Subgroups — #261⋊(C₁₁²⋊C₃) #34038418

Order 18876.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊(C₁₁²⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₁₁²×#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊(C₁₁²⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁²×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₁²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₄×C₁₁²⋊C₃	—	13	1	no	maximal, Hall
7	C₂×C₁₁²⋊C₃	—	13	1	no	—
8	C₁₁×#261	—	3	4	no	—
9	C₄×C₁₁²	—	13	1	no	Hall
10	C₁₁²⋊C₃	—	52	1	no	Hall
11	C₁₁×D₁₃	—	3	4	no	—
12	C₂×C₁₁²	—	13	1	no	—
13	AGL(1,𝔽₁₃)	—	121	1	no	maximal, Hall
14	C₁₁×C₁₃	—	3	4	no	—
15	C₁₁²	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
16	D₁₃⋊C₃	—	121	1	no	—
17	#261	C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₄×C₁₁	—	39	4	no	—
19	C₁₃⋊C₃	—	121	1	no	Hall
20	D₁₃	C₂×C₁₁²⋊C₃	1	1	yes	characteristic
21	C₂×C₁₁	—	39	4	no	—
22	C₁₃	C₄×C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₄	—	1573	1	no	Hall
24	C₁₁	—	3	4	no	—
25	C₂×C₃	—	1573	1	no	—
26	C₄	—	13	1	no	Sylow
27	C₃	—	1573	1	no	Sylow
28	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁²×C₁₃	C₃×C₄
prime radical	D₁₃⋊(C₁₁²⋊C₃)	C₂
cosocle	C₁₁²×D₁₃	C₂×C₃
LCS	G ▷ C₁₁²×C₁₃
UCS	C₁

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.