Subgroups — D₆₇×#4296 #37523849

Order 22914.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#4296	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊C₃×D₆₇	C₃	1	1	yes	maximal, characteristic
3	C₁₉⋊C₃×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	C₉×D₆₇	—	19	1	no	maximal, Hall
7	C₉×C₆₇	—	19	1	no	Hall
8	C₃×D₆₇	—	19	1	no	—
9	C₂×#4296	—	67	1	no	maximal, Hall
10	C₃×C₆₇	—	19	1	no	—
11	#4296	D₆₇	1	1	yes	characteristic, direct product factor, Hall
12	D₆₇	#4296	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₁₉⋊C₃	—	67	1	no	—
14	C₆₇	C₂×#4296	1	1	yes	characteristic, complemented, Sylow
15	C₁₉⋊C₃	C₃×D₆₇	1	1	yes	characteristic
16	C₂×C₁₉	—	67	1	no	Hall
17	C₁₉	C₉×D₆₇	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	1273	1	no	Hall
19	C₉	—	19	1	no	Sylow
20	C₂×C₃	—	1273	1	no	—
21	C₃	—	19	1	no	—
22	C₂	—	67	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₉×C₆₇	C₂×C₉
prime radical	C₁₉⋊C₃×D₆₇	C₃
cosocle	C₁₉⋊C₃×C₆₇	C₂×C₃
LCS	G ▷ C₁₉×C₆₇
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.