Subgroups — C₂×C₃⋊D₃₃ #87697

Order 396.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₃₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃₃	—	3	4	no	maximal
4	C₃²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁	D₃	1	4	yes	complemented
6	D₃₃	—	3	8	no	—
7	C₂×D₁₁	—	9	1	no	Hall
8	C₂×C₃⋊D₃	—	11	1	no	maximal, Hall
9	C₃×C₁₁	C₂×D₃	1	4	yes	complemented
10	C₂×C₁₁	C₃⋊D₃	1	1	yes	characteristic, complemented
11	D₁₁	—	9	2	no	—
12	C₂×C₃²	D₁₁	1	1	yes	characteristic, complemented
13	C₃⋊D₃	—	11	2	no	—
14	C₂×D₃	—	33	4	no	—
15	C₁₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
16	C₃²	C₂×D₁₁	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃	D₃₃	1	4	yes	complemented
18	D₃	—	33	8	no	—
19	C₂²	—	99	1	no	Sylow
20	C₃	C₂×D₃₃	1	4	yes	complemented
21	C₂	—	99	2	no	—
22	C₂	C₃⋊D₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₃₃
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁	C₂
LCS	G ▷ C₃²×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.