Subgroups — C₃₇×#10624912 #41004701

Order 26973.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6900	C₃	1	9	yes	maximal, complemented
2	C₃₇×#6898	C₃	1	9	yes	maximal, complemented
3	C₃₇×#6897	C₃	1	18	yes	maximal, complemented
4	C₃₇×#6891	C₃	1	4	yes	maximal
5	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
6	C₃×3₋¹⁺²×C₃₇	C₃²	1	12	yes	—
7	C₃₇×C₉⋊C₉	C₃²	1	72	yes	complemented
8	C₃₇×C₃²⋊C₉	C₃²	1	24	yes	—
9	C₃₇×C₃²⋊C₉	C₃²	1	12	yes	—
10	C₉²×C₃₇	C₃²	1	9	yes	complemented
11	C₃³×C₃₇	—	9	4	no	—
12	C₃³×C₃₇	C₃³	1	2	yes	—
13	C₃³×C₃₇	C₃³	1	1	yes	characteristic
14	C₃³×C₃₇	C₃³	1	1	yes	characteristic
15	3₋¹⁺²×C₃₇	—	9	12	no	—
16	C₃×C₉×C₃₇	C₃³	1	36	yes	—
17	#10624912	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃²×C₃₇	—	3	4	no	—
19	C₃²×C₃₇	—	3	8	no	—
20	C₃²×C₃₇	—	3	4	no	—
21	C₃²×C₃₇	—	9	9	no	—
22	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
23	C₉×C₃₇	—	3	36	no	—
24	#6900	C₃×C₃₇	1	9	yes	complemented
25	#6898	C₃×C₃₇	1	9	yes	complemented
26	#6897	C₃×C₃₇	1	18	yes	complemented
27	#6891	C₃×C₃₇	1	4	yes	—
28	C₃×C₃₇	—	9	1	no	—
29	C₃×C₃₇	—	9	2	no	—
30	C₃×C₃₇	—	9	1	no	—
31	C₃×C₃₇	3₋¹⁺⁴	1	4	yes	—
32	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
33	C₃×3₋¹⁺²	C₃²×C₃₇	1	12	yes	—
34	C₉⋊C₉	C₃²×C₃₇	1	72	yes	complemented
35	C₃²⋊C₉	C₃²×C₃₇	1	24	yes	—
36	C₃²⋊C₉	C₃²×C₃₇	1	12	yes	—
37	C₉²	C₃²×C₃₇	1	9	yes	complemented
38	C₃₇	#10624912	1	1	yes	characteristic, direct product factor, Sylow
39	C₃³	—	9	4	no	—
40	C₃³	C₃³×C₃₇	1	2	yes	—
41	C₃³	C₃³×C₃₇	1	1	yes	characteristic
42	C₃³	C₃³×C₃₇	1	1	yes	characteristic
43	3₋¹⁺²	—	9	12	no	—
44	C₃×C₉	C₃³×C₃₇	1	36	yes	—
45	C₃²	—	3	4	no	—
46	C₃²	—	3	8	no	—
47	C₃²	—	3	4	no	—
48	C₃²	—	9	9	no	—
49	C₃²	C₃⁴×C₃₇	1	1	yes	characteristic
50	C₉	—	3	36	no	—
51	C₃	—	9	1	no	—
52	C₃	—	9	2	no	—
53	C₃	—	9	1	no	—
54	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×#6900	C₃	semidirect
2. C₃₇×#6898	C₃	semidirect
3. C₃₇×#6897	C₃	semidirect
7. C₃₇×C₉⋊C₉	C₃²	semidirect
10. C₉²×C₃₇	C₃²	semidirect
17. #10624912	C₃₇	direct (N × H)
24. #6900	C₃×C₃₇	semidirect
25. #6898	C₃×C₃₇	semidirect
26. #6897	C₃×C₃₇	semidirect
34. C₉⋊C₉	C₃²×C₃₇	semidirect
37. C₉²	C₃²×C₃₇	semidirect
38. C₃₇	#10624912	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×#6900	3
C₃₇×#6898	3
C₃₇×#6897	3
C₃₇×#6891	3
#10624912	37

Subgroups — C37×#10624912 #41004701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624912 #41004701