Subgroups — #72179441

Order 65274.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃⋊C₃×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃⋊AGL(1,𝔽₂₃)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₃×C₂₃⋊C₁₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂₃⋊(D₄₃⋊C₃)	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂₃×C₄₃⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₄₃⋊C₃	—	23	1	no	maximal, Hall
7	D₉₈₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₃×AGL(1,𝔽₂₃)	—	43	1	no	maximal, Hall
9	C₁₁×C₄₃⋊C₃	—	23	1	no	Hall
10	C₂₃×C₄₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₁₁×D₄₃	—	23	1	no	Hall
12	C₃×C₂₃⋊C₁₁	—	43	1	no	Hall
13	AGL(1,𝔽₂₃)	—	43	1	no	Hall
14	C₁₁×C₄₃	—	23	1	no	Hall
15	D₄₃⋊C₃	—	23	1	no	Hall
16	C₂₃⋊C₁₁	D₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃×D₂₃	—	43	1	no	Hall
18	C₄₃⋊C₃	AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Hall
19	D₄₃	—	23	1	no	Hall
20	C₃×C₂₃	—	43	1	no	Hall
21	C₂×C₃×C₁₁	—	989	1	no	Hall
22	D₂₃	—	43	1	no	Hall
23	C₄₃	C₃×AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₁₁	—	989	1	no	Hall
25	C₂₃	C₁₁×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₁	—	989	1	no	Hall
27	C₁₁	—	23	1	no	Sylow
28	C₂×C₃	—	989	1	no	Hall
29	C₃	—	43	1	no	Sylow
30	C₂	—	989	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₃×C₄₃	C₂×C₃×C₁₁
LCS	G ▷ C₂₃×C₄₃
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.