Subgroups — D₂₂₁₅₅ #56004635

Order 44310.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇₃₈₅	—	3	1	no	maximal, Hall
3	D₄₄₃₁	—	5	1	no	maximal, Hall
4	C₅×C₇×C₂₁₁	D₃	1	1	yes	characteristic, complemented, Hall
5	D₃₁₆₅	—	7	1	no	maximal, Hall
6	C₃×C₇×C₂₁₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₂₁₁	D₇	1	1	yes	characteristic, complemented, Hall
8	D₁₄₇₇	—	15	1	no	Hall
9	D₁₀₅₅	—	21	1	no	Hall
10	C₇×C₂₁₁	D₁₅	1	1	yes	characteristic, complemented, Hall
11	D₆₃₃	—	35	1	no	Hall
12	C₅×C₂₁₁	D₂₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₂₁₁	D₃₅	1	1	yes	characteristic, complemented, Hall
14	D₂₁₁	—	105	1	no	Hall
15	C₂₁₁	D₁₀₅	1	1	yes	characteristic, complemented, Sylow
16	D₁₀₅	—	211	1	no	maximal, Hall
17	C₃×C₅×C₇	D₂₁₁	1	1	yes	characteristic, complemented, Hall
18	D₃₅	—	633	1	no	Hall
19	D₂₁	—	1055	1	no	Hall
20	C₅×C₇	D₆₃₃	1	1	yes	characteristic, complemented, Hall
21	D₁₅	—	1477	1	no	Hall
22	C₃×C₇	D₁₀₅₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₁₄₇₇	1	1	yes	characteristic, complemented, Hall
24	D₇	—	3165	1	no	Hall
25	D₅	—	4431	1	no	Hall
26	C₇	D₃₁₆₅	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	7385	1	no	Hall
28	C₅	D₄₄₃₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₇₃₈₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	22155	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇×C₂₁₁	C₂
LCS	G ▷ C₃×C₅×C₇×C₂₁₁
UCS	C₁

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.