Subgroups — C₃×C₃₇×C₉⋊C₂₇ #41004494

Order 26973.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₃²×C₉×C₃₇	C₃²
commutator	C₃	C₃²×C₂₇×C₃₇
Frattini, cosocle	C₃×C₉	C₃³×C₃₇
socle, prime radical	C₃³×C₃₇	C₃×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×C₉⋊C₂₇	C₃	direct (N × H)
13. C₃×C₉×C₃₇	C₂₇	semidirect
20. C₃×C₉⋊C₂₇	C₃₇	direct (N × H)
27. C₉×C₃₇	C₃×C₂₇	semidirect
31. C₉⋊C₂₇	C₃×C₃₇	direct (N × H)
32. C₃×C₃₇	C₉⋊C₂₇	direct (N × H)
43. C₃₇	C₃×C₉⋊C₂₇	direct (N × H)
46. C₃×C₉	C₂₇×C₃₇	semidirect
59. C₉	C₃×C₂₇×C₃₇	semidirect
61. C₃	C₃₇×C₉⋊C₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₇×C₃₇	3
C₃×C₉²×C₃₇	3
C₃₇×C₉⋊C₂₇	3
C₃×C₉⋊C₂₇	37

Subgroups — C3×C37×C9⋊C27 #41004494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₇×C₉⋊C₂₇ #41004494