Subgroups — C₃⋊((C₈₂₃⋊C₃)⋊C₄) #44444209

Order 29628.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈₂₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₄₆₉	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₈₂₃⋊C₃)⋊C₄	—	3	1	no	maximal
4	C₃×C₈₂₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₈₂₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₈₂₃⋊C₃	—	2	1	no	—
7	C₂×C₈₂₃⋊C₃	D₃	1	1	yes	characteristic
8	Dic₈₂₃	—	3	1	no	Hall
9	C₃×C₈₂₃	C₃×C₄	1	1	yes	characteristic, complemented
10	C₈₂₃⋊C₃	—	2	1	no	—
11	C₈₂₃⋊C₃	Dic₃	1	1	yes	characteristic, complemented
12	C₂×C₈₂₃	C₃×D₃	1	1	yes	characteristic
13	C₈₂₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
14	C₃×Dic₃	—	823	1	no	maximal, Hall
15	C₂×C₃²	—	1646	1	no	—
16	C₃×C₄	—	2469	1	no	—
17	Dic₃	—	823	1	no	—
18	C₃²	—	1646	1	no	Sylow
19	C₂×C₃	—	1646	1	no	—
20	C₂×C₃	—	1646	1	no	—
21	C₂×C₃	D₈₂₃⋊C₃	1	1	yes	characteristic
22	C₄	—	2469	1	no	Sylow
23	C₃	—	1646	1	no	—
24	C₃	—	1646	1	no	—
25	C₃	(C₈₂₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
26	C₂	C₃⋊(D₈₂₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(D₈₂₃⋊C₃)
commutator, hypocenter	C₃×C₈₂₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₈₂₃	C₂×C₃
prime radical	C₂×C₃×C₈₂₃⋊C₃	C₂
LCS	G ▷ C₃×C₈₂₃
UCS	C₁ ◁ C₂

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.