Subgroups — #30685161

Order 17082.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22555435	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₉₄₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₇₃	C₂×C₃	1	1	yes	characteristic
4	D₉₄₉	C₉	1	1	yes	characteristic, complemented, Hall
5	#10620321⋊C₂	—	13	1	no	maximal, Hall
6	C₁₃×C₇₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	#10620321	—	13	1	no	Hall
8	C₃×D₇₃	—	39	1	no	—
9	D₁₃⋊C₉	—	73	1	no	maximal, Hall
10	C₃×C₇₃	D₁₃⋊C₃	1	1	yes	characteristic
11	D₇₃	—	39	1	no	Hall
12	C₁₃⋊C₉	—	73	1	no	Hall
13	C₃×D₁₃	—	219	1	no	—
14	C₇₃	D₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₃	D₇₃⋊C₃	1	1	yes	characteristic
16	D₁₃	—	219	1	no	Hall
17	C₂×C₉	—	949	1	no	Hall
18	C₁₃	#10620321⋊C₂	1	1	yes	characteristic, complemented, Sylow
19	C₉	—	949	1	no	Sylow
20	C₂×C₃	—	2847	1	no	—
21	C₃	#19151047	1	1	yes	characteristic
22	C₂	—	2847	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#19151047
commutator, hypocenter	C₁₃×C₇₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₁₃×C₇₃	C₂×C₃
prime radical	C₃×D₉₄₉	C₃
LCS	G ▷ C₁₃×C₇₃
UCS	C₁ ◁ C₃

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.