Subgroups — C₄₁×D₂₇₉ #37504253

Order 22878.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₁×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁×D₉₃	—	3	1	no	maximal
3	C₃×C₃₁×C₄₁	D₃	1	1	yes	characteristic
4	C₄₁×D₃₁	—	9	1	no	Hall
5	C₃₁×C₄₁	D₉	1	1	yes	characteristic, complemented, Hall
6	D₉×C₄₁	—	31	1	no	maximal, Hall
7	D₂₇₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₉×C₄₁	D₃₁	1	1	yes	characteristic, complemented, Hall
9	C₉×C₃₁	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
10	D₃×C₄₁	—	93	1	no	—
11	D₉₃	—	3	1	no	—
12	C₃×C₄₁	D₉₃	1	1	yes	characteristic
13	C₃×C₃₁	D₃×C₄₁	1	1	yes	characteristic
14	C₂×C₄₁	—	279	1	no	Hall
15	D₃₁	—	9	1	no	Hall
16	C₄₁	D₂₇₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₁	D₉×C₄₁	1	1	yes	characteristic, complemented, Sylow
18	D₉	—	31	1	no	Hall
19	C₉	C₄₁×D₃₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	93	1	no	—
21	C₃	C₄₁×D₉₃	1	1	yes	characteristic
22	C₂	—	279	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	D₂₇₉
commutator, cosocle, hypocenter	C₉×C₃₁	C₂×C₄₁
Frattini	C₃	C₄₁×D₉₃
Fitting	C₉×C₃₁×C₄₁	C₂
socle	C₃×C₃₁×C₄₁	D₃
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₄₁

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.