Subgroups — C₂₇×C₃⋊D₉ #13090855

Order 1458.

161 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⋊D₃×C₂₇	—	3	1	no	maximal
3	C₉×C₃⋊D₉	C₃	1	1	yes	maximal, characteristic
4	D₉×C₂₇	—	3	3	no	maximal
5	C₃²×C₂₇	—	2	1	no	—
6	C₃²×C₂₇	D₃	1	1	yes	characteristic
7	C₃×C₉²	C₂×C₃	1	1	yes	characteristic
8	C₉×C₂₇	—	2	3	no	—
9	C₉×C₂₇	D₃	1	3	yes	complemented
10	C₉×C₃⋊D₃	—	3	1	no	—
11	C₃×C₃⋊D₉	C₉	1	1	yes	characteristic
12	D₃×C₂₇	—	9	3	no	—
13	D₃×C₂₇	—	9	1	no	—
14	C₉×D₉	—	3	3	no	—
15	C₃²×C₉	—	2	1	no	—
16	C₃²×C₉	C₂×C₉	1	1	yes	characteristic
17	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
18	C₃×C₂₇	—	2	9	no	—
19	C₃×C₂₇	—	2	3	no	—
20	C₃×C₂₇	—	2	1	no	—
21	C₃×C₂₇	—	2	3	no	—
22	C₃×C₂₇	D₉	1	3	yes	complemented
23	C₃×C₂₇	C₃⋊D₃	1	1	yes	characteristic
24	C₉²	—	2	3	no	—
25	C₉²	C₃×D₃	1	3	yes	—
26	C₃×C₃⋊D₃	—	3	1	no	—
27	C₃⋊D₉	C₂₇	1	1	yes	characteristic, direct product factor
28	D₃×C₉	—	9	3	no	—
29	D₃×C₉	—	9	1	no	—
30	C₃×D₉	—	3	3	no	—
31	C₂×C₂₇	—	27	1	no	—
32	C₃³	D₃×C₉	1	1	yes	characteristic
33	C₃×C₉	—	2	9	no	—
34	C₃×C₉	—	2	3	no	—
35	C₃×C₉	—	2	1	no	—
36	C₃×C₉	—	2	1	no	—
37	C₃×C₉	—	2	3	no	—
38	C₃×C₉	—	2	3	no	—
39	C₃×C₉	C₂×C₂₇	1	1	yes	characteristic, complemented
40	C₃×C₉	C₃×D₉	1	3	yes	—
41	C₃×C₉	D₃×C₉	1	3	yes	—
42	C₃×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
43	C₂₇	—	2	9	no	—
44	C₂₇	—	2	3	no	—
45	C₂₇	—	2	1	no	—
46	C₂₇	C₃⋊D₉	1	1	yes	characteristic, direct product factor
47	C₃⋊D₃	—	3	1	no	—
48	C₃×D₃	—	9	3	no	—
49	C₃×D₃	—	9	1	no	—
50	C₂×C₉	—	27	1	no	—
51	D₉	—	3	3	no	—
52	C₃²	—	2	3	no	—
53	C₃²	—	2	1	no	—
54	C₃²	C₉×D₉	1	3	yes	—
55	C₃²	D₃×C₂₇	1	1	yes	characteristic
56	C₃²	C₉×C₃⋊D₃	1	1	yes	characteristic
57	C₉	—	2	9	no	—
58	C₉	—	2	1	no	—
59	C₉	—	2	3	no	—
60	C₉	—	2	3	no	—
61	C₉	D₃×C₂₇	1	3	yes	complemented
62	C₉	C₃×C₃⋊D₉	1	1	yes	characteristic
63	C₂×C₃	—	27	1	no	—
64	D₃	—	9	3	no	—
65	D₃	—	9	1	no	—
66	C₃	—	2	1	no	—
67	C₃	—	2	3	no	—
68	C₃	D₉×C₂₇	1	3	yes	complemented
69	C₃	C₉×C₃⋊D₉	1	1	yes	characteristic
70	C₃	C₃⋊D₃×C₂₇	1	1	yes	characteristic
71	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₇	C₃⋊D₉
commutator, hypocenter	C₃×C₉	C₂×C₂₇
Frattini	C₃×C₉	C₃×C₃⋊D₃
Fitting	C₃×C₉×C₂₇	C₂
socle	C₃³	D₃×C₉
prime radical	C₃×C₃⋊D₉	C₉
cosocle	C₃×C₉²	C₂×C₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₂₇	C₂	semidirect
9. C₉×C₂₇	D₃	semidirect
22. C₃×C₂₇	D₉	semidirect
27. C₃⋊D₉	C₂₇	direct (N × H)
39. C₃×C₉	C₂×C₂₇	semidirect
46. C₂₇	C₃⋊D₉	direct (N × H)
61. C₉	D₃×C₂₇	semidirect
68. C₃	D₉×C₂₇	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⋊D₃×C₂₇	3
C₉×C₃⋊D₉	3
D₉×C₂₇	3

Subgroups — C27×C3⋊D9 #13090855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₇×C₃⋊D₉ #13090855