Subgroups — C₃₇×#10624911 #41004700

Order 26973.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6899	C₃	1	18	yes	maximal, complemented
2	C₃₇×#6897	C₃	1	9	yes	maximal, complemented
3	C₃₇×#6896	C₃	1	9	yes	maximal, complemented
4	C₃₇×#6891	C₃	1	2	yes	maximal
5	C₃₇×#6891	C₃	1	2	yes	maximal
6	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
7	C₃×3₋¹⁺²×C₃₇	C₃²	1	6	yes	—
8	C₃×3₋¹⁺²×C₃₇	C₃²	1	6	yes	—
9	C₃₇×C₉⋊C₉	C₃²	1	72	yes	complemented
10	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
11	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
12	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
13	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
14	C₃₇×C₃²⋊C₉	C₃²	1	12	yes	—
15	C₉²×C₃₇	C₃²	1	9	yes	complemented
16	C₃³×C₃₇	—	9	2	no	—
17	C₃³×C₃₇	—	9	2	no	—
18	C₃³×C₃₇	C₃³	1	1	yes	characteristic
19	C₃³×C₃₇	C₃³	1	2	yes	—
20	C₃³×C₃₇	C₃³	1	1	yes	characteristic
21	3₋¹⁺²×C₃₇	—	9	6	no	—
22	3₋¹⁺²×C₃₇	—	9	6	no	—
23	C₃×C₉×C₃₇	C₃³	1	18	yes	—
24	C₃×C₉×C₃₇	C₃³	1	18	yes	—
25	#10624911	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₃²×C₃₇	—	3	2	no	—
27	C₃²×C₃₇	—	3	2	no	—
28	C₃²×C₃₇	—	3	2	no	—
29	C₃²×C₃₇	—	3	2	no	—
30	C₃²×C₃₇	—	3	2	no	—
31	C₃²×C₃₇	—	3	4	no	—
32	C₃²×C₃₇	—	3	2	no	—
33	C₃²×C₃₇	—	9	9	no	—
34	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
35	C₉×C₃₇	—	3	18	no	—
36	C₉×C₃₇	—	3	18	no	—
37	#6899	C₃×C₃₇	1	18	yes	complemented
38	#6897	C₃×C₃₇	1	9	yes	complemented
39	#6896	C₃×C₃₇	1	9	yes	complemented
40	#6891	C₃×C₃₇	1	2	yes	—
41	#6891	C₃×C₃₇	1	2	yes	—
42	C₃×C₃₇	—	9	1	no	—
43	C₃×C₃₇	—	9	2	no	—
44	C₃×C₃₇	—	9	1	no	—
45	C₃×C₃₇	3₋¹⁺⁴	1	2	yes	—
46	C₃×C₃₇	3₋¹⁺⁴	1	2	yes	—
47	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
48	C₃×3₋¹⁺²	C₃²×C₃₇	1	6	yes	—
49	C₃×3₋¹⁺²	C₃²×C₃₇	1	6	yes	—
50	C₉⋊C₉	C₃²×C₃₇	1	72	yes	complemented
51	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
52	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
53	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
54	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
55	C₃²⋊C₉	C₃²×C₃₇	1	12	yes	—
56	C₉²	C₃²×C₃₇	1	9	yes	complemented
57	C₃₇	#10624911	1	1	yes	characteristic, direct product factor, Sylow
58	C₃³	—	9	2	no	—
59	C₃³	—	9	2	no	—
60	C₃³	C₃³×C₃₇	1	1	yes	characteristic
61	C₃³	C₃³×C₃₇	1	2	yes	—
62	C₃³	C₃³×C₃₇	1	1	yes	characteristic
63	3₋¹⁺²	—	9	6	no	—
64	3₋¹⁺²	—	9	6	no	—
65	C₃×C₉	C₃³×C₃₇	1	18	yes	—
66	C₃×C₉	C₃³×C₃₇	1	18	yes	—
67	C₃²	—	3	2	no	—
68	C₃²	—	3	2	no	—
69	C₃²	—	3	2	no	—
70	C₃²	—	3	2	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	3	4	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	9	9	no	—
75	C₃²	C₃⁴×C₃₇	1	1	yes	characteristic
76	C₉	—	3	18	no	—
77	C₉	—	3	18	no	—
78	C₃	—	9	1	no	—
79	C₃	—	9	2	no	—
80	C₃	—	9	1	no	—
81	C₃	C₃₇×3₋¹⁺⁴	1	2	yes	—
82	C₃	C₃₇×3₋¹⁺⁴	1	2	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×#6899	C₃	semidirect
2. C₃₇×#6897	C₃	semidirect
3. C₃₇×#6896	C₃	semidirect
9. C₃₇×C₉⋊C₉	C₃²	semidirect
15. C₉²×C₃₇	C₃²	semidirect
25. #10624911	C₃₇	direct (N × H)
37. #6899	C₃×C₃₇	semidirect
38. #6897	C₃×C₃₇	semidirect
39. #6896	C₃×C₃₇	semidirect
50. C₉⋊C₉	C₃²×C₃₇	semidirect
56. C₉²	C₃²×C₃₇	semidirect
57. C₃₇	#10624911	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×#6899	3
C₃₇×#6897	3
C₃₇×#6896	3
C₃₇×#6891	3
#10624911	37

Subgroups — C37×#10624911 #41004700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624911 #41004700