Subgroups — C₂×D₃×D₁₁ #63166

Order 264.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₁	C₂	1	4	yes	maximal, direct product factor
5	C₂²×D₁₁	—	3	1	no	maximal, Hall
6	C₂×C₃×C₁₁	C₂²	1	1	yes	characteristic, complemented
7	D₃₃	C₂²	1	2	yes	complemented
8	C₃×D₁₁	C₂²	1	2	yes	complemented
9	D₃×C₁₁	C₂²	1	2	yes	complemented
10	C₂²×C₁₁	—	3	1	no	—
11	C₂×D₁₁	—	3	1	no	—
12	C₂×D₁₁	—	3	4	no	—
13	C₂×D₁₁	D₃	1	1	yes	characteristic, direct product factor
14	C₃×C₁₁	C₂³	1	1	yes	characteristic, complemented, Hall
15	C₂²×D₃	—	11	1	no	maximal, Hall
16	C₂×C₁₁	—	3	2	no	—
17	C₂×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented
18	D₁₁	—	3	2	no	—
19	D₁₁	C₂×D₃	1	2	yes	direct product factor
20	C₂²×C₃	—	11	1	no	—
21	C₂×D₃	—	11	1	no	—
22	C₂×D₃	—	11	4	no	—
23	C₂×D₃	D₁₁	1	1	yes	characteristic, direct product factor
24	C₁₁	C₂²×D₃	1	1	yes	characteristic, complemented, Sylow
25	C₂³	—	33	1	no	Sylow
26	C₂×C₃	—	11	2	no	—
27	C₂×C₃	C₂×D₁₁	1	1	yes	characteristic, complemented
28	D₃	—	11	2	no	—
29	D₃	C₂×D₁₁	1	2	yes	direct product factor
30	C₂²	—	3	1	no	—
31	C₂²	—	11	1	no	—
32	C₂²	—	33	4	no	—
33	C₂²	—	33	1	no	—
34	C₃	C₂²×D₁₁	1	1	yes	characteristic, complemented, Sylow
35	C₂	—	3	2	no	—
36	C₂	—	11	2	no	—
37	C₂	—	33	2	no	—
38	C₂	D₃×D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×D₁₁
commutator, cosocle, hypocenter	C₃×C₁₁	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁	C₂²
LCS	G ▷ 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.