Subgroups — #30630596

Order 15996.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16860688	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16860688	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₁×C₄₃	C₂×C₃	1	1	yes	characteristic
5	C₃₁×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₄₃⋊C₃)⋊C₄	—	31	1	no	maximal, Hall
7	(C₃₁⋊C₃)⋊C₄	—	43	1	no	maximal, Hall
8	C₂×C₄₃⋊C₃	—	62	1	no	—
9	C₂×C₃₁⋊C₃	—	86	1	no	—
10	Dic₄₃	—	31	1	no	Hall
11	C₄₃⋊C₃	—	62	1	no	Hall
12	Dic₃₁	—	43	1	no	Hall
13	C₃₁⋊C₃	—	86	1	no	Hall
14	C₂×C₄₃	D₃₁⋊C₃	1	1	yes	characteristic
15	C₂×C₃₁	D₄₃⋊C₃	1	1	yes	characteristic
16	C₄₃	(C₃₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1333	1	no	Hall
19	C₂×C₃	—	2666	1	no	—
20	C₄	—	1333	1	no	Sylow
21	C₃	—	2666	1	no	Sylow
22	C₂	#22547870	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#22547870
commutator, hypocenter	C₃₁×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₃₁×C₄₃	C₂×C₃
prime radical	C₂×#16860688	C₂
LCS	G ▷ C₃₁×C₄₃
UCS	C₁ ◁ C₂

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.