Subgroups — #72259113

Order 3960.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#157×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊D₃×C₁₁⋊C₅	C₄	1	1	yes	characteristic
3	C₁₁⋊AGL(1,𝔽₉)	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃²×C₁₁⋊C₅	C₈	1	1	yes	characteristic, complemented, Hall
5	(C₁₁⋊C₅)⋊C₈	—	9	1	no	maximal, Hall
6	C₁₁×#157	C₂×C₅	1	1	yes	characteristic
7	C₅×AGL(1,𝔽₉)	—	11	1	no	maximal, Hall
8	D₃×C₁₁⋊C₅	—	12	1	no	—
9	C₄×C₁₁⋊C₅	—	9	1	no	—
10	C₁₁×C₃⋊D₃	C₄×C₅	1	1	yes	characteristic
11	C₅×#157	—	22	1	no	—
12	C₃×C₁₁⋊C₅	—	4	1	no	—
13	C₂×C₁₁⋊C₅	—	9	1	no	—
14	C₃²×C₁₁	C₅×C₈	1	1	yes	characteristic, complemented, Hall
15	C₅×C₃⋊D₃	—	22	1	no	—
16	C₁₁⋊C₈	—	9	1	no	Hall
17	AGL(1,𝔽₉)	—	11	1	no	Hall
18	D₃×C₁₁	—	12	1	no	—
19	C₁₁⋊C₅	AGL(1,𝔽₉)	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₅	—	22	1	no	Hall
21	C₄×C₁₁	—	9	1	no	—
22	C₅×C₈	—	99	1	no	Hall
23	#157	AGL(1,𝔽₁₁)	1	1	yes	characteristic
24	C₃×C₁₁	—	4	1	no	—
25	C₅×D₃	—	132	1	no	—
26	C₂×C₁₁	—	9	1	no	—
27	C₄×C₅	—	198	1	no	—
28	C₃⋊D₃	Dic₁₁⋊C₅	1	1	yes	characteristic
29	C₃×C₅	—	44	1	no	—
30	C₁₁	C₅×AGL(1,𝔽₉)	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	198	1	no	—
32	C₃²	(C₁₁⋊C₅)⋊C₈	1	1	yes	characteristic, complemented, Sylow
33	C₈	—	99	1	no	Sylow
34	D₃	—	12	1	no	—
35	C₅	—	22	1	no	Sylow
36	C₄	—	9	1	no	—
37	C₃	—	4	1	no	—
38	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₁	C₅×C₈
prime radical	C₃⋊D₃×C₁₁⋊C₅	C₄
cosocle	C₁₁×#157	C₂×C₅
LCS	G ▷ C₃²×C₁₁
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.