Subgroups — C₁₇×#14274262 #44570413

Order 32487.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₃×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×#63271	—	7	8	no	maximal
3	C₁₇×#3861	—	13	1	no	maximal, Hall
4	#14274262	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×C₁₇	ΓL(1,𝔽₈)	1	8	yes	complemented
6	C₇²×C₁₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
7	C₁₇×C₁₃⋊C₃	—	49	1	no	Hall
8	C₇²×C₁₃	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×ΓL(1,𝔽₈)	—	91	8	no	—
10	#63271	—	7	8	no	—
11	C₁₃×C₁₇	#3861	1	1	yes	characteristic, complemented, Hall
12	#3861	—	13	1	no	Hall
13	C₇×C₁₇	#63271	1	8	yes	complemented
14	C₇×C₁₃	C₁₇×ΓL(1,𝔽₈)	1	8	yes	complemented
15	C₃×C₁₇	—	637	1	no	Hall
16	C₇²	C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₁₃⋊C₃	—	49	1	no	Hall
18	ΓL(1,𝔽₈)	—	91	8	no	—
19	C₁₇	#14274262	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₃	C₁₇×#3861	1	1	yes	characteristic, complemented, Sylow
21	C₇	C₁₇×#63271	1	8	yes	complemented
22	C₃	—	637	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	#14274262
commutator, cosocle, hypocenter	C₇²×C₁₃	C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₇²×C₁₃×C₁₇	C₃
LCS	G ▷ C₇²×C₁₃
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.