Subgroups — C₂×C₉×#4296 #72210941

Order 3078.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#4296	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×#4296	C₃	1	3	yes	maximal
3	C₂×C₉×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃×#4296	C₂×C₃	1	3	yes	—
5	C₉×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
7	C₂×#4296	C₉	1	9	yes	direct product factor
8	C₂×C₉×C₁₉	C₉	1	1	yes	characteristic, complemented
9	C₂×#4294	C₉	1	2	yes	complemented
10	C₃×C₁₉⋊C₃	C₂×C₃²	1	1	yes	characteristic
11	#4296	C₂×C₉	1	9	yes	direct product factor
12	C₉×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
13	#4294	C₂×C₉	1	2	yes	complemented
14	C₂×C₉²	—	19	1	no	maximal, Hall
15	C₂×C₃×C₁₉	C₃×C₉	1	1	yes	characteristic
16	C₂×C₁₉⋊C₃	C₃×C₉	1	3	yes	—
17	C₉²	—	19	1	no	Sylow
18	C₃×C₁₉	C₂×C₃×C₉	1	1	yes	characteristic
19	C₁₉⋊C₃	C₂×C₃×C₉	1	3	yes	—
20	C₂×C₃×C₉	—	19	3	no	—
21	C₂×C₃×C₉	—	19	1	no	—
22	C₂×C₁₉	C₉²	1	1	yes	characteristic, complemented, Hall
23	C₃×C₉	—	19	3	no	—
24	C₃×C₉	—	19	1	no	—
25	C₁₉	C₂×C₉²	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃²	—	19	1	no	—
27	C₂×C₉	—	19	9	no	—
28	C₂×C₉	—	19	2	no	—
29	C₂×C₉	#4296	1	1	yes	characteristic, direct product factor
30	C₃²	—	19	1	no	—
31	C₉	—	19	9	no	—
32	C₉	—	19	2	no	—
33	C₉	C₂×#4296	1	1	yes	characteristic, direct product factor
34	C₂×C₃	—	19	3	no	—
35	C₂×C₃	C₃×#4296	1	1	yes	characteristic
36	C₃	—	19	3	no	—
37	C₃	C₂×C₃×#4296	1	1	yes	characteristic
38	C₂	C₉×#4296	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₉	#4296
commutator, hypocenter	C₁₉	C₂×C₉²
Frattini	C₃	C₂×C₃×#4296
Fitting	C₂×C₉×C₁₉	C₉
socle	C₂×C₃×C₁₉	C₃×C₉
prime radical	C₂×C₃×C₁₉⋊C₃	C₃²
cosocle	C₃×C₁₉⋊C₃	C₂×C₃²
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×#4296	C₂	direct (N × H)
7. C₂×#4296	C₉	direct (N × H)
8. C₂×C₉×C₁₉	C₉	semidirect
9. C₂×#4294	C₉	semidirect
11. #4296	C₂×C₉	direct (N × H)
12. C₉×C₁₉	C₂×C₉	semidirect
13. #4294	C₂×C₉	semidirect
22. C₂×C₁₉	C₉²	semidirect
25. C₁₉	C₂×C₉²	semidirect
29. C₂×C₉	#4296	direct (N × H)
33. C₉	C₂×#4296	direct (N × H)
38. C₂	C₉×#4296	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×#4296	2
C₂×C₃×#4296	3
C₂×C₉×C₁₉⋊C₃	3
C₂×C₉²	19

Subgroups — C2×C9×#4296 #72210941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#4296 #72210941