Subgroups — C₃₇×#10624670 #41004459

Order 26973.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6891	C₃	1	4	yes	maximal
2	C₃₇×#6862	C₃	1	9	yes	maximal, complemented
3	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
4	C₃×3₋¹⁺²×C₃₇	—	3	4	no	—
5	C₃₇×C₃²⋊C₉	—	3	4	no	—
6	C₃₇×C₃²⋊C₉	—	3	4	no	—
7	C₃₇×C₃²⋊C₉	C₃²	1	12	yes	—
8	C₃³×C₃₇	—	9	4	no	—
9	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃³×C₃₇	H(3,𝔽₃)	1	2	yes	—
11	C₃³×C₃₇	C₃³	1	1	yes	characteristic
12	3₋¹⁺²×C₃₇	—	9	12	no	—
13	C₃×C₉×C₃₇	—	3	12	no	—
14	#10624670	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃²×C₃₇	—	3	4	no	—
16	C₃²×C₃₇	—	3	4	no	—
17	C₃²×C₃₇	—	3	4	no	—
18	C₃²×C₃₇	—	3	4	no	—
19	C₃²×C₃₇	—	9	9	no	—
20	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
21	C₉×C₃₇	—	9	12	no	—
22	#6891	C₃×C₃₇	1	4	yes	—
23	#6862	C₃×C₃₇	1	9	yes	complemented
24	C₃×C₃₇	—	9	2	no	—
25	C₃×C₃₇	—	9	1	no	—
26	C₃×C₃₇	—	9	1	no	—
27	C₃×C₃₇	#6910	1	4	yes	—
28	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
29	C₃×3₋¹⁺²	—	3	4	no	—
30	C₃²⋊C₉	—	3	4	no	—
31	C₃²⋊C₉	—	3	4	no	—
32	C₃²⋊C₉	C₃²×C₃₇	1	12	yes	—
33	C₃₇	#10624670	1	1	yes	characteristic, direct product factor, Sylow
34	C₃³	—	9	4	no	—
35	C₃³	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
36	C₃³	H(3,𝔽₃)×C₃₇	1	2	yes	—
37	C₃³	C₃³×C₃₇	1	1	yes	characteristic
38	3₋¹⁺²	—	9	12	no	—
39	C₃×C₉	—	3	12	no	—
40	C₃²	—	3	4	no	—
41	C₃²	—	3	4	no	—
42	C₃²	—	3	4	no	—
43	C₃²	—	3	4	no	—
44	C₃²	—	9	9	no	—
45	C₃²	C₃×H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
46	C₉	—	9	12	no	—
47	C₃	—	9	2	no	—
48	C₃	—	9	1	no	—
49	C₃	—	9	1	no	—
50	C₃	C₃₇×#6910	1	4	yes	—

	subgroup	G/H
center, socle	C₃²×C₃₇	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₃₇
prime radical	C₃⁴×C₃₇	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₃₇ ◁ C₃⁴×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#6862	C₃	semidirect
14. #10624670	C₃₇	direct (N × H)
23. #6862	C₃×C₃₇	semidirect
33. C₃₇	#10624670	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×#6891	3
C₃₇×#6862	3
#10624670	37

Subgroups — C37×#10624670 #41004459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624670 #41004459