Subgroups — C₂₃⋊#11925895 #42123721

Order 27830.

52 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	C₁₁×D₂₅₃	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	1	no	maximal
5	D₂₃×C₁₁⋊C₅	—	11	1	no	maximal
6	C₂₃×C₁₁⋊C₅	—	11	1	no	—
7	C₂₃×C₁₁⋊C₅	—	11	1	no	—
8	C₂₃×C₁₁⋊C₅	—	22	5	no	—
9	#11925895	—	23	1	no	maximal, Hall
10	#10597243	D₂₃	1	1	yes	characteristic, complemented, Hall
11	D₂₅₃	C₁₁⋊C₅	1	1	yes	characteristic, complemented
12	C₁₁×D₂₃	—	55	1	no	—
13	C₁₁×C₂₃	—	2	5	no	—
14	C₁₁×C₂₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
15	C₁₁×C₂₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
16	C₁₁×D₁₁	—	23	1	no	Hall
17	C₅×D₂₃	—	121	1	no	Hall
18	C₁₁²	C₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
19	C₅×C₂₃	—	121	1	no	Hall
20	C₂×C₁₁⋊C₅	—	253	1	no	—
21	AGL(1,𝔽₁₁)	—	253	1	no	—
22	C₁₁⋊C₅	—	11	1	no	—
23	C₁₁⋊C₅	—	11	1	no	—
24	C₁₁⋊C₅	—	22	5	no	—
25	D₂₃	—	55	1	no	Hall
26	C₂₃	#11925895	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	—	1265	1	no	—
28	D₁₁	—	23	1	no	—
29	C₁₁	—	2	5	no	—
30	C₁₁	D₂₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
31	C₁₁	C₂₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
32	C₂×C₅	—	2783	1	no	Hall
33	C₅	—	121	1	no	Sylow
34	C₂	—	1265	1	no	Sylow

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