Subgroups — C₁₇×#14274254 #44570404

Order 32487.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×#63270	—	7	1	no	maximal
3	C₁₇×C₄₉⋊C₃	—	13	1	no	maximal, Hall
4	#14274254	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×C₁₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
6	C₁₇×C₄₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
7	C₁₇×C₁₃⋊C₃	—	49	1	no	Hall
8	C₁₃×C₄₉	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×ΓL(1,𝔽₈)	—	91	1	no	—
10	#63270	—	7	1	no	—
11	C₁₃×C₁₇	C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₄₉⋊C₃	—	13	1	no	Hall
13	C₇×C₁₇	#63270	1	1	yes	characteristic
14	C₇×C₁₃	C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₃×C₁₇	—	637	1	no	Hall
16	C₄₉	C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₁₃⋊C₃	—	49	1	no	Hall
18	ΓL(1,𝔽₈)	—	91	1	no	—
19	C₁₇	#14274254	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₃	C₁₇×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₇	C₁₇×#63270	1	1	yes	characteristic
22	C₃	—	637	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	#14274254
commutator, cosocle, hypocenter	C₁₃×C₄₉	C₃×C₁₇
Frattini	C₇	C₁₇×#63270
Fitting	C₁₃×C₁₇×C₄₉	C₃
socle	C₇×C₁₃×C₁₇	ΓL(1,𝔽₈)
LCS	G ▷ C₁₃×C₄₉
UCS	C₁ ◁ C₁₇

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.