Subgroups — C₃₇×#10624707 #41004496

Order 26973.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₂₇⋊C₃	C₃	1	2	yes	maximal
2	C₃²×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic
4	C₃₇×C₉⋊C₂₇	C₃	1	9	yes	maximal, complemented
5	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
6	C₃₇×C₂₇⋊C₃	—	3	6	no	—
7	C₃×C₂₇×C₃₇	—	3	3	no	—
8	C₃×C₂₇×C₃₇	C₃²	1	3	yes	—
9	C₃×C₂₇×C₃₇	C₃²	1	6	yes	—
10	C₃₇×C₉⋊C₉	C₉	1	6	yes	—
11	C₃₇×C₃²⋊C₉	C₉	1	3	yes	—
12	C₉²×C₃₇	C₃²	1	3	yes	—
13	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
15	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
16	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
17	C₃×C₉×C₃₇	3₋¹⁺²	1	6	yes	—
18	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
19	C₂₇×C₃₇	—	3	3	no	—
20	C₂₇×C₃₇	—	3	6	no	—
21	#10624707	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₃²×C₃₇	—	3	3	no	—
23	C₃²×C₃₇	C₉⋊C₉	1	3	yes	—
24	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
25	C₉×C₃₇	—	3	9	no	—
26	C₉×C₃₇	C₉⋊C₉	1	6	yes	—
27	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₉×C₃₇	C₃×3₋¹⁺²	1	2	yes	—
29	C₃×C₂₇⋊C₃	C₃×C₃₇	1	2	yes	—
30	C₃²×C₂₇	C₃×C₃₇	1	1	yes	characteristic
31	#6887	C₃×C₃₇	1	1	yes	characteristic
32	C₉⋊C₂₇	C₃×C₃₇	1	9	yes	complemented
33	C₃×C₃₇	—	3	3	no	—
34	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
35	C₃×C₃₇	#6903	1	3	yes	—
36	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
37	C₂₇⋊C₃	—	3	6	no	—
38	C₃×C₂₇	—	3	3	no	—
39	C₃×C₂₇	C₃²×C₃₇	1	3	yes	—
40	C₃×C₂₇	C₃²×C₃₇	1	6	yes	—
41	C₉⋊C₉	C₉×C₃₇	1	6	yes	—
42	C₃²⋊C₉	C₉×C₃₇	1	3	yes	—
43	C₉²	C₃²×C₃₇	1	3	yes	—
44	C₃₇	#10624707	1	1	yes	characteristic, direct product factor, Sylow
45	C₃³	C₃×C₉×C₃₇	1	1	yes	characteristic
46	C₃×C₉	C₃×C₉×C₃₇	1	9	yes	—
47	C₃×C₉	C₃×C₉×C₃₇	1	2	yes	—
48	C₃×C₉	3₋¹⁺²×C₃₇	1	3	yes	—
49	C₃×C₉	3₋¹⁺²×C₃₇	1	6	yes	—
50	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
51	C₂₇	—	3	3	no	—
52	C₂₇	—	3	6	no	—
53	C₃²	—	3	3	no	—
54	C₃²	C₃₇×C₉⋊C₉	1	3	yes	—
55	C₃²	C₃²×C₉×C₃₇	1	1	yes	characteristic
56	C₉	—	3	9	no	—
57	C₉	C₃₇×C₉⋊C₉	1	6	yes	—
58	C₉	C₃×3₋¹⁺²×C₃₇	1	1	yes	characteristic
59	C₉	C₃×3₋¹⁺²×C₃₇	1	2	yes	—
60	C₃	—	3	3	no	—
61	C₃	C₃×C₃₇×C₉⋊C₉	1	1	yes	characteristic
62	C₃	C₃₇×#6903	1	3	yes	—

	subgroup	G/H
center	C₃×C₉×C₃₇	C₃³
commutator	C₃²	C₃²×C₉×C₃₇
Frattini, cosocle	C₃×C₉	C₃³×C₃₇
socle	C₃²×C₃₇	C₃²×C₉
prime radical	C₃³×C₃₇	C₃×C₉
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₇×C₉⋊C₂₇	C₃	semidirect
21. #10624707	C₃₇	direct (N × H)
32. C₉⋊C₂₇	C₃×C₃₇	semidirect
44. C₃₇	#10624707	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×C₃₇×C₂₇⋊C₃	3
C₃²×C₂₇×C₃₇	3
C₃₇×#6887	3
C₃₇×C₉⋊C₂₇	3
#10624707	37

Subgroups — C37×#10624707 #41004496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624707 #41004496