Subgroups — C₁₁⋊(D₇₉⋊C₉) #30627708

Order 15642.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₇₉⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₈₆₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₁×C₇₉	C₂×C₃	1	1	yes	characteristic
4	D₈₆₉	C₉	1	1	yes	characteristic, complemented, Hall
5	D₇₉⋊C₉	—	11	1	no	maximal, Hall
6	C₁₁×C₇₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₇₉⋊C₉	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₃×D₇₉	—	11	1	no	—
9	C₃×C₇₉	C₃×D₁₁	1	1	yes	characteristic
10	C₉×D₁₁	—	79	1	no	maximal, Hall
11	D₇₉	—	11	1	no	Hall
12	C₉×C₁₁	—	79	1	no	Hall
13	C₇₉	C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
14	C₃×D₁₁	—	237	1	no	—
15	C₃×C₁₁	D₇₉⋊C₃	1	1	yes	characteristic
16	D₁₁	—	237	1	no	Hall
17	C₂×C₉	—	869	1	no	Hall
18	C₁₁	D₇₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
19	C₉	—	79	1	no	Sylow
20	C₂×C₃	—	2607	1	no	—
21	C₃	C₁₁⋊(D₇₉⋊C₃)	1	1	yes	characteristic
22	C₂	—	2607	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₁⋊(D₇₉⋊C₃)
commutator, hypocenter	C₁₁×C₇₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₁₁×C₇₉	C₂×C₃
prime radical	C₃×D₈₆₉	C₃
LCS	G ▷ C₁₁×C₇₉
UCS	C₁ ◁ C₃

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

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