Subgroups — C₂₃⋊#11759817 #37552233

Order 23322.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#92788	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₉₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂₃⋊(D₁₃⋊C₃)	—	13	1	no	maximal
5	C₁₃⋊C₃×D₂₃	—	13	1	no	maximal
6	#11759817	—	23	1	no	maximal, Hall
7	C₂₃×C₁₃⋊C₃	—	13	1	no	—
8	C₂₃×C₁₃⋊C₃	—	13	1	no	—
9	C₂₃×C₁₃⋊C₃	—	26	6	no	—
10	D₂₉₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
11	C₁₃×D₂₃	—	39	1	no	—
12	#92788	D₂₃	1	1	yes	characteristic, complemented, Hall
13	C₁₃×D₁₃	—	23	1	no	Hall
14	C₁₃×C₂₃	—	2	6	no	—
15	C₁₃×C₂₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₁₃×C₂₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
17	C₁₃²	C₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₂₃	—	169	1	no	Hall
19	C₂×C₁₃⋊C₃	—	299	1	no	—
20	D₁₃⋊C₃	—	299	1	no	—
21	C₃×C₂₃	—	169	1	no	Hall
22	D₂₃	—	39	1	no	Hall
23	C₁₃⋊C₃	—	13	1	no	—
24	C₁₃⋊C₃	—	13	1	no	—
25	C₁₃⋊C₃	—	26	6	no	—
26	C₂×C₁₃	—	897	1	no	—
27	D₁₃	—	23	1	no	—
28	C₂₃	#11759817	1	1	yes	characteristic, complemented, Sylow
29	C₁₃	—	2	6	no	—
30	C₁₃	C₁₃⋊C₃×D₂₃	1	1	yes	characteristic, complemented
31	C₁₃	C₂₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
32	C₂×C₃	—	3887	1	no	Hall
33	C₃	—	169	1	no	Sylow
34	C₂	—	897	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²×C₂₃	C₂×C₃
LCS	G ▷ C₁₃²×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.