Subgroups — D₉₅₃₇ #34061697

Order 19074.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁₇₉	—	3	1	no	maximal, Hall
3	C₁₁×C₂₈₉	D₃	1	1	yes	characteristic, complemented, Hall
4	D₈₆₇	—	11	1	no	maximal, Hall
5	D₅₆₁	—	17	1	no	maximal
6	C₃×C₂₈₉	D₁₁	1	1	yes	characteristic, complemented, Hall
7	D₂₈₉	—	33	1	no	Hall
8	C₃×C₁₁×C₁₇	D₁₇	1	1	yes	characteristic
9	D₁₈₇	—	51	1	no	—
10	C₂₈₉	D₃₃	1	1	yes	characteristic, complemented, Sylow
11	C₁₁×C₁₇	D₅₁	1	1	yes	characteristic
12	D₅₁	—	187	1	no	—
13	D₃₃	—	289	1	no	Hall
14	C₃×C₁₇	D₁₈₇	1	1	yes	characteristic
15	D₁₇	—	561	1	no	—
16	C₃×C₁₁	D₂₈₉	1	1	yes	characteristic, complemented, Hall
17	D₁₁	—	867	1	no	Hall
18	C₁₇	D₅₆₁	1	1	yes	characteristic
19	C₁₁	D₈₆₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3179	1	no	Hall
21	C₃	D₃₁₇₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	9537	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₁₁×C₂₈₉	C₂
Frattini	C₁₇	D₅₆₁
socle	C₃×C₁₁×C₁₇	D₁₇
LCS	G ▷ C₃×C₁₁×C₂₈₉
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.