Subgroups — D₂₄₃⋊C₃ #13090583

Order 1458.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×D₈₁	—	3	1	no	maximal
3	D₂₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₈₁	D₃	1	1	yes	characteristic
5	C₂₄₃	—	2	1	no	—
6	C₂₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₂₇	—	9	1	no	—
8	D₈₁	—	3	1	no	—
9	C₃×C₂₇	D₉	1	1	yes	characteristic
10	C₈₁	—	2	1	no	—
11	C₈₁	C₃×D₃	1	1	yes	characteristic
12	C₃×D₉	—	27	1	no	—
13	D₂₇	—	9	1	no	—
14	C₃×C₉	D₂₇	1	1	yes	characteristic
15	C₂₇	—	2	1	no	—
16	C₂₇	C₃×D₉	1	1	yes	characteristic
17	C₃×D₃	—	81	1	no	—
18	D₉	—	27	1	no	—
19	C₃²	D₈₁	1	1	yes	characteristic
20	C₉	—	2	1	no	—
21	C₉	C₃×D₂₇	1	1	yes	characteristic
22	C₂×C₃	—	243	1	no	—
23	D₃	—	81	1	no	—
24	C₃	—	3	1	no	—
25	C₃	C₃×D₈₁	1	1	yes	characteristic
26	C₂	—	243	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂₄₃	C₂×C₃
Frattini	C₈₁	C₃×D₃
Fitting	C₂₄₃⋊C₃	C₂
socle	C₃	C₃×D₈₁
LCS	G ▷ C₂₄₃
UCS	C₁

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

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