Subgroups — C₂²⋊#14555739 #22580309

Order 8892.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#14555739	—	4	1	no	maximal, Hall
3	C₂×C₁₃×C₁₉⋊C₃	—	3	1	no	—
4	C₂²×C₁₃×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₁₉⋊C₃	A₄	1	1	yes	characteristic
6	C₂²⋊#4296	—	13	1	no	maximal, Hall
7	C₂×C₁₃×C₁₉	—	3	1	no	—
8	C₂²⋊(C₁₃⋊C₉)	—	19	1	no	maximal, Hall
9	C₁₃×C₁₉	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₁₉⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic
11	#4296	—	52	1	no	Hall
12	C₂²×C₃×C₁₃	—	19	1	no	—
13	C₁₃⋊C₉	—	76	1	no	Hall
14	C₂×C₁₉⋊C₃	—	3	1	no	—
15	C₂×C₃×C₁₃	—	57	1	no	—
16	C₂²×C₁₉	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
17	C₁₉⋊C₃	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
18	C₂²×C₁₃	#4296	1	1	yes	characteristic, complemented, Hall
19	C₃×C₁₃	—	19	1	no	—
20	C₂×C₁₉	—	3	1	no	—
21	C₂²⋊C₉	—	247	1	no	Hall
22	C₂×C₁₃	—	3	1	no	—
23	C₁₉	C₂²⋊(C₁₃⋊C₉)	1	1	yes	characteristic, complemented, Sylow
24	C₁₃	C₂²⋊#4296	1	1	yes	characteristic, complemented, Sylow
25	C₂²×C₃	—	19	1	no	—
26	C₉	—	988	1	no	Sylow
27	C₂×C₃	—	57	1	no	—
28	C₂²	#14555739	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	19	1	no	—
30	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂²×C₁₃×C₁₉	C₉
LCS	G ▷ C₂²×C₁₃×C₁₉
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.