Subgroups — C₂²×#14555739 #22580304

Order 8892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²	#14555739
commutator, hypocenter	C₁₃×C₁₉	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₁₉	C₉
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#14555739	C₂	direct (N × H)
3. #14555739	C₂²	direct (N × H)
5. C₂²×C₁₃×C₁₉	C₉	semidirect
8. C₂×C₁₃×C₁₉	C₂×C₉	semidirect
11. C₁₃×C₁₉	C₂²×C₉	semidirect
19. C₂²×C₁₉	C₁₃⋊C₉	semidirect
21. C₂²×C₁₃	#4296	semidirect
23. C₂×C₁₉	C₂×C₁₃⋊C₉	semidirect
25. C₂×C₁₃	C₂×#4296	semidirect
26. C₁₉	C₂²×C₁₃⋊C₉	semidirect
28. C₁₃	C₂²×#4296	semidirect
32. C₂²	#14555739	direct (N × H)
34. C₂	C₂×#14555739	direct (N × H)

Subgroups — C22×#14555739 #22580304

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14555739 #22580304