Subgroups — C₂²×C₃×C₈₂₃⋊C₃ #44444232

Order 29628.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈₂₃⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₈₂₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂²×C₃×C₈₂₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₈₂₃⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₈₂₃	C₂×C₃	1	3	yes	complemented
6	C₂×C₈₂₃⋊C₃	C₂×C₃	1	9	yes	direct product factor
7	C₂²×C₈₂₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₈₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
9	C₈₂₃⋊C₃	C₂²×C₃	1	3	yes	direct product factor
10	C₂×C₈₂₃	C₂×C₃²	1	3	yes	complemented
11	C₈₂₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₃²	—	823	1	no	maximal, Hall
13	C₂×C₃²	—	823	3	no	—
14	C₂²×C₃	—	823	3	no	—
15	C₂²×C₃	C₈₂₃⋊C₃	1	1	yes	characteristic, direct product factor
16	C₃²	—	823	1	no	Sylow
17	C₂×C₃	—	823	9	no	—
18	C₂×C₃	C₂×C₈₂₃⋊C₃	1	3	yes	direct product factor
19	C₂²	C₃×C₈₂₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₃	—	823	3	no	—
21	C₃	C₂²×C₈₂₃⋊C₃	1	1	yes	characteristic, direct product factor
22	C₂	C₂×C₃×C₈₂₃⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₈₂₃⋊C₃
commutator, cosocle, hypocenter	C₈₂₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₈₂₃	C₃
LCS	G ▷ C₈₂₃
UCS	C₁ ◁ C₂²×C₃

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.