—	9	9	no	—
18	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
19	C₉×C₃₇	—	9	12	no	—
20	#6891	C₃×C₃₇	1	4	yes	—
21	#6862	C₃×C₃₇	1	9	yes	complemented
22	C₃×C₃₇	—	9	1	no	—
23	C₃×C₃₇	—	9	2	no	—
24	C₃×C₃₇	—	9	1	no	—
25	C₃×C₃₇	#6910	1	4	yes	—
26	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
27	C₃×3₋¹⁺²	—	3	4	no	—
28	C₃²⋊C₉	—	3	8	no	—
29	C₃²⋊C₉	C₃²×C₃₇	1	12	yes	—
30	C₃₇	#10624675	1	1	yes	characteristic, direct product factor, Sylow
31	C₃³	—	9	4	no	—
32	C₃³	H(3,𝔽₃)×C₃₇	1	2	yes	—
33	C₃³	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
34	C₃³	C₃³×C₃₇	1	1	yes	characteristic
35	3₋¹⁺²	—	9	12	no	—
36	C₃×C₉	—	3	12	no	—
37	C₃²	—	3	4	no	—
38	C₃²	—	3	8	no	—
39	C₃²	—	3	4	no	—
40	C₃²	—	9	9	no	—
41	C₃²	C₃×H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
42	C₉	—	9	12	no	—
43	C₃	—	9	1	no	—
44	C₃	—	9	2	no	—
45	C₃	—	9	1	no	—
46	C₃	C₃₇×#6910	1	4	yes	—

	subgroup	G/H
center, socle	C₃²×C₃₇	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₃₇
prime radical	C₃⁴×C₃₇	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₃₇ ◁ C₃⁴×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#6862	C₃	semidirect
13. #10624675	C₃₇	direct (N × H)
21. #6862	C₃×C₃₇	semidirect
30. C₃₇	#10624675	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×#6891	3
C₃₇×#6862	3
#10624675	37

Subgroups — C37×#10624675 #41004464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624675 #41004464