Subgroups — C₂₃×#13049960 #44471908

Order 29946.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#10620252	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×D₂₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₂₃×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂₃×D₃₁⋊C₃	—	7	1	no	maximal, Hall
5	C₂₃×C₃₁⋊C₃	—	7	1	no	Hall
6	C₂₃×D₃₁	—	7	1	no	Hall
7	#13049960	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₃×AGL(1,𝔽₇)	—	31	1	no	maximal, Hall
9	C₂₃×C₃₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
10	#10620252	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	ΓL(1,𝔽₈)×C₂₃	—	31	1	no	Hall
12	D₂₁₇	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
13	D₇×C₂₃	—	31	1	no	Hall
14	C₇×C₃₁	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
15	D₃₁⋊C₃	—	7	1	no	Hall
16	C₇×C₂₃	D₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₂₃	—	217	1	no	Hall
18	C₃₁⋊C₃	—	7	1	no	Hall
19	C₃×C₂₃	—	217	1	no	Hall
20	D₃₁	—	7	1	no	Hall
21	C₂×C₂₃	—	217	1	no	Hall
22	AGL(1,𝔽₇)	—	31	1	no	Hall
23	C₃₁	C₂₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
24	C₂₃	#13049960	1	1	yes	characteristic, direct product factor, Sylow
25	ΓL(1,𝔽₈)	—	31	1	no	Hall
26	D₇	—	31	1	no	Hall
27	C₇	C₂₃×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	217	1	no	Hall
29	C₃	—	217	1	no	Sylow
30	C₂	—	217	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	#13049960
commutator, cosocle, hypocenter	C₇×C₃₁	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₇×C₂₃×C₃₁	C₂×C₃
LCS	G ▷ C₇×C₃₁
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.