Subgroups — #4296×D₁₀₉ #49152137

Order 37278.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#4296	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊C₃×D₁₀₉	C₃	1	1	yes	maximal, characteristic
3	C₁₉⋊C₃×C₁₀₉	C₂×C₃	1	1	yes	characteristic
4	C₁₉×D₁₀₉	C₉	1	1	yes	characteristic, complemented, Hall
5	C₁₉×C₁₀₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	C₉×D₁₀₉	—	19	1	no	maximal, Hall
7	C₉×C₁₀₉	—	19	1	no	Hall
8	C₃×D₁₀₉	—	19	1	no	—
9	C₂×#4296	—	109	1	no	maximal, Hall
10	C₃×C₁₀₉	—	19	1	no	—
11	D₁₀₉	#4296	1	1	yes	characteristic, direct product factor, Hall
12	#4296	D₁₀₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₁₉⋊C₃	—	109	1	no	—
14	C₁₀₉	C₂×#4296	1	1	yes	characteristic, complemented, Sylow
15	C₁₉⋊C₃	C₃×D₁₀₉	1	1	yes	characteristic
16	C₂×C₁₉	—	109	1	no	Hall
17	C₁₉	C₉×D₁₀₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	2071	1	no	Hall
19	C₉	—	19	1	no	Sylow
20	C₂×C₃	—	2071	1	no	—
21	C₃	—	19	1	no	—
22	C₂	—	109	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₉×C₁₀₉	C₂×C₉
prime radical	C₁₉⋊C₃×D₁₀₉	C₃
cosocle	C₁₉⋊C₃×C₁₀₉	C₂×C₃
LCS	G ▷ C₁₉×C₁₀₉
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.