Subgroups — C₃₇×#10624476 #41004265

Order 26973.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6891	C₃	1	2	yes	maximal
2	C₃₇×#6866	C₃	1	2	yes	maximal
3	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
4	C₃×3₋¹⁺²×C₃₇	—	3	2	no	—
5	C₃₇×C₃²⋊C₉	—	3	6	no	—
6	C₃₇×C₃²⋊C₉	—	3	2	no	—
7	C₃³×C₃₇	—	3	2	no	—
8	C₃³×C₃₇	—	3	2	no	—
9	C₃³×C₃₇	—	9	3	no	—
10	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
11	3₋¹⁺²×C₃₇	—	9	2	no	—
12	3₋¹⁺²×C₃₇	—	9	4	no	—
13	C₃×C₉×C₃₇	—	3	6	no	—
14	C₃×C₉×C₃₇	—	9	2	no	—
15	#10624476	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃²×C₃₇	—	3	6	no	—
17	C₃²×C₃₇	—	9	1	no	—
18	C₃²×C₃₇	—	9	6	no	—
19	C₃²×C₃₇	—	9	4	no	—
20	C₃²×C₃₇	—	9	1	no	—
21	C₃²×C₃₇	AΣL(1,𝔽₂₇)	1	2	yes	—
22	C₃²×C₃₇	#732	1	2	yes	—
23	C₉×C₃₇	—	9	6	no	—
24	C₉×C₃₇	—	27	2	no	—
25	#6891	C₃×C₃₇	1	2	yes	—
26	#6866	C₃×C₃₇	1	2	yes	—
27	C₃×C₃₇	—	3	2	no	—
28	C₃×C₃₇	—	3	2	no	—
29	C₃×C₃₇	—	9	3	no	—
30	C₃×C₃₇	#6856	1	1	yes	characteristic
31	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
32	C₃×3₋¹⁺²	—	3	2	no	—
33	C₃²⋊C₉	—	3	6	no	—
34	C₃²⋊C₉	—	3	2	no	—
35	C₃₇	#10624476	1	1	yes	characteristic, direct product factor, Sylow
36	C₃³	—	3	2	no	—
37	C₃³	—	3	2	no	—
38	C₃³	—	9	3	no	—
39	C₃³	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
40	3₋¹⁺²	—	9	2	no	—
41	3₋¹⁺²	—	9	4	no	—
42	C₃×C₉	—	3	6	no	—
43	C₃×C₉	—	9	2	no	—
44	C₃²	—	3	6	no	—
45	C₃²	—	9	1	no	—
46	C₃²	—	9	6	no	—
47	C₃²	—	9	4	no	—
48	C₃²	—	9	1	no	—
49	C₃²	C₃₇×AΣL(1,𝔽₂₇)	1	2	yes	—
50	C₃²	C₃₇×#732	1	2	yes	—
51	C₉	—	9	6	no	—
52	C₉	—	27	2	no	—
53	C₃	—	3	2	no	—
54	C₃	—	3	2	no	—
55	C₃	—	9	3	no	—
56	C₃	C₃₇×#6856	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₃₇	#6856
commutator, Frattini, cosocle	C₃⁴	C₃²×C₃₇
prime radical	C₃⁴×C₃₇	C₃²
LCS	G ▷ C₃⁴ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₃₇ ◁ C₃³×C₃₇ ◁ C₃⁴×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
15. #10624476	C₃₇	direct (N × H)
35. C₃₇	#10624476	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×#6866	3
#10624476	37

Subgroups — C37×#10624476 #41004265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624476 #41004265