Subgroups — C₃⋊(C₉⋊D₂₇) #13090859

Order 1458.

404 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(C₃⋊D₂₇)	—	3	3	no	maximal
3	C₃⋊(C₉⋊D₉)	—	3	1	no	maximal
4	C₉⋊D₂₇	—	3	9	no	maximal
5	C₃²×C₂₇	D₃	1	3	yes	—
6	C₃×C₉²	D₃	1	1	yes	characteristic
7	C₉×C₂₇	D₃	1	9	yes	complemented
8	C₃⋊(C₃⋊D₉)	—	9	3	no	—
9	C₃⋊(C₃⋊D₉)	—	9	1	no	—
10	C₃⋊D₂₇	—	9	27	no	—
11	C₃⋊D₂₇	—	9	9	no	—
12	C₉⋊D₉	—	9	6	no	—
13	C₉⋊D₉	—	9	3	no	—
14	C₃²×C₉	D₉	1	3	yes	—
15	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
16	C₃×C₂₇	D₉	1	27	yes	complemented
17	C₃×C₂₇	C₃⋊D₃	1	9	yes	—
18	C₉²	D₉	1	6	yes	—
19	C₉²	C₃⋊D₃	1	3	yes	—
20	C₃⋊(C₃⋊D₃)	—	27	1	no	—
21	C₃⋊D₉	—	27	27	no	—
22	C₃⋊D₉	—	27	2	no	—
23	C₃⋊D₉	—	27	9	no	—
24	C₃⋊D₉	—	27	9	no	—
25	C₃⋊D₉	—	27	1	no	—
26	D₂₇	—	27	27	no	—
27	C₃³	C₃⋊D₉	1	1	yes	characteristic
28	C₃×C₉	D₂₇	1	27	yes	complemented
29	C₃×C₉	C₃⋊D₉	1	2	yes	—
30	C₃×C₉	C₃⋊D₉	1	9	yes	—
31	C₃×C₉	C₃⋊D₉	1	9	yes	—
32	C₃×C₉	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
33	C₂₇	C₃⋊D₉	1	27	yes	complemented
34	C₃⋊D₃	—	81	3	no	—
35	C₃⋊D₃	—	81	9	no	—
36	C₃⋊D₃	—	81	1	no	—
37	D₉	—	81	6	no	—
38	D₉	—	81	27	no	—
39	D₉	—	81	3	no	—
40	C₃²	C₉⋊D₉	1	3	yes	—
41	C₃²	C₃⋊D₂₇	1	9	yes	—
42	C₃²	C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
43	C₉	C₉⋊D₉	1	6	yes	—
44	C₉	C₃⋊D₂₇	1	27	yes	complemented
45	C₉	C₃⋊(C₃⋊D₉)	1	3	yes	—
46	D₃	—	243	9	no	—
47	D₃	—	243	1	no	—
48	D₃	—	243	3	no	—
49	C₃	C₉⋊D₂₇	1	9	yes	complemented
50	C₃	C₃⋊(C₉⋊D₉)	1	1	yes	characteristic
51	C₃	C₃⋊(C₃⋊D₂₇)	1	3	yes	—
52	C₂	—	729	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₉×C₂₇	C₂
Frattini	C₃×C₉	C₃⋊(C₃⋊D₃)
socle	C₃³	C₃⋊D₉
LCS	G ▷ C₃×C₉×C₂₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₂₇	C₂	semidirect
7. C₉×C₂₇	D₃	semidirect
16. C₃×C₂₇	D₉	semidirect
28. C₃×C₉	D₂₇	semidirect
33. C₂₇	C₃⋊D₉	semidirect
44. C₉	C₃⋊D₂₇	semidirect
49. C₃	C₉⋊D₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₂₇	2
C₃⋊(C₃⋊D₂₇)	3
C₃⋊(C₉⋊D₉)	3
C₉⋊D₂₇	3

Subgroups — C3⋊(C9⋊D27) #13090859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₉⋊D₂₇) #13090859