Subgroups — C₃₇×#10624913 #41004702

Order 26973.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6898	C₃	1	18	yes	maximal, complemented
2	C₃₇×#6896	C₃	1	18	yes	maximal, complemented
3	C₃₇×#6891	C₃	1	4	yes	maximal
4	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
5	C₃×3₋¹⁺²×C₃₇	C₃²	1	12	yes	—
6	C₃₇×C₉⋊C₉	C₃²	1	72	yes	complemented
7	C₃₇×C₃²⋊C₉	C₃²	1	12	yes	—
8	C₃₇×C₃²⋊C₉	C₃²	1	24	yes	—
9	C₉²×C₃₇	C₃²	1	9	yes	complemented
10	C₃³×C₃₇	—	9	4	no	—
11	C₃³×C₃₇	C₃³	1	2	yes	—
12	C₃³×C₃₇	C₃³	1	2	yes	—
13	3₋¹⁺²×C₃₇	—	9	12	no	—
14	C₃×C₉×C₃₇	C₃³	1	36	yes	—
15	#10624913	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃²×C₃₇	—	3	4	no	—
17	C₃²×C₃₇	—	3	8	no	—
18	C₃²×C₃₇	—	3	4	no	—
19	C₃²×C₃₇	—	9	9	no	—
20	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
21	C₉×C₃₇	—	3	36	no	—
22	#6898	C₃×C₃₇	1	18	yes	complemented
23	#6896	C₃×C₃₇	1	18	yes	complemented
24	#6891	C₃×C₃₇	1	4	yes	—
25	C₃×C₃₇	—	9	2	no	—
26	C₃×C₃₇	—	9	2	no	—
27	C₃×C₃₇	3₋¹⁺⁴	1	4	yes	—
28	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
29	C₃×3₋¹⁺²	C₃²×C₃₇	1	12	yes	—
30	C₉⋊C₉	C₃²×C₃₇	1	72	yes	complemented
31	C₃²⋊C₉	C₃²×C₃₇	1	12	yes	—
32	C₃²⋊C₉	C₃²×C₃₇	1	24	yes	—
33	C₉²	C₃²×C₃₇	1	9	yes	complemented
34	C₃₇	#10624913	1	1	yes	characteristic, direct product factor, Sylow
35	C₃³	—	9	4	no	—
36	C₃³	C₃³×C₃₇	1	2	yes	—
37	C₃³	C₃³×C₃₇	1	2	yes	—
38	3₋¹⁺²	—	9	12	no	—
39	C₃×C₉	C₃³×C₃₇	1	36	yes	—
40	C₃²	—	3	4	no	—
41	C₃²	—	3	8	no	—
42	C₃²	—	3	4	no	—
43	C₃²	—	9	9	no	—
44	C₃²	C₃⁴×C₃₇	1	1	yes	characteristic
45	C₉	—	3	36	no	—
46	C₃	—	9	2	no	—
47	C₃	—	9	2	no	—
48	C₃	C₃₇×3₋¹⁺⁴	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₃₇×#6898	C₃	semidirect
2. C₃₇×#6896	C₃	semidirect
6. C₃₇×C₉⋊C₉	C₃²	semidirect
9. C₉²×C₃₇	C₃²	semidirect
15. #10624913	C₃₇	direct (N × H)
22. #6898	C₃×C₃₇	semidirect
23. #6896	C₃×C₃₇	semidirect
30. C₉⋊C₉	C₃²×C₃₇	semidirect
33. C₉²	C₃²×C₃₇	semidirect
34. C₃₇	#10624913	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×#6898	3
C₃₇×#6896	3
C₃₇×#6891	3
#10624913	37

Subgroups — C37×#10624913 #41004702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624913 #41004702