Subgroups — Dic₃×C₂₃×C₈₉ #37589553

Order 24564.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₃×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×C₈₉	—	3	1	no	maximal, Hall
3	C₃×C₂₃×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₃×C₈₉	D₃	1	1	yes	characteristic
5	C₂₃×C₈₉	Dic₃	1	1	yes	characteristic, direct product factor, Hall
6	Dic₃×C₈₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₈₉	C₂×C₂₃	1	1	yes	characteristic
8	C₄×C₈₉	—	3	1	no	Hall
9	Dic₃×C₂₃	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₈₉	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₈₉	D₃×C₂₃	1	1	yes	characteristic
12	C₂×C₃×C₂₃	C₂×C₈₉	1	1	yes	characteristic
13	C₄×C₂₃	—	3	1	no	Hall
14	C₈₉	Dic₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₂₃	C₄×C₈₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₂₃	D₃×C₈₉	1	1	yes	characteristic
17	C₂₃	Dic₃×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₃	C₂₃×C₈₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₂₃×C₈₉	1	1	yes	characteristic
20	C₄	—	3	1	no	Sylow
21	C₃	C₄×C₂₃×C₈₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×C₂₃×C₈₉	1	1	yes	characteristic

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.