Finite Group Databasebeta

← C₉×C₃₉₇⋊C₃ #24924303

Subgroups — C₉×C₃₉₇⋊C₃ #24924303

Order 10719.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₉₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₃₉₇	C₃	1	1	yes	maximal, characteristic, complemented
3	#16813208	C₃	1	2	yes	maximal, complemented
4	C₃×C₃₉₇	C₃²	1	1	yes	characteristic
5	C₃₉₇⋊C₃	C₉	1	3	yes	direct product factor
6	C₃₉₇	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
7	C₃×C₉	—	397	1	no	maximal, Sylow
8	C₃²	—	397	1	no	—
9	C₉	—	397	2	no	—
10	C₉	C₃₉₇⋊C₃	1	1	yes	characteristic, direct product factor
11	C₃	—	397	3	no	—
12	C₃	C₃×C₃₉₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₉	C₃₉₇⋊C₃
commutator, hypocenter	C₃₉₇	C₃×C₉
Frattini	C₃	C₃×C₃₉₇⋊C₃
Fitting	C₉×C₃₉₇	C₃
socle, cosocle	C₃×C₃₉₇	C₃²
prime radical	C₃×C₃₉₇⋊C₃	C₃
LCS	G ▷ C₃₉₇
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
2. C₉×C₃₉₇	C₃	semidirect
3. #16813208	C₃	semidirect
5. C₃₉₇⋊C₃	C₉	direct (N × H)
6. C₃₉₇	C₃×C₉	semidirect
10. C₉	C₃₉₇⋊C₃	direct (N × H)