Subgroups — Dic₃×D₂₇ #10619540

Order 648.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₂₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊Dic₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃×D₉	—	3	1	no	maximal
5	C₄×D₂₇	—	3	1	no	maximal
6	C₂×C₃×C₂₇	C₂²	1	1	yes	characteristic
7	C₃×D₂₇	C₄	1	2	yes	complemented
8	C₂×C₃×D₉	—	3	1	no	—
9	C₃⋊Dic₉	—	3	1	no	—
10	C₉×Dic₃	D₃	1	1	yes	characteristic
11	C₂×D₂₇	D₃	1	1	yes	characteristic
12	C₄×C₂₇	—	3	1	no	—
13	Dic₂₇	—	3	1	no	—
14	Dic₂₇	—	6	1	no	—
15	C₃×C₂₇	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	D₃×Dic₃	—	9	1	no	—
17	C₄×D₉	—	9	1	no	—
18	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
19	C₃×D₉	—	3	2	no	—
20	C₂×C₂₇	—	2	1	no	—
21	C₂×C₂₇	C₂×D₃	1	1	yes	characteristic
22	D₂₇	Dic₃	1	2	yes	direct product factor
23	C₂×C₃×D₃	—	9	1	no	—
24	C₃⋊Dic₃	—	9	1	no	—
25	C₃×Dic₃	D₉	1	1	yes	characteristic
26	C₂×D₉	—	3	1	no	—
27	C₄×C₉	—	3	1	no	—
28	Dic₉	—	9	1	no	—
29	Dic₉	—	18	1	no	—
30	C₃×C₉	C₄×D₃	1	1	yes	characteristic
31	C₂₇	—	2	1	no	—
32	C₂₇	C₂×Dic₃	1	1	yes	characteristic, complemented
33	C₂×Dic₃	—	27	1	no	—
34	C₄×D₃	—	27	1	no	—
35	C₂×C₃²	C₂×D₉	1	1	yes	characteristic
36	C₃×D₃	—	9	2	no	—
37	C₂×C₉	—	2	1	no	—
38	C₂×C₉	D₃²	1	1	yes	characteristic
39	D₉	—	3	2	no	—
40	C₂²×C₃	—	27	1	no	—
41	C₂×D₃	—	9	1	no	—
42	C₃×C₄	—	3	1	no	—
43	Dic₃	—	27	1	no	—
44	Dic₃	—	27	1	no	—
45	Dic₃	—	54	1	no	—
46	Dic₃	D₂₇	1	1	yes	characteristic, direct product factor
47	C₃²	C₄×D₉	1	1	yes	characteristic
48	C₉	—	2	1	no	—
49	C₉	D₃×Dic₃	1	1	yes	characteristic
50	C₂×C₄	—	81	1	no	Sylow
51	C₂×C₃	—	2	1	no	—
52	C₂×C₃	—	27	2	no	—
53	C₂×C₃	C₂×D₂₇	1	1	yes	characteristic
54	C₂×C₃	D₃×D₉	1	1	yes	characteristic
55	D₃	—	9	2	no	—
56	C₂²	—	27	1	no	—
57	C₄	—	3	1	no	—
58	C₄	—	81	1	no	—
59	C₃	—	2	1	no	—
60	C₃	C₄×D₂₇	1	1	yes	characteristic, complemented
61	C₃	Dic₃×D₉	1	1	yes	characteristic
62	C₂	—	27	2	no	—
63	C₂	D₃×D₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₃×D₂₇
commutator, hypocenter	C₃×C₂₇	C₂×C₄
Frattini	C₂×C₉	D₃²
Fitting, cosocle	C₂×C₃×C₂₇	C₂²
socle	C₂×C₃²	C₂×D₉
prime radical	C₂×C₃×D₂₇	C₂
LCS	G ▷ C₃×C₂₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊Dic₂₇	C₂	semidirect
3. Dic₃×C₂₇	C₂	semidirect
7. C₃×D₂₇	C₄	semidirect
15. C₃×C₂₇	C₂×C₄	semidirect
22. D₂₇	Dic₃	direct (N × H)
32. C₂₇	C₂×Dic₃	semidirect
46. Dic₃	D₂₇	direct (N × H)
60. C₃	C₄×D₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₂₇	2
C₃⋊Dic₂₇	2
Dic₃×C₂₇	2
Dic₃×D₉	3
C₄×D₂₇	3

Subgroups — Dic3×D27 #10619540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×D₂₇ #10619540