Subgroups — C₁₇⋊#14524209 #49145652

Order 36822.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#11762246	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₃₂₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#14524209	—	17	1	no	maximal, Hall
5	C₁₇⋊(D₁₉⋊C₃)	—	19	1	no	maximal
6	D₁₇×C₁₉⋊C₃	—	19	1	no	maximal
7	#11762246	D₁₇	1	1	yes	characteristic, complemented, Hall
8	C₁₇×C₁₉⋊C₃	—	19	1	no	—
9	C₁₇×C₁₉⋊C₃	—	19	1	no	—
10	C₁₉×D₁₉	—	17	1	no	Hall
11	D₃₂₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented
12	C₁₉×D₁₇	—	19	1	no	—
13	C₁₉²	C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
14	C₁₇×C₁₉	—	6	3	no	—
15	C₁₇×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
16	C₁₇×C₁₉	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
17	C₂×C₁₉⋊C₃	—	323	1	no	—
18	D₁₉⋊C₃	—	323	1	no	—
19	C₃×D₁₇	—	361	1	no	Hall
20	C₁₉⋊C₃	—	19	1	no	—
21	C₁₉⋊C₃	—	19	1	no	—
22	C₃×C₁₇	—	361	1	no	Hall
23	C₂×C₁₉	—	323	1	no	—
24	D₁₉	—	17	1	no	—
25	D₁₇	—	19	1	no	Hall
26	C₁₉	—	6	3	no	—
27	C₁₉	D₁₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
28	C₁₉	C₁₇⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
29	C₁₇	#14524209	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	6137	1	no	Hall
31	C₃	—	361	1	no	Sylow
32	C₂	—	323	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₁₉²	C₂×C₃
LCS	G ▷ C₁₇×C₁₉²
UCS	C₁

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.