Subgroups — C₂₃⋊#11759813 #37552221

Order 23322.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#92789	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₉₉	—	3	1	no	maximal, Hall
3	C₁₃²×C₂₃	D₃	1	1	yes	characteristic, complemented, Hall
4	#11759813	—	23	1	no	maximal, Hall
5	C₂₃×C₁₃⋊C₃	—	26	1	no	—
6	D₂₉₉	—	3	1	no	—
7	C₁₃×D₂₃	—	39	1	no	—
8	#92789	D₂₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×D₁₃	—	69	1	no	Hall
10	C₁₃×C₂₃	—	2	1	no	—
11	C₁₃×C₂₃	—	6	1	no	—
12	C₁₃×C₂₃	—	6	1	no	—
13	C₁₃×C₂₃	—	6	1	no	—
14	C₁₃²	D₆₉	1	1	yes	characteristic, complemented, Sylow
15	D₆₉	—	169	1	no	maximal, Hall
16	C₃×C₂₃	—	169	1	no	Hall
17	D₂₃	—	39	1	no	Hall
18	C₁₃⋊C₃	—	26	1	no	—
19	C₂×C₁₃	—	897	1	no	—
20	D₁₃	—	69	1	no	—
21	C₂₃	#11759813	1	1	yes	characteristic, complemented, Sylow
22	C₁₃	—	2	1	no	—
23	C₁₃	—	3	1	no	—
24	C₁₃	—	6	1	no	—
25	C₁₃	—	6	1	no	—
26	D₃	—	3887	1	no	Hall
27	C₃	—	338	1	no	Sylow
28	C₂	—	897	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂₃×#92789	C₂
Fitting, socle	C₁₃²×C₂₃	D₃
LCS	G ▷ C₂₃×#92789
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.