Subgroups — D₆₆₃₃ #27210697

Order 13266.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₁×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₂₁₁	—	3	1	no	maximal
3	C₃×C₁₁×C₆₇	D₃	1	1	yes	characteristic
4	D₇₃₇	—	9	1	no	Hall
5	D₆₀₃	—	11	1	no	maximal, Hall
6	C₁₁×C₆₇	D₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₆₇	D₁₁	1	1	yes	characteristic, complemented, Hall
8	D₂₀₁	—	33	1	no	—
9	C₃×C₆₇	D₃₃	1	1	yes	characteristic
10	D₉₉	—	67	1	no	maximal, Hall
11	D₆₇	—	99	1	no	Hall
12	C₉×C₁₁	D₆₇	1	1	yes	characteristic, complemented, Hall
13	C₆₇	D₉₉	1	1	yes	characteristic, complemented, Sylow
14	D₃₃	—	201	1	no	—
15	C₃×C₁₁	D₂₀₁	1	1	yes	characteristic
16	D₁₁	—	603	1	no	Hall
17	D₉	—	737	1	no	Hall
18	C₁₁	D₆₀₃	1	1	yes	characteristic, complemented, Sylow
19	C₉	D₇₃₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	2211	1	no	—
21	C₃	D₂₂₁₁	1	1	yes	characteristic
22	C₂	—	6633	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁×C₆₇	C₂
Frattini	C₃	D₂₂₁₁
socle	C₃×C₁₁×C₆₇	D₃
LCS	G ▷ C₉×C₁₁×C₆₇
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.