Subgroups — C₁₂₁×C₃⋊#261 #34038340

Order 18876.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic
2	#261×C₁₂₁	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₁₂₁	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₁₂₁	D₃	1	1	yes	characteristic
5	C₁₁×C₃⋊#261	C₁₁	1	1	yes	maximal, characteristic
6	C₁₃×C₁₂₁	Dic₃	1	1	yes	characteristic, complemented, Hall
7	Dic₃×C₁₂₁	—	13	1	no	maximal, Hall
8	C₃×C₁₁×D₁₃	C₂×C₁₁	1	1	yes	characteristic
9	C₂×C₃×C₁₂₁	—	13	1	no	—
10	C₁₁×#261	—	3	1	no	—
11	C₄×C₁₂₁	—	39	1	no	Hall
12	C₃×C₁₁×C₁₃	C₄×C₁₁	1	1	yes	characteristic
13	C₃×C₁₂₁	#261	1	1	yes	characteristic, complemented, Hall
14	C₁₁×D₁₃	D₃×C₁₁	1	1	yes	characteristic
15	C₂×C₁₂₁	—	13	1	no	—
16	C₃⋊#261	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
17	C₁₁×C₁₃	C₁₁×Dic₃	1	1	yes	characteristic
18	C₁₁×Dic₃	—	13	1	no	—
19	C₁₂₁	C₃⋊#261	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×D₁₃	C₂×C₁₂₁	1	1	yes	characteristic
21	C₂×C₃×C₁₁	—	13	1	no	—
22	#261	—	3	1	no	Hall
23	C₄×C₁₁	—	39	1	no	—
24	C₃×C₁₃	C₄×C₁₂₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁	C₁₁×#261	1	1	yes	characteristic
26	D₁₃	D₃×C₁₂₁	1	1	yes	characteristic
27	C₂×C₁₁	—	13	1	no	—
28	C₁₃	Dic₃×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	13	1	no	Hall
30	C₁₁	C₁₁×C₃⋊#261	1	1	yes	characteristic
31	C₂×C₃	—	13	1	no	—
32	C₄	—	39	1	no	Sylow
33	C₃	#261×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁₂₁	C₃⋊#261
commutator, hypocenter	C₃×C₁₃	C₄×C₁₂₁
Frattini	C₁₁	C₁₁×C₃⋊#261
Fitting	C₃×C₁₃×C₁₂₁	C₄
socle	C₃×C₁₁×C₁₃	C₄×C₁₁
prime radical, cosocle	C₃×C₁₁×D₁₃	C₂×C₁₁
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₁₂₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₃×C₁₂₁	C₄	semidirect
6. C₁₃×C₁₂₁	Dic₃	semidirect
13. C₃×C₁₂₁	#261	semidirect
16. C₃⋊#261	C₁₂₁	direct (N × H)
19. C₁₂₁	C₃⋊#261	direct (N × H)
24. C₃×C₁₃	C₄×C₁₂₁	semidirect
28. C₁₃	Dic₃×C₁₂₁	semidirect
33. C₃	#261×C₁₂₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₁₃×C₁₂₁	2
#261×C₁₂₁	3
C₁₁×C₃⋊#261	11
Dic₃×C₁₂₁	13

Subgroups — C121×C3⋊#261 #34038340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₁×C₃⋊#261 #34038340