Subgroups — C₁₁⋊C₅×C₄₉⋊C₉ #37564671

Order 24255.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic
2	C₁₁×C₄₉⋊C₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁⋊C₅×C₇⋊C₉	—	7	1	no	maximal
4	C₄₉×C₁₁⋊C₅	C₉	1	1	yes	characteristic, complemented, Hall
5	C₅×C₄₉⋊C₉	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₄₉	C₃×C₅	1	1	yes	characteristic
7	C₃×C₇×C₁₁⋊C₅	ΓL(1,𝔽₈)	1	1	yes	characteristic
8	C₃×C₅×C₄₉	—	11	1	no	—
9	C₁₁×C₇⋊C₉	—	7	1	no	—
10	C₁₁×C₄₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
11	C₉×C₁₁⋊C₅	—	49	1	no	Hall
12	C₄₉⋊C₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₁₁⋊C₅	C₇⋊C₉	1	1	yes	characteristic
14	C₅×C₇⋊C₉	—	77	1	no	—
15	C₅×C₄₉	—	11	1	no	Hall
16	C₃×C₇×C₁₁	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₃×C₁₁⋊C₅	C₄₉⋊C₃	1	1	yes	characteristic
18	C₃×C₄₉	C₃×C₁₁⋊C₅	1	1	yes	characteristic
19	C₃×C₅×C₇	—	11	1	no	—
20	C₉×C₁₁	—	49	1	no	Hall
21	C₇×C₁₁	C₅×C₇⋊C₉	1	1	yes	characteristic
22	C₇⋊C₉	—	7	1	no	—
23	C₁₁⋊C₅	C₄₉⋊C₉	1	1	yes	characteristic, direct product factor, Hall
24	C₄₉	C₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₉	—	539	1	no	Hall
26	C₅×C₇	—	11	1	no	—
27	C₃×C₁₁	C₅×C₄₉⋊C₃	1	1	yes	characteristic
28	C₃×C₇	ΓL(1,𝔽₈)×C₁₁⋊C₅	1	1	yes	characteristic
29	C₃×C₅	—	11	1	no	—
30	C₁₁	C₅×C₄₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
31	C₉	—	49	1	no	Sylow
32	C₇	C₁₁⋊C₅×C₇⋊C₉	1	1	yes	characteristic
33	C₅	—	11	1	no	Sylow
34	C₃	C₁₁⋊C₅×C₄₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃	C₁₁⋊C₅×C₄₉⋊C₃
commutator, hypocenter	C₁₁×C₄₉	C₅×C₉
Frattini	C₃×C₇	ΓL(1,𝔽₈)×C₁₁⋊C₅
Fitting, cosocle	C₃×C₁₁×C₄₉	C₃×C₅
socle	C₃×C₇×C₁₁	C₅×ΓL(1,𝔽₈)
prime radical	C₃×C₇×C₁₁⋊C₅	ΓL(1,𝔽₈)
LCS	G ▷ C₁₁×C₄₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₄₉⋊C₉	C₅	semidirect
4. C₄₉×C₁₁⋊C₅	C₉	semidirect
10. C₁₁×C₄₉	C₅×C₉	semidirect
12. C₄₉⋊C₉	C₁₁⋊C₅	direct (N × H)
23. C₁₁⋊C₅	C₄₉⋊C₉	direct (N × H)
24. C₄₉	C₉×C₁₁⋊C₅	semidirect
30. C₁₁	C₅×C₄₉⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₉×C₁₁⋊C₅	3
C₁₁×C₄₉⋊C₉	5
C₁₁⋊C₅×C₇⋊C₉	7
C₅×C₄₉⋊C₉	11

Subgroups — C11⋊C5×C49⋊C9 #37564671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊C₅×C₄₉⋊C₉ #37564671