Subgroups — C₃₇×#10624706 #41004495

Order 26973.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₂₇⋊C₃	C₃	1	3	yes	maximal
2	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃₇×C₉⋊C₂₇	C₃	1	9	yes	maximal, complemented
4	C₃²×C₉×C₃₇	C₉	1	3	yes	—
5	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
6	C₃₇×C₂₇⋊C₃	—	3	9	no	—
7	C₃×C₂₇×C₃₇	C₃²	1	9	yes	—
8	C₉²×C₃₇	C₉	1	2	yes	—
9	C₉²×C₃₇	C₉	1	3	yes	—
10	C₉²×C₃₇	C₉	1	1	yes	characteristic
11	C₉²×C₃₇	C₃²	1	3	yes	—
12	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
13	C₃×C₉×C₃₇	—	3	9	no	—
14	C₃×C₉×C₃₇	C₃×C₉	1	6	yes	—
15	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
18	C₃×C₉×C₃₇	3₋¹⁺²	1	9	yes	—
19	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
20	C₂₇×C₃₇	—	3	9	no	—
21	#10624706	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₃²×C₃₇	—	3	3	no	—
23	C₃²×C₃₇	C₉⋊C₉	1	3	yes	—
24	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
25	C₉×C₃₇	—	3	6	no	—
26	C₉×C₃₇	C₉⋊C₉	1	3	yes	—
27	C₉×C₃₇	C₉⋊C₉	1	3	yes	—
28	C₉×C₃₇	C₂₇⋊C₃	1	9	yes	complemented
29	C₉×C₃₇	C₃×3₋¹⁺²	1	3	yes	—
30	C₃×C₂₇⋊C₃	C₃×C₃₇	1	3	yes	—
31	C₃×C₉²	C₃×C₃₇	1	1	yes	characteristic
32	C₉⋊C₂₇	C₃×C₃₇	1	9	yes	complemented
33	C₃×C₃₇	—	3	3	no	—
34	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
35	C₃×C₃₇	C₃×C₂₇⋊C₃	1	3	yes	—
36	C₃²×C₉	C₉×C₃₇	1	3	yes	—
37	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
38	C₂₇⋊C₃	—	3	9	no	—
39	C₃×C₂₇	C₃²×C₃₇	1	9	yes	—
40	C₉²	C₉×C₃₇	1	2	yes	—
41	C₉²	C₉×C₃₇	1	3	yes	—
42	C₉²	C₉×C₃₇	1	1	yes	characteristic
43	C₉²	C₃²×C₃₇	1	3	yes	—
44	C₃₇	#10624706	1	1	yes	characteristic, direct product factor, Sylow
45	C₃³	C₃×C₉×C₃₇	1	1	yes	characteristic
46	C₃×C₉	—	3	9	no	—
47	C₃×C₉	C₃×C₉×C₃₇	1	6	yes	—
48	C₃×C₉	C₃×C₉×C₃₇	1	1	yes	characteristic
49	C₃×C₉	C₃×C₉×C₃₇	1	1	yes	characteristic
50	C₃×C₉	C₃×C₉×C₃₇	1	3	yes	—
51	C₃×C₉	3₋¹⁺²×C₃₇	1	9	yes	—
52	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
53	C₂₇	—	3	9	no	—
54	C₃²	—	3	3	no	—
55	C₃²	C₃₇×C₉⋊C₉	1	3	yes	—
56	C₃²	C₃²×C₉×C₃₇	1	1	yes	characteristic
57	C₉	—	3	6	no	—
58	C₉	C₃₇×C₉⋊C₉	1	3	yes	—
59	C₉	C₃₇×C₉⋊C₉	1	3	yes	—
60	C₉	C₃₇×C₂₇⋊C₃	1	9	yes	complemented
61	C₉	C₃×3₋¹⁺²×C₃₇	1	3	yes	—
62	C₃	—	3	3	no	—
63	C₃	C₃×C₃₇×C₉⋊C₉	1	1	yes	characteristic
64	C₃	C₃×C₃₇×C₂₇⋊C₃	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
3. C₃₇×C₉⋊C₂₇	C₃	semidirect
21. #10624706	C₃₇	direct (N × H)
28. C₉×C₃₇	C₂₇⋊C₃	semidirect
32. C₉⋊C₂₇	C₃×C₃₇	semidirect
44. C₃₇	#10624706	direct (N × H)
60. C₉	C₃₇×C₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃₇×C₂₇⋊C₃	3
C₃×C₉²×C₃₇	3
C₃₇×C₉⋊C₂₇	3
#10624706	37

Subgroups — C37×#10624706 #41004495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624706 #41004495