Subgroups — C₄₃×#10587722 #37553525

Order 23478.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#63270	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×D₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₄₃×D₁₃⋊C₃	—	7	1	no	maximal, Hall
5	AGL(1,𝔽₇)×C₄₃	—	13	1	no	maximal, Hall
6	C₁₃⋊C₃×C₄₃	—	7	1	no	Hall
7	D₁₃×C₄₃	—	7	1	no	Hall
8	ΓL(1,𝔽₈)×C₄₃	—	13	1	no	Hall
9	D₇×C₄₃	—	13	1	no	Hall
10	C₁₃×C₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
11	#10587722	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₄₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
13	#63270	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₄₃	—	91	1	no	Hall
15	D₉₁	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄₃	—	91	1	no	Hall
17	C₇×C₁₃	C₂×C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₃	—	91	1	no	Hall
19	D₁₃⋊C₃	—	7	1	no	Hall
20	C₄₃	#10587722	1	1	yes	characteristic, direct product factor, Sylow
21	AGL(1,𝔽₇)	—	13	1	no	Hall
22	C₁₃⋊C₃	—	7	1	no	Hall
23	D₁₃	—	7	1	no	Hall
24	ΓL(1,𝔽₈)	—	13	1	no	Hall
25	D₇	—	13	1	no	Hall
26	C₁₃	AGL(1,𝔽₇)×C₄₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₄₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	91	1	no	Hall
29	C₃	—	91	1	no	Sylow
30	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₃	#10587722
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₄₃

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.