Subgroups — C₃₇×#10624712 #41004501

Order 26973.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic
2	C₃₇×C₉⋊C₂₇	C₃	1	6	yes	maximal, complemented
3	C₃₇×C₃²⋊C₂₇	C₃	1	3	yes	maximal
4	C₃₇×#6864	C₃	1	2	yes	maximal, complemented
5	C₉×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
7	C₃×C₂₇×C₃₇	C₃²	1	3	yes	—
8	C₃×C₂₇×C₃₇	C₃²	1	6	yes	—
9	C₃₇×C₉⋊C₉	C₉	1	6	yes	—
10	C₃₇×C₃²⋊C₉	C₉	1	3	yes	—
11	C₉²×C₃₇	C₃²	1	1	yes	characteristic
12	C₉²×C₃₇	C₃²	1	2	yes	—
13	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₃₇	—	3	3	no	—
15	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
16	C₃×C₉×C₃₇	C₃×C₉	1	6	yes	—
17	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
18	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
19	C₂₇×C₃₇	—	3	3	no	—
20	C₂₇×C₃₇	—	3	6	no	—
21	#10624712	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₃²×C₃₇	—	3	1	no	—
23	C₃²×C₃₇	—	3	3	no	—
24	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
25	C₉×C₃₇	—	3	2	no	—
26	C₉×C₃₇	—	3	3	no	—
27	C₉×C₃₇	—	3	6	no	—
28	C₉×C₃₇	#737	1	3	yes	—
29	#6887	C₃×C₃₇	1	1	yes	characteristic
30	C₉⋊C₂₇	C₃×C₃₇	1	6	yes	complemented
31	C₃²⋊C₂₇	C₃×C₃₇	1	3	yes	—
32	#6864	C₃×C₃₇	1	2	yes	complemented
33	C₉×C₂₇	C₃×C₃₇	1	1	yes	characteristic, complemented
34	C₃×C₃₇	—	9	1	no	—
35	C₃×C₃₇	#6887	1	1	yes	characteristic
36	C₃×C₃₇	#6903	1	3	yes	—
37	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
38	C₃×C₂₇	C₃²×C₃₇	1	3	yes	—
39	C₃×C₂₇	C₃²×C₃₇	1	6	yes	—
40	C₉⋊C₉	C₉×C₃₇	1	6	yes	—
41	C₃²⋊C₉	C₉×C₃₇	1	3	yes	—
42	C₉²	C₃²×C₃₇	1	1	yes	characteristic
43	C₉²	C₃²×C₃₇	1	2	yes	—
44	C₃₇	#10624712	1	1	yes	characteristic, direct product factor, Sylow
45	C₃³	C₃×C₉×C₃₇	1	1	yes	characteristic
46	C₃×C₉	—	3	3	no	—
47	C₃×C₉	C₃×C₉×C₃₇	1	3	yes	—
48	C₃×C₉	C₃×C₉×C₃₇	1	6	yes	—
49	C₃×C₉	C₃×C₉×C₃₇	1	2	yes	—
50	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
51	C₂₇	—	3	3	no	—
52	C₂₇	—	3	6	no	—
53	C₃²	—	3	1	no	—
54	C₃²	—	3	3	no	—
55	C₃²	C₃²×C₉×C₃₇	1	1	yes	characteristic
56	C₉	—	3	2	no	—
57	C₉	—	3	3	no	—
58	C₉	—	3	6	no	—
59	C₉	C₃₇×#737	1	3	yes	—
60	C₃	—	9	1	no	—
61	C₃	C₃₇×#6887	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
2. C₃₇×C₉⋊C₂₇	C₃	semidirect
4. C₃₇×#6864	C₃	semidirect
5. C₉×C₂₇×C₃₇	C₃	semidirect
21. #10624712	C₃₇	direct (N × H)
30. C₉⋊C₂₇	C₃×C₃₇	semidirect
32. #6864	C₃×C₃₇	semidirect
33. C₉×C₂₇	C₃×C₃₇	semidirect
44. C₃₇	#10624712	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×#6887	3
C₃₇×C₉⋊C₂₇	3
C₃₇×C₃²⋊C₂₇	3
C₃₇×#6864	3
C₉×C₂₇×C₃₇	3
#10624712	37

Subgroups — C37×#10624712 #41004501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624712 #41004501