Subgroups — D₂₂₂₃ #17984635

Order 4446.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇₄₁	—	3	1	no	maximal
3	C₃×C₁₃×C₁₉	D₃	1	1	yes	characteristic
4	D₂₄₇	—	9	1	no	Hall
5	D₁₇₁	—	13	1	no	maximal, Hall
6	C₁₃×C₁₉	D₉	1	1	yes	characteristic, complemented, Hall
7	D₁₁₇	—	19	1	no	maximal, Hall
8	C₉×C₁₉	D₁₃	1	1	yes	characteristic, complemented, Hall
9	C₉×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
10	D₅₇	—	39	1	no	—
11	D₃₉	—	57	1	no	—
12	C₃×C₁₉	D₃₉	1	1	yes	characteristic
13	C₃×C₁₃	D₅₇	1	1	yes	characteristic
14	D₁₉	—	117	1	no	Hall
15	D₁₃	—	171	1	no	Hall
16	C₁₉	D₁₁₇	1	1	yes	characteristic, complemented, Sylow
17	D₉	—	247	1	no	Hall
18	C₁₃	D₁₇₁	1	1	yes	characteristic, complemented, Sylow
19	C₉	D₂₄₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	741	1	no	—
21	C₃	D₇₄₁	1	1	yes	characteristic
22	C₂	—	2223	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃×C₁₉	C₂
Frattini	C₃	D₇₄₁
socle	C₃×C₁₃×C₁₉	D₃
LCS	G ▷ C₉×C₁₃×C₁₉
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.