Subgroups — D₄₁×C₃₁⋊C₉ #37504255

Order 22878.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₃₁⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₃₁×D₄₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₃₁×C₄₁	C₂×C₃	1	1	yes	characteristic
4	C₃₁×D₄₁	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃₁×C₄₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	C₉×D₄₁	—	31	1	no	maximal, Hall
7	C₂×C₃₁⋊C₉	—	41	1	no	maximal, Hall
8	C₉×C₄₁	—	31	1	no	Hall
9	C₃₁⋊C₉	D₄₁	1	1	yes	characteristic, direct product factor, Hall
10	C₃×D₄₁	C₃₁⋊C₃	1	1	yes	characteristic
11	C₂×C₃×C₃₁	—	41	1	no	—
12	C₃×C₄₁	C₂×C₃₁⋊C₃	1	1	yes	characteristic
13	C₃×C₃₁	C₃×D₄₁	1	1	yes	characteristic
14	D₄₁	C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃₁	—	41	1	no	Hall
16	C₄₁	C₂×C₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	C₉×D₄₁	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	1271	1	no	Hall
19	C₉	—	31	1	no	Sylow
20	C₂×C₃	—	41	1	no	—
21	C₃	D₄₁×C₃₁⋊C₃	1	1	yes	characteristic
22	C₂	—	41	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₄₁×C₃₁⋊C₃
commutator, hypocenter	C₃₁×C₄₁	C₂×C₉
Fitting, socle, cosocle	C₃×C₃₁×C₄₁	C₂×C₃
prime radical	C₃×C₃₁×D₄₁	C₃
LCS	G ▷ C₃₁×C₄₁
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.