Subgroups — C₁₇²×D₃₃ #34061707

Order 19074.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇²×D₁₁	—	3	1	no	maximal, Hall
3	C₁₁×C₁₇²	D₃	1	1	yes	characteristic, complemented, Hall
4	D₃×C₁₇²	—	11	1	no	maximal, Hall
5	C₁₇×D₃₃	C₁₇	1	18	yes	maximal, direct product factor
6	C₃×C₁₇²	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₇²	—	33	1	no	Hall
8	C₃×C₁₁×C₁₇	C₂×C₁₇	1	18	yes	complemented
9	C₁₇×D₁₁	—	3	18	no	—
10	C₁₇²	D₃₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₁₁×C₁₇	D₃×C₁₇	1	18	yes	complemented
12	D₃×C₁₇	—	11	18	no	—
13	D₃₃	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₇	C₁₇×D₁₁	1	18	yes	complemented
15	C₂×C₁₇	—	33	18	no	—
16	C₃×C₁₁	C₂×C₁₇²	1	1	yes	characteristic, complemented, Hall
17	D₁₁	—	3	1	no	Hall
18	C₁₇	C₁₇×D₃₃	1	18	yes	direct product factor
19	C₁₁	D₃×C₁₇²	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	11	1	no	Hall
21	C₃	C₁₇²×D₁₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇²	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₁₇²
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₇²	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₁₇²

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.