Subgroups — #37562016

Order 23994.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26046341	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₃₃₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₃₁×C₄₃	C₂×C₃	1	1	yes	characteristic
4	D₁₃₃₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃₁×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	D₄₃⋊C₉	—	31	1	no	maximal, Hall
7	D₃₁⋊C₉	—	43	1	no	maximal, Hall
8	C₄₃⋊C₉	—	31	1	no	Hall
9	C₃₁⋊C₉	—	43	1	no	Hall
10	C₃×D₄₃	—	93	1	no	—
11	C₃×D₃₁	—	129	1	no	—
12	C₃×C₄₃	D₃₁⋊C₃	1	1	yes	characteristic
13	C₃×C₃₁	D₄₃⋊C₃	1	1	yes	characteristic
14	D₄₃	—	93	1	no	Hall
15	D₃₁	—	129	1	no	Hall
16	C₄₃	D₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	D₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	1333	1	no	Hall
19	C₉	—	1333	1	no	Sylow
20	C₂×C₃	—	3999	1	no	—
21	C₃	#22547870	1	1	yes	characteristic
22	C₂	—	3999	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#22547870
commutator, hypocenter	C₃₁×C₄₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₃₁×C₄₃	C₂×C₃
prime radical	C₃×D₁₃₃₃	C₃
LCS	G ▷ C₃₁×C₄₃
UCS	C₁ ◁ C₃

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.