Subgroups — #37523830

Order 22914.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26039282	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×D₆₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₉×C₆₇	C₂×C₃	1	1	yes	characteristic
4	C₁₉×D₆₇	C₉	1	1	yes	characteristic, complemented, Hall
5	C₁₉×C₆₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	D₆₇⋊C₉	—	19	1	no	maximal, Hall
7	C₆₇⋊C₉	—	19	1	no	Hall
8	C₃×D₆₇	C₁₉⋊C₃	1	1	yes	characteristic
9	C₂×#4294	—	67	1	no	maximal, Hall
10	C₃×C₆₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic
11	#4294	—	67	1	no	Hall
12	D₆₇	#4294	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₉	—	201	1	no	—
14	C₆₇	C₂×#4294	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₉	D₆₇⋊C₃	1	1	yes	characteristic
16	C₂×C₁₉	—	201	1	no	Hall
17	C₁₉	D₆₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	1273	1	no	Hall
19	C₉	—	1273	1	no	Sylow
20	C₂×C₃	—	201	1	no	—
21	C₃	#21439405	1	1	yes	characteristic
22	C₂	—	201	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#21439405
commutator, hypocenter	C₁₉×C₆₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₁₉×C₆₇	C₂×C₃
prime radical	C₃×C₁₉×D₆₇	C₃
LCS	G ▷ C₁₉×C₆₇
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.