Subgroups — C₉×D₁₂₄₃ #36375408

Order 22374.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₁×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₂₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₁×C₁₁₃	C₂×C₃	1	1	yes	characteristic
4	D₁₂₄₃	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₉×D₁₁₃	—	11	1	no	maximal, Hall
6	C₁₁×C₁₁₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₁₁₃	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₃×D₁₁₃	—	11	1	no	—
9	C₃×C₁₁₃	C₃×D₁₁	1	1	yes	characteristic
10	D₁₁₃	—	11	1	no	Hall
11	C₉×D₁₁	—	113	1	no	maximal, Hall
12	C₁₁₃	C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
13	C₉×C₁₁	D₁₁₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₁₁	—	113	1	no	—
15	C₃×C₁₁	C₃×D₁₁₃	1	1	yes	characteristic
16	D₁₁	—	113	1	no	Hall
17	C₂×C₉	—	1243	1	no	Hall
18	C₁₁	C₉×D₁₁₃	1	1	yes	characteristic, complemented, Sylow
19	C₉	D₁₂₄₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	1243	1	no	—
21	C₃	C₃×D₁₂₄₃	1	1	yes	characteristic
22	C₂	—	1243	1	no	Sylow

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.