Subgroups — C₃₇×#10624553 #41004342

Order 26973.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₉⋊C₉	C₃	1	3	yes	maximal
2	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃₇×#6855	C₃	1	9	yes	maximal
4	C₃²×C₉×C₃₇	C₃²	1	9	yes	—
5	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
6	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
7	C₃₇×C₉⋊C₉	—	3	9	no	—
8	C₉²×C₃₇	C₉	1	9	yes	complemented
9	C₃³×C₃₇	C₃³	1	1	yes	characteristic
10	C₃×C₉×C₃₇	—	3	9	no	—
11	C₃×C₉×C₃₇	—	3	9	no	—
12	C₃×C₉×C₃₇	—	3	27	no	—
13	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
14	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
15	C₃×C₉×C₃₇	3₋¹⁺²	1	9	yes	—
16	#10624553	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
18	C₃²×C₃₇	C₃×3₋¹⁺²	1	3	yes	—
19	C₃²×C₃₇	#737	1	9	yes	—
20	C₉×C₃₇	—	3	9	no	—
21	C₉×C₃₇	—	9	9	no	—
22	C₉×C₃₇	C₉⋊C₉	1	9	yes	—
23	C₃×C₉⋊C₉	C₃×C₃₇	1	3	yes	—
24	C₃×C₉²	C₃×C₃₇	1	1	yes	characteristic
25	#6855	C₃×C₃₇	1	9	yes	—
26	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
27	C₃×C₃₇	#6887	1	3	yes	—
28	C₃×C₃₇	#6899	1	9	yes	—
29	C₃²×C₉	C₃²×C₃₇	1	9	yes	—
30	C₃²×C₉	C₃²×C₃₇	1	3	yes	—
31	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
32	C₉⋊C₉	—	3	9	no	—
33	C₉²	C₉×C₃₇	1	9	yes	complemented
34	C₃₇	#10624553	1	1	yes	characteristic, direct product factor, Sylow
35	C₃³	C₃³×C₃₇	1	1	yes	characteristic
36	C₃×C₉	—	3	9	no	—
37	C₃×C₉	—	3	9	no	—
38	C₃×C₉	—	3	27	no	—
39	C₃×C₉	C₃×C₉×C₃₇	1	9	yes	—
40	C₃×C₉	C₃×C₉×C₃₇	1	3	yes	—
41	C₃×C₉	3₋¹⁺²×C₃₇	1	9	yes	—
42	C₃²	C₃²×C₉×C₃₇	1	1	yes	characteristic
43	C₃²	C₃×3₋¹⁺²×C₃₇	1	3	yes	—
44	C₃²	C₃₇×#737	1	9	yes	—
45	C₉	—	3	9	no	—
46	C₉	—	9	9	no	—
47	C₉	C₃₇×C₉⋊C₉	1	9	yes	—
48	C₃	C₃×C₃₇×C₉⋊C₉	1	1	yes	characteristic
49	C₃	C₃₇×#6887	1	3	yes	—
50	C₃	C₃₇×#6899	1	9	yes	—

	subgroup	G/H
center, socle, prime radical	C₃³×C₃₇	C₃³
commutator	C₃²	C₃²×C₉×C₃₇
Frattini, cosocle	C₃³	C₃³×C₃₇
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₉²×C₃₇	C₉	semidirect
16. #10624553	C₃₇	direct (N × H)
33. C₉²	C₉×C₃₇	semidirect
34. C₃₇	#10624553	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃₇×C₉⋊C₉	3
C₃×C₉²×C₃₇	3
C₃₇×#6855	3
#10624553	37

Subgroups — C37×#10624553 #41004342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624553 #41004342