Subgroups — #34061852

Order 19092.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18012031	C₂	1	1	yes	maximal, characteristic
2	Dic₁₅₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#18012031	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×C₄₃	C₂×C₃	1	1	yes	characteristic
5	C₃₇×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₄₃⋊C₃)⋊C₄	—	37	1	no	maximal, Hall
7	Dic₃₇⋊C₃	—	43	1	no	maximal, Hall
8	C₂×C₄₃⋊C₃	—	74	1	no	—
9	C₂×C₃₇⋊C₃	—	86	1	no	—
10	Dic₄₃	—	37	1	no	Hall
11	Dic₃₇	—	43	1	no	Hall
12	C₄₃⋊C₃	—	74	1	no	Hall
13	C₃₇⋊C₃	—	86	1	no	Hall
14	C₂×C₄₃	D₃₇⋊C₃	1	1	yes	characteristic
15	C₂×C₃₇	D₄₃⋊C₃	1	1	yes	characteristic
16	C₄₃	Dic₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1591	1	no	Hall
19	C₂×C₃	—	3182	1	no	—
20	C₄	—	1591	1	no	Sylow
21	C₃	—	3182	1	no	Sylow
22	C₂	#23750875	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#23750875
commutator, hypocenter	C₃₇×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₃₇×C₄₃	C₂×C₃
prime radical	C₂×#18012031	C₂
LCS	G ▷ C₃₇×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.