Subgroups — C₁₆₇×C₃⋊D₃₃ #45683406

Order 33066.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₃×C₁₆₇	—	3	4	no	maximal
3	C₃×C₁₁×C₁₆₇	D₃	1	4	yes	complemented
4	D₁₁×C₁₆₇	—	9	1	no	Hall
5	C₃⋊D₃×C₁₆₇	—	11	1	no	maximal, Hall
6	C₁₁×C₁₆₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₁₆₇	D₁₁	1	1	yes	characteristic, complemented, Hall
8	D₃×C₁₆₇	—	33	4	no	—
9	C₃×C₁₆₇	D₃₃	1	4	yes	complemented
10	C₂×C₁₆₇	—	99	1	no	Hall
11	C₃⋊D₃₃	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₆₇	C₃⋊D₃₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²×C₁₁	C₂×C₁₆₇	1	1	yes	characteristic, complemented, Hall
14	D₃₃	—	3	4	no	—
15	C₃×C₁₁	D₃×C₁₆₇	1	4	yes	complemented
16	D₁₁	—	9	1	no	Hall
17	C₃⋊D₃	—	11	1	no	Hall
18	C₁₁	C₃⋊D₃×C₁₆₇	1	1	yes	characteristic, complemented, Sylow
19	C₃²	D₁₁×C₁₆₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	33	4	no	—
21	C₃	D₃₃×C₁₆₇	1	4	yes	complemented
22	C₂	—	99	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₆₇	C₃⋊D₃₃
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂×C₁₆₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₆₇	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₁₆₇

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.