Subgroups — #63143

Order 264.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₃	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×Dic₃	C₂	1	1	yes	maximal, characteristic
4	Dic₂₂	—	3	1	no	maximal, Hall
5	C₂×C₃×C₁₁	C₂²	1	1	yes	characteristic
6	C₄×C₁₁	—	3	1	no	—
7	Dic₁₁	—	3	1	no	—
8	Dic₁₁	D₃	1	1	yes	characteristic
9	C₃×C₁₁	Q₈	1	1	yes	characteristic, complemented, Hall
10	Dic₆	—	11	1	no	maximal, Hall
11	C₂×C₁₁	C₂×D₃	1	1	yes	characteristic
12	C₃×C₄	—	11	1	no	—
13	Dic₃	—	11	1	no	—
14	Dic₃	D₁₁	1	1	yes	characteristic
15	C₁₁	Dic₆	1	1	yes	characteristic, complemented, Sylow
16	Q₈	—	33	1	no	Sylow
17	C₂×C₃	C₂×D₁₁	1	1	yes	characteristic
18	C₄	—	3	1	no	—
19	C₄	—	11	1	no	—
20	C₄	—	33	1	no	—
21	C₃	Dic₂₂	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₁
commutator, Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₁	C₂²
hypocenter	C₃×C₁₁	Q₈
LCS	G ▷ C₂×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂

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.