Subgroups — C₃₇⋊#10624562 #41005180

Order 26973.

2138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃²⋊(C₃₇⋊C₃)	C₃	1	12	yes	maximal, complemented
2	C₃²×H(3,𝔽₃)×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₃₇⋊C₃	C₃²	1	9	yes	—
4	C₃×C₃²⋊(C₃₇⋊C₃)	—	3	36	no	—
5	C₃×C₃²⋊(C₃₇⋊C₃)	—	3	108	no	—
6	C₃⁴×C₃₇	C₃²	1	4	yes	—
7	C₃×H(3,𝔽₃)×C₃₇	—	3	12	no	—
8	C₃³×C₃₇	—	3	12	no	—
9	C₃³×C₃₇	—	3	36	no	—
10	C₃³×C₃₇	H(3,𝔽₃)	1	12	yes	complemented
11	C₃³×C₃₇	C₃³	1	1	yes	characteristic
12	C₃²×C₃₇⋊C₃	—	3	72	no	—
13	C₃²×C₃₇⋊C₃	—	3	36	no	—
14	C₃²×C₃₇⋊C₃	H(3,𝔽₃)	1	27	yes	complemented
15	H(3,𝔽₃)×C₃₇	—	3	27	no	—
16	C₃²⋊(C₃₇⋊C₃)	—	3	324	no	—
17	#10624562	—	37	1	no	maximal, Sylow
18	C₃²×C₃₇	—	3	36	no	—
19	C₃²×C₃₇	—	3	12	no	—
20	C₃²×C₃₇	—	9	36	no	—
21	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	9	yes	—
22	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	4	yes	—
23	C₃×C₃₇⋊C₃	—	3	108	no	—
24	C₃×C₃₇⋊C₃	—	9	72	no	—
25	C₃×C₃₇⋊C₃	—	9	9	no	—
26	C₃²×H(3,𝔽₃)	—	37	12	no	—
27	C₃²×H(3,𝔽₃)	C₃₇⋊C₃	1	1	yes	characteristic, complemented
28	C₃×C₃₇	—	9	12	no	—
29	C₃×C₃₇	C₃²⋊H(3,𝔽₃)	1	12	yes	—
30	C₃×C₃₇	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
31	C₃₇⋊C₃	—	9	27	no	—
32	C₃⁴	—	37	9	no	—
33	C₃⁴	C₃×C₃₇⋊C₃	1	4	yes	—
34	C₃×H(3,𝔽₃)	—	3	12	no	—
35	C₃×H(3,𝔽₃)	—	111	108	no	—
36	C₃×H(3,𝔽₃)	—	111	36	no	—
37	C₃₇	#10624562	1	1	yes	characteristic, complemented, Sylow
38	C₃³	—	3	36	no	—
39	C₃³	—	3	12	no	—
40	C₃³	—	37	27	no	—
41	C₃³	—	111	72	no	—
42	C₃³	—	111	36	no	—
43	C₃³	C₃²⋊(C₃₇⋊C₃)	1	12	yes	complemented
44	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
45	H(3,𝔽₃)	—	3	27	no	—
46	H(3,𝔽₃)	—	111	324	no	—
47	C₃²	—	3	36	no	—
48	C₃²	—	3	12	no	—
49	C₃²	—	9	36	no	—
50	C₃²	—	333	72	no	—
51	C₃²	—	333	9	no	—
52	C₃²	—	111	108	no	—
53	C₃²	H(3,𝔽₃)×C₃₇⋊C₃	1	9	yes	—
54	C₃²	C₃×C₃²⋊(C₃₇⋊C₃)	1	4	yes	—
55	C₃	—	9	12	no	—
56	C₃	—	333	27	no	—
57	C₃	(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	1	12	yes	—
58	C₃	#22582550	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₇⋊C₃
commutator, socle, cosocle	C₃³×C₃₇	C₃³
Fitting	C₃²×H(3,𝔽₃)×C₃₇	C₃
hypercenter	C₃²×H(3,𝔽₃)	C₃₇⋊C₃
hypocenter	C₃₇	#10624562
LCS	G ▷ C₃³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃²⋊(C₃₇⋊C₃)	C₃	semidirect
2. C₃²×H(3,𝔽₃)×C₃₇	C₃	semidirect
10. C₃³×C₃₇	H(3,𝔽₃)	semidirect
14. C₃²×C₃₇⋊C₃	H(3,𝔽₃)	semidirect
27. C₃²×H(3,𝔽₃)	C₃₇⋊C₃	semidirect
37. C₃₇	#10624562	semidirect
43. C₃³	C₃²⋊(C₃₇⋊C₃)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₃²⋊(C₃₇⋊C₃)	3
C₃²×H(3,𝔽₃)×C₃₇	3
#10624562	37

Subgroups — C37⋊#10624562 #41005180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇⋊#10624562 #41005180