Subgroups — #56004642

Order 44310.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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