Subgroups — #63140

Order 264.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊D₁₁	—	3	1	no	maximal, Hall
5	C₂×C₃×C₁₁	C₂²	1	1	yes	characteristic
6	C₃×D₁₁	—	2	1	no	—
7	D₃×C₁₁	—	2	1	no	—
8	C₂²×C₁₁	—	3	1	no	—
9	C₂×D₁₁	D₃	1	1	yes	characteristic, complemented
10	Dic₁₁	—	3	1	no	—
11	C₃×C₁₁	D₄	1	1	yes	characteristic, complemented, Hall
12	#67	—	11	1	no	maximal, Hall
13	C₂×C₁₁	—	6	1	no	—
14	C₂×C₁₁	C₂×D₃	1	1	yes	characteristic
15	D₁₁	—	2	1	no	—
16	C₂²×C₃	—	11	1	no	—
17	C₂×D₃	D₁₁	1	1	yes	characteristic, complemented
18	Dic₃	—	11	1	no	—
19	C₁₁	#67	1	1	yes	characteristic, complemented, Sylow
20	D₄	—	33	1	no	Sylow
21	C₂×C₃	—	22	1	no	—
22	C₂×C₃	C₂×D₁₁	1	1	yes	characteristic
23	D₃	—	2	1	no	—
24	C₂²	—	3	1	no	—
25	C₂²	—	11	1	no	—
26	C₄	—	33	1	no	—
27	C₃	C₂²⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
28	C₂	—	6	1	no	—
29	C₂	—	22	1	no	—
30	C₂	D₃×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₁
commutator, Fitting, socle, cosocle	C₂×C₃×C₁₁	C₂²
hypocenter	C₃×C₁₁	D₄
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.