Subgroups — C₂₃×#11925892 #42123718

Order 27830.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#10597243	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×C₁₁⋊D₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂₃×AGL(1,𝔽₁₁)	—	11	12	no	maximal
5	C₂₃×C₁₁⋊C₅	—	11	12	no	—
6	#11925892	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	#10597243	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
8	D₁₁×C₂₃	—	11	12	no	—
9	C₁₁×C₂₃	AGL(1,𝔽₁₁)	1	12	yes	complemented
10	C₁₁⋊D₁₁	C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₂₃	—	121	1	no	Hall
12	C₁₁²	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
13	C₅×C₂₃	—	121	1	no	Hall
14	AGL(1,𝔽₁₁)	—	11	12	no	—
15	C₁₁⋊C₅	—	11	12	no	—
16	C₂×C₂₃	—	121	1	no	Hall
17	C₂₃	#11925892	1	1	yes	characteristic, direct product factor, Sylow
18	D₁₁	—	11	12	no	—
19	C₁₁	C₂₃×AGL(1,𝔽₁₁)	1	12	yes	complemented
20	C₂×C₅	—	121	1	no	Hall
21	C₅	—	121	1	no	Sylow
22	C₂	—	121	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	#11925892
commutator, cosocle, hypocenter	C₁₁²	C₂×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₁₁²×C₂₃	C₂×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂₃

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.