Subgroups — C₂²×D₂₄₃ #14515708

Order 1944.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₄₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₈₁	—	3	1	no	maximal
4	C₂×C₂₄₃	C₂²	1	3	yes	complemented
5	D₂₄₃	C₂²	1	4	yes	direct product factor
6	C₂²×C₈₁	D₃	1	1	yes	characteristic
7	C₂×D₈₁	—	3	6	no	—
8	C₂₄₃	C₂³	1	1	yes	characteristic, complemented, Sylow
9	C₂²×D₂₇	—	9	1	no	—
10	C₂×C₈₁	C₂×D₃	1	3	yes	—
11	D₈₁	—	3	4	no	—
12	C₂²×C₂₇	D₉	1	1	yes	characteristic
13	C₂×D₂₇	—	9	6	no	—
14	C₈₁	C₂²×D₃	1	1	yes	characteristic
15	C₂²×D₉	—	27	1	no	—
16	C₂×C₂₇	C₂×D₉	1	3	yes	—
17	D₂₇	—	9	4	no	—
18	C₂²×C₉	D₂₇	1	1	yes	characteristic
19	C₂×D₉	—	27	6	no	—
20	C₂₇	C₂²×D₉	1	1	yes	characteristic
21	C₂²×D₃	—	81	1	no	—
22	C₂×C₉	C₂×D₂₇	1	3	yes	—
23	D₉	—	27	4	no	—
24	C₂²×C₃	D₈₁	1	1	yes	characteristic
25	C₂×D₃	—	81	6	no	—
26	C₉	C₂²×D₂₇	1	1	yes	characteristic
27	C₂³	—	243	1	no	Sylow
28	C₂×C₃	C₂×D₈₁	1	3	yes	—
29	D₃	—	81	4	no	—
30	C₂²	—	243	6	no	—
31	C₂²	D₂₄₃	1	1	yes	characteristic, direct product factor
32	C₃	C₂²×D₈₁	1	1	yes	characteristic
33	C₂	—	243	4	no	—
34	C₂	C₂×D₂₄₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₂₄₃
commutator, cosocle, hypocenter	C₂₄₃	C₂³
Frattini	C₈₁	C₂²×D₃
Fitting	C₂²×C₂₄₃	C₂
socle	C₂²×C₃	D₈₁
LCS	G ▷ C₂₄₃
UCS	C₁ ◁ C₂²

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.