Finite Group Databasebeta

← C₂×C₁₁×C₃₉₇⋊C₃ #39910652

Subgroups — C₂×C₁₁×C₃₉₇⋊C₃ #39910652

Order 26202.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃₉₇⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁×C₃₉₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₃₉₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₉₇⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃₉₇⋊C₃	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃₉₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₃₉₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₁₁	—	397	1	no	maximal, Hall
9	C₃×C₁₁	—	397	1	no	Hall
10	C₂×C₁₁	C₃₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁	C₂×C₃₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	397	1	no	Hall
13	C₃	—	397	1	no	Sylow
14	C₂	C₁₁×C₃₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₁	C₃₉₇⋊C₃
commutator, cosocle, hypocenter	C₃₉₇	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₃₉₇	C₃
LCS	G ▷ C₃₉₇
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₃₉₇⋊C₃	C₂	direct (N × H)
2. C₂×C₁₁×C₃₉₇	C₃	semidirect
3. C₁₁×C₃₉₇	C₂×C₃	semidirect
4. C₂×C₃₉₇⋊C₃	C₁₁	direct (N × H)
5. C₃₉₇⋊C₃	C₂×C₁₁	direct (N × H)
6. C₂×C₃₉₇	C₃×C₁₁	semidirect
7. C₃₉₇	C₂×C₃×C₁₁	semidirect
10. C₂×C₁₁	C₃₉₇⋊C₃	direct (N × H)
11. C₁₁	C₂×C₃₉₇⋊C₃	direct (N × H)
14. C₂	C₁₁×C₃₉₇⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₃₉₇⋊C₃	2
C₂×C₁₁×C₃₉₇	3
C₂×C₃₉₇⋊C₃	11
C₂×C₃×C₁₁	397