Subgroups — D₂₆₂₅₇ #72289618

Order 52514.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₇₅₁	—	7	1	no	maximal, Hall
3	D₂₃₈₇	—	11	1	no	maximal
4	C₃₁×C₁₂₁	D₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₁×C₃₁	D₁₁	1	1	yes	characteristic
6	D₈₄₇	—	31	1	no	maximal, Hall
7	C₇×C₁₂₁	D₃₁	1	1	yes	characteristic, complemented, Hall
8	D₃₄₁	—	77	1	no	—
9	D₂₁₇	—	121	1	no	Hall
10	C₁₁×C₃₁	D₇₇	1	1	yes	characteristic
11	D₁₂₁	—	217	1	no	Hall
12	C₇×C₃₁	D₁₂₁	1	1	yes	characteristic, complemented, Hall
13	D₇₇	—	341	1	no	—
14	C₁₂₁	D₂₁₇	1	1	yes	characteristic, complemented, Sylow
15	C₇×C₁₁	D₃₄₁	1	1	yes	characteristic
16	D₃₁	—	847	1	no	Hall
17	C₃₁	D₈₄₇	1	1	yes	characteristic, complemented, Sylow
18	D₁₁	—	2387	1	no	—
19	D₇	—	3751	1	no	Hall
20	C₁₁	D₂₃₈₇	1	1	yes	characteristic
21	C₇	D₃₇₅₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	26257	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₃₁×C₁₂₁	C₂
Frattini	C₁₁	D₂₃₈₇
socle	C₇×C₁₁×C₃₁	D₁₁
LCS	G ▷ C₇×C₃₁×C₁₂₁
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.