Subgroups — #42119952

Order 27588.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉⋊(C₁₁²⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊Dic₂₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉⋊(C₁₁²⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₁₁²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₁₁⋊Dic₁₁)⋊C₃	—	19	1	no	maximal, Hall
7	Dic₂₀₉	—	33	4	no	—
8	C₂×C₁₁²⋊C₃	—	38	1	no	—
9	C₁₁⋊Dic₁₁	—	19	1	no	Hall
10	C₂×C₁₁×C₁₉	—	3	4	no	—
11	C₁₁²⋊C₃	—	38	1	no	Hall
12	C₂×C₁₁²	D₁₉⋊C₃	1	1	yes	characteristic
13	(C₁₉⋊C₃)⋊C₄	—	121	1	no	maximal, Hall
14	C₁₁×C₁₉	—	3	4	no	—
15	C₁₁²	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉⋊C₃	—	242	1	no	—
17	Dic₁₉	—	121	1	no	Hall
18	C₁₉⋊C₃	—	242	1	no	Hall
19	Dic₁₁	—	627	4	no	—
20	C₂×C₁₉	(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
21	C₂×C₁₁	—	3	4	no	—
22	C₁₉	(C₁₁⋊Dic₁₁)⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₄	—	2299	1	no	Hall
24	C₁₁	—	3	4	no	—
25	C₂×C₃	—	4598	1	no	—
26	C₄	—	2299	1	no	Sylow
27	C₃	—	4598	1	no	Sylow
28	C₂	#28352261	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#28352261
commutator, hypocenter	C₁₁²×C₁₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₁²×C₁₉	C₂×C₃
prime radical	C₂×C₁₉⋊(C₁₁²⋊C₃)	C₂
LCS	G ▷ C₁₁²×C₁₉
UCS	C₁ ◁ C₂

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.